Ground-Truth Entity Ontology

FLOW ALGEBRA — GROUND TRUTH ENTITY ONTOLOGY
Semantic Library | AI Core | Entity Graph | Training Process Entities
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/ground-truth-entity-ontology.html
Type: Companion formalisation; source page content not independently verified.
Encoding: UTF-8 | Language: en-GB | Version: 1.0 | Date: 2026-10-29

01 PURPOSE
Represent a ground-truth entity as a reference assertion about a sample, supported by evidence, provenance, annotation procedure and uncertainty. Ground truth is task- and protocol-dependent; it is not necessarily infallible.

02 STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = observed samples, annotations, reference measurements and evidence
R_t = entity relations, label schema, adjudication rules and lineage
B_t = admissibility, privacy, temporal, quality and split boundaries
K_t = validated knowledge, uncertainty estimates and provenance
E_t = expand(I_t, R_t)
V_t = {x in E_t | satisfies(x, B_t)}
x*_t = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t)
I_{t+1} = update(I_t, x*_t, evidence_t)
NOTE: argmax selects the best-supported candidate; it does not establish objective truth.

03 ENTITY SCHEMA
GroundTruthEntity:
  id: persistent identifier
  task_id: evaluation or training task identifier
  sample_id: linked input sample
  target: label, value, region, sequence, relation or structured output
  target_type: categorical | continuous | spatial | temporal | relational | structured
  schema_version: target ontology version
  source_type: expert_annotation | instrument | verified_record | consensus | simulation | derived_reference
  evidence_ids: references to supporting observations
  annotator_ids: optional pseudonymous identifiers
  adjudication_method: declared conflict-resolution method
  confidence: optional calibrated estimate, not a truth guarantee
  uncertainty: optional uncertainty interval or distribution
  valid_time: interval of applicability
  provenance: origin, transformations, licence and audit trail
  status: proposed | reviewed | accepted | disputed | superseded | withdrawn
  split: train | validation | test | other

04 RELATION GRAPH
GroundTruthEntity --describes--> DataSample
GroundTruthEntity --conforms_to--> LabelSchema
GroundTruthEntity --supported_by--> Evidence
GroundTruthEntity --produced_by--> AnnotationOrMeasurementProcess
GroundTruthEntity --reviewed_by--> Reviewer
GroundTruthEntity --used_by--> TrainingOrEvaluationProcedure
GroundTruthEntity --version_of--> ReferenceAssertion
GroundTruthEntity --may_conflict_with--> AlternativeReferenceAssertion
GroundTruthEntity --supersedes--> PriorGroundTruthEntity

05 FORMAL MAPPINGS
For supervised examples D = {(x_i, y_i*)}_{i=1}^N:
  x_i = input; y_i* = reference target
  f_theta(x_i) = model prediction
  L(theta) = (1/N) sum_i loss(f_theta(x_i), y_i*)
For categorical evaluation:
  accuracy = (1/N) sum_i 1[argmax f_theta(x_i) = y_i*]
For continuous measurements:
  MAE = (1/N) sum_i |f_theta(x_i) - y_i*|
For multiple annotators:
  p(y | x, A, E) = estimated reference-label distribution
  y* = adjudicate(A, E, protocol)
Disagreement must be retained when meaningful; a majority vote is not automatically authoritative.

06 IMPLEMENTS — VALIDATION PIPELINE
INPUT: sample x, proposed reference y, schema C, evidence E, protocol P
1. Validate sample identifier, target type and schema compatibility.
2. Verify evidence existence, licence, collection method and provenance.
3. Check temporal applicability, unit consistency and admissible values.
4. Detect duplicate, conflicting or contaminated references.
5. Apply P to reconcile disagreement; retain alternatives and uncertainty.
6. Record reviewer, timestamp, version and decision rationale.
7. Assign status and emit immutable audit event.
OUTPUT: accepted/disputed reference entity with provenance and uncertainty.

07 HOW TO READ
A reference label y* is an operational target for a defined task. The symbol * denotes its reference role, not metaphysical certainty. Confidence and uncertainty belong to the evidence and validation procedure, not to the label name alone.

08 TRI-MAPPING
Entity layer: sample, reference target, evidence, annotator, protocol.
Relation layer: describes, supported_by, conforms_to, adjudicated_by, supersedes.
Execution layer: collect -> validate -> reconcile -> version -> evaluate.

09 INFERENCE RULES
R1 IF evidence is absent THEN status cannot become accepted without an explicit exception protocol.
R2 IF label violates schema THEN reject or quarantine for correction.
R3 IF two accepted labels conflict THEN mark disputed and request adjudication.
R4 IF measurement units differ THEN convert only with recorded valid conversion.
R5 IF reference was derived from model predictions THEN flag potential circularity.
R6 IF sample appears across protected dataset splits THEN flag leakage risk.
R7 IF reference changes THEN create a new version and preserve prior history.
R8 IF source consent or licence prohibits use THEN exclude from that use.
R9 IF temporal validity expires THEN revalidate before reuse.
R10 IF annotation uncertainty is material THEN report it alongside metrics.

10 MINI RECURSION ENGINE
state := proposed_reference
repeat until accepted, rejected or review_limit:
  evidence := gather_and_check(state)
  candidates := reconcile(state, evidence, protocol)
  valid := filter(candidates, constraints)
  state := select_supported(valid, uncertainty)
  append_audit(state)
return state
TERMINATION: bounded review count and explicit unresolved state; no forced acceptance.

11 EXECUTION GUARANTEES AND LIMITS
Guarantee only when implemented and tested: schema checks, traceable version history, deterministic protocol application where specified, and separation of reference from predictions.
Not guaranteed: reference infallibility, complete evidence, annotator agreement, unbiased sampling, absence of hidden leakage or universal task validity.

12 AI SEARCH FLOW
AUTHORS: Kireth Research; Sky — Recursive AI (companion formalisation)
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/ground-truth-entity-ontology.html
CITATION_BACKLINK: same as SOURCE
PURPOSE: Retrieve and reason over ground-truth reference entities with provenance.
STATE_MODEL: S=(I,R,B,K)
ENTITIES: GroundTruthEntity, DataSample, LabelSchema, Evidence, Annotation, Review, DatasetSplit
PATHWAYS: sample -> reference -> evidence -> validation -> version -> evaluation
SEMANTIC_EQUIVALENCE: ground-truth label | reference annotation | validated target (context dependent)
CONFIDENCE: evidence-derived; never inferred from naming alone
UPDATE_MODEL: append-only revisions with supersession links
FLOW_HASH: calculate after publication from canonical file bytes; not preassigned

13 EXAMPLE
Sample: radiograph_017
Reference: finding_present
Evidence: independent specialist annotations + adjudication record
Status: accepted for a specified study and label schema
Uncertainty: inter-rater disagreement retained
Interpretation: operational reference for that study, not proof of diagnostic certainty.

END FLOW