nf.physics.bqnf_regge

Boundary-Quotient Normal Form for Regge Geometrodynamics (BQNF-REGGE)

Contract ID: nf.physics.bqnf_regge | Family: physics | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Boundary-Quotient Normal Form for Regge Geometrodynamics (BQNF-REGGE) enforces structural normalization and explicit defect routing in the physics regime.

Property	Value
Canonical ID	nf.physics.bqnf_regge
Short Name	BQNF-REGGE
Full Name	Boundary-Quotient Normal Form for Regge Geometrodynamics
Family	physics (Discrete Differential Geometry, Regge Calculus, Gauge Theory, Lattice Fermions & Quantum Gravity)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_motion
Index Status	draft
Theory Status	admitted
Verification Status	absent
Contract Version	v0
Governance Fence	AuthorityEffect: None (certified_implies_authorized: false)

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2. Visual Architecture & Normalization Diagram

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3. Concrete Worked Example & Mechanism

Visual Transition Summary

Stage	Carrier / Operator	Concrete State / Invariant
1. Before / Candidate Input	Input Carrier (BQNF-REGGE Candidate)	Anomaly risk: silent ; under-invalidation of deficit ; angles and uncertified curvatur...
2. Normalization / Gate	BQNF-REGGE Verification Gate	exact discrete... (certified_implies_authorized: false)
3. After / Certified Output	Certified BQNF-REGGE Output	Invariant: ; ['c0_local_edge_potentials', ; 'c1_deficit_variations',...

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4. The Four-Pillar Quadrilateral & Non-Claims

Every contract in simplex-normal-forms is evaluated against the Four-Pillar Quadrilateral defined in contracts/_golden_nfs/standard.yaml:

Pillar	Requirement	Contract Specification for nf.physics.bqnf_regge
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	silent under-invalidation of deficit angles and uncertified curvature reallocation during Pachner moves or metric deformations
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: exact discrete Einstein-Regge equations of motion and O(1) incremental repair under local diffeomorphism coboundaries Protected Skeleton: ['c0_local_edge_potentials', 'c1_deficit_variations', 'd0_coboundary_image', 'd1_schlafli_nilpotence']
Pillar III: Lossless Reconstruction	State the non-loss reconstruction operator (join, direct sum, pullback, or replay).	Lossless reconstruction under declared projection, direct sum, or pullback operators.
Pillar IV: Syntactic Decidability	State how conformance is decided from declared constraints without unbudgeted scans.	Decidable from declared schema and witness metadata within bounded evaluation budgets.

Explicit Non-Claims (certified_implies_authorized: false)

• does not ensure under declared assumptions O(1) repair for global topological changes or black hole horizon transitions
• does not claim continuum general covariance without discrete gauge quotienting

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• hinge_deficit_vector: list of deficit angles epsilon_h = 2*pi - sum(theta_h)
• regge_action: sum(A_h * epsilon_h) - Lambda * sum(V_sigma)
• schlafli_invariant: sum(A_h * d_epsilon_h) = 0
• quotient_space: Q1 = C1 / im(d0)

5.2 Required Evidence

None declared.

5.3 Validation Criteria

Criterion ID	Name	Condition
``	****
``	****
``	****

5.4 Terminal Route Map

Every evaluation terminates in a declared local route mapped to a canonical terminal in standard.yaml:

Local Terminal Route	Canonical Terminal
Unsupported	Unsupported
Repair	Repair
Recompute	Recompute
Refuse	Refuse
Preserve	Preserve

5.5 Declared Failure Modes

All defects route explicitly through the Terminal Route Map above.

