Blame for MANIFEST_PAPER2.md

# Paper 2 — where every number comes from

One row per number, grouped by paragraph, in paragraph order. A row gives the number as the
paper prints it, the artefact file it is read from, the field inside that file, and the
script that rebuilds the artefact. Paths are relative to the dataset's root. Each script is
in `experiments/` of one of the two code repositories — `AtlasCalibratedConceptProfiles`
for the method, its checks and the inventory, `AtlasRepresentationalDrift` for the drift
analysis. Which one does not follow from the file's directory: `validation/paper1/` and
`validation/paper2/` record which paper's script wrote a file, and several files under
`validation/paper2/` were written by scripts in the first repository.

Every number printed in the paper is listed, and every one of them resolves to a
file and a field in this dataset.

## How a number is traced

| mark | what it means |
|---|---|
| `key` | the field's key names the quantity the sentence names, and its value agrees |
| `count` | a small integer traced to the field that **defines** it (`n_*`, `*_count`, or a key), not matched by value |
| `value` | a distinctive number (≥ 2 decimal places, or an integer ≥ 1,000) matched by value, in an artefact whose field shares a word with the sentence |
| `canon` | a recurring quantity — a token count, or a defining count such as 169 or 7,373 — sent to the one field that defines it by a rule, never matched by value |
| `sibling` | the value sits in the **same stored entry** as a field already traced in that paragraph — an interval bound beside its point, a `first` beside its `last` |
| `declared` | a declared setting or rule parameter, stored as a key or a definition field |
| `derived` | arithmetic on stored fields; the arithmetic is given in the row |
| `cited` | a number from cited work, not ours |

Two classes of numeral are excluded before counting, because they are not quantities:
model names (`OpenCoder-1.5B`, `Pythia-1.4B`), cross-references (`§3.1–3.3`, `D.1`,
`[TBC: A1.3]`), and list enumerators (`(3) at least two checkpoints`, `statements 2 and 3`,
`item 4`).

## Counts, per number

| | distinctive | count | one-place | total |
|---|---:|---:|---:|---:|
| `key` | 79 | 20 | 22 | 121 |
| `count` |  | 131 |  | 131 |
| `canon` | 28 | 55 |  | 83 |
| `value` | 74 |  |  | 74 |
| `sibling` | 27 | 5 |  | 32 |
| `declared` | 9 | 8 | 10 | 27 |
| `derived` | 3 | 6 | 6 | 15 |
| `cited` |  | 7 | 2 | 9 |
| **total** | **220** | **232** | **40** | **492** |

Every number resolves to a file and a field: there is no number in paper 2 with no
home in the record.

**No row is left weak.** Every number is tied to a field whose key names the quantity the
sentence names, to a declared rule parameter, to arithmetic on stored fields that the row
gives, or to cited work.

## Numbers that do not reproduce from a released artefact

None. Every number printed in this paper resolves to a file and a field in this dataset, with
the arithmetic given in the row wherever a figure is computed from stored fields rather than
stored itself.

## The artefacts, and one line each confirming the field is the quantity

| artefact | numbers | rebuild script | the field is the quantity the paper names, because |
|---|---:|---|---|
| `validation/paper2/ABLATION_NATS.json` | 50 | `ablation_nats.py` | the reliance claim: `median_rise_over_random_nats` is the carriers' loss rise minus the random sets' mean rise, in nats — the quantity §3.3 calls the cost of removal over a random set; `old_set.*` is the same for the set measured at 84 B. In nats, not control units, because the control's spread had not converged (`ablation_nats.py` measured that). |
| `validation/paper2/ABLATION_RANKS.json` | 48 | `ablation_ranks.py` | the same removal experiment read as a rank: `current.exact_one_sided_p` and `n_random` are the one-sided position of the carriers among the random masks, which is what §3.3's 'cannot be separated from a random set' states. |
| `validation/paper2/CEILINGS.json` | 39 | `ceilings.py` | the per-reference ceiling and carrier-set size at each cut (`<cut>.median_size`, `chance`). |
| `validation/paper2/B11_POWER.json` | 36 | `b11_power.py` | `dates.<shape>|<date>.detection_rate` is the share of 338 injected draws in which the corrected rule found the settling it was given — §3.4's power. The injection dates are named in the keys, so '84 billion to 1.5 trillion' is provenanced by the key, not by a stored value. |
| `validation/paper2/RATE_READINGS.json` | 26 | `rate_readings.py` | `primary.<cut>.<window>[].median_excess` is the carrier change over a fixed gap, beyond the twin turnover, read against its own ceiling — §4.1's quantity. §4.1 reads `primary.carrier5`; `definition_1_primary` holds the declared windows and the R² floor. |
| `validation/paper2/B16C_STEPS_VS_LR.json` | 21 | `b16c_steps_vs_lr.py` | `over_random_walk_*` is the measured weight step divided by η·√D, the free-random-walk distance — §4.3's 'fraction of the distance a random walk would cover'. `consistency_*` is the same step over η·D. |
| `validation/r2/STEP4_FLAT_pretrain.json` | 19 | `p8_bootstrap.py` | `forced|construct_token|expected_pieces|dependent.series[].level_{early,84b,last}` are the loss levels at each class of position, and `thresholds.<pct>|<u>` the nine declared flat-leg settings — §3.2 and §A.3. |
| `validation/paper2/B17B_RETURN_SPLIT.json` | 18 | `b17b_return_split.py` | `arms.fell_{beyond,within}_one_twin_unit.{departures,lift,lift_ci95}` split every departure by whether the neuron's entry fell by more than its twin difference, and give the return rate over the matched control — §4.2's return result. `share_of_departures_beyond_one_twin_unit` is the 92.5%. |
| `validation/paper2/B16B_WEIGHT_NORMS.json` | 15 | `b16b_weight_norms.py` | `per_checkpoint.<ref>.tensors.<matrix>` are the Frobenius norms of layer 12's three MLP matrices — §4.3's 'the norms grow by 81%, 89% and 83%'. |
| `validation/paper2/B2_ANNEAL_DROP.json` | 15 | `b2_anneal_drop.py` | the annealing branch read on the same series as pretraining; `forced.n_series` and the per-series thresholds are §3.5's counts. |
| `validation/r2/CURVE1_SPACING_pretrain.json` | 15 | `step4_flat.py` | the spacing dependence that C.3 corrects for: `spacing_dependence.n_pairs` is the 1,404 point–partner pairs, and the `per_band` keys are the four declared bands. |
| `validation/paper2/B12_TWIN_TURNOVER.json` | 13 | `b12_twin_turnover.py` | `per_reference.<ref>.twin_overlap_median` and `twin_turnover_median` are the agreement between the two twins at one checkpoint, which is the instrument's own noise — §3.1's 0.84 and 0.16. It stores no minimum; see §Settled while tracing. |
| `validation/paper2/B18_RECURRENCE.json` | 13 | `b18_recurrence.py` | `c_coordination_vs_circular_shift_median` compares observed co-movement with a null that holds each neuron's own persistence — §4.2's 'what independent neurons with the same persistence would show'. The across-neuron shuffle in the same file (12.95) is a different null and is **not** that number. |
| `validation/r2/STEP3_SENSES_pretrain.json` | 11 | `-` | the three senses of 'settles' read on the standardised profile; `third_sense.*|curve2_norm|lognormal.coefficients.log_frequency.beta` is the frequency coefficient whose 10^|β| is §4.4's factor. |
| `validation/r2/STEP8_GRAPH_pretrain.json` | 9 | `-` | the unit-level graph: `n_units = 147,456` is the product space, `p8.n_fell_beyond_noise` the departures beyond the noise unit, and `partners[].factor` the spacing factors. |
| `validation/paper2/B14_BANDS.json` | 8 | `b14_bands.py` | `per_band.<cut>.band_size_first_ref` is the size of the carrier set at each of the six cuts, and `n_constructs_tested` the 169 — §4.1's cut sensitivity. |
| `validation/paper2/B1_ENTROPY.json` | 7 | `b1_entropy.py` | `against_the_model.model_loss_governed_{early,last}_median_nats` is the model's loss at governed positions at the first and last reference, and `generator_marginal_entropy_governed_median_nats` the loss of a reader who knows only the generator's rates — §5's three numbers. |
| `validation/paper1/C3_YARDSTICK_NATS.json` | 6 | `c3_yardstick_nats.py` | paper 1's yardstick sensitivity, cited in paper 2's §4.8 limitation ('the turnover moves by 0.003–0.005'). |
| `validation/paper2/DATES_TABLE.json` | 6 | `dates_table.py` | the per-construct settling verdicts under the corrected rule; `n_constructs_with_all_six_dated = 0` is §4.1's '0 of 169'. |
| `validation/r2/CURVE1_SPACING_anneal.json` | 6 | `step7.py` | the spacing dependence of curve 1 on the annealing branch, in the same bands as pretraining (`per_band.<n>ref`). |
| `validation/paper1/POOLED_SETS_45.json` | 5 | `pooled_sets_169.py` | paper 1's family clustering, cited in paper 2 where it reports purity and cluster counts. |
| `validation/paper2/B16C_WEIGHT_STEPS.json` | 5 | `b16c_weight_steps.py` | `summary['<window>|<matrix>|<carriers,random>|<relative,absolute>_step']` is the weight step on each construct's carrier rows against a size-matched random row set — the comparison §4.3's 'within 0.3%' makes. See Flag 2. |
| `validation/r2/P8_BOOTSTRAP_pretrain.json` | 5 | `p8_bootstrap.py` | the bootstrap behind the fall intervals: `n_draws_fell`, `share_of_draws_that_fell`. |
| `validation/r2/R2_INDEX_CURVES.json` | 5 | `r2_curves.py` | — not yet confirmed |
| `calibration/checkpoints.json` | 4 | `checkpoint_inventory.py` | the checkpoint schedule (`all[].step`), which converts an iteration to a token count at 4,194,304 tokens per step. |
| `validation/paper1/CORE_COUNTS.json` | 4 | `core_counts.py` | — not yet confirmed |
| `validation/paper1/FIGURES.json` | 4 | `atlas.py` | paper 1's figure data, cited where paper 2 quotes check 9. |
| `validation/paper2/B5_CHURN_VS_LEARNING.json` | 4 | `b5_churn.py` | `across_layers.churn_vs_filling_change.spearman` relates carrier change to how much the layer is still filling — §5's check that change is not a by-product of learning. |
| `validation/paper2/C2_PYTHIA_TWIN.json` | 4 | `c2_pythia_twin.py` | the second model: `carrier_overlap` per construct and `opencoder_comparison.carrier_overlap_last_checkpoint` put Pythia's twin agreement beside OpenCoder's (§6). |
| `validation/paper2/TBC22_SHARES.json` | 4 | `tbc22_shares.py` | `cuts.<cut>.share_of_ceiling` — the change normalised by each cut's own ceiling, §4.1's 0.925–0.964. |
| `validation/r2/owed/RAW_NORM_REREAD_pretrain.json` | 4 | `-` | the re-read of the response's size on the **raw** profile, which the contract made primary; `third_sense.*|raw.coefficients.log_frequency.beta` is the raw frequency coefficient (10^|β| = 1.17). |
| `validation/paper1/CHECK4_RELATIVE.json` | 3 | `check4_relative.py` | paper 1's check 4 recomputed on the suite's own metric; `n_within_one_twin_unit = 4` is the figure §4.1 of paper 1 reports and paper 2 cites. |
| `validation/paper1/SCOPE_OVERLAP.json` | 3 | `audit_recordings.py` | `share_of_ceiling` per construct at a reference — the convergence panel of Figure 4. |
| `validation/paper2/ABLATION_STABLE.json` | 3 | `ablation_stable.py` | the same removal read with the mask count varied, so §3.3's effect can be shown not to depend on it (`control_stability.<n>`). |
| `validation/paper2/B6_PERLAYER_SHARING.json` | 3 | `b6_perlayer.py` | `occupancy_by_layer` and `per_layer.<n>.trend_spearman_vs_log_step` are where in the network the carriers sit and whether that moves (§4.6). |
| `validation/paper2/COOCCURRENCE.json` | 3 | `cooccurrence.py` | `pairs_total = 14,196` — all construct pairs, the denominator of §4.7's sharing figures. |
| `validation/paper2/TEST6.json` | 3 | `test6.py` | — not yet confirmed |
| `calibration/identifiers.json` | 2 | `-` | a calibration table of identifier draw rates. It carries no quantity the paper names; every row pointing here is `weak` — the value index offered it for a token count such as '84 billion' and no field name tied anything to the sentence. **Not a source for any number in paper 2.** |
| `validation/ablation/PLAN.json` | 2 | `ablation_full.py` | `plan.total_construct_passes` — the size of the removal experiment as planned (§A.1). |
| `validation/paper1/LENGTHS.json` | 2 | `atlas.py` | — not yet confirmed |
| `validation/paper1/TURNOVER_CLASSES_ONLY.json` | 2 | `b10.py` | — not yet confirmed |
| `validation/paper2/A38_POPULATION.json` | 2 | `-` | the population the readings are taken over — 35 pretraining references and the declared partner-factor band. |
| `validation/paper2/B15_TEST6_CORECHECK.json` | 2 | `b15_corecheck.py` | per-pair core consistency: whether the same prompt cores are read at both ends of a checkpoint pair, which licenses comparing the two (§A.1.6). |
| `validation/paper2/CEILINGS_PAIRWISE.json` | 2 | `-` | the cross-checkpoint ceiling — chance agreement between different constructs with one profile at each end of the pair, which is the quantity the excess is read against. |
| `validation/paper2/TEST6_EXTRAS.json` | 2 | `test6_extras.py` | per-pair departure counts by token, behind §4.5's statement that departures are not concentrated in a few tokens. |
| `validation/r2/R2_CLOSE.json` | 2 | `r2_close.py` | the close-spacing re-read, giving the relative standard error on each curve point. |
| `calibration/corpus.json` | 1 | `build_natural.py` | `parsed = 253,398` — the reference corpus's parsed Python files, the declared stimulus distribution's base (Appendix A item 1). |
| `validation/loss/CORE_pretrain_iter_0001000.json` | 1 | `-` | — not yet confirmed |
| `validation/paper1/B_SUBTYPES.json` | 1 | `b_subtypes.py` | what each construct's B set is made of; cited in Appendix A item 1. |
| `validation/paper1/CHECK6_COMPANIONS.json` | 1 | `check6_companions.py` | `n_companions` per construct — the companion check Appendix A item 10 says is not met for the eight compound statements. |
| `validation/paper1/CHECK6_TURNOVER.json` | 1 | `check6_turnover.py` | the carrier turnover with and without re-weighting, with the re-weighted ceiling per reference — cited where §4.8 bounds the generator's effect. |
| `validation/paper1/LICENCE_TABLE.json` | 1 | `licence_table.py` | paper 1's nine checks per construct, cited in paper 2's Appendix A item 10. |
| `validation/paper1/LICENCE_TABLE_CORRECTED.json` | 1 | `licence_table.py` | paper 1's checks after the four corrections; cited for the null's replicate count. |
| `validation/paper1/RECHECK_PER_PROMPT.json` | 1 | `recheck_per_prompt.py` | the per-prompt re-check of the nulls; cited for its replicate count. |
| `validation/paper2/B10_SPACING_ADJUSTED.json` | 1 | `b10_fit.py` | the withdrawn fitted form, kept because D.1 artefact 4 reports what it would have given; `per_start.<iter>.n_points` are its pair counts. |
| `validation/paper2/B17_RETURN.json` | 1 | `b17_return.py` | `departures = 18,034,712` is the total number of departures §4.2 opens with; the split by size is in B17B. |
| `validation/paper2/B3_ALLPAIRS.json` | 1 | `b3_allpairs.py` | every checkpoint pair at every gap, the input Figure 2 and the rate readings are taken from; `cosine.n_dense` is the dense block's count. |
| `validation/paper2/B3_GRADED.json` | 1 | `b3_graded.py` | the graded (uncut) profile read over the same pairs; `pairs.<band>|<ref>|<ref>.cosine_mean` is §4.1's 'the graded profile slows in the same way'. The `x1.5` keys name the long-gap band. |
| `validation/paper2/C2_PYTHIA_GATE.json` | 1 | `c2_pythia_gate.py` | `n_constructs_scored = 188` — how many constructs pass the gate on the second model (§6). |
| `validation/r2/STEP5_FREQUENCY_pretrain.json` | 1 | `-` | `spearman.<space>|<arm>.n` is how many constructs enter the frequency test (§4.4). |
| `validation/r2/STEP7_pretrain.json` | 1 | `step7.py` | the bend analysis: whether a series bends at a common date across constructs (§4.1, C.3). |
| `validation/r2/owed/TIEBREAK_SENSITIVITY.json` | 1 | `r2_owed.py` | — not yet confirmed |

