[petalas]

Summary

Finite certificate: construct the h=22 disjoint-triple map with 30,676 additions and 32,216 reversible roles, 22 fewer of each than ToikY's #981. The complete historical three-stage scalar bound decreases by 1,252,204,800. No new kappa or selected-frontier change.

#981 root recipe stays fixed
D_(2,2)(11), split 5+6, channel (1,1): reverse the 146/146 factor-order tie
30,698 additions -> 30,676
32,238 roles     -> 32,216

The new step enters the proper-descendant domain explicitly excluded by #981. Credit ToikY's root traversal, Curtis Dransfield's #863 tied-root construction and Douglas R. Colkitt's recurrence, interning, compiler, phase enclosure and historical accounting. The contribution was produced by Nick Petalas. Predecessor values are cited; their circuit censuses and verifiers are not replayed. The search stopped at the first exact improvement.

Evidence

Before: #981 reports 30,698 additions and 32,238 roles. After: the new literal-DAG checker derives 30,676 additions and checks every one of the 2,371,600 integer coefficient positions, including zeros. Separate symbolic slot replay checks the complete compiled embedding and counts 61,352 literal disjoint-mixer additions. Both physical frame orientations pass, with 104,897 distinct nontrivial transitions. A written elementary inverse covers arbitrary dirty values; one dense integer roundtrip supplements it.

Six rejecting controls cover an incorrect output, duplicate summand, cycle, corrupt cached support, missing paid role and aliased fanout. Warning-strict isolated normal and optimized runs pass on CPython 3.12.15, each locally timed below one second. Both registered checks, metadata/live pins, committed-byte/source-history preflight, export integrity/input coverage and a Git-free optimized exported replay pass. All sixteen exported files remain byte-identical after replay.

Exact reproduction from the repository root:

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

Other machines may substitute their CPython 3.12 executable. Expected marker: PASS_DISJOINT_DESCENDANT_TRAVERSAL additions=30676 roles=32216 no_new_kappa. The read-only replay emits a computed receipt bound to all package and live-input SHA256 hashes.

The complete retained historical bill includes every mixer/inverse, source access, weighted injection, restoration, intersection-two role, 23 centres, join and recursive child. The new signed invocation bound is 409,880 and the three-stage bound is 2,916,214,224,000. Exact W/s/E and stopped-recurrence guards are checked.

Limitations

This is a finite historical circuit and its complete inherited invoice, not a current P104 supplier or multiplication theorem. No global circuit optimum is claimed. Physical frame checks use the retained enclosure case proof; explicit h22 residual orthonormal bases are unrun. Current supplier admission, all-size/compiler, ownership, all-column native, precision/tape and analytic recovery obligations remain. No selected cold replay, Lean or full historical suite was run. Independent human and formal proof-kernel review are unclaimed.

Only the new scoped package is added. Canonical base is de5ec2e, priority 8. The selected binding-only orientation passes. Source pins and predecessor credit are retained.

Open next questions

• Can this sharing mechanism improve a named disjoint-subset component in a competitive physical caller? First identify its complete boundary and bill; compatibility with selected P104 is unproved.
• How much can one proper descendant's factor-order change save under first-decomposition interning? Start with the supports in the two 146-cost factorizations; this example supplies no universal sharing bound.

Neither follow-up is reserved.

Related open work

Refreshed this account's open PRs created since the advance CLAIM at 2026-10-27T13:25:04Z. None remain open, so there is no additional same-object entry. The earlier complete 470-open-PR body corpus and targeted searches found no open PR studying this h=22 disjoint-triple circuit or its descendant factor ordering. #863 and #981 are merged predecessors. Unposted work and arbitrary diffs are outside that coverage.

CI notes

For commit 78c77c5e8b0d3d1988f4cd9d72b9382d818cff43, run 40513670261 failed plan at Onboarding helper tests. The failed step runs python -B -m unittest discover -s tests -p 'test_research_*.py' -v. Its ten failing cases are all in tests/test_research_current_assignment.py: eight assertion failures and two errors, ending with FAILED (failures=8, errors=2, skipped=22). The errors are KeyError: 'follow_up_steps' and KeyError: 'catalog_first_step'; the assertions include missing resolver rewrites and missing expected validation exceptions. This matches the known shared onboarding failure on base de5ec2e7a6074068452f45b1a191b5c72832df4a. Those tests and all files outside this package are unchanged.

replay was skipped. Hosted replay has not certified this package. Only the local package checks described above have run, including normal/optimized registered checks, committed-byte/source-history checks and exported replay. The merged state does not establish scientific approval or change the selected frontier.

Merge Danger

Door: two-way. Blast radius: package. The change adds an isolated opt-in research package and changes no shared code, frozen evidence or selected record.