[thu-nmrc]

The odd-E8 route leaves a physical producer and complete Gaussian caller unresolved. This PR supplies constructive native components: a full120 E8 native K from an explicit fifteen-cube cover and both full120 source-consuming low-rank E adapters, plus the retained112-root and directed cross-cube components. The new construction lowers the modal-query density per port by about12.6%. The negative E decoder remains unresolved: there is no new kappa or complete Gaussian supplier claim.

Full120 E8 construction

The previous native family used112 root lines in14 cubes. Adding the eight roots2e_i gives M^T M=60I. The Weyl-reflection cube orbit contains9450 valid cubes; an explicit exact cover partitions all120 roots into15 eight-port native blocks. Each has two four-port classes with q-span3 and cross-orthogonality. For C=MM^T/4, the signed-half block matrix K satisfies K^2=I, KM=-M and KC=-C. All eight additional ordinary normalizers and32 entry/exit wrappers include their absolute phases.

The emitted n9 forward and backward words start from240 arbitrary independent original main fields, use no helper/COPY/CLEAR, and each pay H2/H3/H5/H6 exactly120 times. All1440 nonzero operator blocks, all zero blocks and four rejecting mutants are checked. A separate AI-worker interpreter imports no author script and rechecks the entire n9 word using a polynomial affine phase backend, including an unchanged-tableau phase-i mutant. It shares the pinned exact Clifford primitive; this is scoped independent implementation, not independent human review.

The odd3 lift has1,728,000 labels and3375 product cubes in dimension25. Every label,6750 common S9 classes and15,552,000 q/basis dot products are checked. One actual512-owner n25 cube is fully emitted/replayed with H8/H9/H15/H16 each512,38912 ADDs and no helper/COPY/CLEAR. The generic constructor covers all3375 cubes; their full literal streams were not all materialized, and the peer does not independently replay n25. All-width tensor lifting retains absolute phase multiplied by width and scalar owner coefficients applied once.

The nonzero C_odd modes are225/2 with multiplicity21504 and-1350 with multiplicity512. Thus h/v=43/3375 versus5/343 previously, a relative reduction2126/16875, approximately12.6%. The absolute mode count grows to22016. The E corrections are now constructed below. If both three-stage halves are granted independent H73 output, the conditional margin per port per local call is enclosed by

0.089288485130366173 < margin < 0.089288485130366174

The old conditional margin was about.04382074131724228. The grant is not productive target credit. Removing E defects while leaving a K-coded bank is insufficient. A separate factor5 price screen is planning evidence; no factor5 native word or decoder is claimed.

• Full120 construction and scope
• Exact cover proof
• Native all-width proof
• Odd3 construction
• Independent checks and rational budgets

Full120 original-source E adapters

research/full120-e8-lowrank-e-native supplies actual base120 E and inverse words and a structured odd3 extension. At base, E=K+C/14 and E_inverse=K+C; for H(T)=diag(T,Q^-1 T Q), the exact physical contracts are

WF = [[E D,0],[D E Q^-1,D E]] = H(E) F0
WB = [[E_inverse D,-E_inverse R],[0,D E_inverse]] = H(E_inverse) B0
base paid per direction: {2:120,3:120,5:120,6:120,9:8}
odd3 paid per FULL: {8:V,9:V,15:V,16:V,25:22016}, V=120^3

Backward gathers original ground Y before precode. Inverse saves actual native source contacts, finishes the source inverse, restores ground Y and queries it before finishing target work. Forward uses the exact owned linear transpose, including COPY/CLEAR dual rules and ordinary boundaries. No query on unavailable Q^-1 X is assumed. The emitted ordinary E codes check all14400 coefficients each; native inverse/transpose checks use all240 base or1024 cube operator rows. The actual base macros list every paid child and ordinary address word. Their full122880-square physical matrix is not expanded.

The odd3 construction uses the explicit120-owner in-place recoder and all-owner selector loops, with a pinned actual512-owner native template. The unified local upper includes2,829,471,232ADD,29,074,432SCALE and34,905,600SWAP, as well as every address, owned and query operation. Owned peak is at most1,750,528. Four chronological recoder orientations give finite whole-field-l2 macro bounds below2^202 locally and2^764 for N3 with positive exits. A separate review corrects an intermediate arbitrary-scratch estimate to the full shear bound1+7=8; all author's final numerical constants remain valid. Coordinate rounding, recursive child internals and outer machine/storage admission remain separate.

A separate root interpreter imports no author script and executes the actual full F/B macro on six selected original columns: old root0 and new roots112,119 in both banks. It checks all240 returned fields in each orientation and all four tensor-width phase residues, totaling3960 nonzero and7560 zero blocks. It shares the Clifford primitive and uses a separate affine-support phase backend. This is not an all240-input-column or n25 independent reconstruction. A second reviewer audits the exact ordinary invoice,512 contact versions, transpose coefficients and macro norm factors. The sealed author, physical peer and review closures are copied verbatim; only a documented portable review path adapter is added.

