Corpus proof canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Proof cid006105PRF0002canonicalv1

Proof of the Hyperfactorization Theorem

Semi-formal Corpus-addressed proof of the Hyperfactorization Theorem (THM0005). Establishes that every τ-Idx element admits a unique hyperfactorization into the canonical generator system, leveraging earned boundary constants and the iterator ladder.

Payload

We prove the Hyperfactorization Theorem by combining earned boundary constants DEF0001 with lobe-swap invariance LEM0001 on the τ-domain. The unique decomposition of every τ-Idx element into the canonical generator system follows directly from these two ingredients, establishing THM0005.

Proof

mode: semi_formalstatus: completeformality: prose_addressedversion-pinning: pinned

Proof steps

  1. Earned constants pin the boundary.

    The boundary constants for the hyperfactorization construction are available by DEF0001 — earned boundary constants on the τ-domain provide the pinned data the factorization consumes.

    Uses:prrp://def0001@v1 (uses definition)

  2. Lobe-swap invariance fixes the canonical decomposition.

    Apply LEM0001 (lobe-swap invariance) to establish that the factorization preserves boundary-constant identity under the permitted symmetries on B_τ.

    Uses:prrp://lem0001@v1 (uses lemma)

  3. Conclude unique hyperfactorization.

    Combining the pinned earned constants (s1) with lobe-swap invariance (s2), every element decomposes uniquely into the canonical generator system, establishing THM0005.

Identifiers

  • Corpus ID cid006105
  • Primary alias PRF0002
  • Type Proof
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

proof-hyperfactorization

Release lines

corpus_v3_working

Relations

Upstream dependencies (2)

cid000007cid000008

Version & History

  • v1 · 2026-05-10 initial corpus item seed

Status disclaimer

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