We prove that the Conflict-Driven Clause Learning (CDCL) algorithm is formally equivalent to a branching collapse chain: a collection of collapse chains that share information through learned clauses, with globally monotone non-decreasing information content despite local backtracking. The equivalence resolves the backtracking paradox: backtracking does not reverse collapse. It terminates the current chain and initiates a new one from a checkpoint, with the learned clause serving as the irreversible information transfer between chains. The global information content of CDCL is monotone non-decreasing (Information Monotonicity Theorem), consistent with the branching collapse chain definition. Three consequences follow: (1) The Information Monotonicity Theorem — each k-literal learned clause contributes n−k bits of information, explaining why modern CDCL implementations prioritise short clauses; (2) The Gradient Impossibility Theorem — no differentiable collapse operator can improve upon CDCL for SAT near the phase transition, providing a principled explanation for the hard wall; (3) Empirical validation — 47 out of 100 variables exhibit intrinsic uncertainty across satisfying assignments at α=4.2, confirming that residual uncertainty after CDCL is structural, not epistemic. Part of the NSD / MOEH research programme. Companion papers: "Collapse as a Unifying Language for NP-Hard Optimisation" (Zenodo: 10.5281/zenodo.19574013) and "A Landscape-Aware Classification Framework for NP-Hard Optimisation Problems" Version 2.1 (May 2026) — Changes from Version 1 This version was prepared for journal submission. All proofs, definitions, theorems, and empirical results are unchanged from Version 1. The revisions address presentation and self-containment: - Author block formalised. Programme tagline removed; full author identification provided (name, affiliation, location, ORCID, email). - Self-contained framing. Definitions of collapse operator and collapse chain are now stated without external attribution. Section 1.2 retitled "Branching Search with Information Accumulation"; Section 9.3 retitled "Prior Use of the Collapse Terminology". The paper depends only on its own definitions for all results. - Springer-standard declarations added. Funding, Competing Interests, Authors' Contributions, Data Availability, and Ethical Approval statements included. - AI Declaration added as an independent section, replacing the previous inline acknowledgement. - Bibliography corrections. Self-references switched to canonical Zenodo DOIs; "under review" annotations removed for stability across review cycles. (NP Landscape DOI corrected from a clerical error in Version 1: 19456455 → 19653758.) - Table 2 body citations added. Explicit Table 1 / Table 2 references in body text (preventive formatting alignment with Springer editorial requirements). - Pagination. 18 → 20 pages (due to declarations block).
H Y Rao (Wed,) studied this question.