the model

core · V1–V5.4 (C1–C17)

• ▸C1φ optimal S/M ratio (open)

  Golden ratio φ is optimal S/M (protect:project) ratio

  conf openstatus openregister corehome formal spec §17.1
• ▸C2A(τ) logarithmic (open)

  A(τ) should be logarithmic

  conf openstatus openregister corehome formal spec §17.1
• ▸C3challenged

  Edge value is additive

  conf —status challenged (path integral replaces)register corehome formal spec §17.3
• ▸C4resolved

  96 vs 64 discrepancy

  conf —status resolved (holographic + algebraic)register corehome formal spec §17.3
• ▸C5resolved

  ~3,000× ZKP reduction

  conf —status resolved (strengthened by BRAID + holographic bound)register corehome formal spec §17.3
• ▸C6P^1.5 ↔ 96/64 convergent 35%

  P^1.5 ↔ 96/64 is structural

  conf 35%status convergentregister corehome formal spec §17.1
• ▸C7three-axis multiplicative 30% · falsification frontier

  Three-axis separation is multiplicative

  conf 30%status active · V6 falsification frontierregister corehome formal spec §17.1
• ▸C8BRAID reduces R_max 45%

  BRAID compression reduces R_max

  conf 45%status activeregister corehome formal spec §17.1
• ▸C9holographic sufficiency 25%

  Holographic boundary sufficiency

  conf 25%status activeregister corehome formal spec §17.1
• ▸C10O(1) shared-parent 20%

  O(1) shared-parent modifies k

  conf 20%status activeregister corehome formal spec §17.1
• ▸C11behavioural density 55%

  Behavioural density ρ amplifies privacy, indicates maturity

  conf 55%status activeregister corehome formal spec §17.1
• ▸C12hexagram resonance 60%

  Hexagram encoding is structurally resonant

  conf 60%status activeregister corehome formal spec §17.1
• ▸C13bilateral witness quantum-resistant 65%

  Bilateral witness as quantum-resistant primitive

  conf 65%status activeregister corehome formal spec §17.1
• ▸C14Φ_agent ≅ D₂ₙ 75%

  Φ_agent ≅ D₂ₙ dihedral isomorphism

  conf 75%status activeregister corehome formal spec §17.1
• ▸C15T_∫ ≅ UOR pipeline 65%

  T_∫(π) ≅ UOR resolution pipeline

  conf 65%status activeregister corehome formal spec §17.1
• ▸C16Betti invariants 25%

  Topological trust invariants via Betti numbers

  conf 25%status activeregister corehome formal spec §17.1
• ▸C17amnesia > policy 60% · quantitative via C83

  Amnesia-enforced separation tighter than policy-enforced

  conf 60%status active · made quantitative at V6 Run 2register corehome formal spec §17.1

V6 series · April 2026 (C18–C37)

• ▸C18-C21Lorenz dynamical ceiling 10-30%

  C18Sovereignty path exhibits strange attractor dynamics (λ > 0); dynamical reconstruction ceiling

  conf 25%status activeregister sharedhome pvm-v6-lorenz-attractor.md

  C19ρ is Lyapunov divergence accumulated over the walk

  conf 20%status activeregister sharedhome pvm-v6-lorenz-attractor.md

  C20Three axes couple as three Lorenz variables

  conf 30%status activeregister sharedhome pvm-v6-lorenz-attractor.md

  C21Sovereignty manifold has fractal dimension

  conf 10%status activeregister sharedhome pvm-v6-lorenz-attractor.md
• ▸C22-C25EML three ceilings 15-30%

  C22Reconstruction cost grows exponentially with EML tree depth

  conf 20%status activeregister sharedhome pvm-v6-eml-three-ceilings.md

  C23Blade forge grammar isomorphic to restricted EML grammar

  conf 30%status activeregister sharedhome pvm-v6-eml-three-ceilings.md

  C24Sovereignty computation requires complex intermediates

  conf 15%status activeregister sharedhome pvm-v6-eml-three-ceilings.md

  C25Minimal EML tree depth is hard floor for compression spectrum

  conf 25%status activeregister sharedhome pvm-v6-eml-three-ceilings.md
• ▸C26-C29ARCH-1 canonical form 20-40%