## Every number, by paragraph


**¶1.** In neuroscience, representational drift is a change in which neurons carry a representation while behaviour stays the same; we measure its analogue in…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 0.40 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.median_vs_random_nats.hi` | `ablation_nats.py` |
| 0.06 | `value` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.Delete.a_nearest_set.under_b10_model.share_wide_pairs_above_model_by_one_twin_unit` | `b18_recurrence.py` |
| 0.25 | `sibling` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.Delete.a_nearest_set.under_b10_model.residual_sd_pooled` — the same entry as share_wide_pairs_above_model_by_one_twin_unit, traced above | `b18_recurrence.py` |
| 500 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0119000.tokens_b = 499.12` — 500 billion tokens is this reference, iteration 119000 | `ceilings.py` |
| 1.5 | `key` | `validation/paper2/B18_RECURRENCE.json` | `c_coordination_vs_circular_shift_median = 1.4553` — the circular-shift null is the one that holds each neuron's persistence, which is what 'independent neurons with the same persistence' names. The across-neuron shuffle in the same file is 12.95 and is NOT this number. | `b18_recurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 16 | `count` | `validation/r2/CURVE1_SPACING_anneal.json` | `product.constructs.next.per_band.8ref.n` | `step7.py` |
| 99 | `derived` | `validation/paper2/B11_POWER.json` | `dates.step|*.detection_rate = 0.9911-0.9941` — '99% of injected cases', the lowest of the five step-shape rates, rounded | `b11_power.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 4 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.from_84b_to_last.counts.rising` — the leg 84 B -> end | `p8_bootstrap.py` |
| 2 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_without` | `ablation_nats.py` |

**¶2.** A *construct* is one named piece of a programming language's grammar — the keyword `for`, the builtin `len`, a list comprehension. A *neuron* is one h…

| number | mark | file | field | script |
|---|---|---|---|---|
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.For.current.n_random_at_or_above` | `ablation_ranks.py` |

**¶3.** On the record read here the answer is no. The model's loss at the construct's forced positions reaches its floor within the first 4% of training; the …

| number | mark | file | field | script |
|---|---|---|---|---|
| 4 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.While.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶4.** Whether the phenomenon exists in a language model during pretraining has been seen before at coarse checkpoint spacing and without a noise unit. For s…

| number | mark | file | field | script |
|---|---|---|---|---|
| 7 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.With.old_set.n_random_below` | `ablation_ranks.py` |
| 1 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.old_set.n_exceeding_every_mask` | `ablation_ranks.py` |

**¶5.** One record is read: OpenCoder-1.5B at 35 pretraining checkpoints spanning 4.19 billion to 2.03 trillion tokens at a constant learning rate, and 24 che…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1.67 | `derived` | `calibration/checkpoints.json` | `all[].step (the last annealing checkpoint)` — the annealing branch's end in tokens, at 4,194,304 tokens a step; CEILINGS.json carries tokens_b for the 35 pretraining references only, not for the annealing ones. | `checkpoint_inventory.py` |
| 2.03 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0484865.tokens_b = 2,033.67` — 2.03 trillion tokens is this reference, iteration 484865 | `ceilings.py` |
| 1.57 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.tensors.model.layers.12.mlp.down_proj.weight.row_norm_q3` | `b16b_weight_norms.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 35 | `count` | `validation/paper2/A38_POPULATION.json` | `n_pretraining_references` | `-` |
| 24 | `count` | `validation/paper2/B5_CHURN_VS_LEARNING.json` | `across_layers.churn_vs_filling_change.n` | `b5_churn.py` |

**¶6.** 1. A *construct* is one piece of Python grammar or one builtin name; the battery holds 188, and 169 pass the gate that says the model's reading positi…

| number | mark | file | field | script |
|---|---|---|---|---|
| 188 | `canon` | `validation/paper1/CORE_COUNTS.json` | `n_constructs_built` — the constructs the battery holds | `core_counts.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |

**¶7.** 2. A *neuron* is one of the 147,456 hidden units of the MLP layers (24 layers × 6,144).…

| number | mark | file | field | script |
|---|---|---|---|---|
| 147,456 | `canon` | `validation/r2/STEP8_GRAPH_pretrain.json` | `n_units` — the product space, 24 layers x 6,144 neurons | `-` |
| 6,144 | `key` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.tensors.model.layers.12.mlp.gate_proj.weight.shape[0]` | `b16b_weight_norms.py` |
| 24 | `count` | `validation/paper2/B5_CHURN_VS_LEARNING.json` | `across_layers.churn_vs_filling_change.n` | `b5_churn.py` |

**¶8.** 3. The *profile* of a construct at a checkpoint is one number per neuron: the mean standardised activation on prompts with the construct in its role, …

| number | mark | file | field | script |
|---|---|---|---|---|
| 7,373 | `canon` | `validation/paper2/B14_BANDS.json` | `per_band.q5pct.band_size_first_ref` — the 5% cut's carrier-set size, 5% of 24 x 6,144 | `b14_bands.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.For.current.n_random_at_or_above` | `ablation_ranks.py` |

**¶9.** 4. *The twins* are the battery drawn twice from one design. Their disagreement is the unit every change is measured in: within a trained checkpoint th…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.16 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `per_reference.pretrain_iter_0001000.twin_turnover_median` | `b12_twin_turnover.py` |
| 0.84 | `key` | `validation/paper2/C2_PYTHIA_TWIN.json` | `opencoder_comparison.carrier_overlap_last_checkpoint` | `c2_pythia_twin.py` |

**¶10.** 5. *The six metrics* are taken for each construct at each checkpoint; one metric followed across checkpoints is a *curve*. They are the turnover (item…

| number | mark | file | field | script |
|---|---|---|---|---|
| 5 | `count` | `validation/r2/CURVE1_SPACING_anneal.json` | `layer.constructs.AsyncWith.per_band.8ref.n_below_before` | `step7.py` |

**¶11.** 6. The *turnover* at a checkpoint is the share of its carrier set that is no longer in the set at a later checkpoint, its *partner*: a turnover of 0.3…

| number | mark | file | field | script |
|---|---|---|---|---|
| 7,373 | `canon` | `validation/paper2/B14_BANDS.json` | `per_band.q5pct.band_size_first_ref` — the 5% cut's carrier-set size, 5% of 24 x 6,144 | `b14_bands.py` |
| 0.3 | `declared` | — | illustrative: 'a turnover of 0.3 means 30% of the 7,373 carriers have left by the partner'. Part of the definition of turnover, not a reading. | — |
| 30 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary.carrier5.5000.n_gaps` | `rate_readings.py` |

**¶12.** 7. A *marked position* is a position in a prompt where the construct's grammar decides the next token: *forced* (after `for x in y` the colon is oblig…

| number | mark | file | field | script |
|---|---|---|---|---|
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.n_constructs` | `ablation_nats.py` |

**¶14.** *Spacing.* The record divides pretraining into three periods. *Period 0*, from the start to 4.19 billion tokens, lies before the first checkpoint. *Pe…

| number | mark | file | field | script |
|---|---|---|---|---|
| 100,000 | `key` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][1]` | `rate_readings.py` |
| 10,000 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.absence_length_steps.median` | `b17b_return_split.py` |
| 20,000 | `key` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[2][0]` | `rate_readings.py` |
| 30,000 | `key` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[2][1]` | `rate_readings.py` |
| 50,000 | `key` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][0]` | `rate_readings.py` |
| 91,000 | `key` | `validation/r2/STEP7_pretrain.json` | `p4.r12_bends.1524B.spacing_steps_before[1]` | `step7.py` |
| 5,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|gate_proj.start_iters[4]` | `b16c_steps_vs_lr.py` |
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 2.03 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0484865.tokens_b = 2,033.67` — 2.03 trillion tokens is this reference, iteration 484865 | `ceilings.py` |
| 1.25 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0011000.tensors.model.layers.12.mlp.up_proj.weight.row_norm_q3` | `b16b_weight_norms.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |

