Yang–Mills Mass Gap v9.8r2: Bottleneck–First OS-Window Program and an Audited E5-min/v1.3 Witness Interface (Packet r10)

# Overview This record releases **Yang–Mills Mass Gap v9.8r2** together with a **sealed minimal witness packet (r10, no-TeX)**.The project is organized as a *bottleneck-first* program: the proof is reduced to a small number ofexplicit “PASS conditions” (a public proof interface), and the decisive remaining work is to produceat least one **non-toy PASS witness instance** under that interface. **Files in this record**- Main manuscript (PDF): `YM_MG_v9.8r2.pdf`- Sealed minimal witness packet (ZIP, no-TeX): `YM_MG_v9.8_pkt_r10_noTeX.zip` # What is new in v9.8r2 (and packet r10) - **E5-min interface upgrade to v1.3.** The report schema is pinned to a public interface id `E5-min/v1.3` (report schema `e5-min-report/v1.3`), including explicit mode separation: `demo_synthetic` vs `simulation` vs `real_data`. - **BT-10 continuation formalized.** The manuscript introduces a continuation blueprint: a single anchor PASS witness can be transported to a target parameter box PB⋆ along a certified path using an explicit Lipschitz envelope bound. - **Strict simulation / instantiation bridge scaffolding.** Appendix H.9.4 specifies a non-toy instantiation bridge (e.g., `pb_instantiation_report.json`) and a stricter audit profile intended to fail unless a real (simulation or real-data) witness is supplied. - **TCB tightening direction.** The packet is designed so that verification can be executed mechanically and deterministically (hash-bound inputs, schema checks, re-computation checks), with an optional independent verifier. # Proof interface (high-level) The program isolates the decisive remaining bottleneck as an auditable inequality package (“E5-min”).Informally, the intended implication chain is: 1) **E5-min PASS** ⇒ a verified strictly-positive variance lower bound \[ δφ(t_0) ≥ δ_0 > 0, \] for a fixed reference flow-time \(t_0>0\) inside an OS window. 2) Together with OS-window stability and exchange principles, this promotes to a uniform spectral gap, i.e. a **mass gap** in the target regime. The current public release emphasizes the *interface completeness* and *bottleneck identification*:the next milestone is a single non-toy PASS witness instance under `mode = simulation` or `mode = real_data`. # Reproducibility (packet) Unzip the sealed packet and run the mechanical auditor on the bundled demo report: - Unzip: `unzip YM_MG_v9.8_pkt_r10_noTeX.zip`- Audit (demo profile): `python3 -B scripts/audit_all.py --packet_root . --report results/e5_min_report.json --profile demo` Notes:- The included report is a **demo_synthetic** witness intended to validate the interface and audit pipeline.- The **strict_simulation** profile is expected to FAIL until a real witness (simulation or real-data) and its provenance are supplied and bound into the packet. # Scope & status (non-toy vs demo) - This record does **not** claim that the Clay-level Yang–Mills mass gap is already established in full generality.- It does claim a sharply specified, mechanically auditable *proof interface* for the decisive remaining bottleneck: producing a non-toy PASS witness in `mode = simulation` or `mode = real_data`, and (optionally) transporting it to a target PB⋆ via BT-10 continuation. # Keywords Yang–Mills mass gap; Osterwalder–Schrader axioms; reflection positivity; OS window; log-Sobolev inequality;functional-analytic stability; certified computation; reproducible proof artifacts; continuation method.