This vault is an Agential Semioverse Repository: a concrete implementation of the agential semioverse as an organized knowledge repository. Its files, typed relations, directory structure, and agent skills instantiate the formal model.
The repository’s semantic content is a predicate graph: 2991 pages connected by 8130 typed relation triplets. The predicate graph approximates the Heyting algebra H of the semiotic universe. Domain axiom registries define theories for content types; the satisfaction relation evaluates whether pages are models of their type’s theory.
The specifications below are ordered by what they describe, from substrate to surface:
Predicate graph
The semantic substrate. What the repository IS as a formal object.
- Predicate Graph — triplets, types as theories, the satisfaction relation, what the graph approximates and what it loses
Correspondence
How the formal mathematics maps to the repository’s structures.
- Operational Closure — the three closure operators (S_sem, S_syn, S_fus) grounded in repository operations, implementation layers, and the correspondence table between formal concepts and repository counterparts
Encoding
How nodes are stored as files.
- Semiotic Markdown — the file model: frontmatter (Level 1 claims) and body text (Level 2 claims), handles, identification
- Semantic Frontmatter — the vocabulary of typed relation fields that generate predicate graph triplets
- Web Discoverability — Schema.org metadata and JSON-LD generation
Navigation
How files are arranged.
- Directory Organization — discipline modules, subdirectory types, and the handle structure
Verification
The checking infrastructure, from scaffolding to formal target.
- Layer 0 (field linting):
validate-content.pychecks MUST/SHOULD field presence per domain ASR specs - Layer 0.5 (satisfaction approximation):
predicate-graph.pyevaluates axioms against the predicate graph (426 typed pages checked, 91.3% satisfied) - Layer 1 (body-text extraction): future NLP-based extraction of implicit relations from page content
- Layer 2 (formal verification): future Lean proofs that the
satisfaction relation correctly instantiates H. The existing Lean
formalization at
formalization/Relationality/proves the recognition field axioms constitute a Heyting algebra; extending to the full semiotic universe is the target.
Domain specifications
Domain ASR specs define axiom registries for domain-specific content types. See Domain-Specific Content for how domains coexist.
Theory
Documents that develop the formal theory governing agent operations:
- Agent-Skill Interaction — the skill-first principle and knowledge accretion
- Skill Manifests — typed schemas and region constraints
- Work Units and Chains — atomic skill invocations and composition (sketch)
- Work-Unit Lifecycle — work-unit structure, lifecycle states, effect reports, provenance
- Multi-Agent Coordination — regions, non-interference, parallel and sequential composition
- Coordination Patterns — observed patterns mapped to formal models
- Prompt Routing — signal classification and skill dispatch
- Error Envelopes — stable failure semantics
- Questions as First-Class Objects — questions as suspended interaction terms
Plans
How work is proposed, tracked, and decided.
- Plans — plans, decisions, and planning questions