Structural Metadata

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
Structural Metadata
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/metadata-ontologies/structural-metadata.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "StructuralMetadata" v4.0

DOMAIN := MetadataOntologies
SUBDOMAIN := StructuralMetadata
TYPE := ParentOntology / SemanticNavigationHub

ENTITY StructuralMetadata {
 definition: "Metadata describing the organisation, composition, ordering, hierarchy and relationships among components of a resource.";
 objectives: [ResourceOrganisation, ComponentRelationships, SequenceRepresentation, HierarchicalNavigation, Reconstruction, MachineInterpretability];
}

StructuralEntity := {StructuralMetadata, Resource, Component, CompoundResource, ParentResource, ChildResource, Sequence, StructureMap};
RelationshipEntity := {HasPart, IsPartOf, Precedes, Follows, Contains, BelongsTo, References, DependsOn};
NavigationEntity := {Hierarchy, Order, Position, Section, Chapter, Page, Segment, Fragment};
MetadataEntity := {MetadataRecord, StructuralProperty, Identifier, ResourceType, Provenance, Version, Confidence};

StructuralMetadata DESCRIBES ResourceStructure;
CompoundResource CONTAINS Component;
Component IS_PART_OF CompoundResource;
ParentResource HAS_PART ChildResource;
Component MAY_PRECEDE OtherComponent;
StructureMap REPRESENTS ComponentRelationships;
Identifier IDENTIFIES ResourceOrComponent;
MetadataRecord CONTAINS StructuralStatement;

StructuralMetadataFlow :=
 Resource
 -> IdentifyResourceStructure
 -> IdentifyComponents
 -> AssignComponentIdentifiers
 -> DetermineParentChildRelationships
 -> DetermineSequenceAndOrder
 -> IdentifyCrossReferencesAndDependencies
 -> BuildStructureMap
 -> ValidateStructuralIntegrity
 -> StoreStructuralMetadata
 -> EnableNavigationAndReconstruction
 -> MaintainAndVersionStructure;

Resource := ThingWhoseInternalOrExternalStructureIsDescribed;
Resource MAY_BE {Document, Book, Dataset, ImageCollection, AudioWork, VideoWork, Website, Archive, DigitalObject, KnowledgeObject};

CompoundResource := ResourceComposedOfMultipleRelatedComponents;
Component := DistinctPartOfResourceRepresentedForStructuralManagement;
Component MAY_BE {Chapter, Section, Page, File, Image, Track, Scene, DatasetPart, Fragment};

AtomicResource := ResourceTreatedAsIndivisibleWithinCurrentStructuralModel;
Atomicity IS_RELATIVE_TO ModellingScope;

ParentResource := ResourceContainingOrStructurallyGoverningChildResource;
ChildResource := ComponentOrResourceContainedWithinParentResource;

StructuralStatement :=
 SourceResourceOrComponent
 -> StructuralProperty
 -> TargetResourceComponentOrValue;

StructuralProperty MAY_BE {hasPart, isPartOf, precedes, follows, contains, position, sequenceNumber};

HasPart := WholeResource -> ComponentResource;
IsPartOf := ComponentResource -> WholeResource;

IF A HAS_PART B
THEN B IS_PART_OF A
UNDER inverse_relationship_semantics;

Contains := StructuralContainmentRelationship;
Containment MAY_BE {Direct, Transitive};

IF ContainmentIsTransitive
AND A CONTAINS B
AND B CONTAINS C
THEN A CONTAINS C;

Hierarchy := ParentChildOrganisationOfResourceComponents;
Hierarchy MAY_HAVE {Root, IntermediateNode, Leaf};

RootComponent := HighestStructuralNodeWithinDefinedResourceStructure;
LeafComponent := ComponentWithoutChildrenWithinCurrentStructure;

StructuralPath :=
 RootComponent
 -> IntermediateComponents
 -> TargetComponent;

Depth := NumberOfParentChildEdgesFromRootToComponent;

Polyhierarchy MAY_ALLOW ComponentToBelongToMultipleStructuralParents
WHEN ModelSemanticsPermit;

