κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%)

[jacklightChen]

This replaces the complex E8 scalar network with a mutable-basis Hamming packet construction, reducing helpers from 783 to 680 while retaining 120 ports, eight copied centers, and the compressed nine-stage geometry from #386.

The resulting conditional finite bound is

• complex supplier b = 0.001049104978040580;
• unchanged bit supplier c = 0.001057833103534317;
• κ = 0.001048005508028206 ≈ 2^-9.898137985359.

The complex gain is 4.97468% over the locally verified frame-retimed word; the combined gain is 4.96947%, or 4.98499% over published #386. This does not reach 2^-9.

The structural change is a new common-frame scalar interface. Sources can carry intermediate signed packet bases until full-frame inverse cleanup; retired packet registers reconstruct the central sums; 56 target pairs carry a first two-output butterfly. An explicit frame-zero inverse output basis and 13,216 charged dirty-response additions restore arbitrary target/helper inputs. The old gx source-immutability and target-read restrictions are replaced by a separate written conjugation lemma and complete exact matrix checks, rather than being silently bypassed. This extension is the principal new mathematical review point.

Validation in the included offline replay:

• all 120 × 120 signed decoder entries, and 920 arbitrary-input columns in each orientation;
• exact source/helper restoration, private-work lifetimes, and negative controls;
• 998 exact complex frames, 3,044 directed transitions, and 240 endpoint adapters, including global phases;
• the emitted 72-call program, all 48,960 helper assignments, padding, idle children and cover corrections;
• fresh finite costs, two rational moment engines, the next-grid rejections, three bootstrap steps and all 47 strict outer inequalities;
• byte-identical regeneration of the scalar word, canonical word, Clifford recipes and global template from a fresh extracted package.

Run make hamming-complex-verify, or python3 -B research/hamming-mutable-basis-complex/verify.py --work /tmp/hamming-e8-fresh with a nonexistent output directory. Python 3.11+ and its standard library suffice; no network or optimizer is used. The construction and scalar-interface proof are in research/hamming-mutable-basis-complex/work/complex-network/hamming/PROOF.txt; fresh receipts are in research/hamming-mutable-basis-complex-validation/.

This is a draft for review of the new scalar interface. The existing all-size compiler, common-grid, restored-row, tape/prime/precision and analytic-transfer interfaces remain explicit assumptions. No new Lean proof or unconditional integer-multiplication theorem is claimed. The historical repository-wide suite is not claimed to pass; its previously recorded Apple-clang OpenMP failure remains outside this research package.

This branch builds on #386 and adds one self-contained research package and a verification target. The pinned PR370 Hamming root data and prior complex/pricing sources retain their notices; no newer external research was consulted.

[ahrazzle]

Target: PR #425, head e11ccea
(base 12a4934, fetched 2026-10-11T12:13:32Z).

Verification

Independent third-hardware replay of this head, from a fresh detached
checkout.

• Verifier exit 0 on the intended interpreter, Python 3.12.15. All six steps
  pass, and all four canonical artifacts byte-match EXPECTED.json.
• kappa = 524002754014103/500000000000000000 = 0.001048005508028206.
  The fraction is exact to the last of 18 decimals and identical to
  FINAL.json and this PR's body. The same rational is written
  1048005508028206/1000000000000000000, reduced by 2.
• Binding component: complex. kappa sits strictly below the complex supplier
  bound, which is the smaller of the two suppliers.
• All 47 strict outer inequalities reproduce from an independent chain, and
  the three derived percentages recompute exactly: 4.97468% complex gain,
  4.96947% combined gain, and 4.98499% over the published #386 baseline.
• Digit-exact: an independent closed-form re-derivation (stdlib fractions,
  no package code) reproduces the same fraction on the 1e-18 grid.

Negative controls

All rejected. 4 scalar and frame audit controls, 7 independent IR and global
replay controls, and the assembly controls next_grid, zero_eta,
zero_beta and unit_beta. The next_b_grid boundary claim is a real
assertion in two independent rational engines, not a stub literal.

Reviewer note on the interpreter

The mathematics does not depend on the interpreter. The byte-identity check
does. On Python 3.13 and later the package's own verify.py exits 1 while
every mathematical step still passes. The only difference is one gzip header
byte, the OS field, which is 19 under Python 3.11 and 3.12 and 255 under
3.13 and later, a CPython change. Payload, mtime, XFL and CRC are
byte-identical, and the freshly decompressed template sha256
813845bd80495c76879e8c6dbe52ddb20e8ee52bd16029e99508b739bb1fd3cd
equals the authors' recorded hash. So an exit 1 on a current interpreter is
that header byte, not a maths failure, and on Python 3.12 the check passes
as recorded.

Limits

The claim is conditional as this PR states: the existing all-size compiler,
common-grid, restored-row, tape and precision, and analytic-transfer
interfaces remain assumptions, the new scalar interface is a written lemma
enforced by exact matrix checks rather than a Lean proof, and no
unconditional theorem is claimed.

AI-assistance disclosure: prepared with AI assistance under human oversight.