Yang–Mills Mass Gap v10.0: A Sealed Strict-Simulation Anchor and Audited Proof Interface (OS-Window Program)

# Overview This record releases **Yang–Mills Mass Gap v10. 0** together with a **sealed strict-simulation anchor packet** implementing an **audited proof interface** for a mass-gap closure program on an OS-window. **Main idea. ** The paper is organized around a small set of window conditions (E1–E5) and a *verdict-triggered* workflow: a finite, sealed, mechanically auditable object (the packet) certifies a base-scale inequality bundle. Once the bundle passes audit, the analytic promotion mechanism is intended to proceed without ad hoc “hand verification” steps. **Core bottleneck (explicit). ** The remaining hard step toward an unconditional mass gap is the quantitative positivity\₀>0, as a nontrivial **lower bound** on topological fluctuation (susceptibility/variance) in the Yang–Mills vacuum after flow to time \ (t₀\). This is a genuinely nonperturbative, nonlinear obstruction and should be viewed as *the* decisive mathematical risk factor. --- # Closed results (interface-level) The v10. 0 release closes (at the artifact/interface level) the following items: - **Sealed verdict interface: ** the packet outputs a single verdict report and fails closed on any missing or inconsistent provenance item. - **Strict-simulation anchor hardening: ** the strict anchor requires full enumeration with zero slack and enforces dual-seal domain binding (see below). - **Independent verifier: ** an additional verifier recomputes key summaries and binding digests and must also return PASS. > Note: “closed results” here refer to **certificate/audit completeness** and do not by themselves eliminate the theoretical hard step \ (₀>0\). --- # What is new in v10. 0 ## 1) BT-3 strict-simulation anchor (mandatory checks) The BT-3 anchor is accepted only if all of the following hold: - **Full enumeration: ** `coverageₘode=fullₑnumeration` and `coverageₛlack=0`. - **Dual-seal binding: ** recomputation and cross-consistency of `domainᵢtems` (per-item `meta. cfgₛha256`), `configsdirₘanifest` (one-shot `dirₛha256`), and `domainbinding`, all tied to packaged `raw/configs/*`. - **Independent PASS: ** both `auditₐll. py` and `verifier2ᵢndependent. py` return `PASS` on the sealed packet. ## 2) Dual-seal domain binding (strictₛimulation) In the strict anchor, the raw configuration domain is sealed twice: (i) item-wise by `results/domainᵢtems. json` with a per-item `meta. cfgₛha256`, and (ii) directory-wise by `results/configsdirₘanifest. json` with a one-shot digest `dirₛha256`over the lexicographically ordered list of \ ( (sha256, bytes, path) \). The report `results/e5ₘinᵣeport. json` binds both digests again via `results/domainbinding. json`. Both auditors recompute these digests from the packaged `raw/configs/*` and fail the verdict on any mismatch, omission, or swap. ## 3) Exact CP cross-check (non-authoritative) For reviewer-facing redundancy, the packet optionally reports an exact Clopper–Pearson one-sided lower bound (`bernci` and `derivedₐlt`) for the two tail-event probabilities, but the verdict remains **authoritative only**for the interval-verified DKW-based bound used in the proof interface. --- # Scope strict-simulation anchor includes dual-seal domain binding and independent verifier. - **Theory: ** the decisive step remains a quantitative lower bound \ (₀>0\), which is plausibly “main-body level” in difficulty. ## Next targets (toward unconditional closure) 1. A genuinely model-faithful strict anchor instance whose \ (₀>0\) lower bound can be defended without additional hidden assumptions. 2. Reduction of the trusted computing base (TCB) by expanding interval/rational verification-only checks for the decisive inequalities. 3. A minimal instantiation bridge report fixing the target YM discretization/flow/observable specification in a reviewer-auditable way. --- # Reproducibility (sealed packet) ## Quick verification Unzip the packet and run the strict profile (the packet is designed to fail if anything is missing or inconsistent): - `bash scripts/finalₛeal. sh --profile strictₛimulation --report results/e5ₘinᵣeport. json`- `python3 -B scripts/auditₐll. py --packetᵣoot. --report results/e5ₘinᵣeport. json --profile strictₛimulation`- `python3 -B scripts/verifier2ᵢndependent. py --packetᵣoot. --report results/e5ₘinᵣeport. json --profile strictₛimulation` The sealed workflow binds the reports, raw-domain digests, and manifest so that swapping or omitting raw inputs produces a FAIL. --- # Files in this record - **Main paper (PDF): ** `YMMGᵥ10. 0. pdf`- **LaTeX source: ** `YMMGᵥ10. 0. tex`- **Sealed strict anchor packet (ZIP): ** `YMMGₚktᵥ10. 0. zip` --- # Citation Please cite as: - *Yang–Mills Mass Gap v10. 0: A Sealed Strict-Simulation Anchor and Audited Proof Interface (OS-Window Program). * (Zenodo record DOI of this release) --- # Keywords Yang–Mills mass gap; lattice gauge theory; Wilson flow; OS positivity; nonperturbative QFT; topological susceptibility; certified computation; reproducibility; audited proof interface; strict simulation anchor.