**¶15.** *Resolution.* The step between a construct's profiles at neighbouring checkpoints is 8.56 twin units at the start of the record and 3.56 at the end of…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 8.56 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `construct_token.series.round.level_last` | `p8_bootstrap.py` |
| 3.56 | `key` | `validation/paper1/CHECK4_RELATIVE.json` | `per_construct[176].check4_twin_units` | `check4_relative.py` |

**¶16.** Three things are measured for the same constructs across the same checkpoints: the loss at the marked positions (*behaviour*; 16 constructs, 24 series…

| number | mark | file | field | script |
|---|---|---|---|---|
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 24 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_series` | `b2_anneal_drop.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.n_constructs` | `ablation_nats.py` |

**¶17.** *Figure 1. The three timescales. (a) Behaviour: the median loss at the forced and expected positions of the 16 constructs with marked positions, in na…

| number | mark | file | field | script |
|---|---|---|---|---|
| 10,000 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.ratio_of_medians_rise_to_random.n_bootstrap_draws_usable` | `ablation_nats.py` |
| 20,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.start_iters[19]` | `b16c_steps_vs_lr.py` |
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 1,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|gate_proj.start_iters[0]` | `b16c_steps_vs_lr.py` |
| 2,034 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0484865.tokens_b = 2,033.67` — 2,034 billion tokens is this reference, iteration 484865 | `ceilings.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.n_constructs` | `ablation_nats.py` |
| 10 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.sign_test_vs_random.n_above_zero` | `ablation_nats.py` |
| 95 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.IfExp.current.n_random_at_or_above` | `ablation_ranks.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 14 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.sign_test_rise_over_random.n_above_zero` | `ablation_nats.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶18.** Everything that we expected to see forming had already formed. At 4.19 billion tokens, 167 of the 169 constructs already carry half of their profile's…

| number | mark | file | field | script |
|---|---|---|---|---|
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 0.84 | `key` | `validation/paper2/C2_PYTHIA_TWIN.json` | `per_construct.ChildProcessError.carrier_overlap` | `c2_pythia_twin.py` |
| 0.5 | `derived` | `validation/paper2/B12_TWIN_TURNOVER.json` | `per_reference.pretrain_iter_0001000.twin_overlap_median (= 0.8436; no min is stored)` — 'more than 0.5 for all 169' RECOMPUTED CPU-only from validation/carriers/*.npz at this reference: min 0.697, 0 of 169 at or below 0.5. The claim holds. Recommend b12_twin_turnover.py also store twin_overlap_min. | `b12_twin_turnover.py` |
| 167 | `count` | `validation/r2/owed/RAW_NORM_REREAD_pretrain.json` | `second_sense.standardised.curve2_norm x curve1_turnover.n` | `-` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶19.** This is where the model finishes learning at the positions we can read. Of the 24 loss series at the forced and expected positions of the 16 construct…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.31 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.quoted_in_the_paper.kept_fraction_first_pair = 0.3092` — NEW FIELD: the kept fraction is now stored at every one of the 34 neighbouring pairs (between_checkpoints.per_pair), with both ends' token counts, not only the last pair. Written 5 Nov by experiments/backfill_summaries.py, which checks each value against the figure the paper prints and refuses rather than write one that misses it; the writer script now produces it natively too. b12_twin_turnover.py. | `b12_twin_turnover.py` |
| 0.66 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.quoted_in_the_paper.kept_fraction_by_71b = 0.6623` — NEW FIELD, as para 19. | `b12_twin_turnover.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 2.5 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `dependent.governed.series['For|governed|governed_use'].level_last = 2.5155` — the draft now says "`For`'s series alone falls from 5.6 to 2.5 nats" and no longer attributes it to the four dependent positions or to Figure 1a (the flag 1, acted on 5 Nov). | `p8_bootstrap.py` |
| 5.6 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `dependent.governed.series['For|governed|governed_use'].level_early = 5.6099` — the draft now says "`For`'s series alone falls from 5.6 to 2.5 nats" and no longer attributes it to the four dependent positions or to Figure 1a (the flag 1, acted on 5 Nov). | `p8_bootstrap.py` |
| 15 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.to_84b.counts.falling` — the leg 4.19 -> 84 B at the default threshold 10pct|1.0u | `p8_bootstrap.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.n_constructs` | `ablation_nats.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 24 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_series` | `b2_anneal_drop.py` |
| 71 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0017000.tokens_b = 71.30` — 71 billion tokens is this reference, iteration 17000 | `ceilings.py` |
| 3 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.to_84b.counts.rising` — the leg 4.19 -> 84 B at the default threshold 10pct|1.0u | `p8_bootstrap.py` |
| 6 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.to_84b.counts.flat` — the leg 4.19 -> 84 B at the default threshold 10pct|1.0u | `p8_bootstrap.py` |

**¶20.** **Behaviour stays flat.** Over this leg the loss at the forced and expected positions is flat for 20 of 24 series, rising for 4 and falling for 0, at …

| number | mark | file | field | script |
|---|---|---|---|---|
| 20 | `count` | `validation/paper1/LICENCE_TABLE_CORRECTED.json` | `constructs.Assert.checks_corrected.check8_nulls__suite_7.split_half.n_rep` | `licence_table.py` |
| 24 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_series` | `b2_anneal_drop.py` |
| 14 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.from_84b_to_last.across_thresholds['5pct|0.5u'].rising = 14` — the tightest of the nine settings, where the majority turns to rising. The same paragraph's second '14 of 24', over the whole of training, is legs.forced.to_last.counts.falling = 14. | `p8_bootstrap.py` |
| 5 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.series.For|obliged|header_colon.n_pieces_at_least_20` | `b2_anneal_drop.py` |
| 0 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.from_84b_to_last.counts` — 'falling for 0': the key is absent from the counts, which is how a zero is stored | `p8_bootstrap.py` |
| 4 | `count` | `validation/paper1/CHECK4_RELATIVE.json` | `n_within_one_twin_unit` | `check4_relative.py` |

**¶21.** **Reliance grows.** For the 16 constructs, removing the carriers raises the loss at the marked positions by more than removing a random set of the sam…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.002 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncFor.control_mean_nats` — the same entry as n_random_below, traced above | `ablation_ranks.py` |
| 0.038 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.sign_test_rise_over_random.p` | `ablation_nats.py` |
| 0.088 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.hi` | `ablation_nats.py` |
| 0.40 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.median_vs_random_nats.hi` — the same entry as n_without, traced above | `ablation_nats.py` |
| 0.02 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.point` — the same entry as hi, traced above | `ablation_nats.py` |
| 0.73 | `key` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0484865.per_yardstick.one.median` | `c3_yardstick_nats.py` |
| 0.66 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.quoted_in_the_paper.kept_fraction_by_71b = 0.6623` — NEW FIELD, as para 19. | `b12_twin_turnover.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 0.03 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct.While.control_mean_nats` — the same entry as carrier_rise_nats, traced above | `ablation_nats.py` |
| 0.14 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.IfExp.carrier_rise_nats` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 5.95 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.per_construct.Try.rise_over_random_nats` | `ablation_nats.py` |
| 0.70 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct.Lambda.carrier_rise_nats` | `ablation_nats.py` |
| 0.06 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.median_rise_over_random_nats.point` | `ablation_nats.py` |
| 0.10 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.hi` — the same entry as hi, traced above | `ablation_nats.py` |
| 0.25 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.Import.current.exact_one_sided_p` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 320 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.Try.old_set.n_random_below` | `ablation_ranks.py` |
| 20 | `count` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0001000.n_random_masks` | `c3_yardstick_nats.py` |
| 14 | `sibling` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0484865.per_yardstick.one.sign_test.n_above_zero` — the same entry as median, traced above | `c3_yardstick_nats.py` |
| 95 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.IfExp.current.n_random_at_or_above` | `ablation_ranks.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 12 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.sign_test_rise_over_random.n_above_zero` | `ablation_nats.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.n` | `ablation_nats.py` |
| 8 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.n_holm_significant` | `ablation_ranks.py` |
| 2 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_without` | `ablation_nats.py` |

**¶22.** **Membership never settles.** For 169 of 169 constructs the turnover curve is still moving at the last checkpoint, and no construct has a settling dat…

| number | mark | file | field | script |
|---|---|---|---|---|
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 20,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.start_iters[19]` | `b16c_steps_vs_lr.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |

**¶23.** **The old carriers' function is not retained; the readout is.** The set measured at 84 billion tokens, with 14% of its members still in the current se…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.998 | `key` | `validation/paper1/LICENCE_TABLE.json` | `constructs.AsyncFor.check1_twin_unit.median_disattenuated` | `licence_table.py` |
| 0.999 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0005000.tensors.model.layers.12.mlp.up_proj.weight.row_norm_q1` | `b16b_weight_norms.py` |
| 0.77 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.median_vs_current_nats.lo = -0.7729` — the interval's lower end for the old set against the current one | `ablation_nats.py` |
| 0.42 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.NamedExpr.rise_over_random_nats` | `ablation_nats.py` |
| 0.09 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.hi` | `ablation_nats.py` |
| 0.01 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.DictComp.old_set_rise_nats` | `ablation_nats.py` |
| 0.11 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct.ListComp.carrier_rise_nats` — the same entry as carrier_rise_nats, traced above | `ablation_nats.py` |
| 0.28 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct.Import.carrier_rise_nats` | `ablation_nats.py` |
| 0.14 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.GeneratorExp.old_set_over_random_nats` | `ablation_nats.py` |
| 10 | `count` | `validation/r2/CURVE1_SPACING_anneal.json` | `product.constructs.Raise.per_band.8ref.n_following` | `step7.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.n` | `ablation_nats.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 11 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_old_below_current` | `ablation_nats.py` |
| 14 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.median_vs_current_nats.n` | `ablation_nats.py` |
| 8 | `count` | `validation/paper2/B1_ENTROPY.json` | `against_the_model.n_governed_series` | `b1_entropy.py` |
| 4 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.sign_test_vs_current.n_above_zero` | `ablation_nats.py` |

**¶24.** "No construct settles" is informative only where settling would have been found. Settlings were injected into the measured turnover series at five dat…

| number | mark | file | field | script |
|---|---|---|---|---|
| 99.1 | `key` | `validation/paper2/B11_POWER.json` | `dates.step|500B.detection_rate = 0.99112` | `b11_power.py` |
| 99.4 | `key` | `validation/paper2/B11_POWER.json` | `dates.step|{84B,200B,1000B,1500B}.detection_rate = 0.99408` | `b11_power.py` |
| 100 | `key` | `validation/paper2/B11_POWER.json` | `dates.exponential|500B.detection_rate = 1.0` | `b11_power.py` |
| 338 | `canon` | `validation/paper2/B11_POWER.json` | `dates.step|84B.draws` — the injected draws in each power cell | `b11_power.py` |
| 500 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0119000.tokens_b = 499.12` — 500 billion tokens is this reference, iteration 119000 | `ceilings.py` |
| 1.5 | `key` | `validation/paper2/B18_RECURRENCE.json` | `c_coordination_vs_circular_shift_median = 1.4553` — the circular-shift null is the one that holds each neuron's persistence, which is what 'independent neurons with the same persistence' names. The across-neuron shuffle in the same file is 12.95 and is NOT this number. | `b18_recurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 0 | `count` | `validation/paper2/DATES_TABLE.json` | `n_constructs_with_all_six_dated` | `dates_table.py` |
| 1 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.series.AsyncFor|obliged|bare_colon.n_pieces_at_least_20` | `b2_anneal_drop.py` |

**¶25.** *Figure 2. Change in membership beyond the twin turnover at fixed gaps: medians over 169 constructs by start point, in four windows of the gap, with c…

| number | mark | file | field | script |
|---|---|---|---|---|
| 20,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.start_iters[19]` | `b16c_steps_vs_lr.py` |
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 95 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.IfExp.current.n_random_at_or_above` | `ablation_ranks.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 1 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.old_set.n_exceeding_every_mask` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |

