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\[δ_0>0,\]interpreted as a nontrivial **lower bound** on topological fluctuation (susceptibility/variance) in the Yang–Mills vacuum after flow to time \(t_0\). 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 \(δ_0>0\). --- # 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:** `coverage_mode=full_enumeration` and `coverage_slack=0`.- **Dual-seal binding:** recomputation and cross-consistency of `domain_items` (per-item `meta.cfg_sha256`), `configs_dir_manifest` (one-shot `dir_sha256`), and `domain_binding`, all tied to packaged `raw/configs/*`.- **Independent PASS:** both `audit_all.py` and `verifier2_independent.py` return `PASS` on the sealed packet. ## 2) Dual-seal domain binding (strict_simulation) In the strict anchor, the raw configuration domain is sealed twice:(i) item-wise by `results/domain_items.json` with a per-item `meta.cfg_sha256`,and (ii) directory-wise by `results/configs_dir_manifest.json` with a one-shot digest `dir_sha256`over the lexicographically ordered list of \((sha256,bytes,path)\).The report `results/e5_min_report.json` binds both digests again via `results/domain_binding.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(`bern_ci` and `derived_alt`) 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 & non-toy status - The approach is **not** a perturbative/diagrammatic argument: the key objects are *audited inequalities* tied to a sealed configuration domain and flow-time \(t_0\) on an OS-window.- The core mathematical difficulty is not hidden: the program makes explicit that obtaining \(δ_0>0\) is equivalent to proving a quantitative, nontrivial lower bound on YM topological fluctuation at the relevant scale, stable under the continuum/window transfer. --- # Program closure and targets ## Current status- **Artifact/interface:** strong, sealed, audit-failing-on-inconsistency; strict-simulation anchor includes dual-seal domain binding and independent verifier.- **Theory:** the decisive step remains a quantitative lower bound \(δ_0>0\), which is plausibly “main-body level” in difficulty. ## Next targets (toward unconditional closure)1. A genuinely model-faithful strict anchor instance whose \(δ_0>0\) 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/final_seal.sh --profile strict_simulation --report results/e5_min_report.json`- `python3 -B scripts/audit_all.py --packet_root . --report results/e5_min_report.json --profile strict_simulation`- `python3 -B scripts/verifier2_independent.py --packet_root . --report results/e5_min_report.json --profile strict_simulation` 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):** `YM_MG_v10.0.pdf`- **LaTeX source:** `YM_MG_v10.0.tex`- **Sealed strict anchor packet (ZIP):** `YM_MG_pkt_v10.0.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.