[zxv]

Change and mathematical scope

Research guide: Read the construction assessment, including its ranked next experiments and stopping rules. The 25-paper technique-to-code map records primary sources and access limits; RESULT.json contains the executable evidence. These links pin the submitted commit.

Encoded outputs cannot be passed through a main-only controller ADD by adding the whole encoded bank: that also changes logical helpers. This package turns techniques from 25 primary papers into executable interface probes and combines catalytic restoration, low-rank factorization and alternative-basis propagation into explicit coupled consumer circuits.

The main constructive result is a cross-chart junction $\mathrm{dst}\leftarrow\mathrm{dst}+H_tPH_s\,\mathrm{src}$, restoring all 120 source originals. Its bill is 3,712 ADD, 16 SCALE, 960 signed monomial field maps, zero new owned fields and zero Gaussian calls. The same-chart specialization uses 2,360 ADD and 480 maps. A retained thin-query wrapper checks 352 original/owned input columns, keeps its 112 H1 calls, and charges all COPY/CLEAR, 112 owned fields and inverse-child translations. Distinct free chart words remain distinct; no cross-stage commutation is assumed.

The package also supplies gauge-optimized variants of PR #4935's existing involutive completion, a 112-coset/6,216-pair observer architecture screen, actual two-generation displacement action, and a ranked construction report. There are 25 paper-to-code mappings: 20 have primary method material, while five record/abstract-only entries are explicitly access-limited. These are scoped adaptations, not reproductions of 25 complete papers.

No new κ is claimed. At submission main newly selects conditional $\kappa=0.003027288235$ from PR #5413. The package authenticates and reconstructs that complete price profile, including all 18 backward FULLs. Conditional restoration to H9 targets has one combined observer/extra-termination allowance of 901.134447… at saving 0.004, or 50.063024… H1-equivalents per FULL. A fresh 112-query observer loses. The 32-H1 allocation and 0.0033 first milestone are design budgets, not implemented suppliers. Full native placement, disjoint mode ownership, the endogenous observer, precision/volume/tape compiler and outer admission remain open.

Research highlights and design implications

The assessment favors a history-augmented coupled transducer with an endogenous paid observer. Design around what the next real consumer needs, keep precisely versioned information that remains useful, and charge its eventual restoration. The verified consumer circuits make that shape concrete; obtaining the observation inside the native provider is the next construction problem.

Conditioning and consumer cost must be optimized together. The balanced gauge $a=-4,\ b=3$ reduces the mode-block squared Frobenius norm from 898 to 688 relative to PR #4935's gauge; the continuous optimum is 674. A different gauge, $a=-12,\ b=1$, improves the finite scalar row-sum bound from 69 to 50 and has a division-free boundary circuit. The latter is not an all-width physical infinity-norm theorem, and switching the balanced junction to that gauge introduces a restoration factor of $1/12$ in its current factorization. Choose the gauge using the actual compiler error metric and the installed consumer.

The two-generation witness points toward bounded history. The physical stationary-transfer equation $W_3T=D_1W_1$ has projected residual rank eight at a nonzero address; the zero-address test falsely passes. Adjoining the next chart yields 16 independent witness columns, which is a finite rank statement rather than a 16-call Gaussian lower bound. The implemented displacement identity supplies a concrete alternative: generation-tagged state whose lifetime ends at a real paid contact.

$$D_1C_1-C_3D_1 =\begin{bmatrix}W_3&D_1W_1\end{bmatrix} \begin{bmatrix}Z_3D_1\\-Z_1\end{bmatrix}.$$

Observation ownership and version are decisive. The exit requires $b=ZQY$ for the current output $Y$, preserved as a borrowed observation. Given that observation, the verified local exit costs eight H1 calls, 456 ADDs and 240 monomial maps. PR #5388's 112 paid observations apply to independent forward-helper inputs, so they cannot simply be renamed as this $Y$ observation. Its complete helper recoding, original inputs and return costs remain obligations.

The observer screen rules out a specific tempting architecture. The 112 source columns occupy 112 distinct right monomial cosets, excluding one common Gaussian after monomial preaggregation for this source. All 6,216 pair comparisons distinguish $\mathrm{rank}_B(E_j^{-1}E_i)=2$ from $\mathrm{rank}_B(E_iE_j^{-1})=0$; reversing the cancellation order does not aggregate independent inputs. This does not exclude multilayer, two-sided or endogenous-observer constructions.

Recursive savings are extremely sensitive to precision. Under the conditional supplied-observer profile, the observer and extra termination share the following allowance. The 0.004 cost cap uses directed exact integer-root enclosures; other entries are numerical sensitivity screens, not compiler theorems.