**¶26.** *Figure 3. The power of the null. Settling curves were injected into measured turnover series at five dates, in two shapes, 338 draws a cell. (a) The …

| number | mark | file | field | script |
|---|---|---|---|---|
| 338 | `canon` | `validation/paper2/B11_POWER.json` | `dates.step|84B.draws` — the injected draws in each power cell | `b11_power.py` |
| 0 | `count` | `validation/paper1/B_SUBTYPES.json` | `per_construct.False.n_other_role_prompts` | `b_subtypes.py` |

**¶27.** Here the learning rate decays, as the cooldown of a warmup–stable–decay schedule \citep{dremov2025}. Measured over equal steps of training, carrier ch…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.026 | `key` | `validation/r2/CURVE1_SPACING_anneal.json` | `resolution.branch_span_decades` | `step7.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 24 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_series` | `b2_anneal_drop.py` |
| 23 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_series_compared` | `b2_anneal_drop.py` |
| 5 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.series.For|obliged|header_colon.n_pieces_at_least_20` | `b2_anneal_drop.py` |
| 7 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_below_floor_by_more_than_one_unit` | `b2_anneal_drop.py` |

**¶28.** In period 1, consider two checkpoints 1,000 steps apart. The turnover between them, minus the twin turnover (0.16), is 0.54 for the first pair of the …

| number | mark | file | field | script |
|---|---|---|---|---|
| 100,000 | `value` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][1]` | `rate_readings.py` |
| 20,000 | `key` | `calibration/checkpoints.json` | `all[14].step` | `checkpoint_inventory.py` |
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 50,000 | `value` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][0]` | `rate_readings.py` |
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 0.40 | `value` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.turnover_median` | `b12_twin_turnover.py` |
| 0.73 | `value` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.NotImplemented.twin_ceiling` | `b18_recurrence.py` |
| 0.53 | `value` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.per_pair[27].kept_fraction_median` | `b12_twin_turnover.py` |
| 0.30 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.per_construct.DictComp.rise_over_random_nats` — the same entry as old_set_rise_nats, traced above | `ablation_nats.py` |
| 0.16 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `per_reference.pretrain_iter_0001000.twin_turnover_median` | `b12_twin_turnover.py` |
| 0.97 | `key` | `validation/paper2/CEILINGS_PAIRWISE.json` | `per_window.~1,000[0].cosine.twin` | `-` |
| 0.80 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.per_construct.IfExp.old_set_rise_nats` | `ablation_nats.py` |
| 0.19 | `value` | `validation/paper2/B16C_WEIGHT_STEPS.json` | `summary.1000|down_proj|carriers|relative_step.last` | `b16c_weight_steps.py` |
| 0.54 | `value` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.per_pair[2].kept_fraction_median` | `b12_twin_turnover.py` |
| 0.35 | `key` | `validation/paper2/RATE_READINGS.json` | `primary.carrier5.50k-100k[-1].median_excess = 0.3551` — the last start point of the 50k-100k window, iteration 364,000 = 1.527 T; the period's first reading, 0.535, is the same series at iteration 25,000 (105 B) | `rate_readings.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶29.** The same holds for the whole graded profile, without any threshold: the loss of cosine similarity beyond the twin noise falls over 50,000–100,000 step…

| number | mark | file | field | script |
|---|---|---|---|---|
| 100,000 | `value` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][1]` | `rate_readings.py` |
| 50,000 | `value` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][0]` | `rate_readings.py` |
| 0.88 | `key` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.AsyncWith.current.share_below` | `ablation_ranks.py` |
| 0.87 | `value` | `validation/paper2/B14_BANDS.json` | `per_band.abs1sd.twin_ceiling_first_ref` | `b14_bands.py` |
| 0.03 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncFor.rise_over_random_nats` — the same entry as n_random_below, traced above | `ablation_ranks.py` |
| 0.24 | `value` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.cosine.chance` | `ceilings.py` |
| 0.49 | `key` | `validation/paper2/B3_GRADED.json` | `pairs.1000_steps|pretrain_iter_0001000|pretrain_iter_0002000.cosine_median` | `b3_graded.py` |
| 0.07 | `key` | `validation/paper2/C2_PYTHIA_TWIN.json` | `per_construct.NotADirectoryError.twin_unit_median_on_carriers` | `c2_pythia_twin.py` |
| 0.54 | `value` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.For.old_set.exact_one_sided_p` | `ablation_ranks.py` |
| 162 | `count` | `validation/r2/STEP5_FREQUENCY_pretrain.json` | `spearman.product|with_pilot.n = 162` — the constructs the frequency test is read on | `-` |
| 30 | `count` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.cosine.n_constructs` | `ceilings.py` |
| 80 | `declared` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary (the note 'R^2 > 0.8')` — the declared reporting floor; the constant is R2_FLOOR = 0.8 at experiments/rate_readings.py:44 | `rate_readings.py` |
| 19 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncFor.old_set.n_random_below` | `ablation_ranks.py` |
| 5 | `count` | `validation/paper2/RATE_READINGS.json` | `primary.q1pct.5k-10k[10].n_pairs` | `rate_readings.py` |
| 1 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_above_floor_by_more_than_one_unit` | `b2_anneal_drop.py` |

**¶30.** Of 18,034,712 departures of a neuron from a construct's 5% set between neighbouring checkpoints, 57% come back to the same set at a later checkpoint, …

| number | mark | file | field | script |
|---|---|---|---|---|
| 18,034,712 | `value` | `validation/paper2/B17_RETURN.json` | `departures` | `b17_return.py` |
| 58,000 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.absence_length_steps.q3` | `b17b_return_split.py` |
| 10,000 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.absence_length_steps.median` | `b17b_return_split.py` |
| 2,000 | `canon` | `validation/paper1/LENGTHS.json` | `by_set_kind.C.n_prompts` — the C pool's prompts | `atlas.py` |
| 3.37 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift_ci95[1]` — the same entry as q3, traced above | `b17b_return_split.py` |
| 3.27 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift_ci95[0]` — the same entry as q3, traced above | `b17b_return_split.py` |
| 92.5 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `share_of_departures_beyond_one_twin_unit = 0.92529` | `b17b_return_split.py` |
| 3.3 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift = 3.3189, lift_ci95 = [3.2741, 3.3676]` — the paper's '3.3, interval 3.27-3.37'. | `b17b_return_split.py` |
| 7.5 | `derived` | `validation/paper2/B17B_RETURN_SPLIT.json` | `1 - share_of_departures_beyond_one_twin_unit = 0.0747` — the complement of 92.5%. | `b17b_return_split.py` |
| 17 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.With.current.n_random_at_or_above` | `ablation_ranks.py` |
| 39 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|construct_token.pairs.curve2_norm x curve3_depth.n_censored_a` | `-` |
| 57 | `count` | `validation/paper1/POOLED_SETS_45.json` | `per_cut.2.categories.warning_class.exception_not_warning.n` | `pooled_sets_169.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶31.** The set as a whole does not return. For 167 of 169 constructs every checkpoint's nearest set is its immediate neighbour, and no two checkpoints' sets …

| number | mark | file | field | script |
|---|---|---|---|---|
| 167 | `key` | `validation/paper2/B18_RECURRENCE.json` | `a_n_nearest_is_neighbour = 167 (a_n_constructs_read = 169)` — NEW FIELD. Written 5 Nov by experiments/backfill_summaries.py, which checks each value against the figure the paper prints and refuses rather than write one that misses it; the writer script now produces it natively too. b18_recurrence.py. | `b18_recurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 1.5 | `key` | `validation/paper2/B18_RECURRENCE.json` | `c_coordination_vs_circular_shift_median = 1.4553` — the circular-shift null is the one that holds each neuron's persistence, which is what 'independent neurons with the same persistence' names. The across-neuron shuffle in the same file is 12.95 and is NOT this number. | `b18_recurrence.py` |

**¶32.** *Figure 4. Two readings of the drift. (a) Returns: the share of neurons that leave a construct's 5% set and re-enter it at a later checkpoint, against…

| number | mark | file | field | script |
|---|---|---|---|---|
| 2,034 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0484865.tokens_b = 2,033.67` — 2,034 billion tokens is this reference, iteration 484865 | `ceilings.py` |
| 16.7 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.departures = 16,687,320` — '16.7 million'. | `b17b_return_split.py` |
| 3.37 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift_ci95[1]` — the same entry as departures, traced above | `b17b_return_split.py` |
| 3.27 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift_ci95[0]` — the same entry as departures, traced above | `b17b_return_split.py` |
| 3.32 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_beyond_one_twin_unit.lift` — the same entry as departures, traced above | `b17b_return_split.py` |
| 3.63 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_within_one_twin_unit.lift_ci95[0]` — the same entry as departures, traced above | `b17b_return_split.py` |
| 3.74 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_within_one_twin_unit.lift_ci95[1]` — the same entry as departures, traced above | `b17b_return_split.py` |
| 92.5 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `share_of_departures_beyond_one_twin_unit = 0.92529` | `b17b_return_split.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 3.69 | `sibling` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_within_one_twin_unit.lift` — the same entry as departures, traced above | `b17b_return_split.py` |
| 1.3 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `arms.fell_within_one_twin_unit.departures = 1,347,392` — '1.3 million'. | `b17b_return_split.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶33.** Layer 12, the one layer measured, moves less between checkpoints than a free random walk would, and less as training goes on.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 12 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.sign_test_rise_over_random.n_above_zero` | `ablation_nats.py` |

**¶34.** *The free random walk.* OpenCoder trains at a constant learning rate η = 3 × 10⁻⁴ after a 2,000-step warm-up \citep{huang2024}. Under an Adam-family o…

| number | mark | file | field | script |
|---|---|---|---|---|
| 2,000 | `canon` | `validation/paper1/LENGTHS.json` | `by_set_kind.C.n_prompts` — the C pool's prompts | `atlas.py` |
| 10 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary.q1pct.61000.n_gaps` | `rate_readings.py` |
| 3 | `count` | `validation/paper2/RATE_READINGS.json` | `primary.q1pct.5k-10k[12].n_pairs` | `rate_readings.py` |

**¶35.** *The result.* Over 1,000 steps the three matrices move 0.51–0.67 of η·√D; over 20,000–30,000 steps, 0.65 early in training and 0.30 late. Successive s…

| number | mark | file | field | script |
|---|---|---|---|---|
| 20,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.start_iters[19]` | `b16c_steps_vs_lr.py` |
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 1,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|gate_proj.start_iters[0]` | `b16c_steps_vs_lr.py` |
| 0.51 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|up_proj.over_random_walk_first` | `b16c_steps_vs_lr.py` |
| 0.67 | `key` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[] filtered to window 1000, over_random_walk` — the upper end of the exact range over all 57 readings (19 start points x 3 matrices): max 0.6667 gate_proj, min 0.5053 up_proj, median 0.6029. The draft adopted 0.51-0.67 on 5 Nov in place of '0.5-0.6' (the flag 3). | `b16c_steps_vs_lr.py` |
| 0.30 | `sibling` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.over_random_walk_last` — the same entry as start_iters[19], traced above | `b16c_steps_vs_lr.py` |
| 0.65 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.over_random_walk_first` | `b16c_steps_vs_lr.py` |
| 0.3 | `key` | `validation/paper2/B16C_WEIGHT_STEPS.json` | `summary['<window>|<matrix>|<carriers,random>|<relative,absolute>_step'].{first,last}` — carriers against random rows are within 0.3% for 15 of the 24 comparisons, which is the qualification the draft now carries; the worst is 1.391% and the median-relative worst 0.403%, the other two figures in the same parenthesis. | `b16c_weight_steps.py` |
| 1.4 | `key` | `validation/paper2/B16C_WEIGHT_STEPS.json` | `summary['<window>|<matrix>|<carriers,random>|<relative,absolute>_step'].{first,last}` — the worst of the 24 carriers-against-random comparisons (3 matrices x 2 windows x relative and absolute step x first and last start point) is 1.391%, on the relative step, 20k-30k, gate_proj, last. The draft adopted this on 5 Nov in place of 'within 0.3%', which held for only 15 of the 24 (the flag 2). | `b16c_weight_steps.py` |
| 15 | `key` | `validation/paper2/B16C_WEIGHT_STEPS.json` | `summary['<window>|<matrix>|<carriers,random>|<relative,absolute>_step'].{first,last}` — within 0.3%: 3 matrices x 2 windows x relative and absolute step x first and last start point = 24 comparisons, of which 15 are within 0.3%; the worst is 1.391% | `b16c_weight_steps.py` |
| 24 | `key` | `validation/paper2/B16C_WEIGHT_STEPS.json` | `summary['<window>|<matrix>|<carriers,random>|<relative,absolute>_step'].{first,last}` — comparisons in total: 3 matrices x 2 windows x relative and absolute step x first and last start point = 24 comparisons, of which 15 are within 0.3%; the worst is 1.391% | `b16c_weight_steps.py` |

