docs/technical: doctrine_five_axes_aflow (technical ledger behind beatrix-ft2, verified 2026-09-04)

docs/technical/08_doctrine_five_axes_aflow.md

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+<!-- Technical ledger extracted 2026-09-04 from the deep-rewrite of the beatrix-ft2 article (every number verified against its ledger and sources by the ft2-finish pass). This is the technical record behind the human-readable article; it is not the article. -->
+
+## 8. The doctrine
+
+**(2026-09-01, morning.)** Phil's directive — "plan diffusion processing based on the Aleph systems... find out how" — and his steer on the older lineage (the shunt/RCFG family "didn't pan out... not enough tests to converge") produced, in one day and one file, a graded inventory, an injection grammar, a cultivation template, two synthetic benches and a five-axis theory (`canon/aleph_diffusion_conditioning_doctrine.md`). Its grading rule, per the steer: **grade equals convergence evidence**. The certified rows are July's r2 results re-graded, not new measurements; the only numbers minted in this topic on 09-01 are the two aflow batteries.
+
+**(The inventory.)** Eight items are certified. **Residual-stream relays beat matched low-rank adaptation (LoRA) on three substrate classes** — zero-init gated writes at every denoiser block, gate −3, bit-exact bypass: flow-Lune frozen flow-MSE 0.52241 against relay 0.51796 (−0.85%) and LoRA-r32 0.52503, grounding preserved (exp001, candidate s0); eps-SD15 0.124788 against 0.121698 (−2.5%) and LoRA 0.122674 (−1.7%), grounding +0.1809 → +0.2172 (exp006, s0); on the Anima DiT the relay improved 0.1229 → 0.1154 while LoRA-r16 degraded 0.1375 → 0.1424 (exp004). That relay form is the doctrine's write calculus. **Sigma-banding is the certified routing axis**: band lesions surgical 3-for-3 at 50–200× on both seeds (exp008), a step-gated controller grounding +0.2135 against frozen +0.1247 (exp010), and the constants — three bands, edges .35/.75, crossfade .06 — are law (S-1402). **Blob structural supervision pays on flow, not eps**: −5.9%/−3.7% HIGH-band flow-MSE, two seeds, 125–200× the eps effect, blob-on-eps inert both seeds (S-401, the conditioning law; the −5.9%/−3.7% pair is exp013's two seeds at the λ = 0.5 point of the dose curve, and λ≈1, at −8.3%, is the measured operating point). The paired grounding judge (conditioned minus shuffled caption; the exp000 wall was n=24 paired) is certified; the 38-class rosetta fingerprint (.87+ confidence, FLUX.1 its own regime) is certified **as a data-versus-noise and generator-family readout only** — the same evening's bcd bed found it conditioning-blind in five instances (cos_to_wall .982–.9999 for every arm, the random control included), a qualifier the inventory sentence still lacks. Also certified: captionbert-B with the deep-arm chunk wrapper (zero training, no number carried); the KSimplexCrossAttentionPrior — 4.8M parameters, 0.56% of the trunk, Cayley–Menger validity 100% — **elevated the same day after draft 1 wrongly demoted it**, one ~1-epoch run, convergence gate owed; the five-CLIP caption bank with its random-control law (the 512 → 640 enrichment it falsified carries no number); and the constellation core (successor designed, not measured).
+
+**(Never validated; falsified.)** The day's retraction is Phil's, verbatim: the dual-shunt adapters were "an interesting experiment but never stabilized as systemic integrations... they were trained as inference utilities not diffusion trained devices. They were never validated." Trained offline on cached embeddings with the diffusion model never in the loop, zero validation ledgers, checkpoint *ladders* as a strength dial — the signature. Retracted as a conditioning device; the encoder beneath is measured and separable (bert-beatrix-2048: a 2.056B-sample masked pretrain, 26 near-equidistant SHUNT tokens, mask accuracy ~.95). The RCFG pentachoron never ran; the GeoVocabConditioner's bridge is unwired in code (a literal TODO). Falsified, never rebuild: comparative dispatch on diffusion (exp007 flat; exp014 raw addresses kill routing; exp015 address-as-key 2.5e-06 over a repeated-key null; two seeds × three, S-103), cross-encoder sequence substitution (Qwen-for-CLIP-G cosine caps ~0.5), the bounded-alpha attenuator as sole path, and the bertenstein hub (R@1 96.2%, in-sample). The RCFG prehistory's real contribution is restored as the **gauged-state lineage** — a few slots by D diffused under a per-step gauge (center plus unit-mean-edge), readout by cosine against a projected text blueprint — the layer-14 blackboard's ancestry and the aflow bench's bed.