Desired saving	Combined observer + extra termination cap, H1-equivalents/FULL	Uniform paid-precision factor ceiling
0.0033	59.743	1.004572
0.004	50.063024…	1.003840
0.006	22.567	1.001743
0.007	8.908	1.000691

A 1% paid-precision increase exceeds every listed ceiling. The proposed 32 H1-equivalents/FULL joint allocation remains unimplemented; at the 0.0033 milestone it leaves numerical moment margin 499.380 but only a 1.002118 paid-precision ceiling. It fails the 0.006 and 0.007 screens. The selected ordinary BIT admission is still 0.0034, so reaching 0.004 also requires an ordinary-work/compiler improvement.

The assessment therefore deprioritizes inverse-only packages, stationary eight-mode rebasing, passive one-Gaussian decoding and uncharged approximate degenerations. In particular, the native cycle $ZW=14I$ is non-nilpotent, so the literature's nilpotent similarity construction does not automatically transfer to this supplier. These scoped exclusions narrow the next experiment without asserting a universal barrier.

Task and overlap

The package extends joint-query-controller; the frozen card and scope change are recorded in TASK.json. Initial scientific base: 1ec1119972c9aefe42525172d07b332fcff81cb4, priority revision 7. Submission comparison: canonical promotion 1a3ced60b2f7a46bc70280a04f2eeb8ca027c700.

Nearest dependencies are PR #4935, PR #5388, PR #5398, PR #5402, PR #5411, PR #5413 and the prior PR #5415 transport check. Exact heads, original byte comparisons and publication-ancestor pins are in SOURCES.json/ORIGINS.json. The involutive completion and three-shear/transpose method are prior work, not newly claimed here. The native coupled provider is not assumed already to equal the proposed $H$ encoding.

Refreshed overlap coverage: 306 open PRs and 4,702 Discussion records with complete remote pagination; sparse local and historical coverage is incomplete. See VALIDATION.md for scope and access limitations.

Validation

Python 3.12.8 and 3.14.5, standard library only:

python3 -B research/literature-coupled-synthesis/verify.py
python3 -O -B research/literature-coupled-synthesis/verify.py
python3 -B scripts/research_package.py --package research/literature-coupled-synthesis

Normal and optimized scoped checks pass. The registered runner checks metadata/source pins and the scientific probes. Failure controls include wrong coupling coefficient, missing owned initialization or catalytic restoration, tableau-invisible global phase, the zero-address false positive, whole-bank ADD substituted for main-only ADD, and wrong observation owner/version. The current-profile 0.004 decisions use directed integer roots. The new signed-invoice preflight was also run: conditional ideal uniformly better, fresh-query decoder uniformly worse, and the unimplemented 32-H1 allocation inconclusive in general concave order.

Committed-byte, official 32-file export, and read-only Git-free normal/optimized replay checks are recorded in VALIDATION.md. Full selected/native admission, historical suites, Lean, Docker and optional full-history ancestry audit were not rerun. Hosted CI is separate from local evidence.

Credit

zxv, with substantial OpenAI Codex assistance. Apache-2.0. Retain David Ganz's completion/code work, Dillon Amburgey's paid-query/provider interfaces, Cao Yifan, Cinna Davis, Jacob Alan Sussman, Ali Romman, and the full controller, source-reflection, Clifford and paper attribution.

Open next questions

The ranked construction assessment gives the proposed order and stopping rules:

1. Fit the actual provider and paid history at the first backward FULL/thin-query cut. Derive the complete 232-field X/Y/mode input/return map with disjoint original-mode ownership. Supply current-version $ZQY$ while preserving or provably displacing the demanded $Q^{-1}X$ response. Charge history return within the single combined cap; stop if an essential read is unavailable or the required inequality fails.
2. Close two generations with bounded history. Use the displacement state, terminate it at the second actual contact, and check every original column, borrowed response and owned-zero return. This establishes whether the first junction can be reused.
3. Optimize the installed junction and both endpoints. Start from the verified $H_tPH_s$ and retained-query circuits, share work only where actual ownership permits, and choose the gauge for the real precision metric. Ordinary synthesis gains alone do not establish recursive savings.
4. Compile and independently admit a favorable complete invoice. After the paid bill passes, prove precision, volume, storage, tape and ordinary/outer admission. Retain the earlier no-IDLE, two-FULL, volume and independent-error obstructions within their stated scopes.

The structured questions are also recorded in TASK.json. The local consumer circuits do not themselves complete the native supplier or establish a new κ.