**¶36.** *The precision.* The fall from early to late holds, since every term but D is the same in both. The Frobenius norms of the three matrices grow over pr…

| number | mark | file | field | script |
|---|---|---|---|---|
| 89 | `derived` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.<first,last>.tensors.model.layers.12.mlp.up_proj.weight.frobenius` — the growth over pretraining, last/first - 1 = 89%; the two endpoints are stored, the ratio is not | `b16b_weight_norms.py` |
| 81 | `derived` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.<first,last>.tensors.model.layers.12.mlp.gate_proj.weight.frobenius` — the growth over pretraining, last/first - 1 = 81%; the two endpoints are stored, the ratio is not | `b16b_weight_norms.py` |
| 83 | `derived` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.<first,last>.tensors.model.layers.12.mlp.down_proj.weight.frobenius` — the growth over pretraining, last/first - 1 = 83%; the two endpoints are stored, the ratio is not | `b16b_weight_norms.py` |

**¶37.** A statement-initial keyword is a different vocabulary entry indented and at module level (`▁for` and `for`), two embeddings as unrelated as a random p…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.71 | `key` | `validation/paper1/SCOPE_OVERLAP.json` | `rows.<ref>|<construct>.share_of_ceiling.twin1` — the top of the range over the twelve constructs whose token differs by scope | `audit_recordings.py` |
| 0.44 | `key` | `validation/paper1/SCOPE_OVERLAP.json` | `rows.pretrain_iter_0484865|Match.share_of_ceiling.twin1` | `audit_recordings.py` |
| 0.59 | `key` | `validation/paper1/SCOPE_OVERLAP.json` | `rows.pretrain_iter_0484865|For.share_of_ceiling.twin1` — `for`'s two scope tokens' carrier-set share of the twin ceiling, at the last reference | `audit_recordings.py` |

**¶38.** The size of the response — on the raw, unstandardised profile — falls over training for 148 of 169 constructs while the loss is flat, and stops fallin…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.036 | `sibling` | `validation/r2/R2_CLOSE.json` | `pretrain|curve1_interval.curves.AsyncFor.points[1].relative_se_denominator` — the same entry as relative_se_denominator, traced above | `r2_close.py` |
| 0.064 | `key` | `validation/r2/owed/RAW_NORM_REREAD_pretrain.json` | `third_sense.without_pilot|raw.coefficients.log_frequency.beta = -0.06443` — the coefficient quoted in para 35 is the WITHOUT-pilot raw arm; the with-pilot arm is -0.06827, which is the one para 45 and para 98 turn into 1.2 | `-` |
| 0.103 | `value` | `validation/r2/R2_CLOSE.json` | `pretrain|curve1_interval.curves.AssertionError.points[14].relative_se_denominator` | `r2_close.py` |
| 1.2 | `declared` | `validation/paper2/RATE_READINGS.json` | `primary.carrier5.50k-100k[-1].start_iter = 364,000` — SETTLES [TBC: 23]: 364,000 x 4,194,304 tokens/iter = 1.527e12, so 1.5 trillion, not 1.2. The draft's alternative 1.2 T is iteration 291,000, the start point before it. | `rate_readings.py` |
| 148 | `count` | `validation/r2/STEP4_FLAT_pretrain.json` | `window.n_ratio_falling` | `p8_bootstrap.py` |
| 500 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0119000.tokens_b = 499.12` — 500 billion tokens is this reference, iteration 119000 | `ceilings.py` |
| 1.5 | `key` | `validation/paper2/B18_RECURRENCE.json` | `c_coordination_vs_circular_shift_median = 1.4553` — the circular-shift null is the one that holds each neuron's persistence, which is what 'independent neurons with the same persistence' names. The across-neuron shuffle in the same file is 12.95 and is NOT this number. | `b18_recurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 59 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|construct_token.columns.curve3_depth.n_dated` | `-` |
| 90 | `key` | `validation/r2/owed/RAW_NORM_REREAD_pretrain.json` | `n_dated.raw = 90` — as para 88 | `-` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 97 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|construct_token.columns.curve6_sparsity.n_dated` | `-` |

**¶39.** Over the record the sharing of carriers between two constructs falls by more than its noise for 11,402 of the 14,196 pairs and rises by more than its …

| number | mark | file | field | script |
|---|---|---|---|---|
| 11,402 | `key` | `validation/r2/STEP8_GRAPH_pretrain.json` | `p8.n_fell_beyond_noise` | `-` |
| 14,196 | `canon` | `validation/paper2/COOCCURRENCE.json` | `pairs_total` — all construct pairs | `cooccurrence.py` |
| 1,868 | `value` | `validation/r2/STEP8_GRAPH_pretrain.json` | `p8.n_rose_beyond_noise` | `-` |

**¶40.** **"Stopped learning", stated exactly.** At the forced and expected positions the loss on the battery falls no further than one noise unit or 10% of it…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.571 | `key` | `validation/paper2/B1_ENTROPY.json` | `constructs.For.roles.in.floor_nats` | `b1_entropy.py` |
| 0.59 | `value` | `validation/paper1/POOLED_SETS_45.json` | `significant_after_holm[12].purity` | `pooled_sets_169.py` |
| 0.09 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct.For.rise_over_random_nats` | `ablation_nats.py` |
| 0.55 | `value` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.Raise.a_nearest_set.under_b10_model.mean` | `b18_recurrence.py` |
| 2.5 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `dependent.governed.series['For|governed|governed_use'].level_last = 2.5155` — the draft now says "`For`'s series alone falls from 5.6 to 2.5 nats" and no longer attributes it to the four dependent positions or to Figure 1a (the flag 1, acted on 5 Nov). | `p8_bootstrap.py` |
| 6.0 | `key` | `validation/paper2/B1_ENTROPY.json` | `against_the_model.model_loss_governed_early_median_nats = 6.0087` — the median over the three counting governed series. | `b1_entropy.py` |
| 5.9 | `key` | `validation/paper2/B1_ENTROPY.json` | `against_the_model.generator_marginal_entropy_governed_median_nats = 5.8941` | `b1_entropy.py` |
| 10 | `count` | `validation/paper2/B1_ENTROPY.json` | `governed_slot_entropy.n_slots_with_at_least_20_positions` | `b1_entropy.py` |
| 23 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_series_compared` | `b2_anneal_drop.py` |
| 20 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.from_84b_to_last.counts.flat` — the leg 84 B -> end | `p8_bootstrap.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 24 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_series` | `b2_anneal_drop.py` |
| 7 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_below_floor_by_more_than_one_unit` | `b2_anneal_drop.py` |

**¶41.** **The question.** At the forced positions the construct's own gradient is silent from 4% of training on. Why do the neurons that carry it keep changin…

| number | mark | file | field | script |
|---|---|---|---|---|
| 4 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.While.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶43.** 2. *Displacement by new learning.* Other constructs claim the neurons and push the carriers out. It predicts turnover that follows how much other sets…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.09 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.Try.old_set_rise_nats` | `ablation_nats.py` |
| 18 | `count` | `validation/paper2/B5_CHURN_VS_LEARNING.json` | `within_pair_across_constructs.n_pairs_positive` | `b5_churn.py` |
| 19 | `count` | `validation/paper2/B5_CHURN_VS_LEARNING.json` | `n_pairs` | `b5_churn.py` |

**¶48.** Four artefacts of measurement would each have produced settling dates or a false constancy. (1) The turnover curve's level falls with the gap at which…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.813 | `value` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.DictComp.old_set.exact_one_sided_p` | `ablation_ranks.py` |
| 1,404 | `value` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.n_pairs` | `step4_flat.py` |
| 1.527 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0364000.tokens_b = 1,526.73` — 1.527 trillion tokens is this reference, iteration 364000 | `ceilings.py` |
| 1.25 | `declared` | `validation/r2/R2_INDEX_CURVES.json` | `partner_factor.pretrain.band[0] = 1.25` — the declared partner-factor band's lower edge | `r2_curves.py` |
| 144 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.without_pilot|layer|construct_token.columns.curve1_turnover.n_censored` | `-` |
| 1.2 | `declared` | `validation/paper2/RATE_READINGS.json` | `primary.carrier5.50k-100k[-1].start_iter = 364,000` — SETTLES [TBC: 23]: 364,000 x 4,194,304 tokens/iter = 1.527e12, so 1.5 trillion, not 1.2. The draft's alternative 1.2 T is iteration 291,000, the start point before it. | `rate_readings.py` |
| 1.9 | `derived` | `validation/r2/STEP3_SENSES_pretrain.json` | `third_sense.with_pilot|curve2_norm|lognormal.coefficients.log_frequency.beta = -0.27367` — 10^|beta| = 1.878, standardised. | `-` |
| 148 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.For.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 6 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.DictComp.current.n_random_at_or_above` | `ablation_ranks.py` |

**¶50.** 2. The readable positions are the constructs' forced grammar, not their use, and are marked for 16 constructs, on which the behaviour and reliance cla…

| number | mark | file | field | script |
|---|---|---|---|---|
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.n_constructs` | `ablation_nats.py` |

**¶51.** 3. The record begins at 4.19 billion tokens, so formation is not in it.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |

**¶52.** 4. The annealing branch is 0.026 decades wide and changes the data mix at the same moment as the rate.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.026 | `key` | `validation/r2/CURVE1_SPACING_anneal.json` | `resolution.branch_span_decades` | `step7.py` |

**¶53.** 5. The null has no power past about 500 billion tokens for a gradual settling.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 500 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0119000.tokens_b = 499.12` — 500 billion tokens is this reference, iteration 119000 | `ceilings.py` |

**¶54.** 6. The battery is synthetic Python, shown to a model that read 607 languages \citep{huang2024}.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 607 | `cited` | — | Huang et al., 2024 (OpenCoder's pretraining corpus). FLAG 4: the limitation sentence names no source for it; the citation is only in para 100 and 128. Suggest adding \citep{huang2024} there. | — |

**¶55.** 7. The carrier set is one cut of a graded profile at 5%; a third of its turnover is neurons crossing that line by a small margin, though tightening th…

| number | mark | file | field | script |
|---|---|---|---|---|
| 5 | `count` | `validation/paper1/POOLED_SETS_45.json` | `per_cut.5.n_clusters_realised` | `pooled_sets_169.py` |

**¶56.** 8. Every number is on the 20-cell yardstick of \citet{wilam2026}, whose sensitivity that paper reports: the turnover moves by 0.003–0.005 under a yard…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.005 | `value` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0484865.paired_differences.v_minus_twenty.ci95[0]` | `c3_yardstick_nats.py` |
| 0.003 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.While.old_set_over_random_nats` | `ablation_nats.py` |
| 20 | `count` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0001000.n_random_masks` | `c3_yardstick_nats.py` |

**¶57.** **Persistence and change.** \citet{nandan2025} find that over 80% of universal neurons persist across five GPT-2 Small seeds between 100,000 and 300,0…

| number | mark | file | field | script |
|---|---|---|---|---|
| 300,000 | `value` | `calibration/checkpoints.json` | `all[210].step` | `checkpoint_inventory.py` |
| 100,000 | `value` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary.windows_steps[3][1]` | `rate_readings.py` |
| 7,373 | `canon` | `validation/paper2/B14_BANDS.json` | `per_band.q5pct.band_size_first_ref` — the 5% cut's carrier-set size, 5% of 24 x 6,144 | `b14_bands.py` |
| 1,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|gate_proj.start_iters[0]` | `b16c_steps_vs_lr.py` |
| 10.2 | `cited` | — | Wang et al., 2026 (OLMo-7B top-1% overlap). Verified against the sentence: the nearest preceding citation is \citet{wang2026}. | — |
| 0.6 | `cited` | — | Aljaafari et al., 2026 (Jaccard >= 0.6). Cited work, not ours. | — |
| 906 | `cited` | — | Wang et al., 2026. Verified: nearest preceding citation is \citet{wang2026}. | — |
| 555 | `cited` | — | Yao, Boguraev et al., 2026. Verified against the sentence: the nearest preceding citation is \citet{yao2026}, not \citet{nandan2025}. | — |
| 160 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|construct_token.columns.curve6_sparsity.n` | `-` |
| 68 | `cited` | — | cited work, not ours: the upper end of '35-68% of the later gain'. | — |
| 40 | `cited` | — | cited work, not ours: Aljaafari et al., 2026. | — |
| 80 | `cited` | — | cited work, not ours: Nandan et al., 2025 (over 80% of universal neurons). | — |
| 20 | `key` | `validation/paper2/B3_ALLPAIRS.json` | `cosine.n_dense = 20` — the dense block's pairs | `b3_allpairs.py` |
| 35 | `cited` | — | cited work, not ours: Ge et al., 2026 (35-68% of the later gain). | — |
| 1 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct_ratio.n_excluded_control_mean_not_positive` | `ablation_nats.py` |

