🧮 The Conjecture Register

The living register of the privacy-value model — 97 conjectures (C1–C97) across eight bands. Numbers are never reassigned; each page is forkable. Source of truth: agentprivacy-docs/research/CONJECTURE_REGISTER_V6.md.

Band I · V1–V5.3 core

• Conjecture C1 — Golden ratio φ is optimal S/M (protect:project) ratio (open)
• Conjecture C2 — A(τ) should be logarithmic (open)
• Conjecture C3 — Edge value is additive (challenged (path integral replaces))
• Conjecture C4 — 96 vs 64 discrepancy (resolved (holographic + algebraic))
• Conjecture C5 — ~3,000× ZKP reduction (resolved (strengthened by BRAID + holographic bound))
• Conjecture C6 — P^1.5 ↔ 96/64 is structural (convergent)
• Conjecture C7 — Three-axis separation is multiplicative (active)
• Conjecture C8 — BRAID compression reduces R_max (active)
• Conjecture C9 — Holographic boundary sufficiency (active)
• Conjecture C10 — O(1) shared-parent modifies k (active)
• Conjecture C11 — Behavioural density ρ amplifies privacy, indicates maturity (active)
• Conjecture C12 — Hexagram encoding is structurally resonant (active)
• Conjecture C13 — Bilateral witness as quantum-resistant primitive (active)
• Conjecture C14 — Φ_agent ≅ D₂ₙ dihedral isomorphism (active)
• Conjecture C15 — T_∫(π) ≅ UOR resolution pipeline (active)
• Conjecture C16 — Topological trust invariants via Betti numbers (active)
• Conjecture C17 — Amnesia-enforced separation tighter than policy-enforced (active)

Band II · V6 research series

• Conjecture C18 — Sovereignty path exhibits strange attractor dynamics (λ > 0); dynamical reconstruction ceiling (active)
• Conjecture C19 — ρ is Lyapunov divergence accumulated over the walk (active)
• Conjecture C20 — Three axes couple as three Lorenz variables (active)
• Conjecture C21 — Sovereignty manifold has fractal dimension (active)
• Conjecture C22 — Reconstruction cost grows exponentially with EML tree depth (active)
• Conjecture C23 — Blade forge grammar isomorphic to restricted EML grammar (active)
• Conjecture C24 — Sovereignty computation requires complex intermediates (active)
• Conjecture C25 — Minimal EML tree depth is hard floor for compression spectrum (active)
• Conjecture C26 — ARCH-1 is canonical form of NAND, EML, succ as co-instances (active)
• Conjecture C27 — ρ is the activation mechanism; Ω without ρ is inert (active)
• Conjecture C28 — Three ceilings independent because ARCH-1 factors into β / μS / Ω (active)
• Conjecture C29 — The Second Person Lift: You := μS.(β ∨ Ω(S,S)) (active)
• Conjecture C30 — Trust half-life begins at inscription; decays until renewed (active)
• Conjecture C31 — Half-life differs by inscription register (shielded vs transparent) (active)
• Conjecture C32 — Productive trust-edges have higher half-life than transactional (active)
• Conjecture C33 — Half-lives compose multiplicatively across the three axes (active)
• Conjecture C34 — Convergence requires a bijective cap (active)
• Conjecture C35 — The wound is where the architectural asymmetry lives (active)
• Conjecture C36 — The cap is where the bijection lives or breaks (active)
• Conjecture C37 — Convergence is recognition, not coincidence (active)

Band III · Bound Collection (Tomes IV–V)

• Conjecture C38 — Bilateral ARCH-1: Σ_ij := μS.(β_ij ∨ Ω(S_i, S_j)) preserves fixpoint (active)
• Conjecture C39 — Kindred-blade as ecosystem-layer primitive (active)
• Conjecture C40 — Zcash dual-ledger preserves Eight Cloak Properties (active)
• Conjecture C41 — 61.8/38.2 transparent/shielded inscription ratio as cultural norm (observation)
• Conjecture C42 — Stake economics generate Sybil resistance ≥ tier accumulation (active)
• Conjecture C43 — Per-VRC viewing-key disclosure strictly more private than unscoped (active)
• Conjecture C44 — Productive VRC ≈ hash-exchange VRC in trust strength (active)
• Conjecture C45 — Four-chain publication beats single-chain reconstruction resistance (active)
• Conjecture C46 — Productive trust-edge has higher half-life than transactional (alias of C32 (restatement; retained for tome continuity))

Band IV · Post-V5.4 coherence

• Conjecture C47 — Ages progressively: the dynamical ceiling is a fourth aging category beyond Bakhta's taxonomy (active)
• Conjecture C48 — Reconstruct-later threat model isomorphic to Bakhta TM-1 (active)
• Conjecture C49 — Behavioural Mosca Inequality binds for long-horizon behavioural evidence (active)
• Conjecture C50 — PVM multiplicative gating ≡ Bakhta compositional defense at different substrates (active)
• Conjecture C51 — The ⿻ remains max-betweenness across trust-graph evolutions (occupied)
• Conjecture C52 — Aether = Quintessence = the Gap (occupied)
• Conjecture C53 — Every bnot-pair on the lattice has a mythological reading (occupied)
• Conjecture C54 — Phi-Adjacency: bnot-pair disclosure ratios cluster near 1/φ (occupied)
• Conjecture C55 — Privacy is the seventh kind of capital, foundationally; its character is land-based RENTIER cap… (occupied)

