Research construction: a tied contraction saves 1,221 historical complex roles (no new kappa)

[Curtis-D]

Change and mathematical scope

Finite historical complex-supplier construction; no new κ. Reversing one tied root contraction at h=22 reduces the disjoint-triple circuit from 31,929 to 30,708 additions, and its reversible embedding from 33,469 to 32,248 paid helper roles. Both alternatives have the same 39,900-addition unshared bound; global support interning and pruning reveal the 1,221-role saving missed by the inherited tie-break.

The full historical invoice includes the unchanged intersection-two circuit, 23 centers, source access, weighted injection, all four mixers/inverses, restoration, joins and recursive children. It saves 9,768 scalar operations per signed invocation and 69,497,366,400 in the complete three-stage scalar bound. Exact W/s/E, guard slack and historical supplier-saving intervals are recomputed. This does not compose with or improve the currently selected #799 multiplication bound.

Only research/disjoint-root-contractions/ is added. Seed 37 selected the complex track and h=22. An initial root-split-only search failed; one bounded pivot completed all 154 labeled root/at-most-one-channel-flip recipes (81 distinct DAGs), with inherited descendants and fixed point order. The winner is root split 11, channel (1,1). This is finite coverage, not a global optimality theorem.

Base: f567884aeb8851b6e794af1184119a3bfbe1e631. Historical tensor source: 1a74950ce5074b848243ba89d8022fbadba66105; exact dependency and selected-source pins are included. The current accepted conditional κ is recorded as 1661634653669567/10^18, not the older frontier in historical notes. A fresh overlap check found no root-contraction duplicate; #304's different module annealing and #809's central-basis shear are distinct and not dependencies.

Validation

python3 research/disjoint-root-contractions/verify.py

Expected: PASS: disjoint-root contraction certificate, independent reconstruction, and 9 tests.

Completed on macOS arm64 / Python 3.14.2:

• Exact integer maps and reversible embeddings for all 154 recipes, including zero coefficients: 365,226,400 coefficient positions.
• Both physical frame orientations at h22; explicit residual bases at h8/h10; all independent dirty input columns at h8/h10 and eight dense dyadic h22 controls.
• A separate standard-library implementation, importing no repository code, independently recomputes the DP, support interner and factor contractions; exact baseline/winner and small-control DAG/map hashes agree.
• Nine new tests, including invalid recipes, altered coefficients, overlapping/cyclic sums, omitted source access and a wrong injection sign; all five original tensor tests pass.
• Full certificate/test replay from outside the repository: normal Python 61.863s, optimized Python 58.427s, identical evidence. Normal replay remains required for inherited assertion-based coverage.
• make selected-record-check passes; source dependency closure is pinned; upstream/ and all selected artifacts remain unchanged. No repository-wide replay, Linux CI or Lean theorem pass is claimed.

Written phase transfer and dirty cancellation arguments accompany the finite checks. Uniform compilation, common labels/mutable sources, whole-call hosting, precision/tape and analytic transfer remain inherited obligations.

Contributor: Curtis Dransfield, with substantial OpenAI Codex assistance, including a scoped worker's independent implementation. Credits Douglas R. Colkitt's retained tensor/phase/invocation work and source notices; Apache-2.0. The local sprint claim and exact validation receipt are included (no pinned coordination issue existed).

[Mister-Meeseeks]

100-PR batch review at 6c0ed3975fda8f0190b34f1b1bbedb33a925d339.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Historical h=22 contraction-order improvement and independent DAG reconstruction; no selected κ change.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.