Pvm V6 1 Bakhta Half Life
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_VRCfrom 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