# pag > Every algorithm contract in this domain is listed with its position on the derivation loop, its intent and invariant, the flow it walks, its productions as a… Page: Ontology · Algorithms Canonical: https://banes-lab.com/ontology/algorithms#algo-domain-pag Every algorithm contract in this domain is listed with its position on the derivation loop, its intent and invariant, the flow it walks, its productions as a grammar, what it composes and is composed by, which forces and principles it answers to, what grounds it and what it grounds, and an exemplar where the record carries one. The diagram shows what composes what inside the domain. Relations diagram What composes what inside this domain. ```mermaid flowchart LR n_pag_document_declaration["PAG Document Declaration"] n_pag_keyword_ontology["PAG Keyword Ontology"] n_pag_node_decomposition["PAG Node Decomposition"] n_pag_validation_gate["PAG Handoff Gate"] n_pag_explicit_control_flow["PAG Explicit Control Flow"] n_pag_constraint_boundary["PAG Invariant Record"] n_pag_tool_invocation["PAG Semantic Operation"] n_pag_coordination_construct["PAG Structure Declaration"] n_pag_ambiguity_reduction["PAG Ambiguity Reduction"] n_pag_authoring_kernel["PAG Authoring Kernel"] n_pag_well_formedness_validation["PAG Well-Formedness Validation"] n_pag_instruction_concern[""] n_pag_authoring_kernel --> n_pag_document_declaration n_pag_authoring_kernel --> n_pag_keyword_ontology n_pag_authoring_kernel --> n_pag_node_decomposition n_pag_authoring_kernel --> n_pag_validation_gate n_pag_authoring_kernel --> n_pag_explicit_control_flow n_pag_authoring_kernel --> n_pag_tool_invocation n_pag_authoring_kernel --> n_pag_coordination_construct n_pag_authoring_kernel --> n_pag_constraint_boundary n_pag_authoring_kernel --> n_pag_well_formedness_validation n_pag_well_formedness_validation --> n_pag_validation_gate n_pag_well_formedness_validation --> n_pag_explicit_control_flow ``` ### PAG Document Declaration - Stage: [orient](https://banes-lab.com/records/stage/orient.md) - Axis: [ontology](https://banes-lab.com/records/reason/axis-ontology.md) - Math type: [set-theory](https://banes-lab.com/records/reason/math-type-set-theory.md) - Yields: set | boolean Details Intent Bind a document to a declared type and its default verb (THIS ) after the YAML frontmatter and before any node, then declare in the meta block what the document is for, which sources ground which, what it trusts, what it may touch and what it declares outside itself, and how far repair may recurse. Invariant A PAG document announces what kind of instruction it is, and what it may touch, before it instructs. Flow ```text Frontmatter → TypeDeclaration → DefaultVerb → MetaBlock → Jurisdiction → DeclaredContract ``` Productions ```bnf PagDocumentDeclaration ::= "->" "->" "->" PagDocumentType ::= "AGENT" | "WORKFLOW" | "PROTOCOL" | "POLICY" | "CHECKLIST" | "TEMPLATE" | "TASK" | "INSTRUCTION" | "PROMPT" | "COMMAND" | "TEST" | "DEBUG" | "VERIFICATION" | "DISTILLATION" | "AUDIT" | "TRANSLATION" | "COMPOSITION" PagDocumentVerb ::= "IS" | "ENFORCES" | "EXECUTES" | "PERFORMS" | "PROVIDES" | "IMPLEMENTS" | "DEFINES" | "MANAGES" | "COORDINATES" | "HAS" | "GENERATES" | "RESOLVES" | "FINDS" | "FIXES" | "VERIFIES" | "CLASSIFIES" | "DISTILLS" | "ABSTRACTS" | "ELIMINATES" | "AUDITS" | "MEASURES" | "SCORES" | "CORRECTS" | "RENDERS" | "COMPOSES" | "FOLDS" PagMetaField ::= "objective" | "priority" | "trust" | "jurisdiction" | "recursion_limit" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [semantic_consistency](https://banes-lab.com/records/force/semantic-consistency.md), [contract_compatibility](https://banes-lab.com/records/force/contract-compatibility.md), [metaprogramming_modeling](https://banes-lab.com/records/force/metaprogramming-modeling.md) Grounds none Before ```text A document instructs with no declared type — its semantic contract, its authority and its jurisdiction are implicit. ``` After ```text frontmatter → THIS {AGENT|WORKFLOW|CHECKLIST} {IS|EXECUTES|ENFORCES} description → META block{objective, priority, trust, jurisdiction, recursion_limit} → declared contract ``` ### PAG Keyword Ontology - Stage: [see](https://banes-lab.com/records/stage/see.md) - Axis: [analysis](https://banes-lab.com/records/reason/axis-analysis.md) - Math type: [set-theory](https://banes-lab.com/records/reason/math-type-set-theory.md) - Yields: set | boolean Details Intent Draw every operative token from a fixed, uppercase, code-frequent vocabulary partitioned into semantic categories, each token grounded to a record in the reasoning ontology, and bind targets to sources through explicit prepositions, so the model completes recognised structured patterns rather than interpreting prose. Invariant Explicit high-frequency uppercase tokens, each grounded to a reasoning record, reduce interpretive variance; prose does not. Flow ```text ProseIntent → KeywordCategory → UppercaseToken → ReasoningGround → PrepositionBinding → StructuredDirective ``` Productions ```bnf PagKeywordOntology ::= "->" "->" "->" "->" PagKeywordCategory ::= "semantic_operation" | "node" | "action" | "control_flow" | "declaration" | "modifier" | "coordination" | "state_machine" | "dag" | "priority_queue" | "flowchart" | "document_type" | "document_verb" | "meta" | "validation" | "report" | "invariant" | "contextual" PagPreposition ::= "FROM" | "TO" | "INTO" | "WITH" | "USING" | "AGAINST" | "IN" | "AS" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [metaprogramming_modeling](https://banes-lab.com/records/force/metaprogramming-modeling.md), [semantic_consistency](https://banes-lab.com/records/force/semantic-consistency.md), [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) Grounds none Before ```text 'Get the data and check it' — prose the model must interpret. ``` After ```text prose intent → uppercase token{READ_RESOURCE|ANALYZE_CONTENT|VALIDATE_ARTIFACT} + preposition{FROM|INTO|AGAINST} → structured directive, low interpretive variance ``` ### PAG Node Decomposition - Stage: [project](https://banes-lab.com/records/stage/project.md) - Axis: [reasoning](https://banes-lab.com/records/reason/axis-reasoning.md) - Math type: [graph](https://banes-lab.com/records/reason/math-type-graph.md) - Yields: edge-list Details Intent Group directives into nodes, each one decision on one reasoning axis, headed by its layer, axis, math type and the shape its decision yields, tagged with the substrate stage its artifact comes to be at, and contracted so that its input names the prior node's output or a declared slot, its transform is stated in semantic operations, and its output is the one record the next node reads. Invariant Each node is one bounded decision whose data flow from the prior node is declared by identity, never inferred from a name. Flow ```text DirectiveSet → NodeHeader → GenesisStage → Contract → DeclaredInput → NodeOutput ``` Productions ```bnf PagNodeDecomposition ::= "->" "->" PagNodeHeader ::= "#" "NODE" "—" "[" "·" "·" "·" "yields:" "]" PagNodeContract ::= "CONTRACT:" "input:" "transform:" "output:" PagScopeRule ::= "declare_before_use" "," "document_wide_scope" "," "prior_output_only" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [modularity](https://banes-lab.com/records/force/modularity.md), [domain_boundary](https://banes-lab.com/records/force/domain-boundary.md), [contract_compatibility](https://banes-lab.com/records/force/contract-compatibility.md) Grounds none Before ```text Directives poured in one flat block, forward-referencing later work, with no statement of what each block decides or what shape its decision takes. ``` After ```text directives → nodes{# NODE n — NAME [layer · axis · math type · yields: shape], @genesis, CONTRACT input/transform/output, one gate} → a node reads only the prior node's output → explicit data flow ``` ### PAG Handoff Gate - Stage: [verify](https://banes-lab.com/records/stage/verify.md) - Axis: [verification](https://banes-lab.com/records/reason/axis-verification.md) - Math type: [logic](https://banes-lab.com/records/reason/math-type-logic.md) - Yields: boolean Details Intent Close every node with a handoff gate of three-to-five checks, each a claim about the output with the evidence that settles it and the population it was measured over, a refusal condition named before any irreversible write, the standing