  C26ARCH-1 is canonical form of NAND, EML, succ as co-instances

  conf 40%status activeregister sharedhome pvm-v6-arch1-canonical-form.md

  C27ρ is the activation mechanism; Ω without ρ is inert

  conf 35%status activeregister sharedhome pvm-v6-arch1-canonical-form.md

  C28Three ceilings independent because ARCH-1 factors into β / μS / Ω

  conf 30%status activeregister sharedhome pvm-v6-arch1-canonical-form.md

  C29The Second Person Lift: You := μS.(β ∨ Ω(S,S))

  conf 20%status activeregister sharedhome pvm-v6-arch1-canonical-form.md
• ▸C30-C33Bakhta half-life 45-60%

  C30Trust half-life begins at inscription; decays until renewed

  conf 60%status activeregister sharedhome pvm-v6-1-bakhta-half-life.md

  C31Half-life differs by inscription register (shielded vs transparent)

  conf 55%status activeregister sharedhome pvm-v6-1-bakhta-half-life.md

  C32Productive trust-edges have higher half-life than transactional

  conf 50%status active · C46 restates thisregister sharedhome pvm-v6-1-bakhta-half-life.md

  C33Half-lives compose multiplicatively across the three axes

  conf 45%status activeregister sharedhome pvm-v6-1-bakhta-half-life.md
• ▸C34-C37wound and cap 50-60%

  C34Convergence requires a bijective cap

  conf 55%status activeregister sharedhome pvm-v6-convergence-wound-and-cap.md

  C35The wound is where the architectural asymmetry lives

  conf 60%status activeregister sharedhome pvm-v6-convergence-wound-and-cap.md

  C36The cap is where the bijection lives or breaks

  conf 55%status activeregister sharedhome pvm-v6-convergence-wound-and-cap.md

  C37Convergence is recognition, not coincidence

  conf 50%status activeregister sharedhome pvm-v6-convergence-wound-and-cap.md

the bound collection (C38–C46)

• ▸C38bilateral ARCH-1 40%

  Bilateral ARCH-1: Σ_ij := μS.(β_ij ∨ Ω(S_i, S_j)) preserves fixpoint

  conf ~40%status activeregister sharedhome formal spec §17.2.1 · Tome IV Act III
• ▸C39kindred-blade 50%

  Kindred-blade as ecosystem-layer primitive

  conf ~50%status activeregister sharedhome formal spec §17.2.1 · Tome IV Act V
• ▸C40Zcash dual-ledger 70%

  Zcash dual-ledger preserves Eight Cloak Properties

  conf ~70%status active · KEEPS this number (see G1 disposition 1)register sharedhome formal spec §17.2.1
• ▸C41observation

  61.8/38.2 transparent/shielded inscription ratio as cultural norm

  conf —status observationregister sharedhome formal spec §17.2.1
• ▸C42stake sybil resistance 50%

  Stake economics generate Sybil resistance ≥ tier accumulation

  conf ~50%status active · V6 Run 5 adversary-regime contextregister sharedhome formal spec §17.2.1
• ▸C43per-VRC viewing-key 60%

  Per-VRC viewing-key disclosure strictly more private than unscoped

  conf ~60%status activeregister sharedhome formal spec §17.2.1
• ▸C44productive VRC 55%

  Productive VRC ≈ hash-exchange VRC in trust strength

  conf ~55%status activeregister sharedhome formal spec §17.2.1
• ▸C45four-chain 70%

  Four-chain publication beats single-chain reconstruction resistance

  conf ~70%status activeregister sharedhome formal spec §17.2.1
• ▸C46alias of C32

  Productive trust-edge has higher half-life than transactional

  conf ~50%status alias of C32 (restatement; retained for tome continuity)register cityhome formal spec §17.2.1

post-V5.4 coherence (C47–C55)

