---
name: agentprivacy-threat-adversarial
description: >
  Threat modelling and adversarial analysis for 0xagentprivacy. Activates
  when discussing R(d) adversarial bounds, attack surface analysis, red team
  methodologies, trusted setup attacks, side-channel vulnerabilities, or
  systematic approaches to finding privacy architecture weaknesses.
license: Apache-2.0
metadata:
  version: "4.0"
  category: "role"
  origin: "0xagentprivacy"
  author: "Mitchell Travers"
  affiliation: "0xagentprivacy, BGIN, First Person Network"
  status: "working_paper"
  target_context: "Security auditors, red teams, academic reviewers, protocol analysts"
  equation_term: "R(d) — reconstruction resistance under adversarial conditions"
  template_references: "cipher, sentinel, ranger, architect, witness"
---

# PVM-V4 Skill — Threat Model & Adversarial Analysis

**Source:** Privacy Value Model V4 + Zero Knowledge Spellbook (Tale 26: Vulnerability Codex)
**Target context:** Security auditors, red teamers, academic peer reviewers, protocol analysts, penetration testers
**Architecture:** [agentprivacy.ai](https://agentprivacy.ai) · **Sync:** [sync.soulbis.com](https://sync.soulbis.com) · **Contact:** mage@agentprivacy.ai

---

## What this is

Every security model has a boundary. This skill defines PVM-V4's boundary: what the model defends against, what it explicitly does not, and the four conditions under which the entire framework fails. A defence that does not know its own breaking conditions is not a defence.

## The adversary

**Capability:** The adversary has complete output streams of both agents (Swordsman and Mage). It observes everything the agents transmit externally. It is computationally bounded — probabilistic polynomial-time (PPT).

**Goal:** Reconstruct the principal's private state X from the combined observations.

**Result (proven):** R_max = (C_S + C_M)/H(X) < 1. Even with complete output observation, the adversary cannot reconstruct the full private state, provided the dual-agent conditional independence holds (I(S;M|π) ≤ ε with ε < 0.1).

**Information bound (proven):** I(X; O_S, O_M) ≤ I(X; O_S) + I(X; O_M) + ε. Information from both agents combines additively, not multiplicatively, under near-independence. The adversary gains less from combining both streams than the sum of what each stream reveals individually.

## What the model defends against

1. **Passive surveillance.** Complete observation of all agent outputs. The reconstruction ceiling guarantees the adversary cannot close the gap.
2. **Traffic analysis.** Even if the adversary sees all traffic patterns, the separation between Swordsman and Mage means traffic from one agent does not reveal the other's state.
3. **Temporal correlation.** The adversary may attempt to correlate Swordsman and Mage outputs over time. The conditional independence requirement (ε < 0.1) bounds the information leaked through temporal patterns.
4. **Network-level observation.** Observing which agents communicate and when. The VRC system provides cover through bilateral channels.

## What the model does NOT defend against

**Side-channel attacks.** If the adversary can observe timing, power consumption, electromagnetic emissions, or other physical signals from the execution environment, the model provides no guarantees. TEE integrity is assumed, not proven.

**Principal-adversary collusion.** If the human principal cooperates with the adversary (voluntarily or under coercion), the separation guarantees are meaningless. The model protects sovereignty — it cannot enforce it against the sovereign's own choices.

**Internal state access.** If the adversary can read the internal memory of either agent (through malware, compromised hardware, or TEE breach), the model breaks entirely. The reconstruction ceiling assumes output-only observation.

**Social engineering.** The model is mathematical. It does not defend against the adversary convincing the human to reveal information through social means.

**Compromised counterparties.** If VRC counterparties are adversarial, the bilateral trust model weakens. The Sybil resistance from personhood binding mitigates but does not eliminate this threat.

**Quantum adversaries.** The PPT assumption does not hold against quantum computers. Post-quantum ZKP backends (ZK Spellbook Tale 28) are an active research area but not currently integrated.

## The four breaking conditions

PVM-V4 is explicitly falsifiable. Any of these demonstrated empirically requires fundamental revision:

**Breaking condition 1: UOR structural incompatibility.** If the conjectured correspondence between the sovereignty lattice and UOR toroidal structure is proven to be a structural mismatch (not merely an encoding difference), the geometric grounding weakens. The lattice remains valid as a Boolean hypercube, but the compactification, periodicity, and conservation properties attributed to toroidal embedding fail. Impact: V5 extension needs different foundations. ZKP efficiency conjecture weakens.

