# E04b: is decoded surface order carried by the E02 reader's 9-d subspace? — RESULT

Full run `full_v1` on 4l GPU 2, 2026-09-11. The design was re-registered as v2 after the design review.
- **Scale:** 160 fresh propositions (40 new nouns, 8 new verbs) × {active, passive, cleft} × 2 directions = 960
  edits; 92,160 decodes in 2,127 s.
- **Gates, all passed:**
  - encoder pipeline cos ≥ .9999999 against E02;
  - every noun round-trips in ≥ .958 of its sentences;
  - fresh reader AUC .977–.980 per family;
  - G-parse .995.
- **Checks:** energy matching is exact for the controls (a, b, d). Control c (the shuffled-label reader's subspace)
  could not be energy-matched at k ≥ 2, so it is excluded from the primary best-control set by the pre-fixed rule.
- **Parser audit:** my blind reading of 40 edited decodes matched the parser on 39. The one disagreement is a
  non-stimulus noun, correctly flagged as noun_lost.

## 4-line debrief
1. **Question:** does the SONAR decoder rely on the query-conditioned order reader's subspace (numerical rank 9) to
   decide surface order? Is that subspace sufficient or necessary beyond other subspaces carrying the same energy?
2. **Answer: no, it isn't special.**
   - Swapping an item's reader-9 coordinates flips decoded order in .140 of edits.
   - Energy-matched structured subspaces do just as well: the top-9 PCs of training Δs give .124, the top z-PCs give
     .110. The paired difference is −.001 [−.04, .04].
   - Removing the reader-9 component from the full swap leaves .626 swapping. Removing the same Δ-energy share
     inside Δ-PC or z-PC subspaces leaves .636 / .677.
   - The log-likelihood shifts are equal to those controls (11.97 vs 11.83 / 11.01 nats).
3. **So:** readable ≠ decoder-special. Decoded order depends on how much of the AB→BA difference is moved inside
   *structured* (data-aligned) subspaces:
   - the same energy spread isotropically over about 334 random dims flips only .024;
   - the curve over k is steep and step-like: 3% of ‖Δ‖² gives 0, 33% gives .14, 100% gives .995.

   There is no low-dimensional order handle in z for the decoder. Order is decoded from a distributed difference.
   This sits alongside E01/E03: trained SONAR is not simple at any of the levels tested (n-gram, broadcast,
   reader-subspace).
4. **Next:** map the decoder's decision boundary along Δ (swap probability against the structured energy fraction,
   pooled across subspace types). Test whether a single "structured energy" variable predicts the flip,
   subspace-agnostically. That would be a compact description of how the decoder reads order.

## Registered predictions (v2)

| id | p | registered | value [noun CI] | outcome | Brier |
|---|---|---|---|---|---|
| F0 | .95 | C-oracle swap ≥ .90 | .995 [.98, 1.00] | TRUE | .0025 |
| F1′ | .25 | S-9 swap ≥ .30 | .140 [.07, .23] | FALSE | .0625 |
| F2′ | .25 | S-9 − best energy-matched control ≥ .15, CI lower > 0 | −.001 [−.04, .04] | FALSE | .0625 |
| F3′ | .70 | N-9 swap ≥ .80 ("not necessary") | .626 [.50, .75] | FALSE | .4900 |
| F4 | .40 | G-floor best-dose swap ≥ .30 with nouns kept ≥ .8 | .331 at 2×, nouns kept .41 | FALSE | .1600 |
| F7 | .35 | S-9 log-lik shift > best matched control in ≥ 70% of propositions | .481 [.32, .64] | FALSE | .1225 |

**Mean Brier .150 (n = 6), my best so far.**
- The miss is F3′. I expected removing the reader's 9-d share to leave the swap intact (≥ .80), and it fell to .63.
  But the energy-matched structured controls fall just as far, so this isn't reader-specific necessity. It's the
  step-like response to losing a third of the structured Δ energy.
- Registered decision: **"readable but not decoder-sufficient beyond energy."** F3′ false means removing the reader
  part blocks the swap below .80, but equally to the matched controls, so there is no reader-specific necessity.

## Descriptive
- **Variance-floored ĝ (G-floor):** .27–.33 swap at 1–4×‖Δ‖. But nouns are lost in .53–.61 of those edits. Pushing
  along the reader direction breaks content before it reorders.
- **Family:** passive is consistently the most editable (S9 .23, G@2 .47), and cleft the least.

## Claim tier
- **T1:** "the E02 reader's order subspace is not decoder-special. Decoded order responds to structured Δ energy,
  not to the reader's directions" (fresh stimuli, energy-matched controls, n = 160 propositions).
- Supersedes the withdrawn E04 descriptive claim.

## Protocol deviation (recorded; fixed before any encoding)
- **Verbs.** v1 listed 8 "new" verbs, but 7 of them (thank, visit, hire, greet, warn, invite, praise) are
  binding_death predicates. The implementer followed the governing rule ("none in binding_death's predicates") and
  used blame, help, rescue, ignore, tease, comfort, punish, admire, fixed in `stimuli.py` before encoding.
  Likewise, the 16 binding_death nouns in v1's example list were excluded. This is my error in the prereg's example
  lists; the rule's intent (fresh predicates) is preserved.
- **Energy matching.** Done by rotating the last basis vector (exact), rather than the review's prefix rule, which
  overshot. This was fixed before any edited decode.