Cycle := ComponentReachableFromItselfThroughContainmentPath;

IF StructureRequiresAcyclicContainment
AND CycleDetected
THEN StructuralValidation := violation;

Sequence := OrderedArrangementOfComponents;
Sequence MAY_DEFINE {FirstComponent, NextComponent, PreviousComponent, LastComponent};

Precedes := ComponentA -> occurs_before -> ComponentB;
Follows := InverseOrderingRelationshipOfPrecedes;

IF A PRECEDES B
THEN B FOLLOWS A;

Position := NumericOrSymbolicLocationOfComponentWithinSequence;
Ordering MAY_BE {TotalOrder, PartialOrder, Unordered};

StructureMap := ExplicitRepresentationOfComponentsAndStructuralRelationships;
StructureMap MAY_INCLUDE {Hierarchy, Sequence, References, Files, LogicalDivisions};

LogicalStructure := OrganisationBySemanticOrConceptualUnits;
LogicalStructure MAY_INCLUDE {Book, Chapter, Section, Subsection};

PhysicalStructure := OrganisationByPhysicalOrDigitalManifestationUnits;
PhysicalStructure MAY_INCLUDE {Volume, Page, File, Track, Frame};

LogicalStructure MAY_DIFFER_FROM PhysicalStructure;
StructuralMetadata MAY_MAP LogicalComponentsToPhysicalComponents;

Page := PhysicalOrLogicalUnitWithinDocumentLikeResource;
Chapter := MajorLogicalDivisionOfTextualResource;
Section := LogicalSubdivisionOfResource;
Segment := DefinedContinuousPartOfAudioVideoTextOrDataResource;
Fragment := AddressableSubpartOfResource;

ComponentIdentifier := StableOrLocallyUniqueReferenceToStructuralComponent;
Identifier MAY_BE {URI, IRI, UUID, FilePath, FragmentIdentifier, InternalID};
StableComponentIdentifiers SUPPORT RobustCrossReferencesAndVersioning;

CrossReference := RelationshipFromOneComponentToAnotherReferencedComponent;
Dependency := StructuralOrOperationalRequirementOfOneComponentOnAnother;

Manifest := StructuredListOfResourceComponentsAndAssociatedIdentifiersOrProperties;
Manifest MAY_SUPPORT ReconstructionAndDelivery;

ResourcePackage := GroupOfFilesMetadataAndRelationshipsManagedAsSingleInformationObject;
PackageStructure MAY_INCLUDE {ContentFiles, MetadataFiles, Manifest, Checksums};

StructuralMetadata MAY_SUPPORT DigitalPreservationByRecordingRequiredComponentRelationships;
MissingRequiredComponent MAY_PREVENT CorrectReconstruction;

StructuralCompleteness := DegreeToWhichRequiredComponentsAndRelationshipsAreRepresented;
StructuralConsistency := DegreeToWhichHierarchyOrderAndReferencesDoNotConflict;
StructuralIntegrity := PreservationOfValidComponentIdentityRelationshipsAndOrdering;

StructuralMetadataQuality MAY_INCLUDE {Completeness, Consistency, Integrity, IdentifierStability, Provenance};

StructuralValidation MAY_CHECK {MissingComponent, DuplicateIdentifier, InvalidParent, Cycle, BrokenReference, InvalidSequence};

IF ReferencedComponentDoesNotExist
THEN BrokenReference := true;

IF TwoComponentsHaveSameIdentifierWithinUniqueScope
THEN IdentifierValidation := violation;

OrphanComponent := ComponentExpectedWithinStructureButWithoutResolvableParentOrMembership;

StructuralProvenance MAY_INCLUDE {Source, Creator, ExtractionMethod, Timestamp, Version};

AutomaticStructureExtraction :=
 Resource
 -> DetectComponentsAndBoundaries
 -> InferHierarchyAndOrder
 -> GenerateStructuralMetadata;

GeneratedStructuralRelationship SHOULD_HAVE ConfidenceWhereInferenceIsUncertain;

