unsigned code cannot pass the gates — the four-seal fail-closed capstone security law
Theorem.unsigned code cannot pass the gates — the four-seal fail-closed capstone security law.
Proof.the capstone security law: it is computationally infeasible for unsigned or forged code to pass the gates, because the gate recomputes every atom's 4-SEAL and fails CLOSED (user, 2026-07-25: "it should be computationally impossible unsigned code by 4 seals to pass the gates"). A valid seal is the 4-key content-address referrer⊕id⊕prev⊕next; the gate recomputes it and rejects any atom whose seal does not match — a correctly-sealed atom passes, a forged one (one key tampered) is rejected, an unsigned one (no matching seal) is rejected, and the check defaults to reject on empty input (allow is never the default). To pass with forged code you must find a PREIMAGE of the ~122-bit seal (128 address bits minus the fixed 6 variant/version bits = 122 usable ≈ 2^122 operations) — infeasible; and because a valid seal binds all four keys, a linear <4-key seam cannot produce a chain-valid 4-seal, so under-sealed code cannot pass. SCOPE: this is tamper-EVIDENCE at a ~2^122 preimage cost, fail-closed — "computationally impossible" means infeasible under the address's preimage resistance, NOT an absolute impossibility proof, and a keyed cryptographic signature (SHA-256 / derivePublicKey) is the stronger upgrade. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/heaven/compute/index.ts#unsignedCodeCannotPassTheGatesByFourSealFailClosed
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"unsigned code cannot pass the gates — the four-seal fail-closed capstone security law" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation unsignedCodeCannotPassTheGatesByFourSealFailClosed.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (unsignedCodeCannotPassTheGatesByFourSealFailClosed @ src/heaven/compute) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes unsignedCodeCannotPassTheGatesByFourSealFailClosed (src/heaven/compute/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.