Band V · City register continuation

• Conjecture C56 — Caduceus as pre-formal dual-agent symbol (active (renumbered from C50 in Threshold chronicle))
• Conjecture C57 — Staff-Mage collapse, held open (observation)
• Conjecture C58 — Forge(t) ∥ Threshold sibling Swordsman-suppliers (active (promoted v1.6.0))
• Conjecture C59 — Create-format as gateway to Mage-tier (active (renumbered from C49 in Threshold chronicle))
• Conjecture C60 — Reconstruct-later threat model for behavioural data (alias of C48 (renumbering eddy: v1.5.0 patch C48 → C60))
• Conjecture C61 — Behavioural Mosca Inequality (planning bound) (alias of C49 (renumbering eddy: v1.5.0 patch C49 → C61))
• Conjecture C62 — Cross-coalition meta-coalition reading (reserved (v1.5.1, no claim authored))
• Conjecture C63 — Attentional workshop register, fourth structural class (active (population-of-one))
• Conjecture C64 — Listener-discipline as the City's structural seventh tier (active (population-of-one, v1.7.0))
• Conjecture C65 — Invitation-posture as fourth tome-posture register (active (population-of-one, v1.7.1))
• Conjecture C66 — The City Key is a reading, not an authority (active)

Band VI · Horizon District

• Conjecture C67 — Cryptographic Mosca for the substrate (extends C30 to C33 + C61; C60 is the X-side) (active)
• Conjecture C68 — Resource-estimate as durability signal, not attack (e^(−λt) reading) (active)
• Conjecture C69 — Held-out gate rejects the tuned claim (nonce-island; C13 at the validation layer) (active)
• Conjecture C70 — Crypto-agility as migration readiness (C30 to C33 migration-window Y) (active)
• Conjecture C71 — The Horizon Vertex V35 (Protection ∧ Computation ∧ Value) (active)

Band VII · Renumbered research blocks

• Conjecture C72 — Traversal ρ of ARCH-1R/T and activation ρ of ARCH-1 are one operator at two scopes (active)
• Conjecture C73 — Terminal-obstruction is a primitive obstruction class; Amnesia Protocol its canonical instance (active)
• Conjecture C74 — Latency (ternary 0) has an algebraic signature on the blade lattice (active)
• Conjecture C75 — Dependency closure under typed propagation models real cascade; hard-vs-soft is the 0-vs-minus… (active)
• Conjecture C76 — UOR-relational instantiation (classifying rel(a,b)) strictly more expressive for sovereignty (active)
• Conjecture C77 — Bakhta's integrity gap and PVM's scales-vs-hides separation are one object (active)
• Conjecture C78 — Specification-intent gap and the irreducible promise are one object, two sides (active)
• Conjecture C79 — Shared frontier: recursive proof composition across providers under heterogeneous trust at runt… (active)
• Conjecture C80 — Bilateral co-signed assumption sets yield strict assurance gain in multi-provider case (active)
• Conjecture C81 — Existence-Leak: a ZK proof of feasibility leaks an upper bound on reconstruction difficulty; I(… (active)

Band VIII · Registered during the V6 runs

• Conjecture C82 — The Moving Ceiling: adversary informational capability grows against fixed archives: the linkag… (active)
• Conjecture C83 — Compositional Leakage Amplification: policy-only separation compounds toward (2^N − 1)ε with ch… (active)
• Conjecture C84 — Existence-Leak Discount: every public feasibility attestation discounts the Behavioural Mosca h… (active)
• Conjecture C85 — Triadic-Constraint Homology (the ARCH-1 bridge, promoted from CM-C47): the three Φ axes and the… (active)
• Conjecture C86 — Obstruction-Theoretic Amnesia: Grade-2 forgetting = non-vanishing obstruction class to gluing l… (active)
• Conjecture C87 — The Key Accumulates: the City Key trust recursion admits an IVC realization (Key = accumulator,… (active)
• Conjecture C88 — The Parity Cube: the stella octangula's two tetrahedra are the even/odd parity classes of the c… (active)
• Conjecture C89 — The Octahedral Gap: the tetrahedra's intersection (volume 1/6 of the cube) is the geometric loc… (active)
• Conjecture C90 — The Limitative Inversion: completeness ⇒ Φ → 0 ⇒ collapse is the value-sign reversal of complet… (observation)
• Conjecture C91 — Gödel ↔ Φ_agent: zero-memory (Selene) is the Φ_agent instance of Gödel's first theorem; a witne… (active)
• Conjecture C92 — Tarski ↔ Φ_inference: existence-leak is the Tarski-undefinability instance loading on Φ_inferen… (active)
• Conjecture C93 — Content-addressed liveness leak: a live content-address is an existence claim about its content… (active)
• Conjecture C94 — Separation Principle in a Second Substrate: s ⊥ m | X realised as a running build on Archon d… (active)
• Conjecture C95 — The Evidence Graph as the Anti-Score: issuer-attested disclosure — a signed, decomposable evide… (active)
• Conjecture C96 — Control-Plane ⊥ Data-Plane: the Sovereign authorizes the rules the Warden enforces; splitting t… (active)
• Conjecture C97 — Structural Inalienability by Non-Reconstruction (the C55 ↔ C82 bridge): a scoped disclosure doe… (active)

---

← Welcome Visitors