Frédéric Riesz (1907), Comptes rendus hebdomadaires des séances de l’Académie des sciences 144:1409–1411 — https://archive.org/details/comptes-rendus-hebdomadaires-academie-des-sciences_1907-06-24_144_25
Standing in the record
Registered on 2026-09-29 at the owner’s request, because the owner’s prior-art novelty map (a private working document on concepts as projectors, the linear representation hypothesis and their neighbours) cites it: row 10 / R2: “Riesz-forced unique factorization” behind the Universal Convergence claim; the docs already cite Riesz. It is seeded from metadata and published descriptions and has not been read here.
The map names this reference only loosely; this entry is one reasonable reading of it, and the choice is the owner’s to revise.
Identification notes: Nucleation ALREADY covers the theorem via LIT-230 (Riesz representation theorem, Wikipedia) and LIT-243 (Adler 2021 REU exposition), plus the Riesz→RKHS cluster (LIT-248, 249, 252, 258, 260, 261) — but not the primary paper. Owner decides whether the primary is wanted or LIT-230 suffices. Issue text verified on the Internet Archive scan (séance of 24 June 1907); Fréchet’s simultaneous note “Sur les ensembles de fonctions et des opérations linéaires” (C. R. 144:1414–1416, same issue) not registered. No DOI exists; Gallica returned 403.
It was filed Deferred, unread. NOTE-289 is the close reading of 2026-09-29, and it placed the work: Active — worth reading only as the historical first statement of the Riesz representation theorem on L², and it takes three minutes. It states and does not prove. For the theorem itself, and for anything the record argues from it, a modern proof (LIT-243, or any functional-analysis text) supersedes it as a source.