[JoyboyBrian]

The adaptive compiler's existing width bound counts all multiplicative products below a cutoff. This adds a bound for each fixed-ratio shell and applies it to the actual level-LCM recurrence. For a fixed alphabet including height base M, with rational valuation rank r, the shell [M^ell,M^(ell+1)) contains at most K(ell+1)^(r-1) products, with an explicit integer K.

For the unchanged adaptive compiler, this gives log B_N = O(N^z(1+log N)^r) when z>0, and retains O((1+log N)^(r+1)) at z=0. The pinned historical p16 profile has r=11 and z=3/5, improving its logarithmic upper-bound degree from 12 to 11. Actual compiler widths, leaf cost and kappa do not change. This answers PR #5962 Open next question 1 using PR #4638's retained level-LCM theorem. It is not a substitution into selected PR #6030 or a discharge of the compiler assumption.

The package contains the quantified proof, a standalone exact checker, source pins and Open next questions. Registered Python 3.12 normal and optimized checks pass: 372 shell fixtures, 21,754 member occurrences, 20,547 fibers, 257 actual compiled ranks and 1,856 batch rows, plus ten rejecting controls. Independent semigroup/minor oracles agree; a separate read-only AI review independently confirms the p16 determinant -1 and the proof. Three disposable optimized code mutations reject. Committed bytes/source history, official 10-file export integrity, and fresh read-only Git-free normal/optimized replays pass without changed bytes.

The scientific statements are conditional on the explicitly retained chronological compiler hypotheses. The full p16 compiler, native execution, owned restoration, physical routing/storage/precision/tape costs, outer transfer and exact recovery are not verified. No Lean, Docker, full selected replay, independent human review or formal-kernel acceptance is claimed. The explicit shell constant can be large, so the asymptotic improvement is not a practical finite-size claim.

Canonical investigation: #6076 . Scientific base: 721c038; reviewed contribution head: f0d9e8d. Prepared by JoyboyBrian with substantial OpenAI Codex assistance. Credit Nick Petalas #5962, codyw912 #4638, Mihir Srivastava #4507/#4586, zxv #4436/#4483, Jacob Alan Sussman, Ryanson Jonathan, Cinna Davis and all retained source-specific predecessors.

Reproduce: python3.12 -B scripts/research_package.py --package research/adaptive-shell-width.

[JoyboyBrian]

CI follow-up for f0d9e8d112359c17c66b84bcc4786fb65f1516af.

The plan failure reproduces on clean canonical main 721c03822c421b7f7fcbb2598993b947c4d88419: the two current-status navigation tests fail before this PR’s scientific replay. Existing PR #6050 (41ac3a47b91b4184e6c54af417bf576bfb429926) fixes both documentation mismatches; its exact two-file change passes all six tests locally, normally and with -O. Awaiting the shared upstream repair and a fresh CI run; this is not a successful scientific-replay claim.