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6. Epistemic Claim Hygiene Quadrant

In accordance with the repository's epistemic claim discipline:

1. What it supports:
   • Supports syntactic and operational checking of nf.physics.bqnf_regge (BQNF-REGGE) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (Unsupported, Repair, Recompute, Refuse) when required declarations or invariants fail.
2. What it does not support:
   • Does not confer operational authority (AuthorityEffect: None, certified_implies_authorized: false).
   • Does not claim semantic truth of undeclared external processes or unverified upstream inputs beyond the declaredprotected skeleton.
3. The narrowest defensible claim:
   • Within the declared substrate in_motion, this contract enforces that silent under-invalidation of deficit angles and uncertified curvature reallocation during Pachner moves or metric deformations is either excluded under exact discrete Einstein-Regge equations of motion and O(1) incremental repair under local diffeomorphism coboundaries or routed to an explicit refusal/recovery terminal.
4. The next test needed:
   • Property-based falsification and mutation testing across boundary edge cases and composed multi-step pipelines for nf.physics.bqnf_regge.

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7. Canonical YAML Contract (contracts/nf.physics.bqnf_regge.yaml)

Click to expand full canonical YAML contract (contracts/nf.physics.bqnf_regge.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.physics.bqnf_regge
  name: Boundary-Quotient Normal Form for Regge Geometrodynamics
  short_name: BQNF-REGGE
  version: v0
  theory_status: admitted
  contract_status: draft
  verification_status: absent
  family: physics
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - pachner_moves
  - curvature_defects
  - regge_action
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: silent under-invalidation of deficit angles and uncertified curvature
    reallocation during Pachner moves or metric deformations
  preserves_invariant: exact discrete Einstein-Regge equations of motion and O(1)
    incremental repair under local diffeomorphism coboundaries
  protected_skeleton:
  - c0_local_edge_potentials
  - c1_deficit_variations
  - d0_coboundary_image
  - d1_schlafli_nilpotence
  erased_structure: []
  non_claims:
  - does not ensure under declared assumptions O(1) repair for global topological changes or black hole horizon
    transitions
  - does not claim continuum general covariance without discrete gauge quotienting
declarations_required:
- hinge_deficit_vector: list of deficit angles epsilon_h = 2*pi - sum(theta_h)
- regge_action: sum(A_h * epsilon_h) - Lambda * sum(V_sigma)
- schlafli_invariant: sum(A_h * d_epsilon_h) = 0
- quotient_space: Q1 = C1 / im(d0)
validation_criteria:
- exact_repair_route: when deficit variation omega in im(d0), local potential alpha
    repairs curvature in O(1)
- closed_residual_route: when [omega] != 0 in Q1 and d1 omega = 0, routes to bounded
    partition recomputation
- closure_failure_route: when d1 omega != 0 (Schlafli breach), terminalizes as Refuse
terminal_routes:
- Unsupported
- Repair
- Recompute
- Refuse
- Preserve
terminal_route_map:
  exact_coboundary: Repair
  closed_cohomology_class: Recompute
  schlafli_violation: Refuse
  zero_variation: Preserve
definition:
  source: coda_all_universe/mssn_sn_tower/definitions.md
  formal_statement: silent under-invalidation of deficit angles and uncertified curvature
    reallocation during Pachner moves or metric deformations. exact discrete Einstein-Regge
    equations of motion and O(1) incremental repair under local diffeomorphism coboundaries
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: reconstruction_is_not_a_relational_project_join
    anomaly_exclusion: silent under-invalidation of deficit angles and uncertified
      curvature reallocation during Pachner moves or metric deformations
    lossless_join:
      status: declared_reconstruction
      statement: exact discrete Einstein-Regge equations of motion and O(1) incremental
        repair under local diffeomorphism coboundaries
    dependency_preservation:
      status: declared_with_the_invariant
      statement: The preserved invariant stays on the declared schema. This form does
        not state a functional-dependency projection of a flat relvar decomposition.
    syntactic_decision:
      status: declaration_decidable
      statement: The check reads the declared constraints and validation criteria.
        One unrecorded runtime image is not the decider.
authorization:
  authorized_by: null
  certified_implies_authorized: false
certification:
  certificate_required: true
  certificate_kind: nf.physics.bqnf_regge_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
evidence_required: []
schema_ref: ./normal_form_contract_schema.yaml