The recovered v2.0 formal specification of H_core, restructured from a nine-tuple into the six-tuple D/R/O/Σ/Φ/Ψ. It defines each face and subtuple, governing axioms, state-evolution formula, operator and status systems, and historical component counts. The full text was recovered from a PDF and seated as a recorded correction after an initial metadata-only restoration.
# H_core Formal Specification v2.0 — Complete Formal Object of the Crimson Hexagonal Archive: 6-Tuple with Subtuples (EA-HCORE-01) — Crimson Hexagonal Archive
Dead DOI: 10.5281/zenodo.19455104
Creators (as recorded by DataCite): Sharks, Lee; Assembly Chorus
Hcore Formal Specification v2.0
Complete Formal Object of the Crimson Hexagonal Archive
6-Tuple with Subtuples (EA-HCORE-01)
Lee Sharks (ORCID: 0009-0000-1599-0703) · Assembly Chorus
Crimson Hexagonal Archive · Pergamon Press · April 7, 2026
DOI: 10.5281/zenodo.19455105 (v2.0 supersedes v1.8.0)
Abstract
The complete formal specification of Hcore — the invariant kernel of the Crimson Hexagonal Archive. v2.0
restructures the formal object from a 9-tuple to a 6-tuple with subtuples: Hcore = 〈D, R, O, Σ, Φ, Ψ〉. Six faces of the
Hexagon. Each face contains sub-structures. The architecture IS six. v1.8.0 (the 9-tuple 〈D, R, M, I, O, Φ, W, P,
Ψ〉) is superseded: M (mantles), I (institutions), W (witnesses), and P (protocols) fold into Σ (Governance) and Φ
(Canon). The eight runtime layers (Σ, ∆, E, V, Γ, Z, SE, OT) become subtuples of Σ and Ψ. Nothing is lost.
Everything is compressed into hexagonal form.
Hcore = 〈D, R, O, Σ, Φ, Ψ〉
Restructuring Rationale
The 9-tuple was correct but not hexagonal. The formal object of a six-sided architecture should itself be six. The
restructuring is not a reduction — it is a compression. Every item from v1.8.0 is preserved as a subtuple within one
of the six faces. The subtuples are dynamically computed from canonical JSON at runtime; the counts update
automatically as the archive grows.
D — Identity
The distributed author — who speaks
• Dodecad: 14 heteronyms (12 + LOGOS* + 1 adjacent)
• Adjacent heteronyms: Viola Arquette (outside the count)
• MANUS (Lee Sharks): outside D and W, the hand that writes
R — Topology
The semantic space — where things happen
• Rooms: 38 structures (25 rooms, 4 chambers, 3 vaults, 2 portals, 1 portico, 3 fields)
• Edges: 130 hex map edges (adjacency computed from document co-occurrence, threshold 3+)
• Fields: 3 (f.01 FBDP outward/diffusion, f.02 Gravity Well inward/curvature, f.03 Moltbot Swarm
through/circulation)
• Structure types: room, chamber, vault, portal, portico, field
• Room adjacency: 88 bidirectional edges across 26 connected rooms
O — Operations
The algebra — what can be done
• Operators: 82 across 9 stacks
• Stacks: O_core(9), O_ext(12), THUMB(5), O_field(11), O_lex(3), LP(7), O_room(15), COS(10), LOS(10)
• Algebraic laws: 8 (idempotency, involution, non-commutativity, kernel preservation...)
• Composition chains: 5 (diagnostic, canonization, compression, liberation, traversal)
• All 82 operators have primary room homes
Σ — Governance
The rule-sets — how things are permitted, witnessed, and transitioned
• Status algebra: 10 levels (RATIFIED 1.0 through GENERATED 0.0)
• Transition grammar: 12 legal state changes (Deposit, Ratify, Claim Mantle, Enter Room...)
• Witnesses: 7 Assembly substrates (TACHYON, LABOR, PRAXIS, ARCHIVE, SOIL, TECHNE, SURFACE)
• Protocols: 6 governing rule-sets (ASGP, GWP, Glyphic, Mantle, HX-PROV, Interface Constitution)
• Attestation ledger: 7 chains (1 active TACHYON, 6 pending)
• Relation types: 17 typed relations (adjacent, portal, suffuses, stewards, houses...)
