[petalas]

Summary

Add research/p104-endpoint-rank-lean/ and its scoped workflow. This formalizes the written matrix implication in #2662 rather than proposing another construction.

actual block-matrix product
  rank B(product) <= sum of declared child charges
  rank B(product)^p <= sum of charge^p, for 0 < p <= 1

independent binary source census
  416 disjoint endpoint runs; rank mass 928

Five Lean theorem roots use only propext, Classical.choice and Quot.sound. The source census uses closed-form symplectic transvections and finite span sets, without importing predecessor executables. Its source-to-matrix binding remains Python evidence, not a kernel certificate.

Credit commdata2338/#2662 for the endpoint-run theorem, rewrite class and histogram; ywz65/#2586 for the physical dual; #2497/#2551, Nick Petalas/#2550 and the retained native/compiler lineage. Exact heads, byte-identical source snapshots and full credit are in the package.

Evidence

• Before: Research: fuse 128 of PR #2586's 416 P104 physical-dual endpoint conversions #2662's matrix/concavity lower-bound implication is a written proof, with ranks checked by its retained native interpreter.
  After: five kernel-checked roots, four altered formal contracts rejected, and all 416 binary run ranks independently reconstructed. This corroborates the existing 928 result; it does not claim a new numerical bound.
• Six package test groups pass normally and optimized, including all 338 consumed frames, 230 small-frame cases, 256 binary matrix pairs, source/receipt corruption and a Git-free export. All 65 research-workflow tests pass. Ruff and YAML validation pass.
• Linux x86_64, CPython 3.12.15, Lean 4.21.0, Mathlib 308445d7985027f538e281e18df29ca16ede2ba3. Existing Mathlib build cache reused; no independent human review or hosted-CI success is claimed.

python3.12 -Werror -B scripts/research_package.py --package research/p104-endpoint-rank-lean
# After fetching the pinned formal/lean Mathlib cache:
python3.12 -Werror -B research/p104-endpoint-rank-lean/check_lean.py

Started from canonical main b5ea56e0a, priority 5. Submission refresh at a76748640 leaves guidance and all consumed inputs unchanged; a virtual merge is conflict-free. Final overlap covered 775 open PRs and 1,333 Discussion records with complete pagination, not arbitrary diffs or unpublished work. The existing investigation is Discussion2619.

Physical/native identification, phases, hosting, idle/residual charges, rounded erasure, precision and all-size admission remain inherited or open. No native/selected cold replay, supplier admission or new kappa is claimed. The next scoped question is a kernel-checked canonical-frame and finite-rank binding.

Merge Danger

Door: two-way

Only an opt-in package and scoped proof workflow are added. Selected records, frozen predecessors and production verifiers are unchanged.

Blast Radius: research