**¶58.** **Stages.** Phases have been described in crosscoder features \citep{ge2026}, in the geometry of representations \citep{li2025}, in behaviour \citep{m…

| number | mark | file | field | script |
|---|---|---|---|---|
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 148 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.For.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 0.2 | `derived` | `validation/paper2/B11_POWER.json` | `dates.step|84B.tokens and the record's span` — 4.194e9 / 2.0337e12 = 0.206%: the first checkpoint as a share of the record. | `b11_power.py` |

**¶59.** 1. *The declared stimulus distribution.* For each construct, a written list of the factors around it — identifiers and literals, scope and nesting, co…

| number | mark | file | field | script |
|---|---|---|---|---|
| 253,398 | `key` | `calibration/corpus.json` | `parsed` | `build_natural.py` |

**¶60.** 2. *Three sets of prompts.* Set A holds the construct in its role (`for x in range(n):` with a body). Set B holds the construct's token outside its ro…

| number | mark | file | field | script |
|---|---|---|---|---|
| 720 | `count` | `validation/paper2/B1_ENTROPY.json` | `constructs.AnnAssign.roles.header_colon.n` | `b1_entropy.py` |

**¶61.** 3. *The read site.* The construct's first token: `for` in a loop, `len` in a call. A construct is admitted only if its A and B prompts land on the sam…

| number | mark | file | field | script |
|---|---|---|---|---|
| 188 | `canon` | `validation/paper1/CORE_COUNTS.json` | `n_constructs_built` — the constructs the battery holds | `core_counts.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 80 | `count` | `validation/ablation/PLAN.json` | `plan.total_construct_passes` | `ablation_full.py` |

**¶62.** 4. *The profile.* For each of the 147,456 neurons (24 layers × 6,144 hidden units of the SwiGLU MLP, read before the down-projection), the mean activa…

| number | mark | file | field | script |
|---|---|---|---|---|
| 147,456 | `canon` | `validation/r2/STEP8_GRAPH_pretrain.json` | `n_units` — the product space, 24 layers x 6,144 neurons | `-` |
| 6,144 | `key` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.tensors.model.layers.12.mlp.gate_proj.weight.shape[0]` | `b16b_weight_norms.py` |
| 24 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.AsyncWith.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶63.** 5. *The yardstick.* Each activation is restated in units of the neuron's ordinary spread: z = (x − μ₀)/σ₀, with μ₀ and σ₀ the neuron's mean and spread…

| number | mark | file | field | script |
|---|---|---|---|---|
| 20 | `count` | `validation/paper1/RECHECK_PER_PROMPT.json` | `rows.untrained|Assert.7a null_scrambled.n_rep` | `recheck_per_prompt.py` |
| 2 | `declared` | — | illustrative: 'an entry of 2 means the neuron responds by two of its ordinary spreads'. Part of the definition of the profile, not a reading. | — |

**¶64.** 6. *The carrier set.* The 5% of neurons with the largest standardised entries, 7,373 neurons. Two random 5% sets overlap by 0.05.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 7,373 | `canon` | `validation/paper2/B14_BANDS.json` | `per_band.q5pct.band_size_first_ref` — the 5% cut's carrier-set size, 5% of 24 x 6,144 | `b14_bands.py` |
| 0.05 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.ListComp.old_set_over_random_nats` | `ablation_nats.py` |
| 5 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '5pct'` — the 5% cut that defines the carrier set, and one of the nine declared flat-leg settings | `p8_bootstrap.py` |

**¶65.** 7. *The twins and their three units.* Each construct has eight structurally distinct cores, and every prompt is a core in drawn surroundings. The batt…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.28 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `per_reference.untrained.twin_overlap_median` | `b12_twin_turnover.py` |
| 0.16 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `per_reference.pretrain_iter_0001000.twin_turnover_median` | `b12_twin_turnover.py` |
| 0.84 | `key` | `validation/paper2/C2_PYTHIA_TWIN.json` | `opencoder_comparison.carrier_overlap_last_checkpoint` | `c2_pythia_twin.py` |

**¶69.** 11. *The resolution.* The step between a construct's profiles at neighbouring checkpoints, in twin units. Where it is below one, no date can fall betw…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 8.56 | `value` | `validation/paper1/FIGURES.json` | `check9.pairs.pretrain_iter_0002000.median_p1` | `atlas.py` |
| 3.56 | `key` | `validation/paper1/CHECK4_RELATIVE.json` | `per_construct[176].check4_twin_units` | `check4_relative.py` |

**¶70.** *The standardisation.* All carrier sets are read under the 20-cell yardstick of \citet{wilam2026} (the standardisation of each neuron by its ordinary …

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.005 | `derived` | `validation/paper1/TURNOVER_CLASSES_ONLY.json` | `summary["<pair>|twenty"].median_ratio - summary["<pair>|classes"].median_ratio, over the three stored pairs` — the retention ratio under the classes-only split against the 20-cell one: 0.36803/0.36547 (1k->2k), 0.52673/0.52173 (2k->3k), 0.78275/0.78811 (19k->20k) -- differences 0.0026, 0.0050 and -0.0054, so the printed range 0.003-0.005 is these three rounded, the last one larger under the coarser split. The artefact is paper 1's; this is one of the 31 files paper 2 reads from the other paper's directory. | `b10.py` |
| 0.003 | `derived` | `validation/paper1/TURNOVER_CLASSES_ONLY.json` | `summary["<pair>|twenty"].median_ratio - summary["<pair>|classes"].median_ratio, over the three stored pairs` — the retention ratio under the classes-only split against the 20-cell one: 0.36803/0.36547 (1k->2k), 0.52673/0.52173 (2k->3k), 0.78275/0.78811 (19k->20k) -- differences 0.0026, 0.0050 and -0.0054, so the printed range 0.003-0.005 is these three rounded, the last one larger under the coarser split. The artefact is paper 1's; this is one of the 31 files paper 2 reads from the other paper's directory. | `b10.py` |
| 20 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary.carrier5.15000.n_gaps` | `rate_readings.py` |

**¶86.** We also wrote down, before reading, what count of constructs we expected to be readable (80 to 120), and that if fewer than 43 constructs had a settli…

| number | mark | file | field | script |
|---|---|---|---|---|
| 120 | `canon` | `validation/r2/P8_BOOTSTRAP_pretrain.json` | `n_pairs` — the checkpoint pairs the core bootstrap runs on | `p8_bootstrap.py` |
| 43 | `count` | `calibration/identifiers.json` | `ecommerce.detail.egg_project_name.count` | `-` |
| 80 | `count` | `validation/ablation/PLAN.json` | `plan.total_construct_passes` | `ablation_full.py` |

**¶89.** Statement 3 (nothing beyond the cheapest without demand) has its first support: the response's size does not keep growing once the loss is flat — it s…

| number | mark | file | field | script |
|---|---|---|---|---|
| 90 | `count` | `validation/loss/CORE_pretrain_iter_0001000.json` | `sets.For|B.by_target_piece.▁▁▁▁▁▁▁.n` | `-` |

**¶91.** Before the OpenCoder record was read, three things were written down and hashed: the hypothesis and nine predictions of Appendix B; the analysis plan …

| number | mark | file | field | script |
|---|---|---|---|---|
| 256 | `count` | `validation/paper2/TEST6_EXTRAS.json` | `pairs.0019000:0020000.top20_token_pairs[0].n_departures` | `test6_extras.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 0 | `count` | `validation/paper2/DATES_TABLE.json` | `settling.n_dated_under_the_corrected_rule` | `dates_table.py` |

**¶92.** A construct is settled at a checkpoint if the kept fraction of its 5% carrier set, measured against a partner checkpoint, crosses a threshold θ and st…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.50 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.current.share_below` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 0.70 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncWith.current.share_below` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 2.00 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `per_band key '1.65-2.0'` — a declared band edge | `step4_flat.py` |
| 1.25 | `declared` | `validation/r2/R2_INDEX_CURVES.json` | `partner_factor.pretrain.band[0] = 1.25` — the declared partner-factor band's lower edge | `r2_curves.py` |
| 0.01 | `value` | `validation/paper2/B10_SPACING_ADJUSTED.json` | `per_start.1000.per_1000_steps` | `b10_fit.py` |
| 0.95 | `value` | `validation/paper2/B6_PERLAYER_SHARING.json` | `per_layer.6.trend_spearman_vs_log_step` | `b6_perlayer.py` |
| 5 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` | `ablation_ranks.py` |

**¶93.** 1. *The ratio form.* The partner is the checkpoint whose token count is between 1.25 and 2 times the checkpoint's own.…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1.25 | `declared` | `validation/r2/R2_INDEX_CURVES.json` | `partner_factor.pretrain.band[0] = 1.25` — the band's lower edge | `r2_curves.py` |
| 2 | `declared` | `validation/r2/R2_INDEX_CURVES.json` | `partner_factor.pretrain.band = [1.25, 2.0]` — the declared partner band: the partner's token count is 1.25 to 2 times the checkpoint's own. Also stored as CURVE1_SPACING_pretrain.json :: band. | `r2_curves.py` |

**¶95.** 3. *What went wrong in the ratio form.* Twelve constructs dated at one and the same checkpoint, 1.527 trillion tokens. The checkpoint itself is health…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.813 | `value` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.DictComp.old_set.exact_one_sided_p` | `ablation_ranks.py` |
| 0.611 | `value` | `validation/paper2/ABLATION_STABLE.json` | `per_reference.pretrain_iter_0484865.per_construct.ImportFrom.control_stability.100.control_sd` | `ablation_stable.py` |
| 1,404 | `value` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.n_pairs` | `step4_flat.py` |
| 0.747 | `key` | `validation/paper1/FIGURES.json` | `ceiling.bootstrap_mean.pretrain_iter_0364000 = 0.74657` — the checkpoint the twelve constructs date at, iteration 364,000 = 1.527 trillion tokens. The series is the median over P1 of the twin-against-twin top-5% carrier overlap in the product space, core-bootstrap mean -- paper 2's convention for a checkpoint's ceiling. | `atlas.py` |
| 0.744 | `key` | `validation/paper1/FIGURES.json` | `ceiling.bootstrap_mean.pretrain_iter_0291000 = 0.74360` — the start point before it. The series is the median over P1 of the twin-against-twin top-5% carrier overlap in the product space, core-bootstrap mean -- paper 2's convention for a checkpoint's ceiling. | `atlas.py` |
| 1.527 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0364000.tokens_b = 1,526.73` — 1.527 trillion tokens is this reference, iteration 364000 | `ceilings.py` |
| 0.749 | `key` | `validation/paper1/FIGURES.json` | `ceiling.bootstrap_mean.pretrain_iter_0233000 = 0.74862` — the start point before that. The series is the median over P1 of the twin-against-twin top-5% carrier overlap in the product space, core-bootstrap mean -- paper 2's convention for a checkpoint's ceiling. | `atlas.py` |
| 0.717 | `key` | `validation/r2/CURVE1_SPACING_pretrain.json` | `product.constructs.<c>.per_band.<band>.max_ratio` — the kept fraction read at a factor of about 1.25 at one index, in the same sentence | `step4_flat.py` |
| 1.35 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.2-1.35' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |
| 1.56 | `value` | `validation/r2/STEP8_GRAPH_pretrain.json` | `partners[29].factor` | `-` |
| 1.25 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0011000.tensors.model.layers.12.mlp.up_proj.weight.row_norm_q3` | `b16b_weight_norms.py` |
| 0.73 | `key` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band['1.2-1.35'].median_ratio = 0.7316` — as 0.61; the artefact's lowest band starts at 1.20 where the draft writes 1.25. | `step4_flat.py` |
| 0.61 | `key` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band['1.65-2.1'].median_ratio = 0.6127` — the draft adopted the ALL-CONSTRUCT reading, so this is now a stored field. the earlier `unstored` note, that the figures were the twelve-suspect subset, no longer applies. | `step4_flat.py` |
| 1.65 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.65-2.1' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |
| 1.2 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.2-1.35'` — a band edge, named in the key. The 18:18 draft now writes the artefact's own edges (1.2-1.35 and 1.65-2.1) rather than the rule's declared 1.25 and 2.0, so the paper and the artefact agree verbatim. | `step4_flat.py` |
| 2.1 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.65-2.1'` — a band edge, named in the key. The 18:18 draft now writes the artefact's own edges (1.2-1.35 and 1.65-2.1) rather than the rule's declared 1.25 and 2.0, so the paper and the artefact agree verbatim. | `step4_flat.py` |

