[petalas]

Summary

Add a fixed literal prefix to Ali Romman's PR #5849 quarter-carry leaf. It lowers the complete uniform bounds from 468V to 1115V/3 transitions and 49V to 24V visited cells, for V=PQS. Claim type: scoped physical construction with a written proof and finite corroboration; no new kappa.

read the next symbol of the canonical Q descriptor
restore the descriptor head
if Q=1: return the unchanged original owner, 4 transitions total
otherwise: enter the retained program, 4 extra transitions

Both directions preserve the valid packet, descriptors, arbitrary spectators, heads and private-storage contract. The nonunit table is preserved instruction by instruction after finite destination relocation. Its correctness and nonunit bounds are cited dependencies, not re-audited results. The new sufficient bounds are not claimed optimal. Sagar Thakrar's PR #3265 already documents Q=1 skipping in a different high-route caller; priority for that general observation is unclaimed.

Evidence

• Before: Complete runtime G20 quarter-carry rotation with tight physical bounds #5849's complete uniform bounds are 468V transitions and 49V visited cells, attained at one bit.
• After: the new unit branch takes exactly 4 transitions and visits 20 cells; the proof combines the four-transition fallback toll with Complete runtime G20 quarter-carry rotation with tight physical bounds #5849's nonunit bounds to obtain 1115V/3 and 24V.
• The verifier passes 1,972 unit executions, 58 separate-interpreter unit checks, eight descriptor-prefix fixtures through 513 bits, every retained row in both source tables, six complete nonunit compositions in both interpreters, and six negative controls. The k=-3,Q=125 composition takes 16,694 transitions and visits 625 cells in either direction.

From the repository root, using CPython 3.12.15 and the standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/unit-modulus-carry-bypass/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/unit-modulus-carry-bypass/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/unit-modulus-carry-bypass
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/unit-modulus-carry-bypass --check-source-history

Normal and optimized direct checks passed in 0.77s and 0.74s. Registered normal/optimized replay and metadata checks passed again at the publication commit in 2.18s total. The verifier emits a generated receipt bound to package and input hashes and writes no files. Committed-byte and declared-source-history preflight passed at 381f5d6146488a20e29e79c2f2dd12630309e258: all 13 publication files match, and the declared base/source commit is an ancestor.

Limitations

The nonunit implementation and its analytic bounds remain inherited from the pinned #5849 table and proof. The unit branch assumes valid inputs and does not validate unused packets or scratch. Nonunit calls pay four extra transitions. This improves the uniform interface envelope; it does not make every call cheaper.

The complete caller has not been installed or repriced. Low-cache packet formation and selection, whole-T staging, low-type commit, physical ROW presentation, ancestor stock/P3 and the full G20 invoice remain open. No predecessor broad replay, formal proof-kernel check, independent human review, selected-frontier change or complete multiplication theorem is claimed. All five framework assumptions retain their status.

Open next questions

Join one actual low-cache row to the supplied packet and this wrapped leaf in a single paid physical execution. Start with #5849's port9 k=-3,Q=125 witness; include row selection, homogeneous routing, packet formation, cache erasure and low-type commit. Whole-T staging and the actual ROW map remain blockers.

Related open work

• Independent review of the G20 BIT chain PR5679/PR5708 #5955 studies admission of the G20 BIT chain; this is a separate literal carry-leaf improvement and does not resolve that audit's native or supplier obligations.

• Prove exact 20-ADD floor for the G20 chain/exchange component (no new κ) #5942 studies the G20 chain/exchange ADD minimum; this changes a physical tape dispatcher, not that algebraic word or its ADD count.

• Exclude 1,981 more G20 helper-split contexts (no new κ) #5983 studies additional helper-split contexts on the final PR5708 G20 word; this contribution changes the literal carry-leaf dispatcher and does not compute its boundary pairing or a competing split count.

CI notes

All checks passed at head 381f5d6146488a20e29e79c2f2dd12630309e258: plan and replay (research/unit-modulus-carry-bypass) in run 40570702728. The run head matches the PR head. This certifies the registered package checks; it does not discharge the inherited mathematical or caller obligations.

Merge Danger

Door: two-way. Blast radius: isolated. Only a new scoped research package is added; shared implementation and frozen evidence are unchanged.