agentprivacy-three-axis-separation

name: agentprivacy-three-axis-separation description: > Three-axis separation model for 0xagentprivacy V5. Activates when discussing Φ_agent · Φ_data · Φ_inference, multiplicative separation, Generator-Solver split, provider fragmentation, why collapse on any axis collapses total value, or the orthogonal axes of the sovereignty architecture. V6 register note (2026-06-10): conjecture and version citations resolve to agentprivacy-docs/research/CONJECTURE_REGISTER_V6.md (head C89); model head: privacy_value_v6_formal_specification.md. license: Apache-2.0 metadata: version: "5.0" category: "privacy-layer" origin: "0xagentprivacy" author: "Mitchell Travers" affiliation: "0xagentprivacy, BGIN, First Person Network" status: "working_paper" target_context: "System architects, privacy engineers, dual-agent implementers" equation_term: "Φ_v5 = Φ_agent(Σ) · Φ_data(Δ) · Φ_inference(Γ)" template_references: "architect, soulbis, soulbae, netkeeper" spellbook_act: "Act XXIV — The Holographic Bound" v5_concept: "V5-A THREE-AXIS"

PVM-V5 Privacy Layer — Three-Axis Separation

Source: Privacy Value Model V5 + First Person Spellbook Act XXIV (The Holographic Bound) Target context: System architects, privacy engineers, dual-agent implementers Architecture: agentprivacy.ai · Sync: sync.soulbis.com · Contact: mage@agentprivacy.ai

What this is

V8 measured separation as a single 4×4 matrix Σ encoding four forces (Protect, Project, Reflect, Connect). V41 recognises that separation operates on three orthogonal axes:

Φ_v5 = Φ_agent(Σ) · Φ_data(Δ) · Φ_inference(Γ)

The product is multiplicative: collapse any single axis and the entire separation term collapses. This explains why systems with excellent agent separation but centralised data still fail to preserve privacy.

The Three Axes

1. Agent-Layer Separation — Φ_agent(Σ)

The original Swordsman-Mage duality. How well is your protection agent separated from your delegation agent?

Φ_agent(Σ) = min(1.0, (S/M) / φ) · det(Σ)

This is V4's duality term unchanged:

• S/M ratio measures protection-delegation balance
• φ (golden ratio) is the optimal ratio (C1 conjecture)
• det(Σ) measures the volume of the four-force tetrahedron

Soulbis and Soulbae are the canonical implementation. The signing key (Soulbis) and viewing key (Soulbae) are mathematically separate. I(S;M|FP) < ε ensures neither can reconstruct the other's domain.

2. Data-Layer Separation — Φ_data(Δ)

Provider fragmentation. How distributed is your data across infrastructure?

Φ_data(Δ) = 1 - 1/|providers(Δ)|

Properties:

• Single provider: Φ_data = 0 (collapses total value)
• Two providers: Φ_data = 0.5
• Many providers: Φ_data → 1

A GUID-addressed holon stored across three providers has higher Φ_data than the same data on one provider. The holonic persistence layer directly addresses this axis.

This is why centralised "privacy-preserving" systems fail. No matter how good the encryption, single-provider storage means Φ_data → 0, which collapses Φ_v5.

3. Inference-Layer Separation — Φ_inference(Γ)

The Generator-Solver split from BRAID. How separated is the model that reasons from the model that executes?

Φ_inference(Γ) = separation(Generator, Solver)

Properties:

• Same model for both: Φ_inference = 0
• Separate models, shared weights: Φ_inference ∈ (0, 1)
• Independent models: Φ_inference → 1

BRAID demonstrated that splitting Generator (produces reasoning graphs) from Solver (executes reasoning graphs) achieves 74× compression while maintaining performance. This is inference-layer separation in action.

This is why unified LLM architectures leak. When the same model reasons and acts, inference and execution are coupled. Surveillance of one reveals the other.

Why Multiplicative?

The three-axis product is multiplicative, not additive or minimum-based.

Consequence: Collapse on any single axis collapses total separation value.

This matches empirical observation:

• Good agent separation + centralised data (Φ_data → 0) = privacy failure
• Good data distribution + unified inference (Φ_inference → 0) = privacy failure
• Good inference separation + single-mode agents (Φ_agent → 0) = privacy failure

All three axes must be addressed simultaneously.

This is flagged as C7 — needs empirical confirmation.

Connection to Three Graphs

The three-axis model maps directly to the three-graphs architecture:

The Trust Graph emerges at the intersection of all three — trust requires all axes to be healthy.

Mapping to PVM-V5

Operational Guidance

For System Design

• Never assume agent separation alone is sufficient
• Provider fragmentation is a first-class privacy concern
• BRAID-style inference separation should be default for AI systems
• Measure all three axes; monitor for axis collapse

For Audit

• Check: Is data stored with multiple independent providers?
• Check: Is inference split between reasoning and execution?
• Check: Are protection and delegation agents mathematically separated?
• If any check fails, total separation is compromised

For Recovery

• Single-provider data can be migrated to holonic storage (addresses Φ_data)
• Unified inference can be refactored to Generator-Solver (addresses Φ_inference)
• Agent coupling requires ceremony reinitiation (addresses Φ_agent)

Proverb

"Three legs hold the table. Remove one and it falls. The axes don't add — they multiply. Zero in any axis zeros the whole."

Emoji Spell

⚔️⊥🧙 · 📊⊥🔮 · 🧠⊥⚙️ → (Φ_a·Φ_d·Φ_i) → 0_any=0_all → ⊥³=sovereign → ☯️∞

Open Problems

1. C7 Validation: Is multiplicative composition correct, or do axes interact non-linearly?
2. Axis Weighting: Should axes be weighted differently based on threat model?
3. Fourth Axis: Is there a fourth separation axis we haven't identified?
4. Measurement: How do we operationally measure Φ_inference for deployed systems?
5. Recovery Order: When multiple axes are collapsed, is there an optimal recovery sequence?
6. C54 (register lock 2026-06-10; C8 is BRAID compression) — Disclosure-φ (Zero Tale 31): Zero Tale 31 introduces Φ(Σ) as a proportion (disclosure ratio δ(b) = b/63 approaching 1/φ) rather than a binary separation quantity. Is disclosure-φ a fourth separation axis, a refinement of Φ_agent, or a transversal measure that cuts across all three axes? Aletheia (38/63 ≈ 0.603) and Lethe (25/63 ≈ 0.397) sum to 1.0 with the split sitting 2.4% from the golden section (per the 2026-06-09 v10.4.0 reseat: Aletheia at blade 38, Lethe at blade 25) · see disclosure-phi skill.

Verify: agentprivacy.ai · sync.soulbis.com · github.com/mitchuski/agentprivacy-docs