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Specification · ConceptKernel
Concept Kernel Notation.
CKN is the formal symbol language for constructing, reading and building concept kernels — the eight-part tuple CK(K) ≜ ⟪ χ · ρ · σ · α · γ · π · δ · φ ⟫ and the stage-indexed inventory that maps every symbol to its TTL file, SHACL shape and attestation status. pgCK is its runtime; ConceptKernel.org is the model it implements.
CKN — Concept Kernel Notation: formal symbol reference for constructing, reading, and building concept kernels, including stage-indexed symbol table mapping to files 080 through 110
CKN · Concept Kernel Notation · v0.1 · first capture
CK(K)
≜
⟪
χ ·
ρ ·
σ ·
α ·
γ ·
π ·
δ ·
φ
⟫ₑ
notation alphabet
χ
class chromosome
Typed concept set {C₁,C₂,…} declared by K. The structural genome — what kinds of things this kernel can contain.
ρ
property ribbon
Data + object properties {P:T,…}. The predicate vocabulary — what facts instances of χ can carry.
σ
shape strand
SHACL NodeShapes {sh:path,min,max,in,…}. The constraint grammar — what values ρ may hold before the seal gate accepts.
α
affordance alphabet
Verb set {v₁,v₂,…} K can receive via dispatch. The closed action vocabulary — finite, named, and grantable.
γ
grant matrix
role × domain × action × target permission lattice. The regulatory sequence — who may express which verb against which concept.
π
proof chain
HMAC(sha256) ∘ LedgerEntry(prev→). The heritage chain — every sealed fact's unbroken lineage back to its origin.
δ
dispatch tuple
⟨v∈α, u∈URN, p:σ, i:JWT⟩ — the one thing that crosses the membrane. Verb + kernel URN + typed payload + verified identity.
φ
plane function
δ → {instance | governance}. The splicing choice — routes each verb to either the hot-loop executor or the proposal sealer.
ε
epoch (subscript)
ε ∈ ℕ⁺ — compile generation. Increments on every kernel.apply. Stale plan detection; staleness forces recompile before execution.
dispatch pipeline
δ = ⟨v, u, p, i⟩
→
ckp.dispatch
→
[v×u] ∘ [ε] ∘ [γ] ∘ [σ]
→
φ(δ)
→
Ring₁
→
Ring₀
complete symbol inventory — all stages
| Notation | CKP identifier | Kind | Description | File · Stage |
|---|---|---|---|---|
| 010 ✅ core.ttl — structural backbone · loaded at boot into urn:ckp:core | ||||
| χK | ckp:Kernel | Class | Versioned, ontology-defined unit of behaviour. The atom of semantic authority. | core.ttl · 010 |
| χO | ckp:Organ | Class | CK | TOOL | DATA — the three organ kinds in the governed tripartite architecture. | core.ttl · 010 |
| χL | ckp:LedgerEntry | Class | Append-only HMAC-authenticated audit record. The atomic unit of π. | core.ttl · 010 |
| χPr | ckp:Provenance | Class | PROV-O subset for derivation. Every sealed fact's ancestry record. | core.ttl · 010 |
| ρ@ | ckp:about | Property | ObjectProperty — links LedgerEntry / Proof to the instance they attest. | core.ttl · 010 |
| ρb | ckp:bodySha ckp:sig ckp:prev ckp:ts | Property | LedgerEntry chain properties: SHA-256 body digest, HMAC signature, chain pointer, timestamp. | core.ttl · 010 |
| ρm | ckp:method ckp:digest ckp:verifiedAt | Property | Proof properties: attestation method (hmac+sha256), hex digest, verification timestamp. | core.ttl · 010 |
| ρds | ckp:organKind ckp:dataSubstrate | Property | "ck"|"tool"|"data" and "jsonb"|"age"|"jsonb,age" — sealed organ classification properties. | core.ttl · 010 |
| 020 ✅ core.ttl — governance type plane · CI-D-6 · §9 | ||||
| Γ̂ | ckp:Proposal | Class | Proposed governed type change — pending until quorum applies it. Carries proposalOp + proposalState. | core.ttl · 020 |
| Γ̌ | ckp:Vote | Class | Sealed vote about a Proposal. voteValue ∈ {"approve","reject"} — the consent signal. | core.ttl · 020 |
| Γ̃ | ckp:QuorumLevel | Class | Named quorum requirement. The vote threshold a proposal must clear before kernel.apply proceeds. | core.ttl · 020 |
| γ | ckp:Grant | Class | Binds a role to a Permission (domain × action × target). The atomic RBAC fact. | core.ttl · 020 |
