Research archive and current public surface

Open maps, bounded claims, live work.

This page collects the research directions that are ready to be shown publicly. The standard here is deliberately conservative: finished artifacts, explicit open problems, reproducible bundles, and clear status labels. When something is not proved, the page says so.

Publication posture Research-stage unless marked otherwise. No Millennium problem proof claims are made here.
Current feature Goldbach is presented as a structural map and expert-review target, not as a proof.
Live engine MIRRIM continues as bounded prime-engine measurement work with explicit guard decisions.

Featured Research Map

The current public-facing priority is a careful Goldbach package. It is relevant enough to show because it isolates a named analytic obstruction; it is not presented as a solved theorem.

Open problem map Public-review candidate Not a proof

A Depth-3 Buchstab Minorant Map for Binary Goldbach

The Goldbach packet isolates a concrete remaining wall in a depth-3 Buchstab route: a Type-III residual shearing problem, sharpened to the one-R-match variance obstruction. The value is the map: what has been reduced, what failed, and exactly what an expert should check next.

  • Claim: structural reduction and obstruction map.
  • Not claimed: proof of Goldbach, almost-proof, or closed Type-III estimate.
  • Expert question: is the one-R-match variance wall structural, or can a pre-L2 identity avoid it?
Open Goldbach Map Expert Review Request Bundle Index

Prime Research

Prime work is organized around bounded measurements and public-safe theorem surfaces. The strongest current pages are the MIRRIM engine and the Goldbach map; other prime directions remain internal or conditional unless explicitly surfaced.

Active measurement Under audit

MIRRIM Prime Engine

Deterministic prime-navigation experiments with bounded guardrails. The current line tracks wall-clock, internal, and probe-side timings separately so noisy wall-only crossings do not masquerade as algorithmic boundaries.

Open MIRRIM Page

Other Mathematical Directions

These pages remain available, but the status labels matter. They are research programs, partial frameworks, or public notes rather than final proofs.

Direction Current public status Open
Riemann Hypothesis Structural approach under audit; no proof claim. View page
Collatz Partial certificate program; global descent not closed. View page
Legendre Current-status page; unresolved theorem direction. View page
P vs NP Structural notes only; no complexity-theorem claim. View page

Research Method

What gets published here

Finished notes, reproducible packages, open-problem maps, public-safe status pages, and artifacts that make the next bottleneck clearer.

What stays internal

Proof-search scaffolding, stale drafts, overclaiming Alpha versions, and internal chains that are useful for research but misleading as public theorem surfaces.