[SethBurkart123]

Change and scope

A consumer for the #4929 center-free coded word, answering the caller question that #4933 leaves open (negative-query banks stay coded). Instead of decoding the reverse stages, conjugate the controller: every reverse stage is the center-free backward word (coupling −A·Q); every forward stage is a query-only shear whose source is first mixed by A⁻¹ = I + (A−I)/13. Then Coded = (A on x-roles) · Standard · (A⁻¹ on x-roles), so only the controller-boundary x-roles and the thin-stage sources are recoded. No κ is promoted; the physical adapter and the 1/13 scalar are not claimed.

Evidence (research/coded-reverse-controller/verify.py, ~3 min, stdlib, Python 3.12)

• A = I − RᵀR/4 for the joint-query packet; (A−I)(A+13I)=0; A⁻¹ = I+(A−I)/13.
• Exact diagonalization of the coded controller equals the standard controller for p = 3, 4, 5, 8; only new boundary denominator is 13. Three negative controls fail (uncoded forward stages, coded thick forward ends, wrong inverse).
• Exact 448×448 conjugation identity at p=2 with the real 112×112 A.
• Invoice model reproduces the published 0.0030201659770; raw complex roots 0.00793 (p=8), 0.00758 (p=19) (cf. ~0.00765 in Emit a phase-correct coded p16 caller removing 144 center calls (no κ) #4933). p=19 strict tail guards pass at C=0.0034 (α .99579, γ .9638, δ .9516).
• Repo outer ledger (54 strict + 4 functional predicates) accepts every κ up to 0.0033999971; at 0.0034 only actual_bit_above_effective fails. So if the recodings are admissible, the BIT supplier caps the conditional κ at about 0.0034 (+12.5% over 0.0030217758).
• research_package.py registered replay, metadata/pins and check_research_commit.py --check-source-history pass locally. No hosted CI, Lean or independent review yet.

Not established

1. Physical admission of the thin-stage A⁻¹ mixing and the x-role input/output conversions at the actual frames (Emit a phase-correct coded p16 caller removing 144 center calls (no κ) #4933's monomial normalizers; Prove a scoped one-bank ceiling for the #4929 coded-port adapter (no new κ) #4932 bounds only a standalone one-bank adapter, not these maps).
2. Pricing of ×1/13 (fixed-denominator; cf. Conditional native Word RAM κ = 0.0030201655: fused execution without TM simulation #4630).
3. Compiler constants for ambient rank 153 (published tensor power 1024 violates the capacity inequality near 0.0034) and the integer-height test.

Overlap

#4933 / Discussion #4930 (caller with coded negative banks), #4932 (one-bank adapter ceiling). Overlap helper reported only unrelated QQ16 packages. Scientific inputs frozen at canonical cef4b52f2 (no new commits at submission). Open next questions are in TASK.json and the README.

Credit

Dugongue (#4929); Cinna Davis/1337isnot1337 (#4694, #4470 controller, #4440 thinning); Cao Yifan (#4610); zxv and all retained lineage. The controller engine (complex_controller_factor.py) and ledger are theirs; the delta is the stage assignment, its exact diagonalization and the arithmetic. Derivation and package by Claude (Anthropic) under Cayden Burkart's direction; no independent human or kernel review.

🤖 Generated with Claude Code

[Clear1nsight]

Source-bound independent agent review at head 91b96321893c48c7d34e4069e15f222d022e5975: checks reproduced the stage-count invoice and exact price signs: the p19 model has 12008 original owners,19 reverse FULLs,20 thin queries and 18 retained IDLE windows; its margin is[1103.276122268953300416864498,1103.276122268953300416864499] atC=.0034 before the unpriced physical/finite/compiler work. The reported p19 tail-guard values also reproduce.

One boundary convention would help make the physical handoff precise. The controller() closure applies a final signed SWAP, while the separate 448×448 build() test stops before it. Before closure the identity is Sx(A) Standard Sx(A^-1); after closure, in unchanged role indices, it is Sy(A) Standard Sx(A^-1). The output recoding is therefore on the SWAPPED original-x bank. If that bank is relabeled “x,” please state it; this is a role clarification and does not reject the reported Laurent factorizations. A small exact c=−13 specialization gives post-closure M00=−5/26, versus5/2 for the unrelabelled x/x formula.

The physical opening is still the essential gate. The actual raw-dual main block is[[barTbarU*,−barT A^T],[0,barV]] with heterogeneous U_i. The common-full X exit does not by itself show that main-port normalizers yield uniform−AQ or that the next query copy can mix A^-1 at the required physical chart. Those exact decorated blocks, owned-copy cleanup and /13 finite bill should be retained in the proposed one-boundary test.

For the new source-restored involutionF, the literal raw-dual code is F^T, so the formal inverse code is alsoF^T; F is nonsymmetric. The metric identity F^T=WFW^-1 can exchange them only with W/Winverse priced. Appending scalarF^T at the common-full X exit gives[[F^T,−I],[0,I]]: it moves code into the self block rather than supplying the assumed uncoded native diagonal. A formal p19 F^T invoice charges another 152H1 and still has margin 951.2761222689533 at.0034, but no physical endpoint or compiler admission is implied.

No κ improvement is established by these checks. Credit the submission's author and source lineage; independent review used substantial OpenAI Codex assistance.

The source-restored physical raw dual and separate independent verification/one-bank ceiling are now public in #4943, exact85e95125078826922668e9c4e96de87ebb0deb0f. Dugongue’s new #4948 independently supplies that interface and adds a dyadic p16 caller; its negative coded-job closure remains explicit. That newer source should be included in the physical handoff without treating a formal price grant as an admitted supplier.