← NS-GSM / v0.6 · Formalization and Cross-Replication

NS-GSM · v0.6 Formalization and Cross-Replication 2026-08-28

NS_GSM Formalization and Cross-Replication v0.6

Does not upgrade the closure status of v0.5’s 12 PROOF assets — only strengthens their auditability. Compiles each one into a machine-readable ‘Formal Intermediate Representation’ (NSGSM-FIR/0.1), then pushes it through a deliberately isolated python -I replicator that imports neither csm_runtime nor the original v0.5 verification module — a genuinely independent second implementation, 12/12 fully MATCH. Also attaches one real external literature citation: ETN-X Prop 8.1’s dependency is formally anchored to Escauriaza–Seregin–Šverák (2003), DOI 10.1070/RM2003v058n02ABEH000609 (a real, well-known critical-L³ regularity criterion in the NS literature), stating explicitly that ‘this is a literature/dependency anchor … it does not re-prove the external theorem.’ Adds four orthogonal authority tiers: FORMALIZED_CORE_ONLY, CROSS_IMPLEMENTATION_REPLICATED, EXTERNAL_THEOREM_ANCHORED, and FORMAL_PROOF (schema reserved). Key point: the FORMAL_PROOF count is 0.

All 12 PROOF assets pass cross-replication by an independent second implementation (12/12 MATCH), with one real external literature anchor attached. The report, verbatim and in bold: ‘The current environment provides no Lean or Coq executable. Therefore: the FORMAL_PROOF tier count is 0; no SymPy computation has been relabeled as a proof-assistant kernel proof.’ Firewall: formalization ≠ formal proof; replication ≠ theorem generalization; external theorem anchor ≠ re-proof.

Connections

Relationship to the other versions, stated as closely as possible in the document's own words, not my interpretation.

NS-GSM progressv0.6 (8 versions total: seed dataset + v0.1–v0.7)

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