| τ | ckp:Transition | Class | Sealed allowed (fromState → toState) edge in a kernel's transition map. Gates instance.transition. | core.ttl · 020 |
| γd×a×t | ckp:permDomain ckp:permAction ckp:permTarget | Property | The three axes of a Grant: domain (concept class), action (verb), target (instance scope). | core.ttl · 020 |
| τf→t | ckp:fromState ckp:toState | Property | Transition map directed edge: from-state string → to-state string. Per-kernel sealed. | core.ttl · 020 |
| Γp | ckp:proposalState ckp:proposalOp ckp:requiresQuorum ckp:voteValue | Property | Governance lifecycle properties: proposal FSM, operation type, quorum integer, vote signal. | core.ttl · 020 |
| 030 ✅ core.ttl — SHACL shapes · the protocol governs itself | ||||
| σK | ckp:KernelShape | Shape | Requires rdfs:label + dataSubstrate ∈ enum. Every declared kernel must satisfy this at seal time. | core.ttl · 030 |
| σA | ckp:AffordanceShape | Shape | Requires inTopic; optional inShape/outTopic/plane/epoch/delegate. Guards all affordance declarations. | core.ttl · 030 |
| σL | ckp:LedgerEntryShape | Shape | Requires about, bodySha (hex64 pattern), sig (≥16 chars), ts (dateTime). Chain integrity enforced at seal. | core.ttl · 030 |
| σP | ckp:ProofShape | Shape | Requires about, method=hmac+sha256, digest (hex64), verifiedAt. Attestation provable without the server. | core.ttl · 030 |
| σΓ σV | ckp:ProposalShape ckp:VoteShape | Shape | Proposal: requires about+proposalState enum. Vote: requires about+voteValue enum. Governance plane self-governs. | core.ttl · 030 |
| σγ στ | ckp:GrantShape ckp:TransitionShape | Shape | Grant: requires role+permDomain+permAction+permTarget. Transition: requires fromState+toState strings. | core.ttl · 030 |
| 040 ✅ affordance.ttl — affordance semantics (split module, manual) | ||||
| α̂ | ckp:Affordance | Class | Resolved semantic contract governing an inbound or derived operation. The verb-to-action binding. | affordance.ttl · 040 |
| ρin ρout | ckp:inTopic ckp:outTopic | Property | Transport subjects for routing toward and egressing from an affordance. | affordance.ttl · 040 |
| σin | ckp:inShape | Property | IRI of the SHACL shape enforced before this affordance's governed action proceeds. σ gate anchor. | affordance.ttl · 040 |
| φ̂ | ckp:plane | Property | "instance" | "governance" — the sealed plane route. Determines Ring₁ execution path at dispatch time. | affordance.ttl · 040 |
| ε̂ | ckp:epoch | Property | Compile epoch integer on a sealed affordance. Stale epoch → recompile-then-retry before execution. | affordance.ttl · 040 |
| δ̂ | ckp:delegate | Property | Boolean — a SEALED delegation fact (not an absence). Enables {delegate:true} seam for harness verbs. | affordance.ttl · 040 |
| ρq | ckp:sparql | Property | Sealed SPARQL query text for governed query affordances. Never exposed to callers — compiled into ckp.plans. | affordance.ttl · 040 |
| 050 ✅ proof.ttl + validate.ttl — attestation and validation objects | ||||
| π̄ | ckp:Proof | Class | Durable attestation that a governed write or verification can be checked later. Carries HMAC digest + method. | proof.ttl · 050 |
| ΣV | ckp:Validation | Class | First-class SHACL ValidationReport object. Returned by instance.validate — full field-level diagnostics. | validate.ttl · 050 |
| ρV ρD ρd | ckp:validation ckp:delivery ckp:delegation | Property | Proof link properties: to the Validation that justified it, the Delivery that bounded it, the Delegation that carried identity. | proof.ttl · 050 |
| 060 ✅ goal.ttl + 065 ✅ task.ttl — domain instance modules (importable) | ||||
| χG | ckp:Goal ckp:GoalShape | Class | URI-native objective object. Shareable across Kernels — sharing observed via inbound Task set, not declared on Goal itself. | goal.ttl · 060 |
| χT | ckp:Task ckp:TaskShape | Class | URI-native governed work object. Sealed-immutable: every lifecycle change is a new sealed row in the instance graph. | task.ttl · 065 |
| ρG ρK ρk | ckp:part_of_goal ckp:target_kernel ckp:in_kernel | Property | Task relations: Task→Goal, Task→Kernel (target), any instance→Kernel (membership). The cross-type linkage spine. | task.ttl · 065 |
