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):** `YM_MG_v10.10.pdf`, `YM_MG_v10.10.tex`- **Sealed packet (ZIP):** `YM_MG_pkt_v10.10.zip` (scripts + schemas + audit + verifier suite) # Closed results (program-level) Within the OS-window setting, the paper formalizes a pipeline of the form: \[(E1--E4) \ \ (E5) m_0>0,\] where \(m_0\) 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: \[PASS (varlb>0)\ \ (E_R ≤ varlb/2)\ \ (δ0,lb>0),\] 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 & non-toy status This record is **not** a claim that the Clay problem is already closed unconditionally in the target continuum theory. Instead, it is a rigorously specified **proof interface**: - The analytic transfer component is presented in the paper under explicit OS-window conditions.- The computational/empirical trigger is encoded as an auditable witness format (E5-min).- The packet enforces strict provenance and fail-closed audits so that “PASS” has a precise meaning as a public, reproducible object. A key intended next milestone is a **physics-strict** instantiation:- `external_source_note.json` marked **REAL** with non-empty citations and a reproducible retrieval recipe,- `pb_instantiation_report.json` elevated to `instantiation_level = physics_validated`,- A sealed **physics_strict** run producing a witness report that passes audit and all verifiers. # Program closure and targets The recommended short path toward a “Clay-grade impression” is: 1. **P0-B (anchor):** produce and seal one **physics_strict PASS** instance with - coverage slack eliminated (full enumeration where applicable), - raw→summary reproducibility enforced by audit, - Verifier2/Verifier3/Verifier4 simultaneous PASS, - contract ↔ core-manifest SHA binding. 2. **P1 (TCB reduction):** expand verification-only interval/rational checking to cover all decisive inequalities, with a “no-warning” policy for enclosures. # Artifacts - `YM_MG_v10.10.pdf` / `YM_MG_v10.10.tex`: main manuscript- `YM_MG_pkt_v10.10.zip`: sealed packet implementing - schemas for witness reports and provenance notes, - `final_seal.sh` sealing routine, - `audit_all.py` fail-closed audit, - independent verifiers: - Verifier2 (recomputation / consistency checks), - Verifier3 (rational/verification-only checks where applicable), - Verifier4 (decimal interval enclosure checks, no-warning policy). # How to reproduce (packet) Unzip the packet and run from the packet root. ## Demo / pipeline sanity checkA demo profile is provided to exercise the full sealing + audit path on internal test inputs. ## Physics-strict instantiation (external configs)To produce a **REAL** external-source binding, supply an external configuration directory and create a REAL `external_source_note.json` with non-empty citations and a retrieval recipe. Then seal with the physics_strict profile. (Exact commands and required file names are documented in `docs/PHYSICS_STRICT_COMMANDS.md` and `docs/PHYSICS_STRICT_IMPORT_GUIDE.md` inside the packet.) # Verification and audit model The packet is designed to be **fail-closed**:- Missing or placeholder provenance fields cause audit failure.- Manifest/core-manifest hashes must match recorded bindings.- Interval enclosure mismatches are treated as failures in the no-warning policy. # Citation / keywords If you reference this record, cite the Zenodo DOI for this release and the main PDF. **Keywords:** Yang–Mills; mass gap; Osterwalder–Schrader; reflection positivity; spectral gap; reproducible research; proof interface; audit; interval arithmetic; lattice gauge theory; SU(2)