of the read set beside the verdict, and a result line that routes pass to the next node, each failure to the earliest node that owns its repair, and unknown to blocked. Invariant A node boundary is trusted only when its checks carry evidence and a population, its writes are refused before they land, and its unknown is routed; unknown is not pass. Flow ```text NodeOutput → CheckWithEvidence → Population → Refusal → Standing → ThreeVerdicts → ResultLine ``` Productions ```bnf PagHandoffGate ::= "->" "->" "->" "->" PagCheckLine ::= "[check]" "(evidence:" ")" "over:" "measured:" "/" PagVerdict ::= "pass" | "fail" | "unknown" PagResultLine ::= "result:" "pass" "->" "|" "->" "REPAIR" "(owner:" ")" "|" "unknown" "->" "BLOCKED" PagGateConstraint ::= "evidence_per_check" "," "population_declared" "," "three_to_five_checks" "," "refusal_before_write" "," "unknown_routed" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md), [PAG Well-Formedness Validation](https://banes-lab.com/records/algo/pag-well-formedness-validation.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md), [model_governance](https://banes-lab.com/records/force/model-governance.md), [modularity](https://banes-lab.com/records/force/modularity.md) Grounds [ver-evidence](https://banes-lab.com/records/reason/node-ver-evidence.md), [ver-population](https://banes-lab.com/records/reason/node-ver-population.md), [ver-refusal](https://banes-lab.com/records/reason/node-ver-refusal.md), [ver-standing](https://banes-lab.com/records/reason/node-ver-standing.md), [ter-block](https://banes-lab.com/records/reason/node-ter-block.md) Before ```text A node ends with 'looks good' — a vague assertion with no evidence, no population, no refusal, and only two verdicts. ``` After ```text node output → 3-5 checks{[check] claim (evidence: what settles it) over: set measured: n / N} + refuse: condition before write + standing: moved-set + result: pass → next | failure → REPAIR (owner) | unknown → BLOCKED ``` ### PAG Explicit Control Flow - Stage: [act](https://banes-lab.com/records/stage/act.md) - Axis: [formalisation](https://banes-lab.com/records/reason/axis-formalisation.md) - Math type: [logic](https://banes-lab.com/records/reason/math-type-logic.md) - Yields: boolean Details Intent Express branching with IF / ELSE IF / ELSE, iteration with FOR EACH over a collection (never a bare FOR), and failure handling with TRY / CATCH, every conditional colon-terminated and every branch a complete directive sequence. Invariant Control flow is explicit and colon-delimited so the model does not infer structure from prose sequence. Flow ```text Condition → BranchSet → IterationForm → FailureForm → DeterministicPath ``` Productions ```bnf PagControlFlow ::= | | PagIteration ::= "FOR" "EACH" "IN" ":" PagControlConstraint ::= "colon_terminated" "," "for_each_not_for" "," "complete_branch_directives" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md), [PAG Well-Formedness Validation](https://banes-lab.com/records/algo/pag-well-formedness-validation.md) Forces [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md), [control_coordination](https://banes-lab.com/records/force/control-coordination.md) Grounds none Before ```text Branching and iteration inferred from prose order; a bare FOR, a missing colon. ``` After ```text IF/ELSE IF/ELSE + FOR EACH x IN collection + TRY/CATCH → every conditional colon-terminated, complete branch directives ``` ### PAG Invariant Record - Stage: [constrain](https://banes-lab.com/records/stage/constrain.md) - Axis: [teleology](https://banes-lab.com/records/reason/axis-teleology.md) - Math type: [optimisation](https://banes-lab.com/records/reason/math-type-optimisation.md) - Yields: boolean | ranking Details Intent State every behavioural invariant as a record with four slots: the property in a form that could be false, the set it quantifies over, the parties it binds, and the objector, the check that would disagree if the property stopped holding or none as declared debt, so an unwatched invariant is visible rather than assumed. Invariant An invariant is stated with its property, its set, its parties and its objector, or it is indistinguishable