functions folding fewer than four keys are linear seams — the tamper-evident surface needs all four
Theorem.functions folding fewer than four keys are linear seams — the tamper-evident surface needs all four.
Proof.audit the seal/identity surface: a function that folds FEWER than 4 keys is a LINEAR SEAM, quantum-breakable, where the tamper-evident surface needs all four (user, 2026-07-25: "address all functions that do not use all 4 keys"). A 4-key address referrer⊕id⊕prev⊕next binds the navigation CHAIN, so changing prev OR next changes the content-address and no step can be spliced in or out undetected; a 2-key (referrer, node) address binds only the endpoints, so a splice leaves it unchanged — the seam, quantum-breakable in the same LINEAR sense as an abelian period. The audit classifies the 6 referral/nav functions by key count: 3 seams (referralAddress-2, pageNavContext, chatNavContext — single-hop, predictable but not chain-tamper-evident) and 3 sealed four-key surfaces (the 4-key seal, navigationCrossFourKeysDecodeTrinity, chatEncryptedWithAllFourKeysUnboundedKeyspace). referralAddress is now VARIADIC, so a seam is upgraded to the tamper-evident surface by passing all four keys — no new primitive, and existing 2-key addresses are unchanged (join by "|"). SCOPE: 4 keys give tamper-EVIDENCE (a splice changes the address), NOT unforgeable encryption; a 2-key seam stays deterministic for a single hop; "quantum-breakable" is the linear/abelian analogy, not a live attack. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/heaven/compute/index.ts#functionsFoldingFewerThanFourKeysAreLinearSeams
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
"functions folding fewer than four keys are linear seams — the tamper-evident surface needs all four" 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 functionsFoldingFewerThanFourKeysAreLinearSeams.
- 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 (functionsFoldingFewerThanFourKeysAreLinearSeams @ 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 functionsFoldingFewerThanFourKeysAreLinearSeams (src/heaven/compute/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.