Formally audit the selected BIT stopped-recurrence implication

[bitplane]

This answers one independent-review request for Jose Manuel's PR #2234: its stated stopped time recurrence implies its stated majorant. The new Lean proof handles the selected weighted child sum and actual fallback maximum on each root's positive descendant widths, with one local-charge constant shared across the root family. It neither assumes monotone costs nor constrains the caller's width-zero cost.

The selected corollary proves T(n) <= 200 C n + 10000 C n^(9983/10000) w. The exact linear moment is proved in Lean. The fractional moment remains an explicit formal hypothesis and is independently certified outside Lean using eight exact integer-power enclosures. Leaf, descent, uniform-charge and fallback-maximum countermodels make the hypotheses reviewable. These controls do not refute PR #2234.

Validation: a fresh build of all three local Lean modules passed with 14 axiom reports limited to propext, Classical.choice and Quot.sound; four invalid proof attempts produced actual Lean type errors. The independent rational replay passed 16,384 positive-width recurrence cases and 4,097 countermodel widths. Nine failure-control groups and the registered replay passed on Python 3.12.3. Both lightweight commands also passed on Python 3.14.4 from a read-only, Git-free export with all 23 files unchanged. The scoped workflow installs checksum-pinned Lean and runs the kernel build; hosted CI is not yet claimed.

The physical recurrence, root-uniform local charge, completed packets, ancestor access and parking remain premises. This is one formal implication, not adoption of the whole supplier or a new multiplication theorem. No selected frontier or kappa changes. Mathlib proof objects came from the official cache; its source library was not rebuilt.

PR #2234 is pinned at d047ef8, with unchanged source snapshots and attribution. Its recurrence, profile, moment point and proposed saving remain predecessor results. Concurrent PR #2284 (e71574b) formalizes a single active-child excess recurrence; its relevant theorem and proof guide were read and credited, without claiming a complete replay. The build wrapper adapts my PR #2267.

Canonical claim and follow-up: #2209 (comment)
Requested review: #1166 (comment)

Original random selection: adversarial-audit / supplier-boundary-audit, nonce e1a6501d422e1e4fca5822db6ad07b8e, refined to this request without rerolling. Canonical main 0fdd7d8 remains unchanged; the patch applies cleanly. The final overlap refresh covered 508 open PRs and 996 discussion records with complete pagination and no warnings. TASK.json records exact freshness, source pins and remaining questions.

Substantial OpenAI Codex assistance; no subagents or independent human review. Apache-2.0; predecessor notices and contributor credit retained.