nf.ddc.loss_ledger

Loss Ledger Normal Form (LLNF)

Contract ID: nf.ddc.loss_ledger | Family: transport | Index Status: active | AuthorityEffect: None

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1. Executive Summary & Metadata

Loss Ledger Normal Form (LLNF) enforces structural normalization and explicit defect routing in the transport regime.

Property	Value
Canonical ID	nf.ddc.loss_ledger
Short Name	LLNF
Full Name	Loss Ledger Normal Form
Family	transport (Scale Ascent/Descent & Representation Transport Ledgers (LNLF, LLNF, GNF))
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: transport
• Runes: ['D']
• Target Runtime Law: Law 6 (Finite Loss Ledger)
• Domain: Scale descent transformations D: H_k -> H_{k-1}.
• Anomaly Excluded: Silent dimension truncation and unaccounted projection energy loss.
• Preserved Invariant: Booked LossLedger record with dropped coordinates, exact rational l^1 loss, and tail bound.
• Reconstruction Theorem: Original state bounded within declared l^1 ball centered at projected 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 (LLNF Candidate)	Anomaly risk: silent dimension ; truncation and unwitnessed ; degree-of-freedom loss during...
2. Normalization / Gate	LLNF Verification Gate	explicit LossLedger... (certified_implies_authorized: false)
3. After / Certified Output	Certified LLNF Output	Invariant: ['initial_dimension_m', ; 'target_dimension_n', ; 'dropped_dimension_count',...

Contract-Declared Worked Cases

- ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
  section: '2.6'

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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.loss_ledger
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	silent dimension truncation and unwitnessed degree-of-freedom loss during representation coarsening
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: explicit LossLedger recording dropped dimensions, tail coordinates, and rational ℓ¹ loss scalar L(x) Protected Skeleton: ['initial_dimension_m', 'target_dimension_n', 'dropped_dimension_count', 'dropped_tail_vector', 'loss_scalar_L', 'is_lossless_flag']
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 coarse representation is equivalent to fine representation when loss_scalar > 0
• does not claim descent is reversible without external auxiliary data
• does not confer operational authority; authority_effect is unconditionally None

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• initial_dim
• target_dim
• dropped_dim
• tail_vector
• loss_scalar
• is_lossless

5.2 Required Evidence

None declared.

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	initial dimension m is strictly greater than or equal to target dimension n
criterion	Check	tail vector length exactly equals m - n
criterion	Check	loss scalar L(x) matches exact rational ℓ¹ sum of dropped components

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
AdmitLossLedger	Preserve
RejectUnbookedDescent	Refuse
RejectTailMismatch	Reject

5.5 Declared Failure Modes

• symptom: dimension reduced without emitting LossLedger record, diagnosis: descent without ledger attempted; violates Law 6, terminal: RejectUnbookedDescent
• symptom: length of tail vector does not match m - n, diagnosis: dropped coordinate count mismatch, terminal: RejectTailMismatch

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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.loss_ledger (LLNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AdmitLossLedger, RejectUnbookedDescent, RejectTailMismatch) 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 silent dimension truncation and unwitnessed degree-of-freedom loss during representation coarsening is either excluded under explicit LossLedger recording dropped dimensions, tail coordinates, and rational ℓ¹ loss scalar L(x) 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.loss_ledger.

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

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

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.ddc.loss_ledger
  name: Loss Ledger Normal Form
  short_name: LLNF
  version: v0
  theory_status: established
  contract_status: active
  status: active
  verification_status: executable
  family: transport
classification:
  hierarchy_level: normal_form
  subject_kind:
    - scale_descent
    - dimension_projection
    - loss_ledger
  data_posture: at_rest
  mathematical_posture: operational
purpose:
  excludes_anomaly: silent dimension truncation and unwitnessed degree-of-freedom loss during representation coarsening
  preserves_invariant: explicit LossLedger recording dropped dimensions, tail coordinates, and rational ℓ¹ loss scalar L(x)
  protected_skeleton:
    - initial_dimension_m
    - target_dimension_n
    - dropped_dimension_count
    - dropped_tail_vector
    - loss_scalar_L
    - is_lossless_flag
  erased_structure:
    - intermediate_subspace_rotation_basis
  non_claims:
    - does not claim coarse representation is equivalent to fine representation when loss_scalar > 0
    - does not claim descent is reversible without external auxiliary data
    - does not confer operational authority; authority_effect is unconditionally None
definition:
  source: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/normal_forms/README.md
  section: '2.0'
  formal_statement: >
    On a representation projection from dimension m to dimension n (with m > n), Loss Ledger Normal Form (LLNF)
    enforces that all dropped coordinates are booked into an explicit LossLedger L_adapter. Scale descent
    rune D is lawful if and only if the ledger records the exact tail vector x_tail and rational ℓ¹ norm
    loss scalar L(x) = ‖x_tail‖₁.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: projection_with_residual_ledger_not_relational_project_join
    anomaly_exclusion: unwitnessed dimension reduction or unbooked topological phase loss
    lossless_join:
      status: direct_sum_reconstruction
      statement: original vector x ∈ ℚᵐ is losslessly reconstructed by concatenating projected vector x↓ ∈ ℚⁿ and dropped tail x_tail ∈ ℚ^{m-n}
    dependency_preservation:
      status: coordinate_projection_preserved
      statement: norm loss L(x) = ‖x_tail‖₁ is calculated strictly on the dropped coordinates
    syntactic_decision:
      status: rational_arithmetic_decidable
      statement: membership is decidable by asserting len(tail) == m - n and L(x) == sum(abs(v))
declarations_required:
  - initial_dim
  - target_dim
  - dropped_dim
  - tail_vector
  - loss_scalar
  - is_lossless
evidence_required: []
validation_criteria:
  - initial dimension m is strictly greater than or equal to target dimension n
  - tail vector length exactly equals m - n
  - loss scalar L(x) matches exact rational ℓ¹ sum of dropped components
terminal_routes:
  - AdmitLossLedger
  - RejectUnbookedDescent
  - RejectTailMismatch
terminal_route_map:
  AdmitLossLedger: Preserve
  RejectUnbookedDescent: Refuse
  RejectTailMismatch: Reject
certification:
  certificate_required: true
  certificate_kind: loss_ledger_receipt
  obstruction_class_required: false
  loss_ledger_required: true
  verifier_required: true
  loss_ledger_trigger_id: scale_descent_with_loss
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
  - symptom: dimension reduced without emitting LossLedger record
    diagnosis: descent without ledger attempted; violates Law 6
    terminal: RejectUnbookedDescent
  - symptom: length of tail vector does not match m - n
    diagnosis: dropped coordinate count mismatch
    terminal: RejectTailMismatch
examples:
  - ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
    section: '2.6'
references:
  - omega_engine_governance/contracts/contracts_omega_engine_crates/mathematics/discrete_deformation_algebra/transport_loss_ledger.contract.yaml