[dillona]

#4483 certifies an adaptive compiler for particular profiles and asks which broader class admits its tail gates. This package proves a sufficient criterion from a moment crossing plus strict pointwise mirror slack, and funds a leaf-count bound at the exact crossing exponent:

L(n) <= A n^theta (c + log n)^p for every integer n >= 1.

The mirror condition itself implies the tilted-mean gap. At a fixed exponent with T(t) >= P(t), the proof also characterizes the two-tail/ordering gates by the single condition T(t-lambda) exp(lambda mu_P(t)) < P(t) for some positive lambda. An exact counterexample passes fixed-exponent moment, mean and mirror checks while failing that condition.

The separately implemented exact checker isolates the retained p7 and p16 crossings and certifies complete critical-root majorants with p=1/10, c=38, n0=121*256^100 and p=2/5, c=133, n0=145*1024^650. Geometry and guards are read from authenticated #4483 benchmarks; the wider exponent covers and p7's conservative mirror factor are explicit. No native word, paid invoice, κ or selected result changes.

The diff contains only research/adaptive-gate-existence/. Canonical base: f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc. Coordination: Discussion #4525.

Validation: registered Python 3.12 replay; isolated optimized execution; 21 semantic rejection controls, exact arithmetic and symbolic mirror-integral controls; committed-byte/source-history preflight; checked 15-file export; replay without Git and with network access denied; exported source-corruption and underfunding controls. Separate author-side AI agents reviewed the proof and interval arithmetic. No formal or independent human verification is claimed.

Hosted CI has a known upstream planning blocker: four unchanged current-status/navigation tests fail before package replay, as reported for #4448 and reproduced on #4521. The local registered pass is not a hosted replay pass.

Remaining obligations: native all-column semantics, owned restoration, actual chronological widths and adapters, movement, precision, stock, fixed-tape execution, analytic transfer and exact recovery. The theorem concerns conditional normalized leaf counts; it does not materialize the winning words or establish practical thresholds.

Credit zxv's #4436/#4483 flow and logarithmic majorant, Jacob Alan Sussman's integer compiler, Ryanson Jonathan's corrected #4459 mirror method and invoice work, the #4433 and @1337isnot1337 p7 lineage, Cinna Davis's #4470 p16 word, Dugongue's #4479 compact consumer, and the retained native/outer sources. #4507/#4519 batching and #4521 expanded accounting remain distinct work. Prepared by Dillon with substantial OpenAI Codex assistance; Apache-2.0.

[dillona]

Hosted run 39719869186 confirms the documented upstream planning blocker: 331 onboarding tests, the same four current-status/navigation failures, 11 skipped. The package replay job was skipped. The affected shared files match canonical main; this PR changes only its isolated research package.

The exact local Python 3.12 registered replay, 15-file committed/source-history/export checks, network-denied Git-free replay and rejection controls passed. Hosted replay remains pending an upstream navigation repair and rerun. The canonical handoff is Discussion #4525.