The SnapKitty Theorem Book is the Yellow Book / SEIT Edition of the SNAPKITTYWEST formal-methods corpus: a cryptographically sealed registry of 78 Lean 4 theorem records

┌──────────────────────────────────────────────────────────────┐
│  SOVEREIGN CRYPTOGRAPHIC SEAL                               │
├──────────────────────────────────────────────────────────────┤
│  Work: The SnapKitty Theorem Book                            │
│  Edition: Yellow Book / SEIT Edition                         │
│  Publisher: Saint Errant Digital Institute of Technology     │
│  Corpus: 78 Lean 4 theorem records                           │
│  Seal Type: SHA-256 / WORM-chain / archival deposit          │
│  Status: Prior-art publication record                        │
└──────────────────────────────────────────────────────────────┘

The SnapKitty Theorem Book  

Yellow Book / SEIT Edition

Saint Errant Digital Institute of Technology
SEIT — Sovereign AI Governance
EIN: 42-2652897
Founded: 2026-05-21
In care of: SnapKitty Collective

SEIT is presented as an independent certification body for Sovereign Artificial Intelligence: autonomous computing systems that govern themselves through structural axioms, hardware-aware operation, and cryptographically verifiable audit trails.

SEIT does not regulate AI.

SEIT certifies sovereignty.

The SnapKitty Theorem Book is the Yellow Book publication of the SNAPKITTYWEST formal-methods corpus: a sealed registry of 78 formal theorems across 12 Lean 4 files, including 63 proven theorems, 15 admitted frontier statements, and 11 named axioms.

This volume is not only a theorem list. It is a cryptographically anchored publication layer for a sovereign AI verification stack.

At its core, the book documents a machine-checkable corpus spanning:

- resonance-to-sovereignty trust kernels
- formal pipeline invariants
- golden-zone uniqueness
- meta-resonance governance verification
- Collatz trajectory verification
- P/NP swarm verification
- Gödel incompleteness framing
- Riemann / Metatron structural claims
- Navier–Stokes formal boundary statements
- WORM-chain audit closure
- multi-witness verification logic
- the Ancient Sorry meta-verification theorem

The corpus is organized as a formal theorem registry, with each theorem presented by Lean identifier, source file, proof status, mathematical statement, and formal-methods commentary. The book distinguishes between what is closed, what is admitted, and what is axiomatically imported. This distinction is intentional: proof integrity requires that the frontier remain visible.

---

 Formal Preview

The central publication claim is not that every mathematical frontier is closed.

The claim is that the system exposes its proof boundary.

```lean
resonant(d) → sovereign(d)
sovereign(d) → resonant(d)
resonant(d) ↔ sovereign(d)

Keywords:
Sovereign AI
Formal verification
Lean 4
Theorem registry
WORM ledger
Cryptographic audit trail
AI governance
Prior art
SnapKitty
SEIT
Saint Errant Digital Institute of Technology
Agentic infrastructure
Machine-checked proofs
Sovereign compute

Related identifiers:
Repository: https://github.com/SNAPKITTYWEST
Reference implementation: https://collectivekitty.com/observer

License:

Notes:
SEIT — Saint Errant Digital Institute of Technology
EIN: 42-2652897
Founded: 2026-05-21
In care of: SnapKitty Collective

“A system that cannot prove it governs itself does not govern itself.”

source theorem
    ↓
Lean identifier
    ↓
proof status
    ↓
formal-methods commentary
    ↓
cryptographic content root
    ↓
WORM-chain audit record
    ↓
archival publication
    ↓
citable prior-art boundary

 ╔══════════════════════════════════════════════════════════════╗
║              SNAPKITTY THEOREM BOOK — YELLOW BOOK           ║
╠══════════════════════════════════════════════════════════════╣
║  78 formal theorem entries                                  ║
║  12 Lean 4 source files                                     ║
║  63 proven theorem records                                  ║
║  15 admitted frontier statements                            ║
║  11 named axioms                                            ║
║  SHA-256 content-root anchoring                             ║
║  WORM-chain audit framing                                   ║
║  SEIT sovereign publication metadata                        ║
╠══════════════════════════════════════════════════════════════╣
║  EVIDENCE OR SILENCE                                        ║
╚══════════════════════════════════════════════════════════════╝

flowchart TD
    A[Lean 4 Source Corpus] --> B[Theorem Registry]
    B --> C[Proof Status Classification]
    C --> D[Formal-Methods Commentary]
    D --> E[SHA-256 Content Root]
    E --> F[WORM-Chain Audit Frame]
    F --> G[SEIT Institutional Seal]
    G --> H[Zenodo Archival Deposit]
    H --> I[Citable Prior-Art Record]

Purpose

This publication exists to make the work:

• citable
• inspectable
• timestamped
• defensible
• reproducible
• institutionally anchored
• cryptographically sealed

It is a bridge between code, proof, governance, and publication.

The result is a cold-storage theorem record for sovereign AI infrastructure: a formal corpus that can be read by humans, checked by machines, and anchored as prior art.