Prime Gaps at Most 186

URL SCAN: Prime Gaps at Most 186
FIRST LINE: This repository contains a Lean 4 formalization of a prime-gap bound and a

THE DISSECTION
This is a conditional formalization and reproducibility package. Lean verifies that the conclusion follows from three admitted project axioms plus standard logical axioms; Python independently reruns a finite numerical certificate. The cited literature and computation support the premises, but they are not kernel-checked proofs of those premises. A successful build proves implementation acceptance, not the unconditional theorem.

THE CORE FALLACY
The headline compresses “if the input estimates and physical bounds hold, then the result follows” into “prime gaps are at most 186.” The body itself largely discloses this limitation. Relative to the Discontinuity Thesis, the analogous error is mistaking validated downstream machinery for control of the bottleneck inputs. The DT lens has no substantive domain here: a prime-gap formalization does not bear on the employment–wage–consumption circuit.

HIDDEN ASSUMPTIONS
- The cited estimates exactly match the formal statements, quantifiers, and normalizations.
- The 104 outer bounds, 45 inner bounds, and cap bounds are correct and sufficient.
- NumPy, FLINT, the corrected signed convolution, the Python certificate, and the execution environment contain no relevant defect.
- The comparator and Lean translation preserve the intended statements without a correspondence bug.
- The conditional derivation covers every case required by the claimed prime-gap bound.

SOCIAL FUNCTION
Partial truth with prestige signaling and auditability. It demonstrates serious formal and computational hygiene while leaving the decisive premises outside Lean. It is not pure copium because the limitations are explicitly stated, but the headline invites readers to treat conditional verification as a completed proof.

THE VERDICT
Serious formal scaffolding, not a completed unconditional Lean proof. The accurate claim is: conditional kernel verification plus an independently checked numerical certificate. Anything stronger is headline compression masquerading as mathematical closure.