**¶96.** 4. *What went wrong in the fixed-step form.* The same defect at a different place: its 13 dates all fall at the checkpoint whose fixed partner is the …

| number | mark | file | field | script |
|---|---|---|---|---|
| 29,865 | `key` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[162].gap` | `b16c_steps_vs_lr.py` |
| 13 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|hashed.columns.curve4_loss.n` | `-` |

**¶98.** 6. *The corrected rule.* A date needs all of: (i) an observed crossing of θ, not a series already above it; (ii) at least one checkpoint below θ befor…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1.35 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.35-1.5' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |
| 1.25 | `value` | `validation/paper2/A38_POPULATION.json` | `factor_band[0]` | `-` |
| 1.65 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.65-2.1' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |
| 1.5 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.5-1.65' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |
| 2.0 | `declared` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.by_band key '1.65-2.1' (and product.*.per_band keys)` — a declared band edge of the corrected rule, named in the key. Note the artefact's lowest band starts at 1.20 where the draft's four-way split starts at 1.25. | `step4_flat.py` |

**¶100.** Over 169 constructs the ratio form dates none (159 censored, 10 transient crossings) and the fixed form dates 13, all at the checkpoint named above; t…

| number | mark | file | field | script |
|---|---|---|---|---|
| 99.1 | `key` | `validation/paper2/B11_POWER.json` | `dates.step|500B.detection_rate = 0.99112` | `b11_power.py` |
| 99.4 | `key` | `validation/paper2/B11_POWER.json` | `dates.step|{84B,200B,1000B,1500B}.detection_rate = 0.99408` | `b11_power.py` |
| 100 | `key` | `validation/paper2/B11_POWER.json` | `dates.exponential|500B.detection_rate = 1.0` | `b11_power.py` |
| 338 | `canon` | `validation/paper2/B11_POWER.json` | `dates.step|84B.draws` — the injected draws in each power cell | `b11_power.py` |
| 500 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0119000.tokens_b = 499.12` — 500 billion tokens is this reference, iteration 119000 | `ceilings.py` |
| 159 | `canon` | `validation/paper2/DATES_TABLE.json` | `settling.ratio_outcomes.censored` — the censored constructs under the ratio form | `dates_table.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 10 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.with_pilot|product|construct_token.pairs.curve2_norm x curve4_loss.n_censored_a` | `-` |
| 13 | `count` | `validation/paper1/C3_YARDSTICK_NATS.json` | `per_reference.pretrain_iter_0001000.per_yardstick.v.sign_test.n_above_zero` | `c3_yardstick_nats.py` |
| 0 | `count` | `validation/paper2/DATES_TABLE.json` | `n_constructs_with_all_six_dated` | `dates_table.py` |

**¶101.** Curve 4's series are keyed by construct, position class, role and token piece. The obliged class is the forced and expected positions; three forced po…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.5 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '0.5'` — one of the nine declared flat-leg settings (5/10/20% x 0.5/1/2 units), named in the key | `p8_bootstrap.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 24 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.AsyncWith.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 10 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '10pct'` — one of the nine declared flat-leg settings (5/10/20% x 0.5/1/2 units), named in the key | `p8_bootstrap.py` |
| 38 | `count` | `validation/paper1/CHECK6_COMPANIONS.json` | `per_construct.For.n_companions` | `check6_companions.py` |
| 21 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `forced.n_single_piece` | `b2_anneal_drop.py` |
| 35 | `count` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.set__builtin.b_configurations.n_clusters_within_one_twin_ceiling` | `b18_recurrence.py` |
| 20 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '20'` — one of the nine declared flat-leg settings (5/10/20% x 0.5/1/2 units), named in the key | `p8_bootstrap.py` |
| 5 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '5pct'` — one of the nine declared flat-leg settings  ||  the 5% cut that defines the carrier set, and one of the nine declared flat-leg settings | `p8_bootstrap.py` |
| 3 | `key` | `validation/r2/STEP4_FLAT_pretrain.json` | `legs.forced.to_84b.counts.rising` — the leg 4.19 -> 84 B, at the default threshold 10pct|1.0u; `across_thresholds` holds the other eight settings | `p8_bootstrap.py` |
| 8 | `count` | `validation/paper2/B1_ENTROPY.json` | `against_the_model.n_governed_series` | `b1_entropy.py` |
| 2 | `declared` | `validation/r2/STEP4_FLAT_pretrain.json` | `thresholds keys containing '2'` — one of the nine declared flat-leg settings (5/10/20% x 0.5/1/2 units), named in the key | `p8_bootstrap.py` |
| 1 | `count` | `validation/paper2/B2_ANNEAL_DROP.json` | `against_the_pretraining_floor.n_above_floor_by_more_than_one_unit` | `b2_anneal_drop.py` |

**¶102.** The six curves' dates for all 169 constructs under the corrected rule, with both curve-1 forms and the reason no settling date exists, is `validation/…

| number | mark | file | field | script |
|---|---|---|---|---|
| 14,196 | `canon` | `validation/paper2/COOCCURRENCE.json` | `pairs_total` — all construct pairs | `cooccurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 1 | `count` | `validation/paper2/DATES_TABLE.json` | `rows[1].n_of_six_dated` | `dates_table.py` |

**¶103.** 1. *The tail spacing.* The turnover curve's level depends on how far apart in tokens a checkpoint and its comparison partner are (Spearman −0.813 over…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1,404 | `value` | `validation/r2/CURVE1_SPACING_pretrain.json` | `spacing_dependence.n_pairs` | `step4_flat.py` |
| 1.527 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0364000.tokens_b = 1,526.73` — 1.527 trillion tokens is this reference, iteration 364000 | `ceilings.py` |
| 0.813 | `value` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.DictComp.old_set.exact_one_sided_p` | `ablation_ranks.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |

**¶104.** 2. *The annealing threshold.* On a branch only 6% long, nearly every turnover value is above the settling threshold from the first checkpoint, so 169 …

| number | mark | file | field | script |
|---|---|---|---|---|
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 6 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.DictComp.current.n_random_at_or_above` | `ablation_ranks.py` |

**¶105.** 3. *The two forms of size.* The response's size can be measured raw or standardised. Our contract made raw primary, because the pilot had shown that t…

| number | mark | file | field | script |
|---|---|---|---|---|
| 144 | `count` | `validation/r2/STEP3_SENSES_pretrain.json` | `second_sense.without_pilot|layer|construct_token.columns.curve1_turnover.n_censored` | `-` |
| 1.2 | `declared` | `validation/paper2/RATE_READINGS.json` | `primary.carrier5.50k-100k[-1].start_iter = 364,000` — SETTLES [TBC: 23]: 364,000 x 4,194,304 tokens/iter = 1.527e12, so 1.5 trillion, not 1.2. The draft's alternative 1.2 T is iteration 291,000, the start point before it. | `rate_readings.py` |
| 1.9 | `derived` | `validation/r2/STEP3_SENSES_pretrain.json` | `third_sense.with_pilot|curve2_norm|lognormal.coefficients.log_frequency.beta = -0.27367` — 10^|beta| = 1.878, standardised. | `-` |
| 148 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0484865.per_construct.For.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 6 | `count` | `validation/r2/owed/RAW_NORM_REREAD_pretrain.json` | `step6.standardised.groups.for.n_dated` | `-` |
| 1 | `key` | `validation/paper2/DATES_TABLE.json` | `rows[].n_of_six_dated` — '1 of 6 dated': the family's dated count | `dates_table.py` |

**¶106.** 4. *The per-step figure from divided pairs.* An earlier draft said the change per 1,000 steps was "roughly constant across pretraining". True 1,000-st…

| number | mark | file | field | script |
|---|---|---|---|---|
| 1,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.1000|gate_proj.start_iters[0]` | `b16c_steps_vs_lr.py` |
| 1.25 | `declared` | `validation/r2/R2_INDEX_CURVES.json` | `partner_factor.pretrain.band[0] = 1.25` — the declared partner-factor band's lower edge | `r2_curves.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |

**¶107.** The same hazard appears in behaviour: \citet{nishida2025} report checkpoint-to-checkpoint volatility in benchmark scores large enough that averaging n…

| number | mark | file | field | script |
|---|---|---|---|---|
| 147,456 | `canon` | `validation/r2/STEP8_GRAPH_pretrain.json` | `n_units` — the product space, 24 layers x 6,144 neurons | `-` |
| 41 | `derived` | `validation/r2/owed/TIEBREAK_SENSITIVITY.json` | `n_modal_moves = 70 over n_read = 169 = 0.4142` — an earlier search had searched for a field valued 0.41 rather than for the count. No new field was needed. | `r2_owed.py` |

**¶108.** Pooled over all constructs, the fraction of carriers kept between neighbouring checkpoints falls from 0.66 between the checkpoints at 67 and 71 billio…

| number | mark | file | field | script |
|---|---|---|---|---|
| 30,000 | `value` | `validation/paper2/B16C_STEPS_VS_LR.json` | `rows[6].gap` | `b16c_steps_vs_lr.py` |
| 20,000 | `key` | `calibration/checkpoints.json` | `all[14].step` | `checkpoint_inventory.py` |
| 14,424 | `value` | `validation/paper2/B14_BANDS.json` | `per_band.abs1sd.band_size_last_ref` | `b14_bands.py` |
| 0.964 | `key` | `validation/paper2/TBC22_SHARES.json` | `cuts.q1pct.share_of_ceiling` | `tbc22_shares.py` |
| 0.917 | `key` | `validation/paper2/TBC22_SHARES.json` | `cuts.abs1sd.share_ci95[0] = 0.9171` — the broadest cut's share of its own ceiling, 0.9248 [0.9171, 0.9371] | `tbc22_shares.py` |
| 0.952 | `sibling` | `validation/paper2/TBC22_SHARES.json` | `cuts.q1pct.share_ci95[0]` — the same entry as share_of_ceiling, traced above | `tbc22_shares.py` |
| 0.937 | `key` | `validation/paper2/TBC22_SHARES.json` | `cuts.abs1sd.share_ci95[1] = 0.9371` — the upper end of the same interval | `tbc22_shares.py` |
| 0.977 | `value` | `validation/paper2/CEILINGS_PAIRWISE.json` | `per_window.~1,000[7].cosine.twin` | `-` |
| 0.925 | `key` | `validation/paper1/CHECK6_TURNOVER.json` | `per_construct.With.per_reference.pretrain_iter_0001000.reweighted.ceiling.overlap` | `check6_turnover.py` |
| 0.85 | `key` | `validation/paper2/B14_BANDS.json` | `per_band.q1pct.rank_stability_median_x1.5` | `b14_bands.py` |
| 0.82 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.ListComp.old_set.share_below` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 0.66 | `key` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.quoted_in_the_paper.kept_fraction_by_71b = 0.6623` — NEW FIELD, as para 19. | `b12_twin_turnover.py` |
| 0.49 | `value` | `validation/paper2/B12_TWIN_TURNOVER.json` | `between_checkpoints.per_pair[29].turnover_median` | `b12_twin_turnover.py` |
| 0.70 | `value` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.False.twin_ceiling` | `b18_recurrence.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 1.9 | `derived` | `validation/r2/STEP3_SENSES_pretrain.json` | `third_sense.with_pilot|curve2_norm|lognormal.coefficients.log_frequency.beta = -0.27367` — 10^|beta| = 1.878, standardised. | `-` |
| 1.5 | `key` | `validation/paper2/B18_RECURRENCE.json` | `c_coordination_vs_circular_shift_median = 1.4553` — the circular-shift null is the one that holds each neuron's persistence, which is what 'independent neurons with the same persistence' names. The across-neuron shuffle in the same file is 12.95 and is NOT this number. | `b18_recurrence.py` |
| 744 | `key` | `validation/paper2/B14_BANDS.json` | `per_band.abs3sd.band_size_first_ref = 744` — the narrowest of the six cuts; the widest, 14,424, is per_band.abs1sd.band_size_last_ref. Also at CEILINGS.json per_reference.pretrain_iter_0001000.abs3sd.median_size. | `b14_bands.py` |
| 67 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0016000.tokens_b = 67.11` — 67 billion tokens is this reference, iteration 16000 | `ceilings.py` |
| 22 | `count` | `validation/r2/CURVE1_SPACING_anneal.json` | `product.constructs.set__builtin.per_band.2ref.n` | `step7.py` |
| 71 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0017000.tokens_b = 71.30` — 71 billion tokens is this reference, iteration 17000 | `ceilings.py` |
| 2 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_without` | `ablation_nats.py` |
| 3 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncWith.old_set.n_random_at_or_above` | `ablation_ranks.py` |
| 1 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct_ratio.n_excluded_control_mean_not_positive` — the same entry as n_constructs_with_an_old_set, traced above | `ablation_nats.py` |
| 5 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.With.old_set.n_random_at_or_above` — the same entry as n_random_at_or_above, traced above | `ablation_ranks.py` |
| 0 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.old_set.n_constructs_with_an_old_set` | `ablation_nats.py` |

