Yang–Mills Mass Gap Program v10.10: OS-Window Proof Interface with Manifest-Core Sealing and No-Warning Interval/Rational Verifiers

# Overview This record releases **Yang–Mills Mass Gap Program v10. 10** as a paper + reproducible packet designed to present the mass-gap route in a **fail-closed proof interface** format. The program is organized around an **OS-window** hypothesis layer (E1–E5) and a public, auditable **witness interface** (E5-min) intended to separate: - **Analytic transfer and reconstruction** (OS framework, operator/semigroup control, exchange/compactness principles), from- **A single auditable trigger object** (a sealed report whose checked inequalities decide PASS/FAIL). The record contains: - **Main paper (PDF + TeX): ** `YMMGᵥ10. 10. pdf`, `YMMGᵥ10. 10. tex`- **Sealed packet (ZIP): ** `YMMGₚktᵥ10. 10. zip` (scripts + schemas + audit + verifier suite) # Closed results (program-level) Within the OS-window setting, the paper formalizes a pipeline of the form: \ (E1--E4) \ \ (E5) m₀>0, \ where \ (m₀\) denotes a positive spectral gap for the reconstructed Hamiltonian (mass gap in the OS/Wightman reconstruction sense), and the only non-analytic trigger is (E5) given as an auditable witness report. The witness interface is expressed as a **PASS/FAIL predicate** on a finite report object. A canonical minimal predicate used in the packet is: (var₋₁>0) \ \ (ER var₋₁/2) \ \ (₀, ₋₁>0), \ where the reported lower bounds and remainder control are checked by mechanical audit and independent verifiers. # What is new in v10. 10 ## (1) “Manifest-core” sealing for cycle-free contract bindingv10. 10 strengthens the sealing impression by introducing a **cycle-free binding** between a strict anchor contract and a stable manifest: - A **core manifest** (excluding volatile outputs such as logs/verifier reports/contract itself) is generated. - The **strict anchor contract** binds the core manifest by SHA256. - The full manifest still includes the contract, but the cycle is avoided by binding only the core manifest. This is intended to reduce ambiguity about “what exactly is sealed” while remaining reproducible. ## (2) E5-min report upgraded to interval/decimal trace (v1. 4) The minimal witness report is upgraded to include: - **Interval enclosures** for decisive scalars, and- **Decimal string representations** suitable for cross-verification. This reduces “float-only” trust and supports verification-only replay. ## (3) Verifier4 policy: no-warning and fail-closed containment checksThe interval/decimal verifier is hardened to treat enclosure mismatches as failures (no warning-only acceptance), aiming to lower the trusted computing base (TCB) for the decisive inequalities. # Scope mass gap; Osterwalder–Schrader; reflection positivity; spectral gap; reproducible research; proof interface; audit; interval arithmetic; lattice gauge theory; SU (2)