THM0191canonicalv1Parseval Identity
Parseval identity: ‖f‖² = Σ_n |⟨f,e_n⟩|². The Pythagorean theorem for orthogonal spectral decomposition. Verified for test functions at N=2,6.
Payload
Parseval Identity
| Parseval identity: ‖f‖² = Σ_n | ⟨f,e_n⟩ | ². The Pythagorean theorem for orthogonal spectral decomposition. Verified for test functions at N=2,6. |
Parseval Identity
Summary
| Parseval identity: ‖f‖² = Σ_n | ⟨f,e_n⟩ | ². The Pythagorean theorem for orthogonal spectral decomposition. Verified for test functions at N=2,6. |
Statement
No manuscript statement was extracted in this pilot run.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 216 - Manuscript source: not matched
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Doors.SpectralDecomp - Name:
parseval_6
Dependencies
- Canonical: III.D81, III.D82
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.T56parseval-identitythm:parsevalRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (2)
Appears in (1)
Downstream uses (computed) (4)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.