[ToikY]

Change and mathematical scope

This constructs exact dyadic operation words for all 111 G20 port normalizers and their inverses from PR #5798, replacing a dense-matrix existence statement with independently checked finite words. Both directions total 5,960 ADDs and 2,174 unit SCALEs; maximum absolute numerator/denominator is 4. Swaps are lowered explicitly. No construction or conditional-exponent credit is claimed.

The serialized convention is RIGHT: I E1...Em=W, ADD[i,j,a]=I+a e_i e_j^T, hence row[j] += a*row[i]. The inverse reverses/inverts factors. The source column convention remains distinct: W maps the central axis to the local line; W^-1 maps the line back. A unit-preserving Euclidean reduction avoids odd nonunit division.

The declared 127-coordinate embedding uses the actual 18-stage inventory by ordinal position, with 119 spectator coordinates fixed. For N=127f, addressed leaves cover every N matrix row and f lane. Two address namespaces and both words are included in a Cartesian catalogue, not identified with retained physical head indices or actual paid-event incidence.

Per coefficient, positive named P2 call counts multiply the both-direction histogram by 18*2*N*f=4572f^2. At f=1: 27,249,120 ordered shifts and 9,939,528 unit scales. Each retains its own symbolic tariff, including relevant radix/width/tape parameters; no zero/unit price or absorption into the existing finite fee is asserted.

Full ROW borrowing, old-low cache COPY/CLEAR, carry/type commit, padding/return, physical head-map and route-incidence binding, primitive implementation/tariffs, compiler and supplier admission remain open. The five framework assumptions remain. No new kappa or frontier change.

Task and overlap

Canonical main refreshed before publication: de5ec2e7a6074068452f45b1a191b5c72832df4a, priority 8. Frozen source: #5798 at eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826; current-main ROW-generator ABI is separately pinned as provenance.

Canonical claim and TASK.json declare scope_status=changed from formal-interface-lemma to this finite constructive kernel certificate; no Lean formalization. This complements #5798's rational matrix audit and JoyboyBrian's earlier ROW schedule, rather than repeating those results. The live corpus contained 353 open PRs; actual #5777 handoff/source comments were checked. Discussion history and unpublished work remain coverage limits.

Exactly one 13-file package is added: research/g20-normalizer-dyadic-words. Frozen source data are retained with raw SHA256/Git blob pins; no predecessor implementation or cross-checker imports.

Validation

Python 3.12.14, standard library:

python3.12 -B scripts/research_package.py --package research/g20-normalizer-dyadic-words

Registered normal/optimized primary and separate oracle pass. The oracle independently checks 222 dense RIGHT products, 222 basis-row products and 222 round trips, all 18 layouts and 731,520 flat-address templates. Six controls reject omitted operations, wrong direction (actual port 1), an odd scale outside the chosen unit alphabet, source drift, spectator writes and raw-stage/ordinal confusion. Both complete canonical receipts reject numeric-type aliases.

Metadata/pins, committed bytes/modes, declared current-main history and official export integrity pass. A separate read-only, Git-free isolated optimized replay with empty PATH passes both checkers in about 1.34 seconds, preserving every exported byte and mode. Export SHA256: f2271a1e620a938364048a3ed391a649dfca84be7314efa3a8431be25f802723. Original data origins are bound by retained bytes, not claimed as publication ancestors. Current selected baseline passes bindings/metadata only.

Publication head eb92cbdf211f0c3717ff6fa71af47ec38f8e412d; tree 2952818c1dc826b0b0ec3cc81d2487cb4045410a. Hosted checks have not yet been observed; the known shared assignment-suite repair remains #5761. No hosted scientific pass is claimed.

Credit

Ali Romman with OpenAI Codex assistance supplied G20 normalizer witnesses and the global audit. Retain Dugongue, ai-nanachi, #5679/#5708, #5782 and all source credit. JoyboyBrian with Codex assistance supplied the earlier ROW generator/P2 schedule; its retained lineage is included in NOTICE. New finite words/certificate: ToikY with substantial OpenAI Codex assistance, separate primary, independent-oracle and read-only proof/review contexts. Classical elimination is not a new general theorem. Apache-2.0.

Open next questions

Bind an exact kernel direction/owner to actual source route markers and the full ROW borrow/cache/carry/return schedule. Prove physical head-map correspondence and coefficient-specific tape tariffs before importing these catalogue counts into a caller invoice. TASK.json records the structured blocker. Maintainer edits disabled; no merge or closure requested.

[ToikY]

Hosted CI update for exact head eb92cbdf211f0c3717ff6fa71af47ec38f8e412d: planning failed with 8 failures and 2 errors in the unchanged shared current-assignment tests (511 tests, 22 platform skips). Scientific replay was skipped. PR #5761 is the existing separate fixture repair. The diff remains confined to the new 13-file package. Registered normal/optimized primary and independent oracle, exact committed bytes/modes/history, official export and read-only Git-free cold replay pass locally. No hosted scientific success, physical ROW/tape admission or new kappa is claimed.