nf.physics.wdwnf

Wheeler-DeWitt Constraint and Kernel Normal Form (WDWNF)

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

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1. Executive Summary & Metadata

Wheeler-DeWitt Constraint and Kernel Normal Form (WDWNF) enforces structural normalization and explicit defect routing in the physics regime.

Property	Value
Canonical ID	nf.physics.wdwnf
Short Name	WDWNF
Full Name	Wheeler-DeWitt Constraint and Kernel Normal Form
Family	physics (Discrete Differential Geometry, Regge Calculus, Gauge Theory, Lattice Fermions & Quantum Gravity)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	at_rest
Index Status	draft
Theory Status	established
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 (WDWNF Candidate)	Anomaly risk: spurious time ; evolution in isolated universe ; models, conflation of small...
2. Normalization / Gate	WDWNF Verification Gate	exact kernel membership... (certified_implies_authorized: false)
3. After / Certified Output	Certified WDWNF Output	Invariant: ; ['timeless_global_state_Psi', ; 'discrete_hamiltonian_constrain...

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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.wdwnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	spurious time evolution in isolated universe models, conflation of small residuals with exact kernel membership, unscaled operator norm vulnerabilities, un-normalized complex wavefunctions, and unverified relational clock transitions
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: exact kernel membership H_global
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)

• an absolute residual ||H |Psi>|| <= 1e-9 does not support membership in ker(H_global); scaling H = 10^{-10} I passes absolute residual tests on every unit state while possessing trivial kernel. Relative residual must be scaled by ||H_global||
• satisfying a single discrete Hamiltonian matrix equation does not alone establish diffeomorphism constraint satisfaction or complete gauge invariance
• relational reconstruction requires an explicitly bound clock decomposition and transition operator; it is not an automatic algebraic consequence of the kernel condition
• does not solve the operator ordering ambiguity in continuous field theory
• does not support a unique quantum gravity vacuum state without boundary conditions

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• clock_subsystem_dimension: integer dimension d_C with orthonormal basis {|k>_C}
• system_geometry_dimension: integer dimension d_S with orthonormal basis {|s>_S}
• global_state_amplitudes: matrix of complex amplitudes Psi(c, s) in C^{d_C x d_S}
• hamiltonian_constraint_matrix: operator matrix H_global acting on H_C (x) H_S
• operator_norm_bound: certified upper bound ||H_global||_op
• relational_clock_transitions: sequence of target unitary operators U(k -> k+1) acting on H_S

5.2 Required Evidence

• state_vector_amplitudes: list
• state_norm_squared: float
• hamiltonian_matrix: list
• hamiltonian_operator_norm: float
• absolute_residual_norm: float
• normalized_relative_residual: float
• exact_nullity_witness: {'exact_zero_mode': 'boolean'}
• relational_transition_matrices: list

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
ExactKernelMembershipCertified	Preserve
BoundedResidualStateAccepted	Repair
ConstraintResidualBreach	Reject
NonNormalizedState	Refuse
RelationalTransitionDefect	Refuse
Unsupported	Unsupported

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.wdwnf (WDWNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (ExactKernelMembershipCertified, BoundedResidualStateAccepted, ConstraintResidualBreach, NonNormalizedState) 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 at_rest, this contract enforces that spurious time evolution in isolated universe models, conflation of small residuals with exact kernel membership, unscaled operator norm vulnerabilities, un-normalized complex wavefunctions, and unverified relational clock transitions is either excluded under exact kernel membership H_global |Psi> = 0 or certified relative residual bound ||H_global |Psi>|| / (||H_global|| * ||Psi||) <= tau_rel, strict complex amplitude normalization sum |Psi_{cs}|^2 = 1, and independently certified relational transition operators 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.wdwnf.

