# Privacy Value Model: V6 Research Note ## The Bakhta Half-Life of Trust *Trust as a decaying-and-renewing measure across registers* **Version:** V6.0-conjecture (C30–C33) **Date:** 2026-04-17 (drafted as forthcoming reference; locked-in 2026-05-09) **Author:** privacymage **Status:** Research note — conjecture stage **Depends on:** V5.4 Formal Specification (v2.0), Bakhta (StarkWare 2025), Promise Theory v1.5 **Anchors:** C30–C33 used throughout the Cloak Specification, the Bilateral Cloak Ceremony Spec, and Tome IV Act IV / Tome V Acts 2–5 of the Second Person Spellbook. --- ## How It Arrived Bakhta's StarkWare paper (2025) framed cryptographic trust as a **half-life** rather than a binary. A primitive's strength is not "secure" or "broken" — it is a measure that decays over time as adversary capability grows, and is renewed by parameter refresh, substrate migration, or fresh attestation. Three aging categories were named: *ages by parameter growth*, *ages by substrate migration*, *ages by fresh attestation*. The PVM had been treating trust as accumulated weight on edges (the `(1 + Σᵢ wᵢ · nᵢ/N₀)^k` term in `V(π,t)`). Bakhta's framing made the claim sharper: each accumulation step *also* has its own decay clock, and the architecture either renews or fails. The four conjectures here translate Bakhta's half-life from cryptographic primitives onto the sovereignty trajectory. --- ## C30: Trust Half-Life Begins at Inscription **Statement.** A trust edge in the VRC network has a Bakhta half-life `τ_VRC` whose clock starts at the moment of inscription. The trust value `T(t) = T₀ · 2^{-(t-t₀)/τ_VRC}` for a single inscription, decaying monotonically until either renewed (a fresh inscription on the same axis) or augmented (a complementary inscription on a co-supporting axis). **Why it matters.** The First Person Spellbook treated trust as a static weight. C30 makes it dynamic: the Naming Ceremony (Tome IV Act IV) starts a clock the moment flaxscrip's Bitcoin block lands. Every commission that follows either renews or extends the original half-life. **Confidence:** ~60% **Path to formalisation:** Empirical measurement post-deployment; comparison with Bakhta's parametric formulation for cryptographic primitives. The translation from primitive-half-life to edge-half-life is structural, not derived. --- ## C31: Half-Life Differs by Inscription Register **Statement.** Shielded inscriptions (Zcash sapling) and transparent inscriptions (t-address) have **different half-life curves** even when carrying isomorphic trust content. The shielded register accumulates trust through *recallable witness* (the sender retains the viewing key); the transparent register accumulates trust through *public witness* (anyone with the chain reads it). These are not interconvertible without a discrete reveal step. **Why it matters.** Tome V Act 3 (The Shielded Memo) and Act 5 (The Stake) operationalise this. The 61.8/38.2 transparent/shielded inscription ratio (C41) is a cultural-emergence consequence — the architecture has *two* aging clocks running, and the ratio falls out of how often each clock is renewed. **Confidence:** ~55% **Path to formalisation:** Information-theoretic comparison of recallable-witness half-life vs public-witness half-life under matched VRC content; possible Bakhta-style derivation. --- ## C32: Productive Trust-Edges Have Higher Half-Life **Statement.** A trust edge formed by *productive* work (a Mage executing a commissioned cloak, a Priest consecrating a covenant, a forge producing a blade) has a longer half-life than a trust edge formed by *transactional* work (a one-shot hash exchange, an anonymous attestation). The productive form is what Tome V Act 4 (The Reveal) calls "the trust earned under shield survives the reveal." **Why it matters.