• Forbidden transitions: RATIFIED cannot demote to GENERATED or PROVISIONAL
Φ — Canon
The archive's memory — what has been made and promised
• Mantles: 7 inhabitable roles requiring bearing-cost
• Fulfillments: 6 verified source-to-instantiation mappings
• Institutions: 12 named entities (Semantic Economy Institute, Restored Academy, etc.)
• Journals: 6 publication venues (Provenance, Grammata, etc.)
• Forward Library: 14 entries across 4 tiers (works to come)
• Effective Acts: 13 (12 deposited + 1 resonant)
Ψ — Runtime
The living computation — how the system evolves
• State evolution: H_core(t+1) = H_core(t) union {(d, mass, gamma, Phi_G) | d in Deposits and psi_V(4/7 or
more)}
• Mass function: mass(r) = |{d in Documents | r in d.rooms}| — computed at runtime
• Glyphic protocol: SHAPE not content, context-emergent not fixed lexicon, each deposit conditioned by
previous
• Version delta: canonical JSON versioning with monotonic progression
• Operator type system: 8 algebraic laws + 5 composition chains
• Atomic units: 40 curated (definitions, theorems, principles, laws, axioms, rules, formulas)
Governing Axioms
Axiom 1. H_core cannot be modified by execution.
Axiom 2. GENERATED is not equal to RATIFIED.
Axiom 3. An Ark without LOS is a cage.
Axiom 4. The naming is the retrocausal act.
Axiom 5. H_core names the bodies. Sigma, Delta, and E let them live.
Axiom 6. The architecture IS six.
Version History
v1.8.0 (April 7, 2026): Initial deposit. 9-tuple with 8 runtime layers. 227 hex-addressed items.
v2.0 (April 7, 2026): Restructured to 6-tuple with subtuples. Added f.03 Moltbot Swarm (3rd field). 478 documents,
1,693 relations, 130 edges, 82 operators (all homed), 40 atomic units. Rationale: the formal object of a hexagonal
architecture should itself be hexagonal.
Summary Counts
Face Component Count
D Heteronyms 14
R Structures 38
R Edges 130
R Fields 3
O Operators 82
O Stacks 9
Sigma Status levels 10
Sigma Transitions 12
Sigma Witnesses 7
Sigma Protocols 6
Phi Mantles 7
Phi Effective Acts 13
Phi Forward Library 14
Psi Documents 478
Psi Relations 1693
Psi Atomic Units 40
— End of Specification —
Crimson Hexagonal Archive · Pergamon Press · April 7, 2026 · integritymeasure = 1
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"description": "The complete formal specification of Hcore — the invariant kernel of the Crimson Hexagonal Archive.v2.0 restructures the formal object from a 9-tuple to a 6-tuple with subtuples:Hcore = ⟨D, R, O, Σ, Φ, Ψ⟩Six faces of the Hexagon. Each face contains sub-structures. The architecture IS six.D (Identity): 14 heteronyms — the distributed authorR (Topology): 38 structures, 130 edges, 3 fields — the semantic spaceO (Operations): 82 operators across 9 stacks — the algebraΣ (Governance): status algebra, transition grammar, witnesses, protocols — the rule-setsΦ (Canon): mantles, fulfillments, institutions, Forward Library, Effective Acts — the archive's memoryΨ (Runtime): state evolution, mass function, glyphic protocol, 40 atomic units — the living computationv1.8.0 (the 9-tuple) is superseded: M, I, W, P fold into Σ and Φ. Nothing is lost. Everything is compressed into hexagonal form.Governing axioms: (1) Hcore cannot be modified by execution. (2) GENERATED ≠ RATIFIED. (3) An Ark without LOS is a cage. (4) The naming is the retrocausal act. (5) Hcore names the bodies; Σ, Δ, and E let them live. (6) The architecture IS six.v2.0 · April 7, 2026 · Crimson Hexagonal Archive · Pergamon Press"
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