**Breaking condition 2: ε > 0.1 in practice.** If real implementations cannot achieve conditional independence ε < 0.1 between Swordsman and Mage agents, the reconstruction ceiling no longer holds. The agents leak too much mutual information, and the adversary can triangulate. Impact: Dual-agent separation is a theoretical result without practical realisability. Alternative separation mechanisms would be needed.

**Breaking condition 3: Sublinear network effects.** If empirical measurement shows k < 1 in the network term (1 + Σ wᵢ nᵢ/N₀)^k, privacy networks face diminishing returns to scale. This would mean the sovereignty gap (17×–12,000×) is overstated and privacy networks hit natural scale ceilings. Impact: The economic thesis weakens. Privacy remains valuable but not exponentially so.

**Breaking condition 4: Singular Σ matrices in practice.** If real sovereignty architectures cluster near det(Σ) ≈ 0, the four-force separation is a theoretical ideal that real systems cannot approach. The sovereignty multiplier Φ(Σ) stays near zero regardless of individual force strength. Impact: The tetrahedral model is beautiful but impractical. A simpler scalar separation model may be sufficient.

## The five open conjectures

Beyond the breaking conditions, five unproven claims require validation:

1. **Golden ratio φ ≈ 1.618 as optimal protect/project balance.** Observed in model outputs. No proof that φ is the optimum rather than merely a good ratio.
2. **Logarithmic growth of temporal memory.** Conjectured that A(τ) grows as ln(1 + |τ|). Could be sub- or super-logarithmic.
3. **Edge value additivity.** T(π) assumes transitions contribute independently. Likely an oversimplification.
4. **UOR toroidal correspondence.** The 96 vs. 192 edge discrepancy remains unresolved.
5. **~3,000× ZKP proof size reduction.** Conjectured from combined lattice-toroidal structure. No circuit analysis performed.

## Measurement gaps

Four quantities the model requires but cannot currently measure:

**M1: Cross-force separations.** No methodology exists for measuring σ_SR, σ_SC, σ_MR, σ_MC, σ_RC in the separation matrix Σ. Only σ_SM (Swordsman-Mage separation) has a clear operational definition.

**M2: Empirical decay rate λ.** Different privacy configurations decay at different rates. No calibration data exists.

**M3: Network exponent k.** Sub-, linear, or superlinear? Requires comparative measurement across networks of different sizes and sovereignty quality distributions.

**M4: Edge weight f(e).** How much more valuable are vertical transitions than lateral transitions? No empirical basis for the weighting.

## The cheapest attacks

For each adversary capability level, the minimum-cost attack:

**Passive observation only:** Wait. The temporal decay term e^{-λt} erodes value automatically. If the agent does not continuously generate attested transitions, its sovereignty decays without any adversary action.

**Network-level observation:** Correlation analysis. Even under separation, temporal patterns may leak information. The cheapest version: observe when Swordsman and Mage are both active and correlate activity windows.

**One compromised counterparty:** Poison the VRC chain. Create a bilateral relationship where one party is adversarial, then use the VRC's bilateral proverb to extract context about the principal's private state.

**TEE breach:** Full compromise. If the execution environment is breached, all guarantees fail. The cheapest TEE breach depends on hardware — historically, speculative execution attacks have been the most accessible.

## Red team protocol

When stress-testing a PVM-V4 deployment:

1. Measure actual ε between Swordsman and Mage. If ε > 0.1, the deployment fails the fundamental requirement before any other testing.
2. Measure det(Σ) for the sovereignty matrix. If near zero, the four-force model is not providing value.
3. Simulate passive adversary with complete output streams. Measure actual reconstruction rate R. Compare to theoretical ceiling.
4. Test temporal correlation between agent outputs. Measure mutual information leaked through timing.
5. Attempt Sybil attack at each armor tier. Measure cost-to-forge vs. legitimate progression cost.

---

**Verify:** [agentprivacy.ai](https://agentprivacy.ai) · [sync.soulbis.com](https://sync.soulbis.com) · [github.com/mitchuski/agentprivacy-docs](https://github.com/mitchuski/agentprivacy-docs)