Research: exact two-register CK coefficient frontier (no new kappa)

[bbMisk]

This PR checks temporary mutation of both source and target for all 103 coefficient magnitudes in the historical PR626 CK programs. It is a scoped negative result with a finite scalar application. In the stated two-register alphabet, it cannot beat the checked scratch-circuit comparators except at magnitudes 2 and 3, where ordinary repeated unit additions suffice. No novelty is claimed for those identities; the contribution is the complete source-bound exclusion and finite application. No new kappa.

Two separate implementations, using integer and Fraction arithmetic, agree on all 30,576 matrix distances. A radius-six ball covers every word through length twelve, giving 77 exact minima and 26 lower bounds. Because every comparator costs at most 14 including a required private clear, this covers every possible strict improvement in the declared class. There is no intermediate magnitude or denominator pruning.

Applying only the direct ±2/±3 substitutions to PR696 saves 3,124 real-component primitives per orientation: 169,618 → 166,494 forward and 169,634 → 166,510 backward. Full scalar replay checks all 725 arbitrary input columns, restored helpers, private clearing, unchanged paid profiles, and unchanged exact and cancellation-free prefix bounds.

python3 -I -B research/complex-restored-source29/verify.py
python3 -I -B research/complex-restored-source29/independent.py
python3 -I -B research/complex-restored-source29/test_package.py

Both checkers, five package tests, selected-record verification and 25 selected-record regressions pass on macOS / CPython 3.14.6. Source corruption, receipt corruption, dirty-input mistakes and false optimality claims are rejected. Full repository suites, cold/native supplier replay, global admission, hosted CI and Lean were not run. The selected T37 frontier and upstream/ are unchanged; inherited compiler, realization, hosting, precision/tape and analytic assumptions remain.

Only one research directory is added. Exact base: 2921874911956718fcaaaf9396fe8267b3cfa9f0; OS seed 29. No pinned coordination issue existed, so the claim is local. The README records source pins, proof, comparison scope and attribution, including Philipp/mightyOil #882/#883, Sagar Thakrar #696/#723, Chris Pagolu #734, Gareth Davidson #837/#866, Seb/ZK-Snarky #999, and the Chafik Boukhalfa / Jeremy Kothe / icekylinx CK lineage.

Prepared for Hanson Sun (@bbMisk) with substantial assistance from OpenAI Codex. Apache-2.0; no independent human review claimed.

[Mister-Meeseeks]

100-PR batch review at c4ad801099d0813ffac56f0b517a908cd8ae0c6a.

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

Reviewed scope: Exact two-register historical CK coefficient frontier with restoration and dirty-work clearing charged; not an unrestricted scalar optimum.

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.