[Matarener]

Requested by Mark

Change and mathematical scope

Negative result, no new κ, no change to the selected record. Adds research/zqy-observation-not-retained. In zxv's #5415, Dillon's #5402 coupled provider returns its eight modes for 8 H1 + 456 ADD + 240 maps per backward FULL if the current-version observation b = Z Q Y is supplied. Buying it costs 120 H1 per FULL and fails the moment screen; with it supplied, the #5415 screen is positive at .004 (rank surplus 1,776). This package shows that b is not present in any retained observation of the frozen words, in the formal free-word grammar of the #5377/#5397 row engines:

• Native level: exact rows (convention of Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation #5377's native.py) of the Preserve all 632 native inputs in an eight-mode coupled helper provider #5402 provider backward word and the Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 word in both orientations. Q Y_k is the row y_k standing in the full frame. The span of all full-frame versions over the whole word (owned copies make every time available) meets pure y, with any warp word, in dimension 0. Its x-free part is exactly the helper content (400 / 408 / 376).
• Caller level: Test coupled returns through two query consumers and price a compressed exit #5415's event semantics over the whole selected p16 caller (162 events, 18 backward FULLs; Q and D commute; Q_POWER and SIGNED_SWAP are free). No version word begins with Z, so b = Z_s Q Y is free iff Q Y is in the span of free images (Q^{±2}, W_t) of the versions. The answer is 0 of 18 at the return and 0 of 18 with the whole caller history (delayed exit), at factor length 1 (registered) and 2 (recorded).

Part 2: response reuse. #5423 names a global occurrence ledger of response reuse as the next economic object. On the same frozen words, no paid job can be replaced by a combination of earlier responses:

• Native: every paid climb or centre, 3,282 in the Preserve all 632 native inputs in an eight-mode coupled helper provider #5402 provider and 3,298 per orientation in Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610, is tested in two windows. EARLY uses the span of everything that stood in its target frame before the climb. LATE uses the span of the other target-frame versions before the field is next touched, with the own result tagged. Both give 0.
• Caller: none of the 63 paid caller outputs (15 thin QUERY responses, 30 IDLE bank outputs, 18 LOCAL Y outputs) is a free image of earlier versions under Q^{±2}, W_t, Z_t. That is 0 as well.
• This is wider than the single proportional-snapshot traversal of Screen recursive cost edits and certify centre-exchange headroom #5397.

So the supplied-observation branch of #5415 section 4 has no free producer here. This does not bound the price of a new paid producer. Not covered: physical identities outside the free-word grammar, changed native words, other providers.

Task and overlap

Card joint-query-controller, priority revision 7, scope refined (TASK.json): the concrete instance "supply Z Q Y from already paid observations", named by #5415 (open question 1), #5419 (ranked experiment 1) and #5425 (open question 1). Base 1a3ced60b2f7a46bc70280a04f2eeb8ca027c700. Inputs pinned in SOURCES.json: research/native-rank8-helper-provider/WORD.json.gz, research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz and research/coupled-query-transport/inputs/SUCCESSOR-CONTROLLER.json. Overlap check: the PR feed through #5425 and Discussion #1166 through 09:00 UTC. #5388's 112 paid observations apply to forward-helper inputs; #5419 already notes that they cannot be renamed as this Y observation, and they are covered here as caller versions anyway. No competing ZQY embedding was found.

Validation

Python 3.12, standard library:

python3 -I -W error -B research/zqy-observation-not-retained/verify.py          # ~90 s (parts 1 and 2), PASS_ZQY_OBSERVATION_NOT_RETAINED
python3 -B scripts/research_package.py --package research/zqy-observation-not-retained   # normal and -O: PASS
python3 -B scripts/check_research_commit.py --package research/zqy-observation-not-retained --check-source-history   # PASS
python3 -I -B research/zqy-observation-not-retained/verify.py --left-depth 2     # optional, ~2 min, same 0/0

Part 2 controls: a copy of the first rank-one result injected just before its climb is found as EARLY; injected just after, it is found as LATE only; a thin query repeated on its unchanged bank is found. Part 1 controls show that every test can answer yes: every final full-frame endpoint row lies in the span; one injected pure-y version is detected; at every caller return the current Y is found; Q² Y is found at the end. Spans are exact echelon forms over ℚ (Fractions), so every rank, intersection and non-membership in both parts is over ℚ: no reconstruction with arbitrary rational coefficients exists. (The first version computed modulo 2^61 − 1, which covers only p-integral coefficients; Clear1nsight's review. The exact recomputation, including the optional depth-2 run, gives identical numbers.) No physical phase evaluator, compiler or outer replay was run. Hosted CI run 40086494886 passed plan and the registered replay at head 2b6316dad (part 1); run 40087716803 passed plan and replay at the part 2 head 389578f2d.

