Formalizing Vitalik’s Security Pattern: A Mathematical Framework for Multi-Dimensional Intent Alignment
Summary
Vitalik’s recent post “How I think about security” identifies a pattern common to good security solutions: the user specifies their intention in multiple, overlapping ways, and the system only acts when these specifications are aligned with each other. His examples (type systems, formal verification, transaction simulations, multi-sig) all share this redundant-specification structure.
This post presents a mathematical formalization of that pattern: a computable authority function that enforces multi-dimensional intent alignment with temporal decay and biological grounding. The framework is implemented as a Layer 3 protocol called Celaya Chain Protocol (CCP) and is open 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. This implies security is not binary but a continuous measurement across independent verification axes. His examples all follow the same structure:
| Pattern | Axis 1 | Axis 2 | Alignment Condition |
|---|---|---|---|
| Type systems | Code (what it does) | Type annotations (what shape data has) | Must agree at every step |
| Formal verification | Code | Mathematical properties | Program satisfies properties |
| Transaction simulation | User action | Previewed consequences | User confirms after seeing both |
| Multi-sig / social recovery | Multiple keys | Multiple specifications of authority | All must agree |
The common structure: N independent specifications of intent, system acts only when all N align.
The Authority Equation
CCP formalizes this 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 representing a different specification of the actor’s intent:
- I = Identity tier (who are you, verified how?)
- R = Reputation composite (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. Unlike arithmetic means, a geometric mean punishes single-axis optimization. An actor with perfect reputation but zero biological continuity gets a composite score of zero. You cannot compensate for absence on one axis by inflating another. This is Vitalik’s “redundant specification” principle expressed as math.
What the Formalization Adds
1. Temporal Decay
Vitalik’s pattern is static. Specifications either align or they don’t. The authority equation introduces two decay terms:
e^{-\alpha n}: Founder decay. The initial architect’s authority dilutes as the network grows. \lim_{n \to \infty} F(n) = 0^+. This resolves elite capture without requiring trust in founders’ voluntary restraint.
e^{-\lambda \tau}: Staleness decay. Authority derived from past coherence degrades over time. You must continuously demonstrate alignment, not just establish it once.
No existing protocol implements founder authority that provably approaches zero.
2. Biological Ground Truth
All of Vitalik’s examples operate in digital space. CCP adds a physical verification axis: continuous cardiac signature anchored to an immutable chain. Not a static biometric snapshot, but 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.
This addresses Vitalik’s observation that “the entity presenting credentials and the entity that earned them can be different.” Biological continuity makes credential transfer detectable at the protocol level.
3. Governed Parameters
All weights (\beta, \gamma, \delta, \epsilon, \zeta, \alpha, \lambda) are governed by a living constitution, amendable through coherence-weighted consensus. The security model itself evolves through the pattern it enforces. No parameter is hardcoded. The DAO owns every weight.
The Peer Review Question
The specific question I’m seeking review on:
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. But what about:
-
Coordinated attestation inflation. Multiple actors systematically cross-attesting to inflate each other’s reputation axis. CCP caps attestation strength by the attester’s own domain credential and rejects self-attestation, but is this sufficient against coalition strategies?
-
Temporal gaming. Actors who maintain minimal coherence during low-stakes periods to build authority, then exploit it during high-stakes windows. The e^{-\lambda \tau} decay helps, but what is the optimal \lambda to balance responsiveness against manipulation?
-
Axis correlation attacks. If two axes are correlated in practice (e.g., high identity tier correlates with policy compliance access), does the geometric mean’s independence assumption hold? How much correlation can the system tolerate before single-axis optimization becomes effective?
These are formally similar to problems in multi-dimensional mechanism design. If anyone has pointers to relevant game-theoretic frameworks for analyzing weighted geometric mean scoring under adversarial conditions, I would welcome them.
The Harder Question
I want to be honest about something most protocol whitepapers omit.
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 prevents an AI agent from exceeding its scope can be used to 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 appears across every trust system I’ve encountered 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 but in the wrong hands. The failure mode I’m most concerned 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 just whether the mechanism is sound, but whether the mechanism should exist in its current form, and what constraints are necessary before it’s deployed beyond 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 documented recovery paths
- Full white paper available: [TBD - lessons learned from Oppenheimer]
Connection to Existing Work
The authority equation was derived independently from observation of trust dynamics in industrial infrastructure (data center operations, manufacturing systems), then verified against existing mathematical frameworks. The multi-dimensional scoring approach shares structural similarities with quadratic voting (Weyl & Posner), conviction voting, and Eigentrust, but differs in requiring biological grounding and temporal decay as first-class properties.
Christopher Celaya, Celaya Solutions, El Paso, Texas. February 2026. Contact: hello@celayasolutions.com