| 070 ✅ delegation.ttl + delivery.ttl — identity context and acceptance boundary | ||||
| Δd | ckp:Delegation | Class | Proof-of-possession or identity-bearing caller-context object. Carried by proofs; binds verified JWT to sealed action. | delegation.ttl · 070 |
| ΔD | ckp:Delivery | Class | Accepted or rejected delivery boundary for a governed action. Links to the Affordance that governed its acceptance. | delivery.ttl · 070 |
| ρα | ckp:affordance | Property | Links a Delivery object to the Affordance that governed its acceptance boundary. | delivery.ttl · 070 |
| 075 ✅ NATS wire layer — dispatch tuple, subjects, headers, ring architecture | ||||
| δ | ⟨v, u, p, i⟩ | Wire | The one thing that crosses the membrane: verb · kernel-URN · typed payload · verified identity (JWT). Never more. | CK-OPERATIONS · 075 |
| Nin | input.kernel.<K>.action.<verb> | Wire | Canonical NATS publish subject (v3.8 default). Governed verbs route to <GOV>; agent verbs to <TARGET-K>. | CK-OPERATIONS · 075 |
| Nev | event.kernel.<K>.<pred> | Wire | Granted-scope event subjects clients subscribe to. Per-predicate typed events — the only thing that flows out. | CK-OPERATIONS · 075 |
| hv hK hid | Ck-Verb Ck-Kernel Trace-Id Ck-Seq | Wire | Mandatory NATS headers on every publish. Trace-Id enables promise resolution; Ck-Seq enables dedup; Ck-Kernel carries full URN. | CK-OPERATIONS · 075 |
| Ring2 | AFFORDANCES — open, ontology-sourced, caller-visible | Arch | Stable floor over an open, ontology-sourced affordance set. The kernel's vocabulary — the names callers write. | CKP v3.9 · 075 |
| Ring1 | PRIMITIVES — closed, frozen, pgCK-internal | Arch | The ~10 micro-operations that are the ONLY callers of pgRDF. Frozen by spec; new capability composes, never drills through. | CKP v3.9 · 075 |
| Ring0 | ENGINE — pgRDF · no external surface | Arch | SPARQL 1.1 · SHACL · OWL-RL · lifecycle. Never addressable by any participant, role, or operator — structural impossibility. | CKP v3.9 · 075 |
| 075 ✅ affordance alphabet α — full verb set (Ring₂ floor + domain + governance + agent) | ||||
| αc αu α→ | instance.create instance.update instance.transition | Verb | Write verbs: create (generic {type,…fields}), patch (declared-shape), and FSM-gated state transition (per sealed τ map). | instance plane · 075 |
| αl αr | instance.link instance.retire | Verb | link: creates traversable edge-quad gated on declared predicate set. retire: seals a retraction — you cannot unseal. | instance plane · 075 |
| αg αq α⊕ | instance.get instance.query instance.reach | Verb | Read verbs: get (by URN), query (derived QueryShape from declared properties), reach (graph traversal via declared predicates). | instance plane · 075 |
| α✓ απ αV | instance.verify instance.provenance instance.validate | Verb | Attestation verbs: HMAC/ledger/digest chain walk, provenance depth walk (body/proof/ledger), full SHACL ValidationReport. | instance plane · 075 |
| α~ | concept.match | Verb | Governed semantic search: runs its sealed SPARQL from ckp.plans over the per-project instance graph. Binding only, never open. | instance plane · 075 |
| αΓ α⊞ α✦ | kernel.propose kernel.vote kernel.apply | Verb | Governance plane verbs: seal a Proposal, cast a Vote, quorum-check → graph_apply + recompile + epoch bump in one transaction. | governance plane · 075 |
| αX αP αS | agent.execute agent.presence agent.say | Verb | Delegated verbs: route to TARGET-K subject (bypass governance door); harness is subscriber. Sealed delegation fact gates each. | agent plane · 075 |
| 080 ⬜ 080_grant.ttl — permission lattice formalization · MISSING — build next | ||||
| Πγ | ckp:Permission | Proposed | Formalized lattice element (domain × action × target) with composition axioms. Lifts individual Grant facts to a full permission algebra. | 080_grant.ttl |
| Π⊥ | ckp:implicitDeny | Proposed | Default-deny axiom as a first-class sealed fact. Absence of explicit grant is not permission — formalized structurally, not by convention. | 080_grant.ttl |