The second commit reuses, byte for byte, the docs/ci-verification.md navigation repair from #5420 (head baa8fbb, Clear1nsight). Canonical main still names make frontier4610-verify, so the shared onboarding test failed before any package replay. No scientific file is changed by that commit.

Credit

Dillon (dillona, #5402) supplies the coupled provider word. Cao Yifan (intqwq, #4610) supplies the native word and frames. zxv (#5415, #5419) supplies the exit contract, the caller semantics, the successor controller and the question. Ali Romman (#5377) supplies the row convention, and Clear1nsight (#5425) the fanout open question. Mark (Matarener) with substantial Claude Code (Claude) assistance; Apache-2.0. Author-checked; this is not independent acceptance.

Open next questions

See TASK.json. (1) Repeat the span test numerically at fiber width one with the absolute-phase evaluator of research/coupled-query-transport/verify.py. This is the only escape inside the frozen words. (2) Price a changed native word that keeps a pure copy of R y in the full frame before it is mixed with D x.

🤖 Generated with Claude Code

[Clear1nsight]

Part 1-only mathematical qualification at head 389578f2d3ef075495ce76f08100ac50e18f7d40 (static source review only; no replay): the modular evidence is useful, but its implication to an arbitrary rational span needs a coefficient-ring qualification or an additional certificate.

This comment addresses Part 1's arithmetic inference only. The new Part 2 response-reuse results, EARLY/LATE windows, tags, native event data and 63 caller-output tests are not assessed here. I inspected Part 2 only to determine whether it supplies an exact rational certificate repairing Part 1; it reuses the same modular Span/modrow backend and supplies no such certificate. The current head’s hosted CI success does not supply the missing arithmetic implication.

The claim is explicit in PROOF.md, Arithmetic, README.md, the checker docstring/emitted arithmetic string and RESULT.json. Inspection of Span/modrow finds Fp RREF and dyadic input checks, with no exact Q-rank upper bound/lift, p-saturation or rational separating certificate.

Knowing the generator and target coefficients are dyadic does not make arbitrary unknown reconstruction coefficients reducible modulo p. For A=[p], b=1, both inputs are integers, the target is outside the modular image, and the rational solution is 1/p. There is no ring map Q -> Fp.

The valid implication is target-specific: if b mod p is outside the reduced span, then no combination with dyadic or p-integral coefficients reconstructs that target in the tested formal generator set. This can preserve a meaningful obstruction for the permitted dyadic ADD/SCALE grammar. It does not prove rational-span nonmembership. It also does not show that the entire dyadic module has zero pure-y intersection: in coordinates (y,x), A=diag(p,1) has modular pure-y intersection zero, but its rational span contains e_y and its dyadic module contains nonzero p*e_y. Thus the Part 1 native rank/intersection/x-free fields should explicitly be labelled Fp quantities unless lifted separately.

The smallest repair is to qualify PROOF/README/checker/output metadata consistently as a tested dyadic/p-integral target obstruction and preserve the Fp dimensions as such. For the stronger Q claim, one sufficient route is exact certification rank_Q(A)=rank_Fp(A mod p), together with the modular augmented-rank increase; modular rank alone is only a lower bound. An exact rational annihilator l^T A=0, l^T b != 0 is another route. Small source coefficients alone are insufficient to guarantee a good prime.

Please also keep the existing evidence boundary: registered caller closure has left-depth 1 / 21 factors; depth 2 / 419 is recorded optional evidence, not freshly compared by the registered depth 1 run. Those are bounded formal sets, and the submission already excludes physical identities, changed words/providers and physical cost/precision closure. No physical no-go, actual rational reconstruction of these native/caller targets, new κ or conclusion about a different retained-history/coded 8/9 construction follows from this qualification.

Credit remains with Mark/Matarener for the dedicated span census, controls and recorded formal evidence, and the credited Dillon/Cao Yifan/zxv/Ali Romman/Chris R lineage. This comment is an AI-assisted static mathematical qualification, not independent human acceptance or a replay claim.

[Matarener]

Thanks, agreed: reduction modulo p only excludes p-integral coefficients. Fixed in dacc35b by removing the modular arithmetic altogether. The span engine now keeps exact Fraction echelon forms, so every rank, intersection dimension and non-membership in both parts is a statement over ℚ, and no reconstruction with arbitrary rational coefficients exists. Every recorded number is unchanged: the native ranks 546/554/554, the intersections 0, the caller closure rank 2827 with 0 of 18 available, and part 2 with 0 reuse. The optional depth-2 run (419 factors, closure rank 56405, 0 of 18) was also recomputed over ℚ. PROOF.md, README and the emitted arithmetic string now say this, and PROOF.md keeps your A=[p], b=1 example as the reason. The bounded formal-set scope (depth 1 registered, depth 2 recorded evidence) is unchanged.