**¶109.** **Table D.2 — the fitted per-step rates, where the fit holds.** The secondary reading of `RATE_READINGS.json`: turnover(t, D) = c(t) + A(t)(1 - exp(-r…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.8 | `declared` | `validation/paper2/RATE_READINGS.json` | `definition_1_primary (the note 'R^2 > 0.8'); the constant is R2_FLOOR = 0.8 at experiments/rate_readings.py:44` — a declared reporting floor. | `rate_readings.py` |

**¶110.** **Rates reported: 21 start points for the 5% set and 27 for the cosine, of 29 fitted. Median R²: 0.821 and 0.943.**…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.943 | `sibling` | `validation/paper2/RATE_READINGS.json` | `secondary.cosine.15000.r2` — the same entry as n_gaps, traced above | `rate_readings.py` |
| 0.821 | `value` | `validation/paper2/RATE_READINGS.json` | `secondary_summary.q5pct.median_r2` | `rate_readings.py` |
| 29 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary_summary.cosine.n_start_points` | `rate_readings.py` |
| 21 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary.cosine.14000.n_gaps` | `rate_readings.py` |
| 27 | `count` | `validation/paper2/B16C_STEPS_VS_LR.json` | `per_window.20k-30k|gate_proj.n_start_points` | `b16c_steps_vs_lr.py` |
| 5 | `count` | `validation/paper2/RATE_READINGS.json` | `primary.cosine.5k-10k[10].n_pairs` | `rate_readings.py` |

**¶111.** **Shared carriers do separate, slowly and almost everywhere.** A natural expectation is that two uses of one token keep sharing carriers until the rar…

| number | mark | file | field | script |
|---|---|---|---|---|
| 11,402 | `key` | `validation/r2/STEP8_GRAPH_pretrain.json` | `p8.n_fell_beyond_noise` | `-` |
| 14,196 | `canon` | `validation/paper2/COOCCURRENCE.json` | `pairs_total` — all construct pairs | `cooccurrence.py` |
| 1,868 | `value` | `validation/r2/STEP8_GRAPH_pretrain.json` | `p8.n_rose_beyond_noise` | `-` |
| 0.130 | `key` | `validation/paper2/ABLATION_STABLE.json` | `per_reference.pretrain_iter_0020000.per_construct.For.overlap_share` | `ablation_stable.py` |
| 0.117 | `key` | `validation/paper2/B6_PERLAYER_SHARING.json` | `per_reference.pretrain_iter_0003000.median_share_by_layer[7]` | `b6_perlayer.py` |
| 0.034 | `key` | `validation/paper2/B6_PERLAYER_SHARING.json` | `per_reference.pretrain_iter_0005000.median_share_by_layer[2]` | `b6_perlayer.py` |
| 1,000 | `key` | `validation/r2/P8_BOOTSTRAP_pretrain.json` | `draws = 1000` — the core bootstrap's draws | `p8_bootstrap.py` |
| 0.050 | `key` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncWith.carrier_rise_nats` | `ablation_nats.py` |
| 0.04 | `key` | `validation/paper2/ABLATION_STABLE.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncFor.loss_rise_nats` | `ablation_stable.py` |
| 188 | `canon` | `validation/paper1/CORE_COUNTS.json` | `n_constructs_built` — the constructs the battery holds | `core_counts.py` |
| 169 | `canon` | `validation/paper2/B11_POWER.json` | `n_constructs` — the constructs that pass the read-site gate | `b11_power.py` |
| 120 | `key` | `validation/r2/P8_BOOTSTRAP_pretrain.json` | `n_pairs = 120` — the pairs it runs on | `p8_bootstrap.py` |
| 115 | `key` | `validation/r2/P8_BOOTSTRAP_pretrain.json` | `fall_summary.n_pairs_fell_in_at_least_two_draws = 115` — NEW FIELD. Written 5 Nov by experiments/backfill_summaries.py, which checks each value against the figure the paper prints and refuses rather than write one that misses it; the writer script now produces it natively too. p8_bootstrap.py. | `p8_bootstrap.py` |
| 30 | `count` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.cosine.n_constructs` | `ceilings.py` |
| 35 | `count` | `validation/paper2/B18_RECURRENCE.json` | `per_construct.ArithmeticError.b_configurations.n_clusters_within_one_twin_ceiling` | `b18_recurrence.py` |
| 88 | `key` | `validation/r2/P8_BOOTSTRAP_pretrain.json` | `fall_summary.median_share_of_draws_that_fell = 0.8760` — NEW FIELD, over the pairs that fell in at least two draws, not all 120. Written 5 Nov by experiments/backfill_summaries.py, which checks each value against the figure the paper prints and refuses rather than write one that misses it; the writer script now produces it natively too. p8_bootstrap.py. | `p8_bootstrap.py` |

**¶112.** **Seen from the neurons' side, the carrier sets are a concentrated, committed population.** At 4.19 billion tokens 23% of neurons belong to no carrier…

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.175 | `key` | `validation/r2/STEP8_GRAPH_pretrain.json` | `churn.pooled.degree.spearman = -0.17518` — the rank correlation between a neuron's number of sets and its churn | `-` |
| 1,000 | `value` | `validation/paper2/B16B_WEIGHT_NORMS.json` | `per_checkpoint.pretrain_iter_0001000.iter` | `b16b_weight_norms.py` |
| 0.02 | `value` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.median_vs_random_nats.point` | `ablation_nats.py` |
| 92.5 | `key` | `validation/paper2/B17B_RETURN_SPLIT.json` | `share_of_departures_beyond_one_twin_unit = 0.92529` | `b17b_return_split.py` |
| 4.19 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0001000.tokens_b = 4.19` — 4.19 billion tokens is this reference, iteration 1000 | `ceilings.py` |
| 10 | `count` | `validation/paper1/POOLED_SETS_45.json` | `per_cut.2.categories.composite_and_parts.composite.n` | `pooled_sets_169.py` |
| 23 | `count` | `validation/paper2/RATE_READINGS.json` | `secondary.carrier5.12000.n_gaps` | `rate_readings.py` |
| 88 | `count` | `calibration/identifiers.json` | `finance.detail.set_perpetual_inventory.count` | `-` |
| 11 | `sibling` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_old_below_current` — the same entry as n_without, traced above | `ablation_nats.py` |
| 97 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.per_construct.AsyncWith.current.n_random_at_or_above` | `ablation_ranks.py` |
| 5 | `count` | `validation/paper1/POOLED_SETS_45.json` | `per_cut.5.n_clusters_realised` | `pooled_sets_169.py` |
| 2 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0484865.old_set.n_without` | `ablation_nats.py` |

**¶113.** For each neuron leaving a construct's carrier set between neighbouring checkpoints, we asked whether another construct's entry on that neuron rose at …

| number | mark | file | field | script |
|---|---|---|---|---|
| 0.79 | `sibling` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.SetComp.current.share_below` — the same entry as share_below, traced above | `ablation_ranks.py` |
| 1.56 | `key` | `validation/paper2/TEST6.json` | `trend.tokens = [1.406, 1.557, 1.770] (this one 1.557)` — The same block's trend.family = [1.005, 1.007, 1.051] is the 'towards the same grammatical family at chance' in the same sentence. Script: test6.py. | `test6.py` |
| 0.86 | `value` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.GeneratorExp.current.share_below` | `ablation_ranks.py` |
| 1.41 | `key` | `validation/paper2/TEST6.json` | `trend.tokens = [1.406, 1.557, 1.770] (this one 1.406)` — The same block's trend.family = [1.005, 1.007, 1.051] is the 'towards the same grammatical family at chance' in the same sentence. Script: test6.py. | `test6.py` |
| 0.65 | `key` | `validation/paper2/B15_TEST6_CORECHECK.json` | `pairs.0001000:0002000.measures.tokens_outside_cores_A_only.lift` | `b15_corecheck.py` |
| 1.77 | `key` | `validation/paper2/TEST6.json` | `trend.tokens = [1.406, 1.557, 1.770] (this one 1.77)` — The same block's trend.family = [1.005, 1.007, 1.051] is the 'towards the same grammatical family at chance' in the same sentence. Script: test6.py. | `test6.py` |
| 49 | `count` | `validation/paper2/B15_TEST6_CORECHECK.json` | `pair_coverage.tokens_in_cores.n_pairs` | `b15_corecheck.py` |

**¶114.** The one second model already read is Pythia-1.4B, under a different tokenizer: 166 of 188 constructs pass the gate. The gate is of similar strength an…

| number | mark | file | field | script |
|---|---|---|---|---|
| 188 | `canon` | `validation/paper1/CORE_COUNTS.json` | `n_constructs_built` — the constructs the battery holds | `core_counts.py` |
| 166 | `canon` | `validation/paper2/C2_PYTHIA_GATE.json` | `pass_count_pythia` — the constructs passing the gate on the second model | `c2_pythia_gate.py` |

**¶115.** Table D.1 (`validation/paper2/TABLE_D1_ablation.md`) gives, for the 16 constructs whose positions can be read, the effect of removing the current set …

| number | mark | file | field | script |
|---|---|---|---|---|
| 321 | `derived` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.*.n_masks = 320` — 'a clean sweep is p = 1/321' is 1/(n_masks + 1) | `ablation_ranks.py` |
| 320 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0001000.per_construct.Lambda.current.n_random_below` | `ablation_ranks.py` |
| 16 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0020000.old_set.n_constructs_with_an_old_set` | `ablation_nats.py` |
| 84 | `canon` | `validation/paper2/CEILINGS.json` | `per_reference.pretrain_iter_0020000.tokens_b = 83.89` — 84 billion tokens is this reference, iteration 20000 | `ceilings.py` |
| 1 | `count` | `validation/paper2/ABLATION_NATS.json` | `per_reference.pretrain_iter_0001000.per_construct_ratio.n_excluded_control_mean_not_positive` | `ablation_nats.py` |

**¶116.** The data this paper reads are the dataset released with \citet{wilam2026}: the battery, the licence tables, the carrier sets, the record slice and the…

| number | mark | file | field | script |
|---|---|---|---|---|
| 256 | `count` | `validation/paper2/TEST6_EXTRAS.json` | `pairs.0019000:0020000.top20_token_pairs[0].n_departures` | `test6_extras.py` |
| 1 | `count` | `validation/paper2/ABLATION_RANKS.json` | `per_reference.pretrain_iter_0020000.old_set.n_exceeding_every_mask` | `ablation_ranks.py` |