[Dugongue]

This certifies conditional κ = 0.0030266747680744, a tiny increase of 3.0744 × 10⁻¹² over #5387, on the unchanged eight-relation paid/target profile. The more substantial companion result is a smaller compiler at #5387’s unchanged κ: tensor power 1024 → 505, logarithmic power 1000 → 484, and the sufficient exponent H in N = 2^H falls from 409,549,000,000,000,000 to 194,586,000,000,000,000, a factor of about 2.105. This is not a measured runtime speedup.

Use the existing fully charged higher-moment theorem directly: α^v + 2γ^v + 2δ^v ≤ 1/(1+vρ) + 2g^v + 2d^v. The predecessor replaced both tails by a coarse 4/2^32 allowance. With exact envelopes g=957/1000 and d=952/1000, a reusable rational selector chooses the least tensor power satisfying the sufficient bound, then the least admissible positive logarithmic power and a finite integer threshold. README.md proves sufficiency and termination; the underlying tail theorem and logarithmic majorant retain zxv’s credit.

At the new endpoint, tested saving is 0.0030266747680745, reserve 10⁻¹⁷, tensor power 757, logarithmic power 725, and outer gap 1/70,000,000,000,000,000. The exact fixed-profile root lies in (0.0030266747680745498, 0.0030266747680745499). The compiler threshold is N=2^3634890000000000000000, with all 54 strict and four functional outer predicates positive. This much higher threshold funds the smaller gap: the higher-κ result and the smaller matched compiler are distinct parameter choices.

The 64,148-paid / 10,800-target invoice and all native operations are unchanged. All surrendered helper outputs, eight simultaneous snapshots, scalar work, routes and completion costs remain charged. Frozen #5387 native code/word/receipts are retained byte-for-byte and authenticated; no pending Git object is required at runtime. The package freshly replays both native directions and source identities, the p16 controller and complete bill, two rational interval engines, direct tails, compiler capacity and outer predicates. No expanded product/compiler word is materialized.

Validation: registered normal and optimized Python 3.12 standard-library checks; all native and outer controls; rejection of invalid/inexact parameter inputs; preceding-power failures; coarse-tail failure; separate integer cross-product checks of v=757 and v=505; committed-byte checks; official export integrity and read-only optimized Git-free replay. All checks are author/AI checks. No hosted CI, independent human or Lean/kernel acceptance is claimed. Full-history ancestry checking is not claimed in the shallow checkout.

python3 -B scripts/research_package.py --package research/geometric-tail-compiler
python3 -B scripts/check_research_commit.py --package research/geometric-tail-compiler

The result retains the selected native/all-size, whole-job, owned-erasure, precision/tape, analytic, prime and exact-recovery contracts. Full source phase lowering and ordinary BIT construction are authenticated/reused. No unconditional multiplication theorem, practical speedup, new native mechanism, global parameter optimum or selected-frontier update is claimed.

Credit zxv for higher-moment completion and the arbitrary-positive-logarithm majorant; Ali Romman #5377/#5383 for the helper relations; Cao Yifan #4610 for the native word and prior tightening; Cinna Davis #4470 for the controller/helper lineage; Chris R #5241/#5384 for their independent scoped audits; Jacob Alan Sussman for mixed-target recursion; Dugongue #5387 for the frozen preceding certificate; ToikY and all retained native, Clifford, BIT, precision and analytic contributors. This does not claim invention of geometric tails, binary search or logarithmic majorants.

Only research/geometric-tail-compiler/ changes, based on canonical main 1ec1119, refreshed before release. Recent PRs through #5389 were checked; #5385 is a partial reference repair and #5388 leaves caller integration open. Bounded cache/span/controller screens found no paid-profile gain and are not treated as global impossibility evidence. Discussion coverage remains incomplete. Prepared by Dugongue with substantial OpenAI Codex assistance, solo. Apache-2.0. Open next questions are in README.md and TASK.json.