• ▸C47ages progressively 50%

  Ages progressively: the dynamical ceiling is a fourth aging category beyond Bakhta's taxonomy

  conf ~50%status active · KEEPS this number (see G1 disposition 2)register corehome v6_1_research_note.md (renumbered from C22-Bakhta, 2026-05-09)
• ▸CM-C47alias of C85

  Triadic-Constraint Homology: Φ-axes × PRISM Datum·Stratum·Spectrum instances of one triadic primitive

  conf ~40%status alias of C85 (promoted Run 4, 2026-06-10); City prose keeps CM-C47 with one erratum at Wave Rregister cityhome Tome V Act 15 · tome-v-conjectures.ts
• ▸C48reconstruct-later 65% (alias C60)

  Reconstruct-later threat model isomorphic to Bakhta TM-1

  conf ~65%status active · C60 restates this (City register)register corehome v6_1_research_note.md (from C23-Bakhta)
• ▸C49Behavioural Mosca 70% (alias C61)

  Behavioural Mosca Inequality binds for long-horizon behavioural evidence

  conf ~70%status active · C61 restates this (City register)register corehome v6_1_research_note.md (from C24-Bakhta)
• ▸C50gating ≡ compositional defense 60%

  PVM multiplicative gating ≡ Bakhta compositional defense at different substrates

  conf ~60%status activeregister corehome v6_1_research_note.md (from C25-Bakhta)
• ▸C51-C55occupied, never reassign

  C51The ⿻ remains max-betweenness across trust-graph evolutions

  conf openstatus occupied · never reassignregister sharedhome CHRONICLE_V5_4_BETWEENNESS_SELENE

  C52Aether = Quintessence = the Gap

  conf openstatus occupied · never reassignregister sharedhome aether-blade-ceremony-circuit.md

  C53Every bnot-pair on the lattice has a mythological reading

  conf ~70%status occupied · never reassignregister sharedhome aletheia-and-lethe.md

  C54Phi-Adjacency: bnot-pair disclosure ratios cluster near 1/φ

  conf ~40%status occupied · never reassign · follows the number (Aletheia at 38 keeps disclosure-φ, 2026-06-09 lock)register sharedhome aletheia-and-lethe.md

  C55Privacy is the seventh kind of capital, foundationally

  conf architecturalstatus occupied · never reassignregister sharedhome poems/tide-orbit-selene.md

the city register (C56–C66)

• ▸C56caduceus 60%

  Caduceus as pre-formal dual-agent symbol

  conf ~60%status active (renumbered from C50 in Threshold chronicle)register cityhome tome-v-conjectures.ts · Tome V Act 16
• ▸C57held open

  Staff-Mage collapse, held open

  conf —status observationregister cityhome tome-v-conjectures.ts
• ▸C58Forge(t) ∥ Threshold 85%

  Forge(t) ∥ Threshold sibling Swordsman-suppliers

  conf ~85%status active (promoted v1.6.0)register cityhome tome-v-conjectures.ts
• ▸C59create-format gateway 70%

  Create-format as gateway to Mage-tier

  conf ~70%status active (renumbered from C49 in Threshold chronicle)register cityhome tome-v-conjectures.ts
• ▸C60alias of C48

  Reconstruct-later threat model for behavioural data

  conf ~65%status alias of C48 (renumbering eddy: v1.5.0 patch C48 → C60)register cityhome tome-v-conjectures.ts
• ▸C61alias of C49

  Behavioural Mosca Inequality (planning bound)

  conf ~70%status alias of C49 (renumbering eddy: v1.5.0 patch C49 → C61)register cityhome tome-v-conjectures.ts
• ▸C62reserved

  Cross-coalition meta-coalition reading

  conf —status reserved (v1.5.1, no claim authored)register cityhome tome-v-conjectures.ts
• ▸C63attentional register 50%

