HLV-DG-001: Pre-Execution Protocol Freeze for Deterministic Reconstruction and Algebraic Certification of the Abstract 0-3 Provenance Chain Complex

This record freezes, before target evaluation, the scientific protocol for HLV-DG-001, the first computational gate of the Dimension-Graded Geometry and Typed Emergence programme.

DG-001 addresses a deliberately narrow theorem-adjacent question:

Can the frozen parent-derived HLV source data be reconstructed deterministically as a complete and internally consistent abstract 0-3 provenance chain complex?

The gate does not test physical spacetime, gravity, gauge emergence, spectral dimension, or HLV-specific physical dynamics. It tests only the algebraic and provenance integrity of the graded source object

C^0 -> C^1 -> C^2 -> C^3.

The controlling source data are inherited from the previously frozen HLV-LAYER-ORIGIN-007F finite-carrier corpus. The relevant source objects include the parent-labelled rank-3 cell ledger, the frozen Freudenthal/Kuhn tetrahedron construction, exact parent-vertex provenance, and associated integrity records. The previously established 007F/007F-CERT face-to-face failure is retained only as a historical geometric constraint and is not re-evaluated or repaired in DG-001.

The prospective DG-001 execution must reconstruct the complete abstract graded incidence object directly from the frozen parent provenance and report, for p = 0,1,2,3:

- the number N_p of distinct p-cells;

- canonical oriented incidence/boundary matrices;

- exact chain-complex checks B_1 B_2 = 0 and B_2 B_3 = 0;

- equivalently, d_1 d_0 = 0 and d_2 d_1 = 0 on cochains;

- exact or mathematically controlled matrix ranks;

- Betti numbers derived from the frozen incidence structure;

- source-cell and tetrahedron provenance checks;

- duplicate, orientation, boundary, and unresolved-class ledgers;

- deterministic reconstruction and integrity hashes;

- a machine-readable final verdict.

The primary positive verdict is permitted only if the complete frozen source corpus is reconstructed without unresolved provenance or incidence classes and all chain identities pass exactly under the declared arithmetic rules.

A failure of source reconstruction, inconsistent incidence, nonzero boundary-of-boundary composition, unresolved provenance, or violation of the frozen parent-cell construction blocks a positive DG-001 verdict.

A successful DG-001 execution would establish only that the tested finite HLV source admits a reproducible abstract provenance-preserving 0-3 chain complex. It would not establish that the corresponding projected tetrahedra form a globally valid embedded simplicial manifold. In particular, it does not override the previously locked FINITE_HFF_FAIL_CERTIFIED result of HLV-LAYER-ORIGIN-007F/007F-CERT.

Likewise, DG-001 cannot establish:

- physical spacetime;

- gravity or Regge gravity;

- gauge fields or Standard-Model interactions;

- physical spinors or fermions;

- spectral dimensional flow;

- a continuum limit;

- physical time;

- experimental validity of HLV;

- physical golden-ratio specificity.

The purpose of this freeze is to preserve prospectivity. The target quantities N_p, matrix ranks, Betti numbers, and final DG-001 verdict are not evaluated or reported in this record. They are reserved for a subsequent locked execution using an implementation whose scientific definitions remain unchanged from this protocol.

This freeze is the first computational step in the prospective sequence DG-001-DG-005. Downstream dimensional-flow, Regge-curvature, and hyperbolic-continuum tests may not use a positive DG-001 result as evidence for a higher physical claim without satisfying their own separately frozen gates.