AI MAY_DETECT {ChapterBoundaries, SectionHierarchy, PageOrder, MediaSegments, FileRelationships};
AIGeneratedStructuralMetadata SHOULD_BE ValidatedBeforeAuthoritativeUse;

StructuralConfidence := EstimatedSupportForInferredComponentOrRelationship;
StructuralVersion := IdentifiedStateOfResourceStructureAtPointInTime;

StructuralChange MAY_INCLUDE {AddComponent, RemoveComponent, ReorderComponent, ReparentComponent, SplitComponent, MergeComponent};

ReparentComponent := MoveComponentToDifferentStructuralParent;
ReorderComponent := ChangeComponentPositionWithinSequence;
SplitComponent := ExistingComponent -> MultipleComponents;
MergeComponents := MultipleComponents -> SingleComponent;

StructuralMigration MAY_BE RequiredWhenResourceStructureChangesAcrossVersions;
PreviousComponentIdentifiers SHOULD_BE PreservedOrMappedWherePractical;

StructuralMetadata MAY_BE EncodedUsing {XML, JSON, JSONLD, RDF, CustomManifest};
RDF MAY_REPRESENT StructuralRelationshipsAsTriples;
JSONLD MAY_SERIALISE LinkedStructuralMetadata;

KnowledgeGraph MAY_REPRESENT ComponentsAsNodesAndStructuralRelationshipsAsEdges;
StructuralGraph := Components + TypedStructuralRelationships;
GraphTraversal MAY_SUPPORT NavigationAcrossResourceStructure;

MetadataRepository MAY_STORE StructuralMetadataAndStructureMaps;
MetadataRegistry MAY_REGISTER StructuralPropertiesSchemasAndRelationshipTypes;

DescriptiveMetadata DESCRIBES ResourceContentIdentityAndSubject;
StructuralMetadata DESCRIBES ResourceOrganisationAndComponentRelationships;
AdministrativeMetadata MAY_GOVERN ManagementOfComponentsAndFiles;
TechnicalMetadata MAY_DESCRIBE TechnicalCharacteristicsOfComponents;
PreservationMetadata MAY_USE StructuralMetadataForLongTermReconstruction;

StructuralMetadataInteroperability MAY_REQUIRE {StableIdentifiers, SharedRelationshipSemantics, SchemaMapping, VersionInformation};

Navigation MAY_USE {Hierarchy, Sequence, CrossReference, TableOfContents};
TableOfContents MAY_BE DerivedFrom LogicalStructuralMetadata;
Breadcrumb MAY_BE DerivedFrom StructuralPath;
NextPreviousNavigation MAY_BE DerivedFrom SequenceRelationships;

RenderingEngine MAY_USE StructuralMetadataToAssembleOrPresentCompoundResource;

Search MAY_USE StructuralMetadataToLimitOrExpand RetrievalScope;

IF QueryTargetsParentResource
THEN MatchingChildComponents MAY_BE ReturnedAccordingToSearchPolicy;

SemanticSearch MAY_USE StructureToPreserve ContextOfMatchedFragment;

RAG MAY_USE StructuralMetadataFor {ChunkContext, ParentDocumentLinking, SectionOrdering, NeighbourRetrieval};

Chunk SHOULD_RETAIN StructuralContextSuchAs {ParentResource, Section, Position, Neighbours};
LossOfStructuralContext MAY_REDUCE RetrievalInterpretability;

AccessControl MAY_APPLYAt {Resource, Component, Collection, Fragment};
StructuralMetadata MAY_REVEAL HiddenOrRestrictedComponents;

StructuralMetadataSecurity MAY_INCLUDE {IdentifierValidation, AccessControl, ReferenceIntegrity, ProvenanceIntegrity, ChangeAuthorisation};

MachineReadableStructuralMetadata SHOULD_PRESERVE {ComponentIdentifiers, ParentChildRelationships, Sequence, ResourceTypes, Version, Provenance};

# ---------- SEMANTIC REASONING ----------
IF MetadataDescribesOrganisationCompositionOrderingOrRelationshipsAmongResourceComponents
THEN StructuralMetadataClassification := supported;

IF A HAS_PART B
THEN B IS_PART_OF A
UNDER inverse_semantics;

