an object may be a combination of objects — closed, recursive, like biology
Theorem.an object may be a combination of objects — closed, recursive, like biology.
Proof.a content-addressed object may be a COMBINATION of objects, recursively, like biology (user, 2026-07-25: "an object may be combinations of objects. like biology"). A composite object is the merkle of its parts and is itself an object, so composition is CLOSED (a monoid on addresses); objects nest — organism ⊃ organs ⊃ cells — each level an object with its own content-address; the combination has its own tamper-evident identity (its address changes if any part changes); and composition is unbounded (K distinct combinations → K distinct addresses). SCOPE: "object = combination of objects" is content-addressed recursive composition (schema.org objects nest, like biology's organism/organ/cell hierarchy), structural; "like biology" is the compositional ANALOGY to the real biological hierarchy, NOT a claim the object is alive. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/mountain/og/index.ts#anObjectMayBeCombinationsOfObjectsLikeBiology
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
"an object may be a combination of objects — closed, recursive, like biology" 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 anObjectMayBeCombinationsOfObjectsLikeBiology.
- 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 (anObjectMayBeCombinationsOfObjectsLikeBiology @ src/mountain/og) 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 anObjectMayBeCombinationsOfObjectsLikeBiology (src/mountain/og/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.