EPISTEMIC DEMARCATION // Tier 2 (Frontier Program)
Inspect Results Ledger →

Constitutional Demarcation: A Research Fabric is a bounded epistemological architecture. Structural formulation, digital execution, and proof-assistant replay declare local invariants; they do not constitute unverified physical validation.

Research Question ​

How can long-horizon frontier mathematical work be organized so that candidate arguments, established external results, unresolved proof obligations, failed routes, publications and future formalization remain distinguishable and traceable?

Current Canonical Scientific Status ​

The current RC34 control plane uses the following scientific-status grammar:

  • ESTABLISHED — external theorem/source accepted within its stated hypotheses;
  • DERIVED — internally proved lemma with explicit assumptions;
  • CONDITIONAL — valid only if named open hypotheses are established;
  • OPEN_MAJOR — load-bearing theorem remains missing;
  • NO_GO — route or implication has been falsified under audited assumptions.

The canonical rule is:

No manuscript is a completed Millennium proof while any load-bearing item remains OPEN_MAJOR or CONDITIONAL.

This current programme status governs the website even where older publication titles use stronger wording such as “complete proof” or “resolution.”

Architecture ​

  1. Live proof manuscripts — editable current proof-development surfaces.
  2. Source/research ledger — external theorem sources, assumptions and iteration notes.
  3. Immutable baseline packs — preserved historical states.
  4. Legacy iterations — prior public or internal releases retained without silent rewriting.
  5. Proof-gate registry — exact load-bearing theorem currently under attack.
  6. Outcome classifier — CLOSE, REDUCE, FALSIFY, or SOURCE_BLOCKED.
  7. Publication layer — Zenodo/preprint records with publication status separated from proof-completion status.
  8. Formalization layer — Lean/Coq or other machine-checking targets where applicable.

Core Invariants ​

  • candidate argument ≠ proof;
  • numerical evidence ≠ theorem;
  • publication ≠ independent validation;
  • title language ≠ canonical proof status;
  • every load-bearing assumption must remain visible;
  • failed/no-go routes remain preserved in the research record;
  • external theorem hypotheses must be checked before import;
  • historical releases are not silently rewritten.

Active Millennium Research Stack ​

The current RC34 programme tracks six problem areas:

  • Riemann Hypothesis;
  • Birch and Swinnerton-Dyer;
  • Hodge Conjecture;
  • Navier–Stokes regularity;
  • Yang–Mills existence and mass gap;
  • P versus NP.

Current control documents record unresolved or conditional bridges on multiple tracks; the web page should therefore present them as active proof research, not settled external mathematics.

Evidence & Status ​

NMF has substantial documentary and publication evidence as a research programme: public preprints, live proof manuscripts, source ledgers, iterative audits and continuation controls.

That is different from proof validation. Independent mathematical acceptance requires external expert review and closure of all load-bearing gaps.

Research / Implementation Path ​

  • attack one exact load-bearing theorem at a time;
  • verify current theorem hypotheses from primary sources;
  • classify each result;
  • update live manuscripts immediately;
  • maintain source and provenance ledgers;
  • formalize closed components where useful;
  • submit mature work for independent mathematical review.

Publications & Primary Materials ​

The following records are attached as programme publications. Their publication titles do not override the current RC34 scientific-status controls.

Canonical programme controls ​

  • RC34 Millennium Proof Program — Master Index
  • START HERE — RC34 Millennium Proof Program
  • live proof manuscripts and research ledger
  • acorpus / UKC
  • CodexStation
  • Trace Reciprocity
  • Extended TQFT
  • Geometric–Structural Layer Closure
Primary Source01_LIBRARY_42/nmf.md
Source SHA-256100771c7cc86dd2a21b7a61810371a400d43bb8a339687cb482f46a52635e030
TRWM BridgeRF-031__nmf__TRWM_BRIDGE_v1.3.md
Corpus StatusSOURCE_GROUNDED_DRAFT_NOT_RELEASED