Riemann Hypothesis AI Research Starting Point v0.2: GAP-ification

Changed from "candidate proof drafts are the unit of research" to "GAP edges G=(A→B) are the unit of research" — establishing 47 first-round GAPs at once, distributed across ten complete routes: Weil-type positivity (W), Nyman–Beurling closure (NB), Li coefficient positivity (LI), Hilbert–Pólya spectral realization (HP), de Bruijn–Newman heat flow (DBN), explicit formulas and prime error (EF), Speiser derivative criterion (SP), random matrix statistics (RMT), Adelic/Connes trace formula (AD), and observation framework and dynamic projection (OD). The subsequent entire W-01~W-20 series is merely the expansion of route W — the GAP Atlas left in this package shows that this is just one of ten parallel routes.

Non-Proof Research Engineering Documents — Self-stated in the "Properties" field of the main document within the package, reproduced as is. "Must not directly demand 'prove RH'"; v0.2 does not use whether RH is proven as the sole criterion for success.

Connections

Regarding its relationship with other packages, I try to use the words from its own documents, not my interpretation.

Previous VersionResearch Starting Point v0.1

Next VersionResearch Starting Point v0.3 · First GAP Closure

Route W expands toW-01 ~ W-20

Research Starting Point Series2 / 23

"Starting from v0.2, the AI no longer generates a full, unaudited RH proof, but continuously maintains Sₜ=(Kₜ,Gₜ,Fₜ,Cₜ,Dₜ)... The next step in the research is not to add more narrative, but to answer point by point: Can this GAP be backfilled?" — Excerpted from Section 6 "Current Conclusions" in the main document of this package.

v0.2 Core Changes

Formal definition of GAP edges, per-round research workflow (definition freeze → literature retrieval → candidate backfill → counterexample search → computational/formal verification → status update), first batch of recommended work nodes (including RH-W-01/02/05, RH-OD-03, RH-HP-05), and six success criteria.

RH GAP Atlas v0.1

The full text of the GAP registry for all ten complete routes — each route's known entries, GAP lists, and route determinations are included as is. Route W (Section 6) is the source specification for the entire subsequent W-01~W-20 series.

Reproduce

Registration consistency check for 47 GAPs:

python validate_registry.py

Files

The previous version's research draft (01_RH_AI_Research Starting Point_v0.1.md) is incorporated into this package as-is. Its content is identical to v0.1's own page and is not rendered again here.

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