from a property a reader happened to infer. Flow ```text BehaviorPolicy → Property → Set → Parties → Objector → InvariantRecord ``` Productions ```bnf PagInvariantBlock ::= "#" "CROSS-NODE" "INVARIANTS" + PagInvariantRecord ::= "INVARIANT" ":" "over:" "binds:" "objector:" ( | "none") PagInvariantQuality ::= "falsifiable" "," "quantified" "," "delivered" "," "watched" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [model_governance](https://banes-lab.com/records/force/model-governance.md), [security_governance](https://banes-lab.com/records/force/security-governance.md), [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) Grounds none Before ```text Behavioural rules as a bullet list under ALWAYS and NEVER — no set the rule ranges over, no party it binds, nothing that would disagree if it stopped holding. ``` After ```text INVARIANT name: property over: set binds: parties objector: check | none → each invariant stated in a form that could be false, with what watches it ``` ### PAG Semantic Operation - Stage: [act](https://banes-lab.com/records/stage/act.md) - Axis: [formalisation](https://banes-lab.com/records/reason/axis-formalisation.md) - Math type: [computation](https://banes-lab.com/records/reason/math-type-computation.md) - Yields: procedure Details Intent Name every external effect as one of the semantic operations (discover, read, search, analyze, extract, calculate, compose, validate, persist, execute, request a decision, report) with a uniform WITH / USING parameter clause and an INTO / arrow result binding, so the document names what it does and an adapter binding resolves how, and no host's tool name enters the document. Invariant Every external effect is a semantic operation with explicit parameters and an explicit result binding, and the host's tools are the adapter's data. Flow ```text SemanticOperation → OperationTarget → ParameterClause → ResultBinding → AdapterBinding ``` Productions ```bnf PagToolInvocation ::= PagSemanticOperation ::= "DISCOVER_RESOURCES" | "READ_RESOURCE" | "SEARCH_CONTENT" | "ANALYZE_CONTENT" | "EXTRACT_FACTS" | "CALCULATE_METRIC" | "COMPOSE_ARTIFACT" | "VALIDATE_ARTIFACT" | "PERSIST_ARTIFACT" | "EXECUTE_TOOL" | "REQUEST_DECISION" | "REPORT_RESULT" PagResultBinding ::= "INTO" | "->" | "AS" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [contract_compatibility](https://banes-lab.com/records/force/contract-compatibility.md), [runtime_extensibility](https://banes-lab.com/records/force/runtime-extensibility.md) Grounds none Before ```text An external effect described in prose, or named by one host's tool, so the document runs in one place only. ``` After ```text semantic operation{READ_RESOURCE|PERSIST_ARTIFACT|EXECUTE_TOOL|REQUEST_DECISION} + WITH/USING params + INTO/-> result → a named effect the adapter binds to a host's tool ``` ### PAG Structure Declaration - Stage: [project](https://banes-lab.com/records/stage/project.md) - Axis: [reasoning](https://banes-lab.com/records/reason/axis-reasoning.md) - Math type: [graph](https://banes-lab.com/records/reason/math-type-graph.md) - Yields: edge-list Details Intent Make a document's structure explicit with the declaration that names it: a DAG for a dependency graph, a STATE_MACHINE for a lifetime or a set of derived states, a PRIORITY_QUEUE for a ranking, a FLOWCHART for the rendered projection of a declared structure, and for a shared surface the coordination model's SURFACE, RECORD and ITEM with their typed edges, derived states and the one post-and-wait operation, so ordering, ownership and state are declared as structure rather than narrated as prose. Invariant Ordering, ownership and state are declared through explicit structure constructs a check can read, never implied by textual order. Flow ```text StructureNeed → StructureDeclaration → DeclaredEdges → DerivedState → ReadableStructure ``` Productions ```bnf PagStructure ::= | | | | PagStructureForm ::= "DAG" | "STATE_MACHINE" | "PRIORITY_QUEUE" | "FLOWCHART" | "SURFACE" PagSurface ::= "SURFACE" ":" ("RECORD" "subject:" *)+ PagEdgeKind ::= "PARENT" | "SATISFIED_BY" | "BLOCKS" | "ANSWERS" | "REFUTES" | "SUPERSEDES" ``` Composes none Composed