nf.ddc.trace_merkle

Trace Merkle Normal Form (TMNF)

Contract ID: nf.ddc.trace_merkle | Family: runtime | Index Status: active | AuthorityEffect: None

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1. Executive Summary & Metadata

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

Property	Value
Canonical ID	nf.ddc.trace_merkle
Short Name	TMNF
Full Name	Trace Merkle 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_motion
Index Status	active
Theory Status	established
Verification Status	executable
Contract Version	v0
Governance Fence	AuthorityEffect: None (certified_implies_authorized: false)

Foundational Treatise Specification

• Family: runtime
• Runes: ['I', 'T']
• Target Runtime Law: Laws 1 & 5 (Non-Empty Trace & Monotonic Identity)
• Domain: Operational execution tapes tau = (w_0, ..., w_n).
• Anomaly Excluded: Un-receipted state transitions, out-of-order execution, and non-reproducible trace execution.
• Preserved Invariant: Immutable RFC 8785 canonical JSON and SHA-256 Merkle chain at each step.
• Reconstruction Theorem: Deterministic replay from initial state and Merkle chain reconstructs identical terminal state.

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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 (TMNF Candidate)	Anomaly risk: non-reproducible, ; un-receipted, out-of-order, or ; mutated execution steps committ...
2. Normalization / Gate	TMNF Verification Gate	append-only cryptographic... (certified_implies_authorized: false)
3. After / Certified Output	Certified TMNF Output	Invariant: ['step_index_sequence', ; 'operational_rune', ; 'previous_tape_hash',...

Contract-Declared Worked Cases

- ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
  section: '2.4'

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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.ddc.trace_merkle
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	non-reproducible, un-receipted, out-of-order, or mutated execution steps committed to trace
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: append-only cryptographic Merkle chaining with SHA-256 digests over RFC 8785 canonical JSON step receipts Protected Skeleton: ['step_index_sequence', 'operational_rune', 'previous_tape_hash', 'current_tape_hash', 'canonical_step_receipt']
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 a valid tape supports truth of outside prose
• does not confer operational authority; authority_effect is unconditionally None
• does not permit post-terminal continuation

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• tape_index
• operation_rune
• step_receipt
• prev_hash
• current_hash

5.2 Required Evidence

None declared.

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	tape entry index increments strictly by one without gaps
criterion	Check	current hash equals SHA-256 digest of previous hash concatenated with RFC 8785 canonical receipt JSON
criterion	Check	step receipt contains non-empty input and output state hashes

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
AdmitTraceMerkle	Preserve
RejectMissingReceipt	Refuse
RejectBrokenHashChain	Invalidate
RejectOutdatedTape	Reject

5.5 Declared Failure Modes

• symptom: step committed to tape without explicit cryptographic receipt, diagnosis: un-receipted transition; violates Law 5, terminal: RejectMissingReceipt
• symptom: recomputed SHA-256 digest does not match declared current_hash, diagnosis: corrupted or out-of-order hash chain, terminal: RejectBrokenHashChain

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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.ddc.trace_merkle (TMNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AdmitTraceMerkle, RejectMissingReceipt, RejectBrokenHashChain, RejectOutdatedTape) 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 non-reproducible, un-receipted, out-of-order, or mutated execution steps committed to trace is either excluded under append-only cryptographic Merkle chaining with SHA-256 digests over RFC 8785 canonical JSON step receipts 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.ddc.trace_merkle.

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7. Canonical YAML Contract (contracts/nf.ddc.trace_merkle.yaml)

Click to expand full canonical YAML contract (contracts/nf.ddc.trace_merkle.yaml)

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.ddc.trace_merkle
  name: Trace Merkle Normal Form
  short_name: TMNF
  version: v0
  theory_status: established
  contract_status: active
  status: active
  verification_status: executable
  family: runtime
classification:
  hierarchy_level: normal_form
  subject_kind:
    - execution_tape
    - merkle_hash_chain
    - step_receipt
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: non-reproducible, un-receipted, out-of-order, or mutated execution steps committed to trace
  preserves_invariant: append-only cryptographic Merkle chaining with SHA-256 digests over RFC 8785 canonical JSON step receipts
  protected_skeleton:
    - step_index_sequence
    - operational_rune
    - previous_tape_hash
    - current_tape_hash
    - canonical_step_receipt
  erased_structure:
    - solver_wallclock_execution_time
    - memory_heap_addresses
  non_claims:
    - does not claim a valid tape supports truth of outside prose
    - does not confer operational authority; authority_effect is unconditionally None
    - does not permit post-terminal continuation
definition:
  source: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/normal_forms/README.md
  section: '2.0'
  formal_statement: >
    On a sequence of discrete operational transitions under alphabet {E, R, C, I, Λ, D, M, T},
    Trace Merkle Normal Form (TMNF) commits transitions into an append-only tape. Integration rune I
    requires an explicit deterministic step receipt (Law 5), computing current tape digest
    h_k = SHA256(h_{k-1} || RFC8785(R_k)). Replay from genesis reproduces the active state losslessly.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: cryptographic_hash_chain_not_relational_project_join
    anomaly_exclusion: missing step receipts, un-recomputed tape digests, silent state mutations, or post-terminal insertions
    lossless_join:
      status: replay_reconstruction
      statement: given initial state s₀ and tape entries T, the full sequence of intermediate states is losslessly and deterministically reconstructed
    dependency_preservation:
      status: step_receipt_hash_preserved
      statement: each step hash h_k = SHA256(h_{k-1} || RFC8785(R_k)) is verifiable locally from adjacent steps
    syntactic_decision:
      status: schema_and_hash_decidable
      statement: membership is decidable by parsing TapeEntry schema and re-evaluating SHA-256 chain equality
declarations_required:
  - tape_index
  - operation_rune
  - step_receipt
  - prev_hash
  - current_hash
evidence_required: []
validation_criteria:
  - tape entry index increments strictly by one without gaps
  - current hash equals SHA-256 digest of previous hash concatenated with RFC 8785 canonical receipt JSON
  - step receipt contains non-empty input and output state hashes
terminal_routes:
  - AdmitTraceMerkle
  - RejectMissingReceipt
  - RejectBrokenHashChain
  - RejectOutdatedTape
terminal_route_map:
  AdmitTraceMerkle: Preserve
  RejectMissingReceipt: Refuse
  RejectBrokenHashChain: Invalidate
  RejectOutdatedTape: Reject
certification:
  certificate_required: true
  certificate_kind: merkle_tape_receipt
  obstruction_class_required: false
  loss_ledger_required: false
  verifier_required: true
  loss_ledger_trigger_id: null
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
  - symptom: step committed to tape without explicit cryptographic receipt
    diagnosis: un-receipted transition; violates Law 5
    terminal: RejectMissingReceipt
  - symptom: recomputed SHA-256 digest does not match declared current_hash
    diagnosis: corrupted or out-of-order hash chain
    terminal: RejectBrokenHashChain
examples:
  - ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
    section: '2.4'
references:
  - omega_engine_governance/contracts/contracts_omega_engine_crates/mathematics/discrete_deformation_algebra/dda_trace_cochain.contract.yaml