+
+**(The grammar and the refit.)** Four clauses of entry: pooled vectors transfer across encoders by one fitted rotation (no numeric column travels with it); sequences **reconstruct native, never substitute** — the seq77 reconstructor reached m_acc .957 / s_cos .734 in one 78-minute run where substitution capped at ~0.5; appended structure pays only where non-redundant — exp002's address was inert beside full text, address-only carried +.0287 at one seed, and the positive half went unsupported on the Lune bed that evening (section 9); the aleph enters as a near-zero-init additive anchor, never a selector (S-103). Two constants ride along: the **Rosetta Stone** — text through the VAE bottleneck reads 2.5–3.5× more geometrically discriminable than images, three encoder families converging (seed count not in the record) — and the omega frame (effective rank ~15.9 across modalities; S_delta 0.29152 from pure noise at epoch 52), whose omega-grid conditioning stays a stub. The two-channel doctrine — A inside the trunk (production today), B on the conditioning stream in pooled, sequence and appended planes, two seeds plus a repeat before any claim — is the program section 9's campaign executed. The five-slot cultivation template puts the velocity tangent to the gauge slice; rectified flow is the Lune convention, x0 = x_t − t·v exact and linear, which is why the conditioning law generalizes from loss to geometry. Phil's **refit recognition** — "we have created nearly identical solutions we can simply refit into diffusion" — recorded nine slot-for-slot correspondences; the new ingredient is thin, continuous t and velocity regression. Two laws bound it: **sign codes have no tangent space** (magnitudes flow, signs address; S-906) and **a refit is not a validation**. The deepest refit — the aleph read *as* the velocity field — stayed a design.
+
+**(Battery 1 — launched 10:42 local.)** The bed is synthetic and known-truth: pentachora in R^[5×64] under the RCFG gauge, ten class blueprints (pairwise cosine asserted below 0.5) with low-rank deformation, Euler sampling in 50 steps, cosine-versus-blueprint readout (chance .10), Cayley–Menger validity in fp64, and spec_cos (top-six singular values, generated against true class clouds) as the recovery gauge. The pre-battery probe opened with a negative: the read as the **sole** velocity path starved, .10 → .19 over 1.2k steps while a plain perceptron reached .98 by step 120, a context-lane fix changing nothing (the doctrine says "~chance"; the plan records .19, twice chance) — V1d re-derived on flows (S-1006): m_hat addresses, it does not carry. Redefined as relay-form — a perceptron carrier plus a gated zero-init read correction, gate −3, 1.35M parameters against the perceptron's 1.48M — it ignited at .993 by 1.2k with spec_cos .999. No ledger, log or script of the sole-path version survives; law_families says 2/2, the plan shows one trajectory. The battery then ran 2×2 at 4,000 steps × 512, pure Adam wd 0, fp32: in-gauge path (A1: gauge both endpoints, re-gauge x_t, target the gauged path's finite-difference velocity) against retraction (A2: naive linear path, gauge only after each sampling step — the RCFG original), perceptron (B1) against relay-form (B2), two seeds and a repeat, every cell sampled raw and projected.
+
+| cell (s0 / s1) | params | val flow-MSE | acc proj | acc raw | erank proj | spec_cos |
+|---|---|---|---|---|---|---|
+| A1B1 | 1,497,280 | .23302 / .22698 | .98770 / .98203 | .97695 / .97656 | 59.4 / 59.5 | .99887 / .99850 |
+| A1B2 | 1,345,921 | .06661 / .06936 | .98652 / .96895 | .98242 / .96699 | 53.4 / 53.1 | .99901 / .99883 |
+| A2B1 | 1,497,280 | .06167 / .06801* | .92227 / .91973 | .97188 / .96855 | 71.2 / 71.1 | .99832 / .99807 |
+| A2B2 | 1,345,921 | .03326 / .03345* | .96465 / .94043 | .98555 / .96699 | 67.3 / 67.7 | .99877 / .99861 |
+| A1B2-s0-REPEAT | 1,345,921 | .06661 | .98652 | .98242 | 53.4 | .99901 |
+
+*A2 val-MSE is on the linear target and is not comparable to A1's gauged target.
+
+**The in-gauge interpolant wins** (S-903): projected, the perceptron cells read .98770/.98203 against .92227/.91973 — +6.54/+6.23 points, two of two, against a seed spread of .0057 (the doctrine's "+6.3 ±0.4": mean 6.39, half-range 0.16; the ±0.4's derivation is not in the record); the relay cells gain +2.19/+2.85. The raw column holds the mechanism, unstated in canon: unprojected, the same nets nearly tie (+0.51/+0.80), and per-step projection *helps* the in-gauge nets (+1.07/+0.55, +0.41/+0.20) while it *costs* the retraction nets 4.96/4.88 and 2.09/2.66 points — a field trained off the gauge integrates its error at every projection, and the ledgered signature is the projected effective rank, 71 against 59. **The read is a tangent-field specialist, not a carrier**: at fewer parameters it fits the gauged field 3.50×/3.27× better (val-MSE .06661/.06936 against .23302/.22698; the doctrine's "3.4×"), and under the wrong geometry it rescues +4.24/+2.07 points (A2B2 against A2B1, two of two). In-gauge its readout is −0.12/−1.31 against the perceptron — a tie under the relay cells' own seed spread (.0176), not under the ~.006 bar the doctrine states; which spread the bar means is not in the record. **Geometric health is uniform** — Cayley–Menger validity 1.000 in all nine cells, spec_cos .99807–.99937 — but verdict 3's "in-gauge raw sampling drift ~10× lower than retraction" is not what the drift column shows: raw drift is 5.7e-4–6.6e-4 for *both* perceptron cells and 7.0e-3–9.4e-3 for *both* relay cells, a ~10× split between velocity forms, not path geometries, which tie; no retraction is minted, and the sentence should be restated. The hardware repeat reproduced A1B2-s0 to every decimal (val-MSE 0.06660972535610199 both; delta exactly 0.000) — S-708's noise floor — so the bar on this bench is the seed spread, never the repeat. Two debits: the nine ~1.4M-parameter nets were never persisted (repaired in battery 2), and the run logs, the only record of per-1k-step train MSE, live in a session scratchpad.
