# Phase 4: Advanced Research

{% hint style="info" %}
**Advanced research.** These items improve long-term safety and scale after the core product path is stable.
{% endhint %}

This phase covers longer-range work where correctness matters more than speed. It focuses on stronger safety checks, backup signature options, compact audit history, and shared approval for high-value agents.

***

## Research Tracks

```mermaid
%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#003399', 'primaryTextColor': '#eff6ff', 'primaryBorderColor': '#1a7fff', 'lineColor': '#3d8bff', 'secondaryColor': '#001650', 'tertiaryColor': '#000d20', 'clusterBkg': '#001650', 'titleColor': '#eff6ff', 'edgeLabelBackground': '#001650'}}}%%
graph TD
    FV["Formal Safety Checks\ncontracts and registry rules"]
    SLH["Backup Signature\nhash-based fallback"]
    REC["Compact Audit History\ncompressed proof trail"]
    THRESH["Shared Approval\nmulti-party control"]
    PARAM["Parameter Monitoring\n2080 horizon"]

    PARAM --> FV
    PARAM --> SLH
    FV --> REC
    SLH --> THRESH
    REC --> THRESH

    style FV fill:#003399,color:#eff6ff,stroke:#1a7fff
    style SLH fill:#003399,color:#eff6ff,stroke:#1a7fff
    style REC fill:#001650,color:#7dd3fc,stroke:#3d8bff
    style THRESH fill:#001650,color:#7dd3fc,stroke:#3d8bff
    style PARAM fill:#003399,color:#eff6ff,stroke:#1a7fff
```

***

## Formal Safety Checks

The CevexRegistry holds public keys, revocation state, and metadata commitments for agent identities. Formal safety checks target machine-checked assurance for the registry rules.

| Property                 | Statement                                                     |
| ------------------------ | ------------------------------------------------------------- |
| Registration uniqueness  | A public key maps to one deterministic agent address          |
| No unauthorized rotation | Key rotation requires authorization under the active key      |
| No reactivation          | A revoked identity cannot return to active status             |
| Integrity                | Public key state changes only through the rotation path       |
| Liveness                 | A valid active agent can rotate or revoke when policy permits |

Candidate methods include K framework specifications, Certora Prover rules, and property-based Solidity tests.

***

## Backup Signature Scheme

SLH-DSA, formerly SPHINCS+, gives CEVEX a conservative hash-based fallback whose security does not rely on lattice assumptions.

| Scheme       | Signature size | Signing profile | Security assumption    |
| ------------ | -------------: | --------------: | ---------------------- |
| Dilithium-3  |        3,293 B |            fast | Module LWE and MSIS    |
| FALCON-512   |          666 B |            fast | NTRU lattice hardness  |
| SLH-DSA-128s |        7,856 B |          slower | Hash function security |

SLH-DSA is best suited for high-value, low-frequency operations where conservative assumptions are worth the added size and signing cost.

***

## Compact Audit History

Recursive proofs compress long action histories into a proof that remains small as the number of verified actions grows.

For a chain of $n$ valid agent actions:

$$\pi\_i \leftarrow \text{Prove}!\left(V(pk\_i,m\_i,\sigma\_i)=1 \land \pi\_{i-1}\text{ valid}\right)$$

The target compression profile is:

$$|\pi\_{\text{recursive}}| = O(1)$$

$$T\_{\text{verify}} = O(1)$$

This matters for long-running agents that need to provide compact audit evidence without replaying every historical signature.

***

## Shared Approval Signing

Shared approval signing allows an agent identity to require $t$ of $n$ authorized parties before producing a valid signature. The design target is distributed control without any participant holding the full signing key.

The Dilithium secret vector can be shared additively over $R\_q$:

$$\mathbf{s}*1 = \sum*{i=1}^{n}\mathbf{s}\_1^{(i)} \pmod q$$

A valid signing response is produced only when enough shares participate:

$$|{i : \mathbf{s}\_1^{(i)} \text{ participates}}| \geq t$$

***

## Research Milestones

| Milestone                      | Status   |
| ------------------------------ | -------- |
| Registry safety specification  | Research |
| Machine-checked safety proofs  | Research |
| Backup signature study         | Research |
| Compact proof feasibility      | Research |
| Shared approval signing design | Research |
| Parameter monitoring process   | Ongoing  |

***

## Next

* [Phase 1: Core Identity](/roadmap/foundation.md)
* [Phase 2: Developer Tools](/roadmap/developer-access.md)
* [Phase 3: Production Integrations](/roadmap/ecosystem-expansion.md)


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