Mathematics Publication Status & Maturity Register
Formal Verification Lifecycle (M0–M5), Proof Obligations & Publication State
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Mathematics Root · Mathematics Publication Status & Maturity Register
Public Status Boundary. This register defines the procedural maturity tiers (M0–M5) for all mathematical theorems, conjectures, and proof obligations across the corpus. Moving a theorem candidate into an active tier indicates formalization progress within our Lean 4 pipeline, not independent journal acceptance.
1. The M0–M5 Mathematical Maturity Scale
To prevent premature equivalence between heuristic derivations and verified proofs, every mathematical claim in the corpus is indexed according to a strict 6-stage maturity ladder:
| Tier | Classification | Definition | Verification Threshold |
|---|---|---|---|
| M0 | Conjectural Extract | Unparsed mathematical notes and initial relational formulations. | Raw notebook extraction. |
| M1 | Syntactically Clean | Explicit algebraic notation with all variables, operators, and domains specified. | Dimensional & type validation. |
| M2 | Analytically Derived | Closed-form analytical proof consistent with corpus axioms. | Internal peer derivation. |
| M3 | Machine Verified | Fully verified in Lean 4 with 0 sorry and 0 unproven axioms. | Clean lake build output. |
| M4 | Numerically Checked | Discretized numerical simulation stress-testing stability and residual bounds. | Solver convergence ( |
| M5 | Published & Sealed | Peer-reviewed external publication or public registered manuscript package. | Standalone LaTeX / DOI artifact. |
2. Active Formalization Portfolio
- Machine-Verified Core (M3): 28 Lean 4 machine-verified proofs across 9 formal modules (
Fabrica.ObserverKnot,Fabrica.InvariantEngineering,Fabrica.TraceReciprocity,Fabrica.FFE,Fabrica.FQFT,Fabrica.PGP,Fabrica.ObserverMonad,Fabrica.Fabricon, andFabrica.Realica). - Standalone Manuscript Packages (M5):
- Manuscript B (
fqft-continuum-core): Dirichlet forms with operator-valued potentials. - Manuscript D (
identifiability-obstructions): Negative identifiability theorems and singular Fisher information.
- Manuscript B (
3. Canonical Continuations
| Direction | Node | Route | Focus / Purpose |
|---|---|---|---|
| Proof Gateway | Lean 4 Formalization Roadmap | /04-mathematics/formalization-roadmap | 28 machine-verified theorem records and lemma dependency DAGs |
| Proof Governance | Proof Governance & Verification Scale | /04-mathematics/proof-governance | Six-stage M0–M5 verification and publication lifecycle |
| Review Gateway | Mathematical Review Gateway | /04-mathematics/review-gateway | Interactive verification readiness dashboard and atlas |
| SFR Review Portal | SFR Public Review Portal | /03-research/sfr-review-portal/ | Dedicated scholarly manuscripts and reviewer dossiers |