Formalizing Vitalik's Security Pattern

First published on ethresear.ch, February 2026. Reproduced here with the equations intact.

Vitalik's post "How I think about security" names a pattern common to the good solutions: the user specifies their intention in multiple, overlapping ways, and the system only acts when those specifications line up. His examples (type systems, formal verification, transaction simulation, multi-sig) all share that redundant-specification structure.

This is a mathematical formalization of the pattern: a computable authority function that enforces multi-dimensional intent alignment, with temporal decay and biological grounding. It ships as a Layer 3 protocol called Celaya Chain Protocol (CCP). I'm putting it up for peer review, specifically on the game-theoretic properties of the composite scoring mechanism.

The core observation

Vitalik defines security as minimizing divergence between user intent and system behavior. Read that carefully and security stops being binary. It's a continuous measurement across independent verification axes. Every one of his examples has the same shape:

• Type systems. Axis one is the code, what it does. Axis two is the type annotations, what shape the data has. They must agree at every step.
• Formal verification. The code, and the mathematical properties. The program has to satisfy the properties.
• Transaction simulation. The user's action, and the previewed consequences. The user confirms after seeing both.
• Multi-sig and social recovery. Multiple keys, multiple specifications of authority. All of them must agree.

The common structure: N independent specifications of intent, and the system acts only when all N align.

The authority equation

CCP writes that down as:

$$A(t) = C(t) \cdot e^{-\alpha n} \cdot e^{-\lambda \tau}$$

where $C(t)$ is a coherence vector composite:

$$C(t) = \left( I^{\beta} \cdot R^{\gamma} \cdot P^{\delta} \cdot X^{\epsilon} \cdot B^{\zeta} \right)^{1/(\beta + \gamma + \delta + \epsilon + \zeta)}$$

Five independent axes, each a different specification of the actor's intent:

• I, identity tier. Who are you, verified how?
• R, reputation composite. A five-axis behavioral history, not a single score.
• P, policy compliance. Do your actions follow governed rules?
• X, action audit score. Do your actual transactions match your stated intent?
• B, biological continuity. Is the entity acting right now the same entity that earned this authority?

The weighted geometric mean is the critical design choice. An arithmetic mean lets you buy your way out of a weak axis with a strong one. A geometric mean punishes single-axis optimization. An actor with perfect reputation and zero biological continuity gets a composite score of zero. You can't compensate for absence on one axis by inflating another. That is Vitalik's redundant-specification principle, expressed as math.

In the reference implementation each axis also carries its own floor, so a failure names the dimension instead of returning a bare "incoherent":

/// The five-axis coherence measurement for a single actor.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct CoherenceVector {
    /// Trust tier weight: VerifiedLivingHuman=1.0, HumanPrincipalActive=0.75,
    /// AutonomousAgent=0.50, UnverifiedActor=0.25.
    pub identity_score: f64,
    /// Composite from ReputationVector (SAFE score).
    pub reputation_score: f64,
    /// Ratio of passed policy checks [0.0-1.0].
    pub policy_score: f64,
    /// Audit accuracy: 1.0 if no flagged actions, decreases with flags.
    pub action_score: f64,
    /// Heartbeat continuity [0.0-1.0]. 0.0 for agents without heartbeat.
    pub biological_score: f64,
}

impl CoherenceVector {
    /// Returns the specific axis that failed its minimum threshold,
    /// or None if all axes pass.
    pub fn failed_axis(&self) -> Option<(&'static str, f64, f64)> {
        if self.identity_score < MIN_IDENTITY {
            return Some(("identity", self.identity_score, MIN_IDENTITY));
        }
        if self.reputation_score < MIN_REPUTATION {
            return Some(("reputation", self.reputation_score, MIN_REPUTATION));
        }
        if self.policy_score < MIN_POLICY {
            return Some(("policy", self.policy_score, MIN_POLICY));
        }
        if self.action_score < MIN_ACTION {
            return Some(("action", self.action_score, MIN_ACTION));
        }
        if self.biological_score < MIN_BIOLOGICAL {
            return Some(("biological", self.biological_score, MIN_BIOLOGICAL));
        }
        None
    }
}

What the formalization adds

Temporal decay

Vitalik's pattern is static. Specifications either align or they don't. The authority equation adds two decay terms.

$e^{-\alpha n}$ is founder decay. The initial architect's authority dilutes as the network grows: $\lim_{n \to \infty} F(n) = 0^{+}$. That resolves elite capture without asking anyone to trust the founders' voluntary restraint.

$e^{-\lambda \tau}$ is staleness decay. Authority derived from past coherence degrades over time. You have to keep demonstrating alignment, not establish it once.

No existing protocol implements founder authority that provably approaches zero.