• Full120 E construction and limits
• Operator/source/checkpoint proof
• Actual physical macro peer
• Precision and invoice qualification

The three-stage endpoint remains Q^-1 E3 E2^-1 E1 D123 on the negative original bank. Only the positive bank is ordinarily decoded to trueH73. Completing the positive E components does not solve the negative terminal.

Retained112-root E and K components

research/odd-e8-lowrank-e-native retains the112-root construction unchanged. With E=K(I-C)^-1, Q=C0, fresh rank24 D and H(T)=diag(T,Q^-1 T Q), its exact contracts are

W_F = H(E) diag(D,D) L(Q^-1)
W_B = H(E^-1) diag(D,D) U(-Q)
paid per FULL: {8:v,9:v,15:v,16:v,25:20480}, v=112^3

The backward correction gathers actual original ground Y before precode/overwrite, pays R25 per nonzero mode and scatters before postX. Forward is built from a genuine source-checkpoint inverse and linear transpose, with COPY/CLEAR dual rules and ordinary D-squared/J boundaries. Root512 contacts, complete small noncommuting Q(i) fixtures and two actual E8 cubes test these interfaces. Explicit structured mode and native loops give field-level ordinary/owned invoices and finite whole-field-l2 norm bounds. Coordinate precision, compiler/storage and outer admission remain open. Proof, review, precision scope.

The actual F1,B2,F3 caller, after its signed swap, has endpoints Q^-1 B_E D123 and B_E D123 Q, where B_E=E3 E2^-1 E1. Ordinary B_E^-1 decodes the positive half to H73. The negative half remains coded. Existing ordinary-decoder obstructions, including #5508, are credited; this construction does not contradict them. The pre-return original-input lever also remains credited to the existing discussion and #5469.

research/odd-e8-whole-k-native retains its original112-root K, exact absolute-phase forward/backward interfaces and scoped terminal-support obstruction. research/odd-e8-polarized-native retains the directed H_ab primitive and its caller obligations. Neither frozen package is altered by the full120 addition.

Reproduction and scientific gate

Python3.12 and the standard library suffice; checks run serially.

python3.12 -B scripts/research_package.py --package research/full120-e8-native
python3.12 -B scripts/check_research_commit.py --package research/full120-e8-native
python3.12 -B scripts/research_package.py --package research/full120-e8-lowrank-e-native
python3.12 -B scripts/check_research_commit.py --package research/full120-e8-lowrank-e-native
python3.12 -B scripts/research_package.py --package research/odd-e8-lowrank-e-native
python3.12 -B scripts/research_package.py --package research/odd-e8-whole-k-native
python3.12 -B scripts/research_package.py --package research/odd-e8-polarized-native

On dcd9a87, the new full120 package passes all four registered hooks (sixteen scientific script runs) and the exact56-file committed-byte check. Its official committed export/check passes. A separate Git-free, empty-PATH replay runs the same four hooks on exported0444 payloads and verifies unchanged bytes. The three source packages and independent peer closure are retained verbatim; canonical decompressed scientific programs are distinguished from gzip container hashes. A full source-history ancestry check is not claimed for this shallow checkout. Earlier registered and cold checks on the unchanged packages remain recorded; hosted CI is separate execution evidence.

On d4b9151, the full120 E package passes all four registered hooks (twenty-two scientific runs plus inventory checks), the exact71-file committed-byte check, official committed export/check and separate Git-free empty-PATH normal/O export replay on unchanged0444 payloads. The current exact-head hosted workflow passes all six jobs: plan and the five registered package replays. These are execution and reproducibility evidence, separate from scientific acceptance.

At refreshed canonical main32890bc5de034ab8fc93ac88ead7279a6a416d04, selected conditional kappa remains0.003027288235 with the retained framework assumptions. Promotion requires a profitable all-width paid negative decoder or genuinely changed caller/target inventory, followed by full ordinary/precision/storage admission. Component validation, conditional margins and archive merges are not scientific promotion.

Bounded primary PR/Discussion searches and reads found no identical full120 native-compatible fifteen-cube package. They are not an exhaustive literature or unpublished priority check. Generic E8 root geometry, Weyl/Clifford algebra, tensor modes and the native/compiler/analytic lineage are inherited. Credit Ali Romman; Dugongue and Dillon Amburgey; Cao Yifan; Cinna Davis, zxv, Jacob Alan Sussman and the retained sources. Prepared for THU New Media Research Center (@thu-nmrc) with substantial OpenAI Codex assistance and separate AI-worker review. Apache-2.0; retained notices remain. No independent human or proof-kernel acceptance is claimed.