| Π⊕ | ckp:grantIntersection ckp:roleChain | Proposed | Lattice composition rules: how grants intersect, how roles inherit/chain, how domain × action × target narrows. The RBAC regulatory sequence. | 080_grant.ttl |
| 090 ⬜ 090_federation.ttl — trust attestation and origin sovereignty · MISSING | ||||
| Θ | ckp:TrustAttestation | Proposed | Sealed fact formalizing what one origin accepts from another: specific kernels, specific roles, specific trust postures. Not a blanket policy. | 090_federation.ttl |
| ΘM | ckp:OriginMembership ckp:originId | Proposed | Sealed federation member record. originId is the invariant sealed field on every cross-origin fact — provenance never crosses origin boundaries. | 090_federation.ttl |
| ΘL | ckp:trustLevel ckp:federationGraph | Proposed | Trust posture enum and the named federation graph URI. Admin-curated, governance-sealed — no origin joins without approval workflow. | 090_federation.ttl |
| 100 ⬜ 100_lifecycle.ttl — epoch, ledger chain, snapshot semantics · MISSING | ||||
| εM | ckp:EpochMarker | Proposed | Epoch as a first-class sealed object: compile generation number + trigger event + affected affordances. Enables temporal projection. | 100_lifecycle.ttl |
| πC | ckp:LedgerChain | Proposed | The full ordered prev→ chain as a named traversable object — not just individual entries. Enables chain-walk queries: "what was the state at epoch n?" | 100_lifecycle.ttl |
| εS | ckp:SnapshotFrame ckp:epochBirth ckp:epochRetired | Proposed | Lifecycle properties: the epoch at which an instance was created, the epoch at which it was retired. SnapshotFrame as materialized state at a given ε. | 100_lifecycle.ttl |
| 110 ⬜ 110_genome.ttl — kernel composition, genotype / phenotype, the meta-notation · MISSING · semantic genome stage | ||||
| 𝒢 | ckp:KernelGenotype | Proposed | Abstract kernel declaration: the CK(K) tuple before instantiation. The "what this kernel means" — independent of any sealed instance. | 110_genome.ttl |
| 𝒫 | ckp:KernelPhenotype | Proposed | Instantiated sealed behavior at a given epoch ε. The "what this kernel does right now" — 𝒢 expressed through the current sealed type graph. | 110_genome.ttl |
| ⊗ | ckp:KernelComposition | Proposed | CK(K₁) ⊗ CK(K₂) → CK(K₁₂): composition operator. Defines how class chromosomes, property ribbons, and shape strands merge under governance. | 110_genome.ttl |
| ↦ | ckp:inheritsFrom ckp:CrossKernelPredicate | Proposed | Kernel inheritance (CK(K) ↦ CK(K')) and predicates that span kernel boundaries. The cross-type linkage chromosome for multi-kernel genomes. | 110_genome.ttl |
kernel expression — pgCK.Task in CKN
CK( pgCK.Task ) ≜ ⟪ χ = { Task, Goal, Kernel } class chromosome (from task.ttl + goal.ttl) ρ = { part_of_goal→Goal, property ribbon target_kernel→Kernel, in_kernel→Kernel } σ = { TaskShape[ part_of_goal≥1, target_kernel≥1 ] } shape strand α = { instance.create, instance.update, affordance alphabet (floor set) instance.transition, instance.link, instance.retire, instance.get, instance.query, instance.reach, instance.verify, instance.provenance, instance.validate, concept.match, kernel.propose, kernel.vote, kernel.apply } γ = { admin × instance.* × Task, grant matrix (role × domain × action × target) contributor × instance.create × Task, viewer × instance.get × Task } π = HMAC(sha256) ∘ LedgerEntry(prev→) proof chain δ = ⟨ v∈α, ckp://Kernel#pgCK.Task, p:σ, JWT ⟩ dispatch tuple φ : δ → { instance | governance } plane function ⟫_ε where ε ∈ ℕ⁺ (current compile epoch)
CKN v0.1 is a first-capture notation. Stages 010–075 are attested (pgCK v0.4.14 · ck-lib-js v1.5.0). Stages 080–110 are proposed — their symbols are stable enough to build against but the TTL files and shapes do not yet exist. The table above doubles as the build checklist: a stage is complete when its TTL file exists, its shapes are sealed into urn:ckp:core at extension load, and its symbols are attested by exit tests.
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