nf.motion.locality_lrb

Lieb-Robinson Locality Normal Form (LRBNF)

Contract ID: nf.motion.locality_lrb | Family: motion | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Lieb-Robinson Locality Normal Form (LRBNF) enforces structural normalization and explicit defect routing in the motion regime.

Property	Value
Canonical ID	nf.motion.locality_lrb
Short Name	LRBNF
Full Name	Lieb-Robinson Locality Normal Form
Family	motion (Flow Control, Horizon Emission & Lieb-Robinson Locality Bounds)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_motion
Index Status	draft
Theory Status	proposed
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 (LRBNF Candidate)	Anomaly risk: instantaneous global ; influence claim across a local ; finite graph
2. Normalization / Gate	LRBNF Verification Gate	propagation claims remain... (certified_implies_authorized: false)
3. After / Certified Output	Certified LRBNF Output	Invariant: ['locality_graph', ; 'graph_metric', ; 'interaction_radius',...

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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.motion.locality_lrb
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	instantaneous global influence claim across a local finite graph
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: propagation claims remain inside a declared finite locality cone or carry a residual suppression ledger Protected Skeleton: ['locality_graph', 'graph_metric', 'interaction_radius', 'velocity_bound', 'decay_bound', 'event_support', 'observation_window']
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 support a Lieb-Robinson theorem for an arbitrary continuum or undeclared Hamiltonian
• does not imply zero influence outside the cone; it requires bounded residual accounting
• does not authorize physical interpretation beyond the finite carrier and declared bound

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• finite_locality_graph
• graph_metric
• local_interaction_or_dependency_radius
• velocity_bound
• decay_bound_or_epsilon
• event_support
• observation_window
• residual_ledger_policy

5.2 Required Evidence

• topology_snapshot
• dependency_or_coupling_bound
• event_support_witness
• observation_time_window
• residual_bound_computation

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	claimed affected support lies within the declared locality cone or emits OutsideConeResidual
criterion	Check	outside-cone effects carry an explicit decay or error budget
criterion	Check	missing topology or coupling evidence terminalizes as BudgetUnknown or LocalityBoundExceeded
criterion	Check	locality cone composition is checked for multi-hop transports

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
WithinLocalityCone	Preserve
ExponentiallySuppressed	Preserve
OutsideConeResidual	Escalate
LocalityBoundExceeded	Refuse
BudgetUnknown	BudgetUnknown
RefuseInstantInfluence	Refuse

5.5 Declared Failure Modes

• symptom: distant cache partition is invalidated or trusted as updated before any declared dependency path can carry the event, diagnosis: unbounded propagation assumption, terminal: RefuseInstantInfluence
• symptom: approximate locality is used without publishing the residual error budget, diagnosis: missing outside-cone residual ledger, terminal: OutsideConeResidual

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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.motion.locality_lrb (LRBNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (WithinLocalityCone, ExponentiallySuppressed, OutsideConeResidual, LocalityBoundExceeded) 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 instantaneous global influence claim across a local finite graph is either excluded under propagation claims remain inside a declared finite locality cone or carry a residual suppression ledger 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.motion.locality_lrb.

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7. Canonical YAML Contract (contracts/nf.motion.locality_lrb.yaml)

Click to expand full canonical YAML contract (contracts/nf.motion.locality_lrb.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.motion.locality_lrb
  name: Lieb-Robinson Locality Normal Form
  short_name: LRBNF
  version: v0
  status: draft
  family: motion
  theory_status: proposed
  contract_status: draft
  verification_status: absent
classification:
  hierarchy_level: normal_form
  subject_kind:
  - locality_graph
  - distributed_write
  - distributed_claim
  data_posture: in_motion
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: instantaneous global influence claim across a local finite graph
  preserves_invariant: propagation claims remain inside a declared finite locality
    cone or carry a residual suppression ledger
  protected_skeleton:
  - locality_graph
  - graph_metric
  - interaction_radius
  - velocity_bound
  - decay_bound
  - event_support
  - observation_window
  erased_structure: []
  non_claims:
  - does not support a Lieb-Robinson theorem for an arbitrary continuum or undeclared
    Hamiltonian
  - does not imply zero influence outside the cone; it requires bounded residual accounting
  - does not authorize physical interpretation beyond the finite carrier and declared
    bound
obstruction_substrate:
  policy_ref: ../substrate/default_finite_obstruction_policy.yaml
  finite_carrier:
    description: finite metric graph with local supports propagation windows velocity
      bounds and residual decay budgets
  cochain_complex:
    C0: local_delays_repair_paths_or_basis_updates
    C1: out_of_cone_influence_or_unbounded_commutator_defects
    C2: locality_cycle_or_noncomposable_bound_closure_failures
    d0: local_repair_to_propagation_defect
    d1: propagation_defect_to_locality_closure_failure
    quotient: Q1 = C1 / im(d0)
  obstruction_class:
    notation: '[omega]'
    exact: '[omega] == 0'
    residual_closed: '[omega] != 0 and d1(omega) == 0'
    open: d1(omega) != 0
  carrier_realization: finite_metric_graph
  geometry_module: null
  gauge_metric_selector:
    weights:
    - distance
    - time
    - residual_bound
    - confidence
    selector_role: choose conservative terminal when suppression evidence is incomplete
declarations_required:
- finite_locality_graph
- graph_metric
- local_interaction_or_dependency_radius
- velocity_bound
- decay_bound_or_epsilon
- event_support
- observation_window
- residual_ledger_policy
evidence_required:
- topology_snapshot
- dependency_or_coupling_bound
- event_support_witness
- observation_time_window
- residual_bound_computation
validation_criteria:
- claimed affected support lies within the declared locality cone or emits OutsideConeResidual
- outside-cone effects carry an explicit decay or error budget
- missing topology or coupling evidence terminalizes as BudgetUnknown or LocalityBoundExceeded
- locality cone composition is checked for multi-hop transports
proof_obligations:
- id: lrbnf.finite_locality_bound
  statement: finite propagation bound is sound for the declared graph metric and dependency
    radius
  status: deferred
terminal_routes:
- WithinLocalityCone
- ExponentiallySuppressed
- OutsideConeResidual
- LocalityBoundExceeded
- BudgetUnknown
- RefuseInstantInfluence
certification:
  certificate_required: true
  certificate_kind: locality_bound_certificate
  obstruction_class_required: true
  loss_ledger_required: conditional
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: distant cache partition is invalidated or trusted as updated before any
    declared dependency path can carry the event
  diagnosis: unbounded propagation assumption
  terminal: RefuseInstantInfluence
- symptom: approximate locality is used without publishing the residual error budget
  diagnosis: missing outside-cone residual ledger
  terminal: OutsideConeResidual
references:
- ../relnf.md
- ../1_normal_forms.md
- ../symbol_dictionary.md
terminal_route_map:
  WithinLocalityCone: Preserve
  ExponentiallySuppressed: Preserve
  OutsideConeResidual: Escalate
  LocalityBoundExceeded: Refuse
  BudgetUnknown: BudgetUnknown
  RefuseInstantInfluence: Refuse
definition:
  source: coda_all_universe/mssn_sn_tower/definitions.md
  formal_statement: instantaneous global influence claim across a local finite graph.
    propagation claims remain inside a declared finite locality cone or carry a residual
    suppression ledger
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: reconstruction_is_not_a_relational_project_join
    anomaly_exclusion: instantaneous global influence claim across a local finite
      graph
    lossless_join:
      status: declared_reconstruction
      statement: propagation claims remain inside a declared finite locality cone
        or carry a residual suppression ledger
    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.
schema_ref: ./normal_form_contract_schema.yaml