Scoped negative result: scratch-free CK/JP8 boundaries need extra primitives

[RossRichardson]

The historical CK/JP8 2+3-cycle boundary costs eight real-component primitives with one temporary register. Removing that register cannot tie the price when the circuit may use exactly the five moved coordinates—even allowing arbitrary mixed dyadic intermediate rows. The scratch-free minimum is between nine and ten; the nine-versus-ten question remains open.

This is a scoped negative result, with no new kappa or supplier substitution. The complete census binds all 168 PR971 boundaries. The restricted scratch-free boundary invoice is at least 238 versus 224 primitives per real component, or at least 28 extra real primitives per orientation.

• Complete radius-four F3 balls: 509,157 states. Separate Python row-table and C++ bit-packed implementations agree on every state and shortest distance. The exact dyadic-to-F3 reduction makes the empty five-dimensional intersection a length-eight exclusion.
• Rational witnesses establish exact costs four and six for the two-/three-cycle cases and a ten-operation upper bound for the combined case. All 37 single-primitive omissions fail.
• Ten test groups pass on CPython 3.14.6 and 3.9.6, including source/receipt corruption and minimal offline relocation. Full receipt regeneration, source pins, selected-record check and five selected-result tests pass after rebase.

Reproduce with Python 3.9+ and a C++17 compiler:

python3 -I -O -B research/complex-scratch-free-boundaries/verify.py

Expected: PASS_COMPLEX_SCRATCH_FREE_BOUNDARIES boundaries=168 states=509157 costs=4,6,>=9 scratch_costs=4,5,8 no_new_kappa.

Research base: ba82555c64e1879e4b7decce28186f208fcb8262; refreshed submission base: ce7ad1b6ab09452c3478723a2e96ed5ff212dc08. All seven historical source inputs are unchanged. Upstream now selects PR1094; this patch does not edit selection or upstream/.

Credit ToikY/Eva Ayala #971, woklerx #1095, Sagar Thakrar #696, Chafik Boukhalfa #626, Jeremy Kothe #622 and the retained lineage. Unlike #1095's one-scratch monomial-prefix class, this result permits mixed rows and forbids scratch. No pending implementation is imported. Prepared for Ross Richardson with substantial OpenAI Codex assistance; Apache-2.0, no independent human review claimed.

Scope excludes borrowed fixed registers, joint optimization across boundaries, restricted incoming states, different primitives and full native/physical/hosting/precision/analytic admission. This is not a formal proof of the multiplication theorem. Hosted CI is pending separately from the completed local checks.

[Mister-Meeseeks]

100-PR batch review at fd4d5ffc448361297e717aa30eafed578caf8e61.

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

Reviewed scope: Scratch-free historical cycle-boundary exclusion via complete mod-three meet-in-the-middle balls and independent C++ census; fixed registers may not be borrowed.

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.