Research Program v0.1.2 2026-08-11

Faithful Global Quantifier Compression: A Proof Research Program from Conjecture-Difficulty Analysis to the Collatz Hard-Zeta Frontier

Local solvability, global quantifiers, exception-faithfulness, and a six-track parallel proof plan. Synthesizes the Mathematical Conjecture Difficulty Matrix (MCDM) v0.2, prior work on global quantifiers and domain closure, existential-quantifier compression from the P/NP Dual-Hypothesis Rehearsal, and the nine completed Collatz OT Series papers, proposing the concept of a "Faithful Globalizer" and "exception-faithfulness" as a necessary design condition for any global-proof compressor. Not the series' Paper 10 — an independent research program built on top of the nine papers. Co-organized with Aletheia.

A research program, not a theorem: proposes the Faithful Globalizer and exception-faithfulness as design conditions Section 43, "Proved / Not Yet Proved Ledger," is reproduced as-is — 6 items proved (the strict-positive atomic-frontier theorem, its equivalence with Zₖ(s)→0, etc.), 8 items not yet proved (any nontrivial global decay rate, uniform block contraction, a Diophantine contradiction for a counterexample, etc.). The document states plainly that this is a research program and a six-track parallel proof plan, not a proof of the Collatz conjecture.

Connections

Relationship to the rest of the series — the source document itself already points to the "next paper," reproduced here as-is.

Builds onPaper 09 · Finite Certificate Frontier

Series progressFollow-on research program, not counted among the nine closed-series papers

"The Hard-Zeta manuscript is not Paper 10 of the closed nine-paper series. It is packaged separately under research_program/." — from SERIES_INDEX.md.

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