  Attentional workshop register, fourth structural class

  conf ~50%status active (population-of-one)register cityhome tome-v-conjectures.ts · Tome V Act 17
• ▸C64listener-discipline tier 50%

  Listener-discipline as the City's structural seventh tier

  conf ~50%status active (population-of-one, v1.7.0)register cityhome cityofmages CHANGELOG
• ▸C65invitation-posture 50%

  Invitation-posture as fourth tome-posture register

  conf ~50%status active (population-of-one, v1.7.1)register cityhome cityofmages CHANGELOG
• ▸C66Key is a reading 55%

  The City Key is a reading, not an authority

  conf ~55%status active · revised Run 5, 2026-06-10 (+10 via ocap lineage citation: SPKI/SDSI, designation without authority) · City register owner confirms at Wave Rregister cityhome 2026-05-28 capstone chronicle · privacy_value_v6_draft.md Part V §V.5

Horizon District · pinned v1.8.0 (C67–C71)

• ▸C67cryptographic Mosca

  Cryptographic Mosca for the substrate (extends C30 to C33 + C61; C60 is the X-side)

  conf stage 1status activeregister cityhome 2026-06-09 horizon district note · grimoire v1.8.0
• ▸C68resource-estimate as durability signal

  Resource-estimate as durability signal, not attack (e^(−λt) reading)

  conf stage 1status activeregister cityhome same
• ▸C69held-out gate

  Held-out gate rejects the tuned claim (nonce-island; C13 at the validation layer)

  conf stage 1status activeregister cityhome same
• ▸C70crypto-agility

  Crypto-agility as migration readiness (C30 to C33 migration-window Y)

  conf stage 1status activeregister cityhome same
• ▸C71Horizon Vertex V35

  The Horizon Vertex V35 (Protection ∧ Computation ∧ Value)

  conf geometricstatus activeregister cityhome same

renumbered at Run 0 (C72–C80)

• ▸C72-C76ARCH-1R/T (was provisional C67-C71)

  C72Traversal ρ of ARCH-1R/T and activation ρ of ARCH-1 are one operator at two scopes

  conf ~35%status activeregister corehome pvm-v6-arch1rt-operational-reachability.md (was C67)

  C73Terminal-obstruction is a primitive obstruction class; Amnesia Protocol its canonical instance

  conf ~50%status active · V6 Run 4 materialregister corehome same (was C68)

  C74Latency (ternary 0) has an algebraic signature on the blade lattice

  conf ~25%status activeregister corehome same (was C69)

  C75Dependency closure under typed propagation models real cascade; hard-vs-soft is the 0-vs-minus distinction lifted

  conf ~35%status activeregister corehome same (was C70)

  C76UOR-relational instantiation (classifying rel(a,b)) strictly more expressive for sovereignty

  conf ~30%status activeregister corehome same (was C71)
• ▸C77-C80integrity-gap convergence (was provisional C70-C73)

  C77Bakhta's integrity gap and PVM's scales-vs-hides separation are one object

  conf ~60%status activeregister corehome pvm-v6-bakhta-integrity-gap-convergence.md (was C70)

  C78Specification-intent gap and the irreducible promise are one object, two sides

  conf ~60%status activeregister corehome same (was C71)

  C79Shared frontier: recursive proof composition across providers under heterogeneous trust at runtime

  conf ~45%status active · V6 Run 5 IVC adjacencyregister corehome same (was C72)

  C80Bilateral co-signed assumption sets yield strict assurance gain in multi-provider case

  conf ~35%status activeregister corehome same (was C73)

registered in the V6 runs (C81–C89)

