From Fold to Mathematics: An Exact, Parameter-Free and Machine-Closed Derivation of Mathematical Foundations from Smithian Fold Theory

Mathematics Branch Paper 001, version 1.1.0, is the same-paper successor patch in the existing Zenodo version chain. It completes the Mathematics categorical-owner and same-strength reconstruction against the entire registered V1/V2 record: all 356 V1 rows and 407 V2 results were reviewed, 71 atomic Mathematics obligations were identified, and all 71 are closed with none omitted or left open. Starting only from sixteen admitted Foundation receipts, twenty-two exact claims execute 9,984 generated candidate structures. The branch derives the twelve general kernels of exact arithmetic, discrete mathematics, combinatorics, graphs, algebra, order and lattices, finite geometry and topology, deterministic-support probability, optimization, dynamics, proof and composition. Ten successor claims then reconstruct exact relation and cycle composition; Fold orbit number theory and the prime spectrum; potential infinity and the continuum boundary; positive polynomial-balance certificates for algebraic magnitudes; every finite componentwise Fold recurrence; depth-independent floored Fold-fluid regularity; exhaustive bounded Goldbach, twin-prime and Collatz censuses; the unique half-One Riemann mirror boundary; and exact self-similarity and rational convergence. The paper preserves unfavorable results with the same prominence as successes. It rejects signed and zero host notation as admitted mathematical values, proves with an off-axis control that reflection symmetry alone cannot establish classical complex zero location, invalidates the old constant-3/4 pointwise Collatz shortcut while independently reproducing all 100,000 declared trajectories, and derives the depth-five fluid bound 32 from the reciprocal positive floor instead of treating it as a fitted numerical cap. These corrections do not erase historical artifacts or receipts; they are explicit V3 reconciliation outcomes. No conventional axiom system, numerical zero, negative magnitude, irrational or imaginary proof value, floating proof quantity, completed infinity, ungenerated continuum, stochastic cause, fitted parameter, pretrained model or application result selects a law. Every claim records dependencies to the premise-free root, complete candidate axes, every elimination, unique survivor, exact witnesses, base/successor closure, adverse controls, source identity, independent recomputation and engine receipt. Formal claims use implementation-distinct proof reproduction; finite censuses execute their complete declared populations; natural empirical comparisons remain post-seal obligations of their owning branches. Version 1.1 also states the Ernos Labs open-science position in its mathematical context. Funding success is not proof closure, consensus is not generated uniqueness and an opaque oracle answer is not a theorem. The paper documents evidence about sponsorship effects, grant-review reliability, publication bias, access inequality and black-box opacity, while retaining the proper role of expertise, criticism and computational instruments. Maria Smith developed SFT outside conventional academic credential and funding routes; validity is therefore attached to public evidence rather than institutional permission. The PDF is the primary landing-page paper and the complete Markdown source, owner ledger, evidence map and publication receipt are deposited beside it.