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

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

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.physics.wdwnf
  name: Wheeler-DeWitt Constraint and Kernel Normal Form
  short_name: WDWNF
  version: v0
  theory_status: established
  contract_status: draft
  verification_status: absent
  family: physics
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - quantum_geometrodynamics
  - hamiltonian_constraint
  - mini_superspace
  data_posture: at_rest
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: spurious time evolution in isolated universe models, conflation
    of small residuals with exact kernel membership, unscaled operator norm vulnerabilities,
    un-normalized complex wavefunctions, and unverified relational clock transitions
  preserves_invariant: exact kernel membership H_global |Psi> = 0 or certified relative
    residual bound ||H_global |Psi>|| / (||H_global|| * ||Psi||) <= tau_rel, strict
    complex amplitude normalization sum |Psi_{cs}|^2 = 1, and independently certified
    relational transition operators
  protected_skeleton:
  - timeless_global_state_Psi
  - discrete_hamiltonian_constraint_H_global
  - operator_norm_scaling
  - complex_inner_product_normalization
  - clock_subsystem_decomposition
  - declared_transition_operators
  erased_structure:
  - absolute_external_newtonian_time
  non_claims:
  - an absolute residual ||H |Psi>|| <= 1e-9 does not support membership in ker(H_global);
    scaling H = 10^{-10} I passes absolute residual tests on every unit state while possessing
    trivial kernel. Relative residual must be scaled by ||H_global||
  - satisfying a single discrete Hamiltonian matrix equation does not alone establish
    diffeomorphism constraint satisfaction or complete gauge invariance
  - relational reconstruction requires an explicitly bound clock decomposition and
    transition operator; it is not an automatic algebraic consequence of the kernel condition
  - does not solve the operator ordering ambiguity in continuous field theory
  - does not support a unique quantum gravity vacuum state without boundary conditions
declarations_required:
- clock_subsystem_dimension: integer dimension d_C with orthonormal basis {|k>_C}
- system_geometry_dimension: integer dimension d_S with orthonormal basis {|s>_S}
- global_state_amplitudes: matrix of complex amplitudes Psi(c, s) in C^{d_C x d_S}
- hamiltonian_constraint_matrix: operator matrix H_global acting on H_C (x) H_S
- operator_norm_bound: certified upper bound ||H_global||_op
- relational_clock_transitions: sequence of target unitary operators U(k -> k+1) acting on H_S
validation_criteria:
- complex_normalization: sum_{c,s} |Psi(c, s)|^2 == 1 within declared tolerance 1e-12
- relative_residual_bound: relative constraint residual ||H_global |Psi>|| / (||H_global||_op * ||Psi||) <= tau_rel
- exact_kernel_nullity: if exact certification is claimed, verify exact zero eigenvalue witness H_global |Psi> == 0 over algebraic or rational field
- relational_transition_fidelity: for non-zero conditional slices |psi_S(k)>, verify that normalized states satisfy || |psi_S(k+1)> - U(k -> k+1) |psi_S(k)> || <= tau_U
terminal_routes:
- ExactKernelMembershipCertified
- BoundedResidualStateAccepted
- ConstraintResidualBreach
- NonNormalizedState
- RelationalTransitionDefect
- Unsupported
terminal_route_map:
  ExactKernelMembershipCertified: Preserve
  BoundedResidualStateAccepted: Repair
  ConstraintResidualBreach: Reject
  NonNormalizedState: Refuse
  RelationalTransitionDefect: Refuse
  Unsupported: Unsupported
extensions:
  condition_to_local_route_map:
    exact_nullity_and_normalized: ExactKernelMembershipCertified
    normalized_residual_bounded: BoundedResidualStateAccepted
    residual_exceeds_bound: ConstraintResidualBreach
    norm_differs_from_one: NonNormalizedState
    relational_transition_mismatch: RelationalTransitionDefect
definition:
  source: coda_all_universe/mssn_sn_tower/definitions.md
  formal_statement: Wheeler-DeWitt constraint normal form establishing operator-scaled
    relative residual bounds or exact kernel membership for normalized global wavefunctions,
    with independently certified relational clock transitions.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: reconstruction_is_not_a_relational_project_join
    anomaly_exclusion: spurious time evolution in isolated universe models, false kernel
      membership under unscaled operators, and un-normalized complex wavefunctions
    lossless_join:
      status: declared_reconstruction
      statement: normalized global state in kernel of Hamiltonian constraint with relational
        clock decomposition
    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.
canonical_terminal_map:
  ExactKernelMembershipCertified: Preserve
  BoundedResidualStateAccepted: Repair
  ConstraintResidualBreach: Reject
  NonNormalizedState: Refuse
  RelationalTransitionDefect: Refuse
  Unsupported: Unsupported
authorization:
  authorized_by: null
  certified_implies_authorized: false
certification:
  certificate_required: true
  certificate_kind: nf.physics.wdwnf_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
evidence_required:
- state_vector_amplitudes: list
- state_norm_squared: float
- hamiltonian_matrix: list
- hamiltonian_operator_norm: float
- absolute_residual_norm: float
- normalized_relative_residual: float
- exact_nullity_witness: {exact_zero_mode: boolean}
- relational_transition_matrices: list
schema_ref: ./normal_form_contract_schema.yaml