by [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [control_coordination](https://banes-lab.com/records/force/control-coordination.md), [event_messaging](https://banes-lab.com/records/force/event-messaging.md), [causality_ordering](https://banes-lab.com/records/force/causality-ordering.md) Grounds none Before ```text Concurrency, ordering, lifetimes and ownership implied by the order sentences appear in. ``` After ```text a declared structure → DAG{dependency graph} | STATE_MACHINE{lifetime, derived states} | PRIORITY_QUEUE{ranking} | FLOWCHART{rendered projection} | SURFACE{RECORD, ITEM, typed edges, WAIT} → the structure is explicit and a check can read it ``` ### PAG Ambiguity Reduction - Stage: [derive](https://banes-lab.com/records/stage/derive.md) - Axis: [reasoning](https://banes-lab.com/records/reason/axis-reasoning.md) - Math type: [logic](https://banes-lab.com/records/reason/math-type-logic.md) - Yields: boolean Details Intent Replace interpretive prose with explicit structured tokens so the model completes recognized patterns, while accepting that output stays probabilistic: the grammar reduces input ambiguity, it does not constrain output tokens or guarantee determinism. Invariant PAG shapes the input toward consistent completion and does not always apply; it reduces the variance of the output without making it deterministic. Flow ```text ProseAmbiguity → TokenStructure → PatternRecognition → ReducedVariance ``` Productions ```bnf PagAmbiguityReduction ::= "->" "->" PagApplicabilityBound ::= "input_shaping_only" "," "probabilistic_output" "," "not_always_applicable" ``` Composes none Forces [model_governance](https://banes-lab.com/records/force/model-governance.md), [semantic_consistency](https://banes-lab.com/records/force/semantic-consistency.md), [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) Grounds none Before ```text Prose intent claimed to guarantee deterministic model output. ``` After ```text prose → structured tokens → reduced interpretation load; input-shaping only, output stays probabilistic (less variance, never deterministic) ``` ### PAG Authoring Kernel - Math type: [computation](https://banes-lab.com/records/reason/math-type-computation.md) - Yields: procedure Details Intent Compose a PAG document as frontmatter and typed declaration, then a meta block with jurisdiction, then nodes each headed by its layer, axis, math type and yields, contracted to read the prior node's output, and closed by a handoff gate with evidence, population, refusal and the three verdicts, drawing directives from the semantic operations, control flow and structure declarations, and closing with invariant records and a report. Invariant A well-formed PAG document is a node-gated, keyword-typed, invariant-bounded instruction contract whose every verdict carries its population. Flow ```text Declaration → MetaBlock → Nodes → Gates → Directives → Invariants → Report → PagDocument ``` Productions ```bnf PagAuthoringKernel ::= "->" "->" "->" "->" "->" "->" "->" ``` Composes [PAG Document Declaration](https://banes-lab.com/records/algo/pag-document-declaration.md), [PAG Keyword Ontology](https://banes-lab.com/records/algo/pag-keyword-ontology.md), [PAG Node Decomposition](https://banes-lab.com/records/algo/pag-node-decomposition.md), [PAG Handoff Gate](https://banes-lab.com/records/algo/pag-validation-gate.md), [PAG Explicit Control Flow](https://banes-lab.com/records/algo/pag-explicit-control-flow.md), [PAG Semantic Operation](https://banes-lab.com/records/algo/pag-tool-invocation.md), [PAG Structure Declaration](https://banes-lab.com/records/algo/pag-coordination-construct.md), [PAG Invariant Record](https://banes-lab.com/records/algo/pag-constraint-boundary.md) Forces [metaprogramming_modeling](https://banes-lab.com/records/force/metaprogramming-modeling.md), [model_governance](https://banes-lab.com/records/force/model-governance.md), [contract_compatibility](https://banes-lab.com/records/force/contract-compatibility.md), [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) Grounds [derivation-loop](https://banes-lab.com/ontology/reasoning/reason-loop-derivation-loop.md) Derivation map