• ▸C81Existence-Leak 70%

  Existence-Leak: a ZK proof of feasibility leaks an upper bound on reconstruction difficulty; I(feasibility; method) > 0

  conf ~70%status active · PROMOTED Run 3 2026-06-10 (Schrottenloher instance + Garg-Jain-Sahai λ<1 impossibility as bookends) · Stage 2 open: held at 70% until a second independent instanceregister corehome schrottenloher-ecdlp-v6-note.md · privacy_value_v6_draft.md Part III
• ▸C82Moving Ceiling 65%

  The Moving Ceiling: frontier capability growth raises C_S(t) + C_M(t) against fixed archives without raising H(X); R(t) drifts upward and every static reconstruction guarantee has a finite shelf life t*

  conf ~65%status active · registered Run 1, 2026-06-10register corehome privacy_value_v6_draft.md Part I §I.3
• ▸C83Compositional Leakage Amplification 55%

  Compositional Leakage Amplification: policy-only separation compounds toward (2^N − 1)ε with chain depth; amnesia separation breaks the Markov chain and caps at Nε; the gap is exponential-to-linear

  conf ~55%status active · registered Run 2, 2026-06-10 · edge C7 → C83 → C17register corehome privacy_value_v6_draft.md Part II §II.3
• ▸C84Existence-Leak Discount 50%

  Existence-Leak Discount: every public feasibility attestation discounts the Behavioural Mosca horizon, Z_b' = Z_b − D(a); migration deadlines tighten on attestation, independent of any actual attack

  conf ~50%status active · registered Run 3, 2026-06-10 · edges C81 → C84 → C49, C84 → C82register corehome privacy_value_v6_draft.md Part III §III.3
• ▸C85Triadic-Constraint Homology (ARCH-1 bridge) 40%

  Triadic-Constraint Homology (the ARCH-1 bridge, promoted from CM-C47): the three Φ axes and the lattice's Datum·Stratum·Spectrum are one triadic primitive; candidate pair map Protection+Delegation→Σ, Memory+Value→Δ, Connection+Computation→Γ; the gap is β

  conf ~40%status active · registered Run 4, 2026-06-10 · CM-C47 becomes alias · two named predictions (bnot-pairs invert all axes; stratum-3 is the no-dominant-axis seat)register corehome privacy_value_v6_draft.md Part IV §IV.2
• ▸C86Obstruction-Theoretic Amnesia 30%

  Obstruction-Theoretic Amnesia: Grade-2 forgetting = non-vanishing obstruction class to gluing local agent views into a global witness of O; Grade-1 = vanishing class with withheld gluing data; amnesia is the only term whose security is independent of t

  conf ~30%status active · registered Run 4, 2026-06-10 · cross-linked C73 (taxonomy placement vs cohomological content) · falsification: any view-composition recovering Grade-2-forgotten Oregister corehome privacy_value_v6_draft.md Part IV §IV.4
• ▸C87The Key Accumulates (IVC) 50%

  The Key Accumulates: the City Key trust recursion admits an IVC realization (Key = accumulator, trust tasks = step circuits, Charge = folding step, V63 = attested invariant); LatticeFold makes the substrate post-quantum-hedged

  conf ~50%status active · registered Run 5, 2026-06-10 · architectural claim, no circuit existsregister corehome privacy_value_v6_draft.md Part V §V.2
• ▸C88Parity Cube 30%

  The Parity Cube: the stella octangula's two tetrahedra are the even/odd parity classes of the cube's vertices; the canonical seat of neg/bnot at 3-bit scale; {0,1}⁶ = {0,1}³ × {0,1}³ gives each agent a cube, with the C85 pair map as candidate factoring

  conf ~30%status active · registered Run 5, 2026-06-10register corehome privacy_value_v6_draft.md Part V §V.4
• ▸C89Octahedral Gap 30%

  The Octahedral Gap: the tetrahedra's intersection (volume 1/6 of the cube) is the geometric locus of the conditional-independence bound; the gap is β is the octahedron, three readings of one thing

  conf ~30%status active · registered Run 5, 2026-06-10 · volume facts are theorems, the correspondence is the conjectureregister corehome privacy_value_v6_draft.md Part V §V.4