Collapse Mathematics (cMth): From Deduction to Durability by Rogério Figurelli
English | October 4, 2025 | ISBN: N/A | ASIN: B0FTTXLBCB | 181 pages | EPUB | 1.44 Mb
This book begins from a simple discomfort: formal mathematics tells us what can be derived; it says much less about what persists when representation is stressed, information is compressed, or interpretation drifts.
Collapse Mathematics (cMth) proposes a complementary discipline organized around that missing question. Instead of asking whether a statement follows from axioms, we ask whether a symbolic structure survives distortion and remains itself after cycles of semantic collapse. The book framed this agenda and supplied the initial apparatus-collapse pressure, curvature-like response, and survivability metrics-out of which this volume grows.
In cMth, survivability is not a metaphor. It is measured. The Symbolic Survivability Index (SSI) records how a hypothesis degrades or stabilizes under iterative collapse; the semantic integrity function (C(t)) integrates recomposability over time.
Together they let us grade structures not by elegance alone but by endurance under epistemic stress. The intuition is that robust objects are those that recompress cleanly; brittle ones disperse into noise. Proof, in this perspective, becomes a special case of persistence, and undecidability becomes a behavior to be observed, not a wall to despair against.
The book introduced collapse manifolds-symbolic spaces where distinct stressors trace trajectories for competing hypotheses. These spaces are not isotropic. They exhibit instability zones and narrow corridors where interpretation remains coherent: "blue paths" that behave as attractors.
A recurring empirical character in that terrain is the configuration long associated with the Riemann critical line, which emerges as collapse-invariant across noise families and filtration schedules. Whether or not one accepts the strongest philosophical reading, the diagnostic fact remains: some structures repeatedly reconstitute; others do not. This book treats that fact as data.
Our ambition is not to enlarge rhetoric around unsolved problems, but to equip readers with a compact, sharable practice for observing symbolic endurance-one that travels across domains and can be audited in detail. If, by the end, you disagree with our readings of specific terrains yet keep the tools, the project will have succeeded.
The attractor, not the axiom, is the anchor; persistence, not presentation, is the test.
Welcome to Collapse Mathematics.
May your structures survive the fall.
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