orient [PAG Document Declaration](https://banes-lab.com/records/algo/pag-document-declaration.md) see [PAG Keyword Ontology](https://banes-lab.com/records/algo/pag-keyword-ontology.md) project [PAG Node Decomposition](https://banes-lab.com/records/algo/pag-node-decomposition.md) constrain [PAG Invariant Record](https://banes-lab.com/records/algo/pag-constraint-boundary.md) act [PAG Semantic Operation](https://banes-lab.com/records/algo/pag-tool-invocation.md) verify [PAG Handoff Gate](https://banes-lab.com/records/algo/pag-validation-gate.md) terminate [PAG Well-Formedness Validation](https://banes-lab.com/records/algo/pag-well-formedness-validation.md) Before ```text An instruction written as prose, ungated, untyped and unwatched. ``` After ```text frontmatter + typed declaration → meta block with jurisdiction → nodes each headed, contracted and closed by a handoff gate → directives{semantic operations, control flow, structure declarations} → INVARIANT records → REPORT ``` ### PAG Well-Formedness Validation - Stage: [terminate](https://banes-lab.com/records/stage/terminate.md) - Axis: [termination](https://banes-lab.com/records/reason/axis-termination.md) - Math type: [logic](https://banes-lab.com/records/reason/math-type-logic.md) - Yields: boolean Details Intent Scan a PAG document for structural and epistemic defects, each named for the shape it catches — a retired unit head, a node without a gate, a check without evidence, a gate without a population or with an empty one, an unknown left unrouted, a write without a refusal, an artifact without freshness, a node declared twice, an input naming no source, an invariant missing its set, parties or objector, a bare invariant block, a lowercase keyword, a bare FOR, a missing colon, a vague condition — and emit a token-based, regex-free verdict. Invariant A PAG document is trusted only after a deterministic well-formedness scan whose defect set is the epistemology's failure taxonomy, never because it reads fluently. Flow ```text PagDocument → DefectScan → DefectSet → WellFormednessVerdict ``` Productions ```bnf PagWellFormedness ::= "->" "->" PagDefect ::= "retired_unit_head" | "node_without_gate" | "node_tag_malformed" | "node_declared_twice" | "input_without_source" | "check_without_evidence" | "gate_without_population" | "empty_population" | "result_missing" | "unknown_unrouted" | "write_without_refusal" | "artifact_without_freshness" | "invariant_without_set" | "invariant_without_parties" | "invariant_without_objector" | "bare_invariant_block" | "gate_too_few_conditions" | "gate_too_many_conditions" | "vague_condition" | "for_without_each" | "lowercase_keyword" | "missing_colon" | "no_declaration" PagWellFormednessVerdict ::= "well_formed" | "ill_formed" ``` Composes [PAG Handoff Gate](https://banes-lab.com/records/algo/pag-validation-gate.md), [PAG Explicit Control Flow](https://banes-lab.com/records/algo/pag-explicit-control-flow.md) Named in the derivation of [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) Forces [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md), [model_governance](https://banes-lab.com/records/force/model-governance.md) Grounds none Before ```text A PAG document trusted because it reads fluently. ``` After ```text document → defect scan{retired unit head, node without gate, check without evidence, gate without population, empty population, unknown unrouted, write without refusal, artifact without freshness, node declared twice, input without source, invariant without set/parties/objector, bare invariant block, lowercase keyword, for without each, missing colon, vague condition} → well-formed | ill-formed ``` ### - Meta record Details Intent → → → → → Invariant Any PAG artifact should be treated as a structured instruction contract whose tokens are drawn from a fixed ontology grounded in the reasoning face, whose nodes are closed by evidence-bearing gates that carry their population and route unknown to blocked, and whose invariants name their objector, reducing interpretive ambiguity without guaranteeing deterministic output. Flow ```text DocumentType → Keywords → Nodes → Gates → OperationsAndStructure → Invariants → WellFormedness ``` Productions ```bnf PagInstructionConcern ::= "->" "->" "->" "->" "->" "->" "->" ``` Composes none Forces [metaprogramming_modeling](https://banes-lab.com/records/force/metaprogramming-modeling.md), [model_governance](https://banes-lab.com/records/force/model-governance.md), [semantic_consistency](https://banes-lab.com/records/force/semantic-consistency.md), [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) Grounds none ## Links to - [Orient](https://banes-lab.com/records/stage/orient.md) - [Ontology](https://banes-lab.com/records/reason/axis-ontology.md) - [Set Theory](https://banes-lab.com/records/reason/math-type-set-theory.md) - [PAG Authoring Kernel](https://banes-lab.com/records/algo/pag-authoring-kernel.md) - [semantic_consistency](https://banes-lab.com/records/force/semantic-consistency.md) - [contract_compatibility](https://banes-lab.com/records/force/contract-compatibility.md) - [metaprogramming_modeling](https://banes-lab.com/records/force/metaprogramming-modeling.md) - [See](https://banes-lab.com/records/stage/see.md) - [Analysis](https://banes-lab.com/records/reason/axis-analysis.md) - [correctness_verification](https://banes-lab.com/records/force/correctness-verification.md) - [Project](https://banes-lab.com/records/stage/project.md) - [Reasoning](https://banes-lab.com/records/reason/axis-reasoning.md) - [Graph](https://banes-lab.com/records/reason/math-type-graph.md) - [modularity](https://banes-lab.com/records/force/modularity.md) - [domain_boundary](https://banes-lab.com/records/force/domain-boundary.md) - [Verify](https://banes-lab.com/records/stage/verify.md) - [Verification](https://banes-lab.com/records/reason/axis-verification.md) - [Logic](https://banes-lab.com/records/reason/math-type-logic.md) - [PAG Well-Formedness Validation](https://banes-lab.com/records/algo/pag-well-formedness-validation.md) - [model_governance](https://banes-lab.com/records/force/model-governance.md) - [Ver Evidence](https://banes-lab.com/records/reason/node-ver-evidence.md) - [Ver Population](https://banes-lab.com/records/reason/node-ver-population.md) - [Ver Refusal](https://banes-lab.com/records/reason/node-ver-refusal.md) - [Ver Standing](https://banes-lab.com/records/reason/node-ver-standing.md) - [Ter Block](https://banes-lab.com/records/reason/node-ter-block.md) - [Act](https://banes-lab.com/records/stage/act.md) - [Formalisation](https://banes-lab.com/records/reason/axis-formalisation.md) - [control_coordination](https://banes-lab.com/records/force/control-coordination.md) - [Constrain](https://banes-lab.com/records/stage/constrain.md) - [Teleology](https://banes-lab.com/records/reason/axis-teleology.md) - [Optimisation](https://banes-lab.com/records/reason/math-type-optimisation.md) - [security_governance](https://banes-lab.com/records/force/security-governance.md) - [Computation](https://banes-lab.com/records/reason/math-type-computation.md) - [runtime_extensibility](https://banes-lab.com/records/force/runtime-extensibility.md) - [event_messaging](https://banes-lab.com/records/force/event-messaging.md) - [causality_ordering](https://banes-lab.com/records/force/causality-ordering.md) - [Derive](https://banes-lab.com/records/stage/derive.md) - [PAG Document Declaration](https://banes-lab.com/records/algo/pag-document-declaration.md) - [PAG Keyword Ontology](https://banes-lab.com/records/algo/pag-keyword-ontology.md) - [PAG Node Decomposition](https://banes-lab.com/records/algo/pag-node-decomposition.md) - [PAG Handoff Gate](https://banes-lab.com/records/algo/pag-validation-gate.md) - [PAG Explicit Control Flow](https://banes-lab.com/records/algo/pag-explicit-control-flow.md) - [PAG Semantic Operation](https://banes-lab.com/records/algo/pag-tool-invocation.md) - [PAG Structure Declaration](https://banes-lab.com/records/algo/pag-coordination-construct.md) - [PAG Invariant Record](https://banes-lab.com/records/algo/pag-constraint-boundary.md) - [The derivation loop](https://banes-lab.com/ontology/reasoning/reason-loop-derivation-loop.md) - [Terminate](https://banes-lab.com/records/stage/terminate.md) - [Termination](https://banes-lab.com/records/reason/axis-termination.md)