The register is the deliverable. Every target carries exactly one label. A target
without a label fails ops/verify.sh check Q7 and the repository will not publish.
Labels
PROVED — a complete proof exists in this repository.ARCHITECTURE — the proof skeleton exists; the intermediate lemmas are named; no proof.CONJECTURE — stated as a claim believed true; no skeleton.OPEN — not even a fixed formulation; the statement itself is under construction.As of v0.1 the register contains no PROVED rows. That is the honest state of the
programme and is stated here rather than discovered by a reviewer.
| Target | Label | Nearest existing tool |
|---|---|---|
| Formal definition of typed directed event hypergraph | ARCHITECTURE | typed hypergraph theory |
| Rewrite grammar L -> R with embedding m: L -> H | ARCHITECTURE | double-pushout / SPO graph rewriting |
| Matching decision procedure and its complexity | OPEN | subgraph isomorphism (NP-complete in general) |
| Locality of rewriting | ARCHITECTURE | DPO locality results |
| Determinism of global evolution under concurrent rewrites | ARCHITECTURE | parallel independence, Church–Rosser for DPO |
| Confluence, or explicit characterisation of non-confluence | OPEN | critical pair / Knuth–Bendix analogues |
| Termination | OPEN | — |
| Consistency (a model satisfying A1–A12 exists) | OPEN | — |
| Independence of A1–A12 | OPEN | — |
| Category Hyp_T, rewrite functors, natural transformations | ARCHITECTURE | adhesive categories |
| Simplicial realisation functor F: Hyp_T -> SSet | ARCHITECTURE | nerve constructions |
| Information invariance I(H) = I(R(H)) | CONJECTURE | — |
| Noether-analogue conserved graph currents | OPEN | — |
| Target | Label | Nearest existing tool |
|---|---|---|
| Graph metric, geodesics, discrete connection, torsion | ARCHITECTURE | discrete differential geometry |
| Discrete exterior derivative, codifferential, Hodge decomposition | ARCHITECTURE | discrete exterior calculus |
| Dirac operator on the hypergraph | OPEN | — |
| Selection of a canonical hypergraph Laplacian | OPEN | competing definitions exist; none selected |
| Spectral convergence to Laplace–Beltrami | CONJECTURE | graph-Laplacian consistency results under manifold sampling |
| Gromov–Hausdorff convergence of the discrete metric space | CONJECTURE | GH convergence theory |
| Benjamini–Schramm, Mosco and Gamma-convergence conditions | ARCHITECTURE | each is a standard notion; none instantiated here |
| Injective metric reconstruction from the spectrum | OPEN | blocked by isospectrality; needs added hypotheses |
| Emergence of an integer dimension (spectral / Hausdorff) | CONJECTURE | spectral dimension of graphs |
| Target | Label | Nearest existing tool |
|---|---|---|
| Causal DAG induces a partial order with Alexandrov topology | ARCHITECTURE | causal set theory |
| Lorentzian signature (-,+,+,+) uniquely forced | OPEN | no known uniqueness argument; the poster marks this Open |
| Bounded propagation speed yields light cones and proper time | ARCHITECTURE | — |
| Discrete Ollivier-Ricci curvature -> Ricci tensor in the limit | CONJECTURE | Ollivier-Ricci; Regge calculus |
| Regge action -> Einstein–Hilbert action | CONJECTURE | Regge calculus convergence results |
| Einstein field equations recovered | OPEN | requires all of the above plus a stress-energy identification |
| Stress-energy tensor from graph strain | OPEN | — |
| Target | Label | Nearest existing tool |
|---|---|---|
| Multiway graph and history space construction | ARCHITECTURE | multiway systems |
| History quotient under commuting rewrites and automorphisms | ARCHITECTURE | — |
| Amplitude functional; emergence of a complex phase | OPEN | the complex structure is not derived, only posited |
| Inner product, completion, Hilbert space | CONJECTURE | — |
| Unitarity of evolution | CONJECTURE | — |
| Born rule (probability = squared amplitude) from path combinatorics | OPEN | Gleason-type uniqueness is the target form; no derivation |
| Decoherence as constraint redistribution | ARCHITECTURE | — |
| No-signalling theorem for A7 constraints | OPEN | required for consistency with relativity |
| Target | Label | Nearest existing tool |
|---|---|---|
| Automorphism groups Aut(P) yield Lie algebras | CONJECTURE | — |
| Recovery of U(1) x SU(2) x SU(3) | OPEN | no selection principle for these groups is given |
| Yang–Mills equations in the continuum limit | OPEN | — |
| Classification of stable topological defects | OPEN | knot / homotopy invariants |
| Spin, statistics, chirality, mass generation | OPEN | — |
| FLRW metric and Friedmann equations | CONJECTURE | — |
| Dimensional cooling to D = 3 macroscopically | CONJECTURE | — |
| Dark energy from node injection rate | CONJECTURE | — |
| Hawking radiation, Page curve, information preservation | OPEN | — |
| Standard Model parameters (CKM, PMNS, couplings) | OPEN | explicitly out of scope for v0.1 |
Of the targets above, none is proved, several rest on standard external machinery that has not yet been instantiated on this substrate, and the four load-bearing ones — confluence, Laplacian selection, forced Lorentzian signature, and the Born rule — are open. A programme is not refuted by having open problems. It would be discredited by presenting them as closed, which this register exists to prevent.
© 1993–2026 Abhishek Choudhary. All rights reserved.