nf.physics.cdt_wick_mc

Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract (CDT-WMC-NF)

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

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1. Executive Summary & Metadata

Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract (CDT-WMC-NF) enforces structural normalization and explicit defect routing in the physics regime.

Property	Value
Canonical ID	nf.physics.cdt_wick_mc
Short Name	CDT-WMC-NF
Full Name	Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract
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	experimental
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 (CDT-WMC-NF Candidate)	Anomaly risk: acausal move ; proposals, invalid analytical ; continuation outside the CDT...
2. Normalization / Gate	CDT-WMC-NF Verification Gate	verified Wick rotation on... (certified_implies_authorized: false)
3. After / Certified Output	Certified CDT-WMC-NF Output	Invariant: ; ['cdt_sandwich_complex', ; 'wick_rotation_continuation_par...

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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.cdt_wick_mc
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	acausal move proposals, invalid analytical continuation outside the CDT domain, detailed balance violations, unaddressed non-ergodicity, and conflation of statistical equilibrium with semiclassical gravitational convergence
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: verified Wick rotation on causal triangulations yielding real Euclidean action S_E, normalizable partition function on volume-fixed ensembles, and reversible MCMC kernel satisfying detailed balance and empirical mixing Protected Skeleton: ['cdt_sandwich_complex', 'wick_rotation_continuation_parameter', 'euclidean_regge_action', 'volume_fixing_constraint', 'transition_kernel_detailed_balance', 'mcmc_trajectory_evidence', 'semiclassical_observable_records']
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)

• detailed balance does not imply sampling convergence; an identity transition satisfies detailed balance while failing to mix or sample the target distribution
• positive Gibbs weights exp(-beta * S_E) do not analytically force the classical Einstein residual to contract; convergence of <||E||>_beta is a distinct empirical hypothesis requiring explicit experimental evidence
• Wick rotation in CDT is an explicit analytical continuation on causal, foliated geometries, not a generic erasure of oscillatory phases
• positive weights alone do not establish a finite partition function; normalizability requires volume-fixing or explicit finite support
• does not claim continuum quantum general relativity without infinite-volume and continuum scaling limits

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• sandwich_complex: spatial Cauchy boundaries Sigma_t, Sigma_{t+1} and causal interior simplices
• wick_continuation: analytical rotation alpha -> -alpha in lower half-plane on strictly foliated simplices
• volume_stabilization: volume-fixing potential V(N_4) = epsilon * (N_4 - N_4^target)^2 ensuring normalizability
• transition_kernel: proposal distribution q(T'|T) and acceptance probability p(T->T')
• coupling_parameter: inverse quantum coupling beta = 1/hbar
• semiclassical_hypothesis: declared threshold tau_E for mean Einstein residual norm <||E||>_beta

5.2 Required Evidence

• sandwich_triangulation_metadata: {'slices': 'integer', 'vertices': 'integer', 'simplices': 'integer'}
• wick_rotation_parameter_alpha: float
• euclidean_action_values: list
• detailed_balance_residuals: list
• chain_autocorrelation_time: float
• gelman_rubin_r_hat: float
• inverse_temperature_beta_series: list
• mean_einstein_residual_series: list
• variance_einstein_residual_series: list
• semiclassical_hypothesis_verdict: string

5.3 Validation Criteria

Criterion ID	Name	Condition
``	****
``	****
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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
StatisticalSamplingValidated	Preserve
SemiclassicalEinsteinHypothesisSupported	Preserve
QuantumFluctuationRegime	Escalate
DetailedBalanceViolation	Reject
ErgodicityOrMixingDefect	Refuse
AcausalMoveRefusal	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.cdt_wick_mc (CDT-WMC-NF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (StatisticalSamplingValidated, SemiclassicalEinsteinHypothesisSupported, QuantumFluctuationRegime, DetailedBalanceViolation) 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 acausal move proposals, invalid analytical continuation outside the CDT domain, detailed balance violations, unaddressed non-ergodicity, and conflation of statistical equilibrium with semiclassical gravitational convergence is either excluded under verified Wick rotation on causal triangulations yielding real Euclidean action S_E, normalizable partition function on volume-fixed ensembles, and reversible MCMC kernel satisfying detailed balance and empirical mixing 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.cdt_wick_mc.

