Blame for validation/paper2/SETTLING_RULE.md

# Appendix C — the settling rule, as pre-registered and as applied

*Written from the analysis plan, `experiments/r1_turnover.py`, `experiments/curve1_spacing.py`
and `DATES_TABLE.json`. Every threshold is named with the date it entered.*

## The rule as pre-registered

A construct is **settled** at a checkpoint if the kept fraction of its 5% carrier set, measured
against a partner checkpoint, crosses and stays above a threshold.

| element | value | where it comes from |
|---|---|---|
| threshold θ | **0.7** | the contract's fallback, inherited from the pilot (A31) |
| threshold grid tested | 0.50 to 0.95 in steps of 0.01 | `r1_turnover.THETA_GRID`, so θ's choice is a sensitivity and not a hinge |
| partner | one checkpoint at a token factor inside the band | |
| factor band | **(1.25, 2.00)** | `construct_token_loss.FACTOR_BAND` |
| crossing | "crosses θ and stays above it to the end of the series" | A31 |

## What went wrong with it, and when

**A31's form was vacuous at the end of the series.** Twelve constructs dated at one and the same
checkpoint, `pretrain_iter_0364000` (1.527 T tokens). The reference itself is healthy — its twin
ceiling runs 0.7486 / 0.7436 / **0.7466** / 0.7414 / 0.7400 across its neighbours and its twin
agreement 0.9245 / 0.9242 / **0.9249** / 0.9225 / 0.9203 — so the checkpoint is not the cause.

**The spacing is.** Curve 1's level falls monotonically with the gap it is read at, Spearman
**−0.837** over 1,584 (point, partner) pairs for those twelve constructs:

| step factor | median ratio |
|---|---|
| 1.20–1.35× | 0.7382 |
| 1.35–1.50× | 0.7128 |
| 1.50–1.65× | 0.6680 |
| 1.65–2.10× | 0.6113 |

And the twelve dates sit exactly where the available spacing shortens: at indices 29–31 the only
in-band partner is ≈1.56×, and at index 32 it is **1.332×**, because the 1.5× partner (2.29 T)
is past the end of training. The same construct at index 29 reads **0.611 at 1.56× and 0.717 at
1.25×** — a gap of 0.106, larger than the whole "jump" at index 32 (0.119). Index 32 is also the
**last point of the series**, so "stays above θ to the end" has nothing left to stay above.

The fixed-step form has the same defect in a different place: its dates concentrate at index 33
(`pretrain_iter_0455000`), **13 of 13** in the product space, whose fixed partner is the smallest
gap in the tail (29,865 steps) and which is likewise the last point of its series. Only **56%**
of the pretraining points carry the nominal 1,000-step spacing at all.

## The rule as corrected

A date needs **all** of:

1. an **observed crossing** of θ = 0.7 — not a series already above it;
2. **at least one checkpoint below θ before** the crossing;
3. **at least two checkpoints after** it, so the crossing can be seen to hold;
4. **agreement between two partner spacings** — the ratio and the fixed form must both date it;
5. and, in `curve1_spacing.py`'s strengthened form, the ratio stays above θ **at every spacing
   available at every index from the crossing to the end**, not only at the partner the band
   happened to pick.

A date in the last two checkpoints is **censored**, not a date.

The band is split into four for clause 5 — [[1.25, 1.35], [1.35, 1.5], [1.5, 1.65], [1.65, 2.0]] — because one
threshold cannot serve a 1.25× and a 2.0× window.

## What the corrected rule yields

| spacing | outcomes over 169 constructs |
|---|---|
| ratio | {"censored": 159, "transient": 10} |
| fixed | {"transient": 150, "censored": 6, "dated": 13} |
| **both agreeing (the rule)** | **0 of 169** |

The zero is the conjunction, not an absence of signal: the fixed spacing dates 13 constructs and
the ratio spacing dates none, so nothing survives clause 4. `DATES_TABLE.json` prints both
columns per construct with a `c1_why_no_date` field, so this can be checked row by row.

Across the six cuts of B14 — the top 1%, 2% and 5%, and entries above 1, 2 and 3 σ₀, sets of
744 to 14,424 neurons — the rule dates **0 of 169 in every band**.

## The position classes

Curve 4's series are keyed `construct|class|role|piece`. The classes and their counts on the
pretraining branch:

| class | series |
|---|---|
| governed | 4,587 |
| obliged | 43 |
| scope | 158 |

## Table C.1

Rendered from `DATES_TABLE.json` as `DATES_TABLE.md` — one row per construct, both curve-1
spacings, curves 2, 3 and 6, curve 4's role counts, and the reason no settling date exists.
Curve 5 has no per-construct date: it is defined on the 14,196 construct **pairs**.