nf.runtime.mtnf

Mazurkiewicz Trace Normal Form (MTNF)

Contract ID: nf.runtime.mtnf | Family: runtime | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Mazurkiewicz Trace Normal Form (MTNF) enforces structural normalization and explicit defect routing in the runtime regime.

Property	Value
Canonical ID	nf.runtime.mtnf
Short Name	MTNF
Full Name	Mazurkiewicz Trace Normal Form
Family	runtime (Exact Rational Zero-Duality-Gap Certifiers & Merkle Trace Execution Contracts)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_transformation
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 (MTNF Candidate)	Anomaly risk: spurious ; interleaving redundancy anomaly ; where causally independent...
2. Normalization / Gate	MTNF Verification Gate	traces are canonicalized... (certified_implies_authorized: false)
3. After / Certified Output	Certified MTNF Output	Invariant: ['trace_records', ; 'independence_relation', ; 'causal_dependency_graph',...

Contract-Declared Worked Cases

- ref: https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/lean4/Derivation/TraceAlgebra.lean
  section: lean4/Derivation/TraceAlgebra.lean
  note: independent event commutation and trace equivalence

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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.runtime.mtnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	spurious interleaving redundancy anomaly where causally independent concurrent events are serialized in arbitrary permutations
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: traces are canonicalized under independent commutation into minimal Foata normal form or causal dependency posets without external clocks Protected Skeleton: ['trace_records', 'independence_relation', 'causal_dependency_graph', 'terminal_state_digest']
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 claim global Newtonian time or continuum clocks
• does not commute events with overlapping state store writes
• does not bypass step-level guard discharges
• does not imply operational authority

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• event_alphabet
• independence_relation
• event_sequence
• initial_state
• accepted_step_semantics
• guard_read_and_write_footprints

5.2 Required Evidence

• transition_records
• commutation_proof_receipt
• foata_normal_form_blocks

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	the declared independence relation is symmetric and irreflexive
criterion	Check	each permitted adjacent swap has both orders accepted and equal post-states at the reached prefix
criterion	Check	guard reads as well as writes are included in any footprint argument
criterion	Check	trace representation matches the declared Foata block decomposition

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
AcceptCanonicalTrace	Preserve
RecomputeFoataDecomposition	Recompute
RejectConflictingCommutation	Reject
Undetermined	Abstain

5.5 Declared Failure Modes

• symptom: events modifying overlapping state stores are commuted, diagnosis: commutation violates causal dependence, terminal: RejectConflictingCommutation
• symptom: trace is presented in an un-normalized interleaving, diagnosis: trace was not reduced to its Foata normal form, terminal: RecomputeFoataDecomposition

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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.runtime.mtnf (MTNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptCanonicalTrace, RecomputeFoataDecomposition, RejectConflictingCommutation, Undetermined) 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_transformation, this contract enforces that spurious interleaving redundancy anomaly where causally independent concurrent events are serialized in arbitrary permutations is either excluded under traces are canonicalized under independent commutation into minimal Foata normal form or causal dependency posets without external clocks 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.runtime.mtnf.

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7. Canonical YAML Contract (contracts/nf.runtime.mtnf.yaml)

Click to expand full canonical YAML contract (contracts/nf.runtime.mtnf.yaml)

# Draft declaration: no bound local contract evaluator is supplied; upstream mathematics and schema checks are separate evidence.
schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.runtime.mtnf
  name: Mazurkiewicz Trace Normal Form
  short_name: MTNF
  version: v0
  status: draft
  family: runtime
  theory_status: established
  contract_status: draft
  verification_status: absent
classification:
  hierarchy_level: form
  subject_kind:
  - event_trace
  - causal_partial_order
  - mazurkiewicz_monoid
  data_posture: in_transformation
  mathematical_posture: operational
purpose:
  excludes_anomaly: spurious interleaving redundancy anomaly where causally independent concurrent events
    are serialized in arbitrary permutations
  preserves_invariant: traces are canonicalized under independent commutation into minimal Foata normal
    form or causal dependency posets without external clocks
  protected_skeleton:
  - trace_records
  - independence_relation
  - causal_dependency_graph
  - terminal_state_digest
  erased_structure:
  - arbitrary_sequential_serialization_order
  non_claims:
  - does not claim global Newtonian time or continuum clocks
  - does not commute events with overlapping state store writes
  - does not bypass step-level guard discharges
  - does not imply operational authority
quadrilateral:
  qualifies_as_true_normal_form: false
  qualification_gap: no_project_join_theorem
  anomaly_exclusion: combinatorial trace proliferation from serializing non-interfering independent events
    in arbitrary orders
  lossless_join:
    status: poset_replay_reconstruction
    statement: under the accepted-swap diamond premises, every linearization of the declared dependency
      poset replays to the same endpoint; original interleaving needs retained history
  dependency_preservation:
    status: causal_order_preserved
    statement: conflicting events sharing state stores retain strict serial order
  syntactic_decision:
    status: declaration_decidable
    statement: finite independence-table and trace checks; semantic independence needs the declared accepted-step
      commutation evidence
declarations_required:
- event_alphabet
- independence_relation
- event_sequence
- initial_state
- accepted_step_semantics
- guard_read_and_write_footprints
evidence_required:
- transition_records
- commutation_proof_receipt
- foata_normal_form_blocks
validation_criteria:
- the declared independence relation is symmetric and irreflexive
- each permitted adjacent swap has both orders accepted and equal post-states at the reached prefix
- guard reads as well as writes are included in any footprint argument
- trace representation matches the declared Foata block decomposition
terminal_routes:
- AcceptCanonicalTrace
- RecomputeFoataDecomposition
- RejectConflictingCommutation
- Undetermined
terminal_route_map:
  AcceptCanonicalTrace: Preserve
  RecomputeFoataDecomposition: Recompute
  RejectConflictingCommutation: Reject
  Undetermined: Abstain
certification:
  certificate_required: true
  certificate_kind: trace_commutation_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: events modifying overlapping state stores are commuted
  diagnosis: commutation violates causal dependence
  terminal: RejectConflictingCommutation
- symptom: trace is presented in an un-normalized interleaving
  diagnosis: trace was not reduced to its Foata normal form
  terminal: RecomputeFoataDecomposition
examples:
- ref: https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/lean4/Derivation/TraceAlgebra.lean
  section: lean4/Derivation/TraceAlgebra.lean
  note: independent event commutation and trace equivalence
references:
- https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/docs/GENESIS_CLOSEOUT.md
- ./README.md