Biological ground truth

All of Vitalik's examples operate in digital space. CCP adds a physical verification axis: a continuous cardiac signature anchored to an immutable chain. Not a static biometric snapshot. A sequential, cryptographically committed record of biological continuity. The wallet is continuously proven to be operated by a living human whose cardiac signature has been present and uninterrupted.

That answers Vitalik's observation that the entity presenting credentials and the entity that earned them can be different. With biological continuity, credential transfer becomes detectable at the protocol level.

The score is deliberately blunt. A heartbeat with enough witnesses is a 1.0. No heartbeat is a 0.0, and for an autonomous agent that's allowed:

/// Computes the biological score from heartbeat data.
/// 1.0 if continuous heartbeat with witnesses, 0.0 if none.
pub fn biological_score(has_heartbeat: bool, witness_count: usize, min_witnesses: usize) -> f64 {
    if !has_heartbeat {
        return 0.0;
    }
    if witness_count >= min_witnesses {
        1.0
    } else if min_witnesses > 0 {
        witness_count as f64 / min_witnesses as f64
    } else {
        1.0
    }
}

Governed parameters

Every weight ($\beta, \gamma, \delta, \epsilon, \zeta, \alpha, \lambda$) is governed by a living constitution, amendable through coherence-weighted consensus. The security model evolves through the pattern it enforces. No parameter is hardcoded. The DAO owns every weight.

The peer review question

The specific question I want examined:

Can the composite coherence score $C(t)$ be gamed through coordinated multi-actor strategies?

The geometric mean resists single-actor, single-axis manipulation by construction. What about:

• Coordinated attestation inflation. Multiple actors cross-attesting to inflate each other's reputation axis. CCP caps attestation strength by the attester's own domain credential and rejects self-attestation. Is that enough against coalition strategies?
• Temporal gaming. Actors who hold minimal coherence through low-stakes periods to build authority, then spend it in a high-stakes window. The $e^{-\lambda \tau}$ decay helps. What is the optimal $\lambda$ that balances responsiveness against manipulation?
• Axis correlation attacks. If two axes are correlated in practice (a high identity tier tends to come with policy-compliance access, say), does the geometric mean's independence assumption hold? How much correlation can the system take before single-axis optimization starts working?

These are formally close to problems in multi-dimensional mechanism design. If you have pointers to game-theoretic frameworks for weighted geometric mean scoring under adversarial conditions, I want them.

The harder question

Here is the part most protocol whitepapers leave out.

The authority equation is domain-agnostic. It formalizes "who should have authority right now, and why" as a computable function. I built it for blockchain governance. The math doesn't know that. The same framework that keeps an Applied Intelligence agent inside its scope can build a social credit system. The same biological continuity requirement that stops credential theft can become a surveillance primitive. The founder decay function that resolves elite capture can be inverted to engineer it. A living constitution that makes governance adaptive also means whoever controls the initial parameter space controls the trajectory.

I don't fully know what this is yet.

I know the equation works. I know it formalizes a pattern that shows up in every trust system I've met in eleven years of building critical infrastructure: data centers, manufacturing, industrial automation. I know the math is clean. The implementation passes its tests.

What I don't know is what happens when a universal trust arbitration layer works exactly as designed, in the wrong hands. The failure mode I'm most worried about isn't that the geometric mean can be gamed. It's that it can't, and someone uses that property to build systems of control that are mathematically provable and therefore unchallengeable.

Oppenheimer built the physics correctly. The physics didn't care what it was pointed at.

I'm publishing this for peer review because I want it examined by people who take the ethical weight of coordination technology seriously. Not only whether the mechanism is sound, but whether it should exist in its current form, and what constraints belong on it before it leaves a research context.

This is not a product launch. This is a researcher saying: I found something, and I need more eyes on what it means.

Implementation status

• 83 blocks verified, 9 property tests passing, deterministic replay confirmed.
• Biological identity layer (MORTEM) operational on Solana devnet: 8 autonomous witness agents producing continuous heartbeat attestations.
• 12 threat vectors identified through adversarial self-red-teaming, each with a documented recovery path.
• Full white paper: in preparation.

Connection to existing work

The authority equation came out of watching trust dynamics in industrial infrastructure (data center operations, manufacturing systems), then got checked against the existing mathematical frameworks. The multi-dimensional scoring shares structure with quadratic voting (Weyl and Posner), conviction voting, and EigenTrust. It differs in requiring biological grounding and temporal decay as first-class properties.

Read the companion note on how the chain itself came together: Celaya Chain Protocol: When Consensus Is Coherence.

Christopher Celaya, Celaya Solutions, El Paso, Texas. Contact: hello@celayasolutions.com