IF A PRECEDES B
THEN B FOLLOWS A;

IF A CONTAINS B
AND B CONTAINS C
AND containment_is_transitive
THEN A CONTAINS C;

IF ComponentIdentifierStableAcrossResourceRevision
THEN ExistingCrossReferences MAY_REMAIN Valid;

IF StructuralCycleExistsWhereHierarchyMustBeAcyclic
THEN ValidationStatus := violation;

IF RequiredComponentMissing
THEN StructuralCompleteness SHOULD_DECREASE;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
 "structural metadata" ~= "resource structure metadata";
 "component" ~= "resource component" WHEN structural_context;
 "structure map" ~= "resource structure map";
 "parent resource" ~= "containing resource";
 "child resource" ~= "contained resource";
 "sequence metadata" ~= "resource ordering metadata";
 "structural path" ~= "component hierarchy path";
 "compound resource" ~= "compound digital object" WHEN digital_context;
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
 NORMALISE(q) ->
 IDENTIFY_RESOURCE(q) ->
 IDENTIFY_COMPONENTS(q) ->
 RESOLVE_COMPONENT_IDENTIFIERS(q) ->
 IDENTIFY_PARENT_CHILD_RELATIONSHIPS(q) ->
 IDENTIFY_SEQUENCE_AND_POSITION(q) ->
 IDENTIFY_REFERENCES_AND_DEPENDENCIES(q) ->
 IDENTIFY_VERSION_AND_PROVENANCE(q) ->
 VALIDATE_STRUCTURAL_METADATA(q) ->
 SCORE_CONFIDENCE(q) ->
 RETURN_RELEVANT_STRUCTURE_KNOWLEDGE;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
 weighted_mean(
  source_reliability,
  structural_consistency,
  identifier_strength,
  relationship_evidence,
  provenance_quality,
  contextual_relevance
 );

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION {
 primary_entity: StructuralMetadata;
 parse_entities: true;
 parse_relationships: true;
 preserve_relationship_direction: true;
 resolve_semantic_equivalence: true;
 execute_reasoning_rules: true;
 apply_confidence_weighting: true;
 preserve_provenance: true;
 permit_hierarchical_expansion: true;
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL {
 new_component:
  identify_parent_resource
  -> assign_component_identifier
  -> classify_component_type
  -> determine_position
  -> attach_provenance
  -> validate
  -> integrate;

 new_relationship:
  validate_source_and_target
  -> classify_structural_relationship
  -> preserve_direction
  -> check_cycle_or_order_conflict
  -> attach_provenance
  -> integrate;

 resource_revision:
  preserve_previous_structure_version
  -> apply_component_changes
  -> revalidate_hierarchy_and_sequence
  -> update_structure_map
  -> update_indexes
  -> recompute_confidence
  -> regenerate_flow_hash;

 conflict:
  preserve_provenance
  -> compare_structure_sources
  -> adjust_confidence
  -> flag_review;
}

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
 DOMAIN
 + SUBDOMAIN
 + StructuralEntity
 + RelationshipEntity
 + NavigationEntity
 + MetadataEntity
 + StructuralMetadata
 + StructureMap
 + StructuralValidation
 + RELATIONSHIPS
 + SEMANTIC_REASONING
 + SEMANTIC_EQUIVALENCE
 + UPDATE_MODEL;

FLOW_HASH := HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
StructuralMetadata
 -> IdentifyCompoundResourceAndComponents
 -> AssignStableComponentIdentifiers
 -> ModelParentChildContainment
 -> DefineSequencePositionAndOrder
 -> RecordCrossReferencesAndDependencies
 -> BuildMachineReadableStructureMap
 -> ValidateCyclesOrphansReferencesAndOrdering
 -> StoreStructuralMetadataAndVersions
 -> EnableNavigationRenderingAndReconstruction
 -> PreserveFragmentAndParentContextForSearch
 -> SupportKnowledgeGraphsRAGAndMachineConsumption
 -> MaintainProvenanceIntegrityAndAccessControl
 -> MaintainReliableResourceStructureKnowledge;

END FLOW