[DanieleCorso]

Retraction following reviewer counterexample

The previously advertised candidate κ = 0.00045019844704 is withdrawn. The proposed three-core first-stage lockstep does not define a valid shared-dirty-scratch execution; its rank-3r histogram and finite moment bound cannot support a multiplication exponent.

Swapnil Jain's review comment correctly identifies cross-core live-data contamination. The same failure led to PR #132's explicit retraction. Thank you to both reviewers.

Correction committed

• Removed the unsupported new-κ result from the executable certificate. The revised verifier reproduces only PR Padded triple covers with sequential dirty reuse: conditional κ = 4.13596233702e-4 CrocSwap/integer-mult-bounds#137's original sequential, fully completed three-core construction and its exact finite assembly.
• Added research/triple-lockstep/lockstep_counterexample.py: a Q(i)-exact, 64-address, three-core regression with mutually orthogonal frame-label subspaces and nontrivial reversible Clifford operations.
• The counterexample verifies both schedules restore all physical scratch and the joint frame algebra commutes, but the proposed lockstep corrupts 192/192 target entries; the sequential schedule has zero errors.
• Updated the research README to document the invalidity and proof gap, and adjusted CI so it expects the counterexample and disallows new-κ claims.

Retained baseline and limits

The frozen PR CrocSwap#137 sequential three-core package is left unchanged, with conditional κ = 0.000413596233702. PR CrocSwap#138 independently reports a slightly tighter parameter choice, κ = 0.000413596659368, which is not claimed by this branch.

No new exponent improvement is claimed. Orthogonality of frame labels does not isolate independent live data in one shared register. Keeping external data-front gates separate cannot repair contaminated intermediate auxiliary streams. Any future improvement needs a genuinely distinct physical schedule or paid separation, with an exact arbitrary-dirty, signed forward/reflected replay before modifying the rank histogram.

Reproduce

python3 research/triple-lockstep/lockstep_counterexample.py
python3 research/triple-lockstep/certificate.py

Status: Draft / negative-control artifact, not ready to merge as a claimed new κ. Source authorship and licenses remain intact; this correction was prepared with OpenAI assistance.