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

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

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.physics.cdt_wick_mc
  name: Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract
  short_name: CDT-WMC-NF
  version: v0
  theory_status: experimental
  contract_status: draft
  verification_status: absent
  family: physics
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - wick_rotation
  - lorentzian_cdt_sandwiches
  - quantum_path_integral_mcmc
  - discrete_einstein_convergence
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: acausal move proposals, invalid analytical continuation outside
    the CDT domain, detailed balance violations, unaddressed non-ergodicity, and conflation
    of statistical equilibrium with semiclassical gravitational convergence
  preserves_invariant: verified Wick rotation on causal triangulations yielding real
    Euclidean action S_E, normalizable partition function on volume-fixed ensembles,
    and reversible MCMC kernel satisfying detailed balance and empirical mixing
  protected_skeleton:
  - cdt_sandwich_complex
  - wick_rotation_continuation_parameter
  - euclidean_regge_action
  - volume_fixing_constraint
  - transition_kernel_detailed_balance
  - mcmc_trajectory_evidence
  - semiclassical_observable_records
  erased_structure:
  - microscopic_sweep_orderings
  - unverified_acausal_triangulations
  non_claims:
  - detailed balance does not imply sampling convergence; an identity transition satisfies
    detailed balance while failing to mix or sample the target distribution
  - positive Gibbs weights exp(-beta * S_E) do not analytically force the classical
    Einstein residual to contract; convergence of <||E||>_beta is a distinct empirical
    hypothesis requiring explicit experimental evidence
  - Wick rotation in CDT is an explicit analytical continuation on causal, foliated
    geometries, not a generic erasure of oscillatory phases
  - positive weights alone do not establish a finite partition function; normalizability
    requires volume-fixing or explicit finite support
  - does not claim continuum quantum general relativity without infinite-volume and
    continuum scaling limits
declarations_required:
- sandwich_complex: spatial Cauchy boundaries Sigma_t, Sigma_{t+1} and causal interior simplices
- wick_continuation: analytical rotation alpha -> -alpha in lower half-plane on strictly foliated simplices
- volume_stabilization: volume-fixing potential V(N_4) = epsilon * (N_4 - N_4^target)^2 ensuring normalizability
- transition_kernel: proposal distribution q(T'|T) and acceptance probability p(T->T')
- coupling_parameter: inverse quantum coupling beta = 1/hbar
- semiclassical_hypothesis: declared threshold tau_E for mean Einstein residual norm <||E||>_beta
validation_criteria:
- analytical_wick_validity: Euclidean action S_E is real-valued and bounded from below on the volume-stabilized carrier
- volume_normalizability: total 4-simplex count N_4 is bounded within declared envelope, ensuring normalizable measure
- detailed_balance_exact: kernel satisfies W(T) * q(T'|T) * p(T->T') = W(T') * q(T|T') * p(T'->T) within declared tolerance
- ergodicity_and_mixing: chain demonstrates finite integrated autocorrelation time and Gelman-Rubin convergence R_hat < 1.05
- foliation_integrity: proposals introducing CTCs, foliation branching, or spatial topology changes are rejected
- semiclassical_hypothesis_test: records whether empirical mean residual <||E||>_beta contracts below tau_E at high beta as a scoped experimental finding
terminal_routes:
- StatisticalSamplingValidated
- SemiclassicalEinsteinHypothesisSupported
- QuantumFluctuationRegime
- DetailedBalanceViolation
- ErgodicityOrMixingDefect
- AcausalMoveRefusal
- Unsupported
terminal_route_map:
  StatisticalSamplingValidated: Preserve
  SemiclassicalEinsteinHypothesisSupported: Preserve
  QuantumFluctuationRegime: Escalate
  DetailedBalanceViolation: Reject
  ErgodicityOrMixingDefect: Refuse
  AcausalMoveRefusal: Refuse
  Unsupported: Unsupported
extensions:
  condition_to_local_route_map:
    sampler_valid_stationary: StatisticalSamplingValidated
    sampler_valid_converged_experimental: SemiclassicalEinsteinHypothesisSupported
    sampler_valid_fluctuating: QuantumFluctuationRegime
    detailed_balance_error: DetailedBalanceViolation
    chain_non_ergodic: ErgodicityOrMixingDefect
    acausal_move_proposed: AcausalMoveRefusal
definition:
  source: coda_all_universe/mssn_sn_tower/definitions.md
  formal_statement: Wick-rotated Lorentzian CDT Monte Carlo contract evaluating analytical
    continuation on causal sandwiches, volume-stabilized positive Gibbs measures, reversible
    Markov kernels satisfying detailed balance and empirical mixing, and scoped testing
    of semiclassical Einstein convergence.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: reconstruction_is_not_a_relational_project_join
    anomaly_exclusion: acausal move proposals, detailed balance violations, non-ergodic
      trapping, and unnormalizable Gibbs measures
    lossless_join:
      status: declared_reconstruction
      statement: stationary distribution sampling of volume-stabilized Euclidean CDT
    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:
  StatisticalSamplingValidated: Preserve
  SemiclassicalEinsteinHypothesisSupported: Preserve
  QuantumFluctuationRegime: Escalate
  DetailedBalanceViolation: Reject
  ErgodicityOrMixingDefect: Refuse
  AcausalMoveRefusal: Refuse
  Unsupported: Unsupported
authorization:
  authorized_by: null
  certified_implies_authorized: false
certification:
  certificate_required: true
  certificate_kind: nf.physics.cdt_wick_mc_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
evidence_required:
- sandwich_triangulation_metadata: {slices: integer, vertices: integer, simplices: integer}
- wick_rotation_parameter_alpha: float
- euclidean_action_values: list
- detailed_balance_residuals: list
- chain_autocorrelation_time: float
- gelman_rubin_r_hat: float
- inverse_temperature_beta_series: list
- mean_einstein_residual_series: list
- variance_einstein_residual_series: list
- semiclassical_hypothesis_verdict: string
schema_ref: ./normal_form_contract_schema.yaml