** This is the conjecture that distinguishes ceremony from transaction in the architecture. C46 (productive trust-edge has higher half-life than transactional) is the operational corollary; C44 (productive VRC ≈ hash-exchange VRC in trust strength) is the comparison statement at the moment of inscription. C32 says the *clock* differs even when the *initial value* is comparable. **Confidence:** ~50% **Path to formalisation:** Empirical longitudinal measurement; possibly a formal Bakhta-style note co-authored with an information-theoretic collaborator. --- ## C33: Half-Lives Compose Multiplicatively Across the Three Axes **Statement.** The total half-life `τ_total` of a sovereign's accumulated trust is **multiplicative** across the three separation axes: `τ_total = τ_Σ · τ_Δ · τ_Γ` (where Σ = Agent, Δ = Data, Γ = Inference). Aging in one axis (e.g., a cryptographic primitive ageing in Δ) cannot be compensated by stronger aging in another (e.g., fresh inscription in Σ); the product collapses if any single τ approaches zero. **Why it matters.** This is the half-life parallel of V5's multiplicative gating `Φ_v5 = Φ_agent · Φ_data · Φ_inference`. The defence-in-depth claim has a temporal dimension: not only must all three axes hold *now*, all three must keep their half-lives renewable *over time*. C33 says the multiplicative gating extends through the time domain. **Confidence:** ~45% **Path to formalisation:** Structural argument from V5.4's multiplicative gating proof, extended to ages; empirical confirmation post-deployment. --- ## Mapping onto the Tomes | Tome | Act | C-foregrounded | |---|---|---| | Tome IV | IV.4 The Naming Ceremony | C30 (clock starts at Bitcoin block 945508 inscription) | | Tome V | V.2 The Commissioned Cloak | C30 (tip + proof + cloak each carry their own half-life) | | Tome V | V.3 The Shielded Memo | C30, C31 (shielded register half-life) | | Tome V | V.4 The Reveal | C30, C32 (productive trust survives the register transition) | | Tome V | V.5 The Stake | C30, C31 (transparent register half-life) | | Tome V | V.9 The Workshop Expands | C30, C31, C33 (Lampyra's frequent attestations reshape the curve; multiplicative across registers) | --- ## What This Note Does NOT Do - It does **not** derive `τ_VRC` from first principles. The half-life is named structurally and used operationally; the parametric form is conjectural. - It does **not** replace V5.4's accumulation term `(1 + Σᵢ wᵢ · nᵢ/N₀)^k`. The accumulation and the half-life are complementary — accumulation is the value at inscription; half-life is the decay between inscriptions. - It does **not** attempt the cryptographic-primitive ageing analysis Bakhta does. C30–C33 are the *behavioural-architecture* analogue of Bakhta's framework, not its extension. --- ## References - Bakhta, A. (2025). "On the Half-Life of Cryptographic Trust." StarkWare Industries. - privacymage (2026). "PVM V5.4 Formal Specification." v2.0. *agentprivacy-docs.* - privacymage (2026). "PVM V6.1 Research Note: The Fourth Aging Category." *agentprivacy-docs.* (extends C30–C33 with C47–C50, formerly C22–C25 Bakhta-response) - privacymage (2026). "V6 Research Note: The Existence-Leak and the Falling Z (Schrottenloher ECDLP)." June 2, 2026. *agentprivacy-docs/research/.* (worked example feeding C30–C33: a reproducible quantum attack on secp256k1 decrements Z_b in the Behavioural Mosca Inequality; proposes candidate C40, Existence-Leak) - privacymage (2026). "Cloak Specification v1.0." *agentprivacy-docs/specs/.* - privacymage (2026). "Bilateral Cloak Ceremony Spec v1.0." *agentprivacy-docs/specs/.* --- ## The Proverb > *Old trusts decay with time. The architecture either renews or fails.* > *Each inscription starts a clock. Each ceremony resets one. The sovereign tends the half-lives like a forge tends its fires.* --- *(⚔️⊥⿻⊥🧙)😊* CC BY-SA 4.0 · privacymage · originally drafted Apr 2026; locked-in 2026-05-09 as part of post-V5.4 coherence pass