[Lean] Certify PR531 ownership, controller windows and width matching

[rohanarun]

This package certifies the selected PR531 ownership table and finite borrowing controller in Lean 4.21.0. The proofs use the actual literal rows and checked inverse indexes, so owner-group and family-list construction are not assumed correct. They establish an injective map from all 728 invocation registers into the 7,168-family live stock for each of the 72 selected calls.

The checked interfaces cover:

• All 36,288 helper rows, 16,128 possible owner groups (15,302 occupied), source widths, complete call/helper census, actual offsets/capacity and inverse group/family links.
• Separation of all 504 helpers from both 112-wire active data banks, as well as helper/helper and data/data ownership injectivity.
• The projected 242-event controller: exact admitted-call sets, idle deadlines, untouched interiors and same-lane separation for all 144 selected borrowing windows. Every helper call lies strictly inside its traced window. The controller has 160 child deadlines; 16 windows host no helpers. Unknown event kinds conservatively block the affected replica or all replicas when unscoped.
• Generic complete matching from sorted width domination, admissible stateful selection, and capacity-preserving compaction with nonaliasing and gap-free occupied-prefix coverage. The package also retains PR527's 29 and PR531's five packing-shape certificates.

Source pins: PR527 2080903b9e6bd01e3f64cc4c7c62ea1b3af0aa6a; the selected PR531 inputs and complete hosted template imported in main db0e57bc7f36b5ac0fc844ad7ce1396165ee6647. The generators reproduce the committed literal definitions and certificates from immutable inputs.

Validation: all 15 project modules were compiled freshly, in three successive validation phases. The combined audit covers all 420 theorem declarations, including finite chunk certificates and rejection controls; each depends only on standard Lean axioms or none. No proof placeholders, custom axioms or native evaluation proof shortcuts are used. Source regeneration, six matching regressions, nine owner-table rejection controls, six controller-window rejection controls, twelve corrupted-source controls and rejection of a false Lean capacity statement passed. The receipt retains source/object hashes, complete axiom reports and the earlier phase receipts. Remote CI is separate from this local evidence.

Scope remains finite and explicit. Python parses/projects source JSON and associates the source primary-wire formula and helper routes with the Lean definitions; the JSON decoder is not formalized. Lean checks the literal-table relations and controller model. The physical implementation of the controller/events, charts, exact recipes, complete scalar endpoints, atomic execution, source Python allocator, uniform compiler, numerical recovery, prime supply and analytic transfer remain open. The per-call one-owner result alone is not a proof of physical scheduling or machine running time. No new kappa or full integer-multiplication theorem is claimed.

FULL-PROOF-STATUS.md preserves the full target: the selected PR531/PR493 saving 1517760977820331/10^18, on one deterministic machine with a fixed finite alphabet and fixed finite number of one-dimensional tapes, exact padded products for every input length and the required worst-case asymptotic runtime. The next integration connects these certified finite interfaces to the physical hosting, charts and asynchronous gathering proofs in incorporated #509/#516.

Attribution: PR527 retains Dugongue #522 and icekylinx #523 predecessor credits. Imported PR531 material retains icekylinx's authorship, GPT-6 Astra disclosure and preceding contributions. New formalization/verifier: Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0. No independent human audit or mathematical-priority claim.

Reproduce from research/lean-owner-transport using a new output directory:

python3 -B verify.py --lean /path/to/lean-4.21.0 --build-dir /absolute/new/output

The default verifier builds all 15 modules without reusing project objects or downloading dependencies.