+
+**(Battery 2 — 11:35 to 12:15 local.)** Two rungs on the winning cell, two seeds each, nets saved. The **birth-book prior** replaced the gauged Gaussian at t=1 with the governed birth process (minsep-projected vertices per sample, radial jitter, then gauge): endpoint accuracy .98535/.97031 against .98652/.96895 (−0.12/+0.14 points) and val-MSE .06742/.06764 against .06661/.06936 (+1.2%/−2.5%) — **an endpoint tie, two of two**, graded law at law_families:198. The other half of that law — ignition .99 at 150 steps against ~1,200 for the Gaussian prior, hence "transit accelerator" and the few-step-regime hook (a candidate) — has no primary record: no ignition field in the ledger, train MSE only every 1,000 steps in the log, no per-step probe in the archived script; the figure is canon-only and carried as such. The ledger does carry the price: 19.5/18.9 minutes per cell against 0.8 for the banded cells, from the per-sample minsep loop. The **sigma-banded velocity** split the consume head into three t-band heads under the law constants at matched parameters (1,344,123 against 1,345,921): val-MSE .06364/.06702 against the battery-1 pair .06661/.06936, −4.45%/−3.38% (the doctrine prints −4.4%/−3.4%, the prior docket −4.5%; against the same-battery birth-book cells, the wrong comparator, −5.6%/−0.9%), accuracy −0.47/−0.35, a tie. Two of two in direction, inside the comparator's own 4.1% seed spread: **candidate**. The banded cells did carry the **difficulty gradient**: per-band held-out error LOW_t (data end) .09684/.09925, MID .06454/.06994, HIGH_t (noise end) .014444/.014417 — 6.70×/6.88× harder near the data than the noise, identical to four decimals across seeds at the noise end. Registered as a constant (law_families:2754); "tight across seeds and arms" rests on two cells of one arm — per-band error was never computed for an unbanded cell. Battery 2 has no repeat cell and no MANIFEST bundle; Cayley–Menger validity 1.000 and spec_cos .99875–.99922 throughout; four nets of ~5.39 MB on the hub.
+
+**(The five axes.)** Phil's question — what makes a proper conditional geometry — was answered from the day's verdicts as a composite law (S-1501) with an effectiveness statement: per noise band, usable information (that band's decision variables, readable by a well-conditioned map, factored for guidance) minus injected nuisance variance. One grade per axis. (1) **Two-regime discrimination** — signs address the head, magnitudes modulate the tail; pooled vectors carry only the head: law, on the probe program's single draw (array ridge R² +.776 yet binding SNR 0.13–0.18; pooled T5 SNR 0.57). (2) **Band-aligned accessibility**: the property holds on the generator side (lesions 14:1 scale-dissociated, blob-on-flow 125–200×), but nothing band-orders the blackboard, and the one organ built to test it read null — banded minus flat −.008/+.001 and −.004/+.001, inside the .026 bar, two seeds (bcd-e002). **Candidate with evidence against at organ size**; S-403 and law_families:2822 keep the pre-ablation law wording; the lesion numbers are instances of the property, not the organ. (3) **Core/residual factorization** — "classifier-free guidance is core/residual arithmetic": minted at law wording in the morning bundle and **downgraded to candidate that afternoon** by the Fable 5.1 review (item 1) — theoretical, unmeasured, its gauge unbuilt; law_families carries both a law row (:2825) and the candidate row (:2869), and candidate is current. (4) **Gauge respect**: law — the one axis with a same-day two-seed known-truth instance, aflow's +6.54/+6.23. (5) **Generator commensurability** — per-target-family columns mandatory: law on the Rosetta Stone and the fingerprint families, but its intended live gauge is the conditioning-blind fingerprint, so the axis has no working conditioning gauge yet.
+
+**(The missing organ.)** Blackboard-plus-arms already has the right shape on four axes — slotted core, gated migratory residual, per-slot gauge, arm-switchable cluster target — and the missing property is the second. The organ that would supply it is a **sigma-banded conditioning readout**: a sequence head trained band-weighted so coarse slots speak at high noise and fine slots at low. Its first attempt came that evening — bcd-e002's HEAD_banded read +.006 in v4 (invalid: two bands untrained) and, valid in v5, tied the flat head inside the bar (section 9). As of 2026-09-04 nothing band-orders the blackboard, aflow-3 (asymmetric band capacity) has not run, the PatchSVAE load-verify behind the omega-grid flow is undone, and the blackboard flow is unbuilt — the standing queue, items 3 and 5.