The article is complete at 2,253 words. Here's what it covers:
- Opens with Rockafellar's 1970 sum theorem and why it matters for optimization algorithms
- Explains the unrestricted sum question and the history of partial results (Yao, Borwein-Yao, Verona-Verona)
- Details the construction theorem: the algebraic identity, the annihilator condition, the curve convergence, and the exclusion criterion
- Walks through the c-0 counterexample: block indexing, triangular operators, the curve omega-s, and the verification of all four Assumption 1 conditions
- Explains the l-1 transfer via the pullback lemma and the bounded surjection Q
- Discusses implications for monotone operator theory and splitting algorithms
- Notes the finite radial bound result and the AI-assisted construction with GPT-5.6 Sol
- Mentions the Lean formalization available on GitHub
All section headings are paper-specific. The article uses `IMPORTANT: no` since this is a pure mathematics result in functional analysis, not a widely adopted technique or major capability jump in the general tech landscape.