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Mathematical Estate

The standing catalogue of governed mathematical domains. It records scope and canonical entry points; it is not a priority list and does not imply current activity.

How to use the estate

The estate answers a different question from Current Work.

  • Current Work shows material obligations now in motion.
  • Mathematical Estate shows the standing domains that the programme preserves.
  • Results and Exemplars shows bounded outputs that crossed a declared checking or publication boundary.

A domain can remain in the estate while no active front is running. An active front can also cross domain or programme boundaries.

Catalogue

Domain Campaign Mathematical status Standing scope
01 · Union-Closed Sets UC Open conjecture Foundational programme demonstration domain with retained local proofs, fixtures, and bounded certificates.
02 · Navier–Stokes Critical Integrability NS-CI-001 Open problem Equation-specific critical-integrability routes and explicit continuation boundaries; no general regularity theorem is claimed.
03 · Hodge Conjecture HC-001 Open conjecture Source, formulation, and equivalence control for the canonical rational projective target; no new algebraicity theorem is claimed.
04 · Birch–Swinnerton-Dyer BSD-001 Open conjecture Rank-one theorem-ledger campaign with a live literal-p=2 route. See Current Work.
05 · Poincaré Reconstruction PC-001 Solved classical theorem Qualified reconstruction and bounded-certification archive; no novelty claim.
06 · Yang–Mills Existence and Mass Gap YM-001 Open problem Source-normalized axiomatic and equivalence dossier; no continuum construction or mass-gap theorem is claimed.
07 · P versus NP PNP-001 Open problem Machine, encoding, reduction, and barrier control; no equality, separation, algorithm, or unrestricted lower bound is claimed.
08 · Riemann Hypothesis RH-001 Open conjecture Function, zero, source, equivalence, and barrier control. WP01/WP02 implemented, merged, and CI-passed, with formal promotion withheld; no proof or disproof is claimed.

Domain authority

DOMAIN_REGISTRY.yaml records the machine-readable domain estate. Each public domain page points to its canonical repository entry.

The public landing page is an orientation artifact. It is not the theorem ledger. Before relying on a mathematical statement, follow the domain page to the relevant source record, Work Package, claim ledger, proof, review, or certificate.

Priority is a separate axis

The estate does not rank domains by importance, difficulty, or current attention.

For example, the current BSD work is one active front inside a standing domain. OZ order-7 certificate work is active programme research but is not represented by one of the eight historical domain slots. VGSE has moved from a bounded mathematical certification result into a separate engineering-discovery lane.

This separation prevents a durable taxonomy from becoming a stale description of present work.

Claim boundary

The programme does not infer theorem status from:

  • presence in the domain catalogue;
  • document count;
  • issue activity;
  • repository merge;
  • CI success;
  • Referee or governance disposition;
  • documentary publication;
  • public visibility.

Mathematical support remains attached to the exact claim and its governed evidence route.