nf.ddc.terminal_partition

Terminal Partition Normal Form (TPNF)

Contract ID: nf.ddc.terminal_partition | Family: authority | Index Status: active | AuthorityEffect: None

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1. Executive Summary & Metadata

Terminal Partition Normal Form (TPNF) enforces structural normalization and explicit defect routing in the authority regime.

Property	Value
Canonical ID	nf.ddc.terminal_partition
Short Name	TPNF
Full Name	Terminal Partition Normal Form
Family	authority (Terminal Partition & Authority Boundary Contracts (TPNF))
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	at_rest
Index Status	active
Theory Status	established
Verification Status	executable
Contract Version	v0
Governance Fence	AuthorityEffect: None (certified_implies_authorized: false)

Foundational Treatise Specification

• Family: authority
• Runes: ['T']
• Target Runtime Law: Law 2 (Terminal Sink)
• Domain: Terminal halting states under authority contracts.
• Anomaly Excluded: Post-terminal mutation, unauthorized continuation, and authority elevation.
• Preserved Invariant: Partition into 4 mutually exclusive axes (SUCCESS, REFUSAL, HALT, ABORT) with can_continue == 0 and AuthorityEffect None.
• Reconstruction Theorem: Terminal certificate uniquely seals the trace; no further morphisms can compose.

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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 (TPNF Candidate)	Anomaly risk: post-terminal ; mutation, continuation past ; halting criteria, or conflating...
2. Normalization / Gate	TPNF Verification Gate	evaluation of 9-way... (certified_implies_authorized: false)
3. After / Certified Output	Certified TPNF Output	Invariant: ; ['routing_terminal_verdict', ; 'continuation_predicate_witness...

Contract-Declared Worked Cases

- ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
  section: '2.9'

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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.terminal_partition
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	post-terminal mutation, continuation past halting criteria, or conflating routing terminal verdicts with sovereign authority
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: evaluation of 9-way CanContinue_n predicate into immutable terminal sink with four-axis separation firewall Protected Skeleton: ['routing_terminal_verdict', 'continuation_predicate_witnesses', 'final_tape_digest', 'authority_effect_sentinel']
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 terminal verdict confers external authority; authority_effect is unconditionally None
• does not claim open residuals can be sealed as resolved
• does not permit further execution once terminal rune T is emitted

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• routing_terminal
• final_phi1
• final_gamma2
• can_continue_eval
• authority_effect

5.2 Required Evidence

None declared.

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	no further step entries follow terminal rune T on the tape
criterion	Check	authority_effect field is set explicitly and unconditionally to 'None'
criterion	Check	terminal route is partitioned strictly into canonical terminal vocabulary

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
AdmitTerminalPartition	Preserve
RejectPostTerminalMutation	Refuse
RejectAuthorityConflation	Invalidate
RejectPredicateFailure	Reject

5.5 Declared Failure Modes

• symptom: step entry attempted after terminal rune T has been committed, diagnosis: post-terminal mutation attempted; violates Law 2 terminal absorption, terminal: RejectPostTerminalMutation
• symptom: terminal verdict claims authority_effect other than 'None', diagnosis: authority conflation defect; violates four-axis separation, terminal: RejectAuthorityConflation

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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.terminal_partition (TPNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AdmitTerminalPartition, RejectPostTerminalMutation, RejectAuthorityConflation, RejectPredicateFailure) 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 post-terminal mutation, continuation past halting criteria, or conflating routing terminal verdicts with sovereign authority is either excluded under evaluation of 9-way CanContinue_n predicate into immutable terminal sink with four-axis separation firewall 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.terminal_partition.

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

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

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.ddc.terminal_partition
  name: Terminal Partition Normal Form
  short_name: TPNF
  version: v0
  theory_status: established
  contract_status: active
  status: active
  verification_status: executable
  family: authority
classification:
  hierarchy_level: normal_form
  subject_kind:
    - terminal_sink
    - halting_predicate
    - four_axis_separation
  data_posture: at_rest
  mathematical_posture: operational
purpose:
  excludes_anomaly: post-terminal mutation, continuation past halting criteria, or conflating routing terminal verdicts with sovereign authority
  preserves_invariant: evaluation of 9-way CanContinue_n predicate into immutable terminal sink with four-axis separation firewall
  protected_skeleton:
    - routing_terminal_verdict
    - continuation_predicate_witnesses
    - final_tape_digest
    - authority_effect_sentinel
  erased_structure:
    - post_terminal_execution_proposals
  non_claims:
    - does not claim terminal verdict confers external authority; authority_effect is unconditionally None
    - does not claim open residuals can be sealed as resolved
    - does not permit further execution once terminal rune T is emitted
definition:
  source: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/normal_forms/README.md
  section: '2.0'
  formal_statement: >
    Terminal Partition Normal Form (TPNF) partitions execution traces into terminal sinks
    via the 9-way CanContinue_n predicate. Terminal rune T closes active mutation (Law 2),
    absorbing all subsequent moves into the identity. TPNF enforces four-axis separation:
    DiagnosticClass != RoutingTerminal != ExtensionStatus != AuthorityStatus, strictly setting
    authority_effect to None.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: halting_sink_partition_not_relational_project_join
    anomaly_exclusion: downstream agent hallucination of continued execution after trace termination, or authority leaks
    lossless_join:
      status: sink_absorption_reconstruction
      statement: once terminalized, any subsequent operation maps identically to the terminal state
    dependency_preservation:
      status: predicate_conjuncts_preserved
      statement: each of the 9 continuation conjuncts is evaluated against explicit step metrics
    syntactic_decision:
      status: boolean_predicate_decidable
      statement: membership is decidable by evaluating CanContinue_n and checking authority_effect == 'None'
declarations_required:
  - routing_terminal
  - final_phi1
  - final_gamma2
  - can_continue_eval
  - authority_effect
evidence_required: []
validation_criteria:
  - no further step entries follow terminal rune T on the tape
  - authority_effect field is set explicitly and unconditionally to 'None'
  - terminal route is partitioned strictly into canonical terminal vocabulary
terminal_routes:
  - AdmitTerminalPartition
  - RejectPostTerminalMutation
  - RejectAuthorityConflation
  - RejectPredicateFailure
terminal_route_map:
  AdmitTerminalPartition: Preserve
  RejectPostTerminalMutation: Refuse
  RejectAuthorityConflation: Invalidate
  RejectPredicateFailure: Reject
certification:
  certificate_required: false
  certificate_kind: null
  obstruction_class_required: true
  loss_ledger_required: false
  verifier_required: true
  loss_ledger_trigger_id: null
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
  - symptom: step entry attempted after terminal rune T has been committed
    diagnosis: post-terminal mutation attempted; violates Law 2 terminal absorption
    terminal: RejectPostTerminalMutation
  - symptom: terminal verdict claims authority_effect other than 'None'
    diagnosis: authority conflation defect; violates four-axis separation
    terminal: RejectAuthorityConflation
examples:
  - ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
    section: '2.9'
references:
  - omega_engine_governance/contracts/contracts_omega_engine_crates/mathematics/discrete_deformation_algebra/dda_packets.contract.yaml