Paradoxes Dissolved: A Canvas Temporal Mathematics Compendium

Classical paradoxes—from Russell's set to Zeno's arrow, from the Liar to Banach–Tarski—have challenged mathematicians, logicians, and philosophers for centuries. Each has generated a cottage industry of proposed solutions, restrictions, and workarounds. Yet none has been definitively resolved within the standard framework of Zermelo-Fraenkel set theory with Choice (ZFC). Canvas Temporal Mathematics (CTM) replaces the assumptions that create paradoxes, rather than adding axioms to restrict them. The six problematic assumptions of classical mathematics are: 1. Boolean equality — truth is either true or false.2. Completed infinity — infinite sets exist as actual totalities.3. Continuum — real numbers as a completed set of zero-size points.4. Axiom of choice — choice functions exist for arbitrary families.5. Static truth — mathematical statements have timeless truth values.6. Local realism — spatially separated systems are independent. CTM replaces each assumption: · Equality is spectral — a resonance amplitude, not a Boolean.· Infinity is asymptotic — a limit as meta-time \tau \to \infty, never actualized.· The continuum is discrete — a voxel lattice with minimum spacing \ell_P.· Choice is deterministic — the canvas provides unique selection.· Truth is dynamical — it evolves in meta-time toward \mathcal{S}-invariant attractors.· Reality is non-local — wave intersections connect distant events. What this compendium provides: · Sixty classical paradoxes and their dissolution in CTM. Each entry states the paradox, the standard resolution (or lack thereof) in ZFC, and the CTM dissolution with the specific axiom or mechanism that resolves it. The paradoxes are organized by domain: Set Theory and Logic, Infinity and Number Theory, Geometry and Measure, Probability and Statistics, Physics, Quantum Mechanics, and Cosmology and Philosophy.· A dissolution, not a resolution. A resolution finds a flaw in the paradoxical argument while keeping the assumptions. A dissolution changes the assumptions so the paradox never arises. CTM does not "solve" the Liar paradox by finding a flaw in the reasoning. It replaces Boolean equality with spectral equality, and the Liar becomes an oscillation—not a contradiction, but a wave.· Comprehensive tables. Two summary tables classify all sixty paradoxes by the primary assumption replaced and by the CTM mechanism that dissolves them. The Liar and its variants dissolve via the Equality Processor. Banach–Tarski and related geometric paradoxes dissolve via Discrete Spacetime. Zeno's paradoxes dissolve via the voxel lattice. EPR and Bell dissolve via the non-local canvas. The measurement problem dissolves via the Threshold Condition. Why this matters: The paradoxes are not bugs in mathematics. They are symptoms of the assumptions. Change the assumptions, and the symptoms disappear. CTM does not "solve" paradoxes by finding flaws in the reasoning while keeping the assumptions. It changes the assumptions. The Liar is not a contradiction to be excluded; it is a wave that oscillates. Banach–Tarski is not a theorem to be accepted; it is an artifact of the continuum. Zeno's arrow is not a puzzle for calculus; motion is discrete. This compendium is a companion to Emergence XXXI (Canvas Temporal Mathematics) and the broader Emergence series. It provides the evidence for the claim that CTM resolves the paradoxes that have resisted resolution in ZFC. The full mathematical machinery—the Equality Processor, the Cheeger–Plank mechanism, the Steering dynamics, the TAC operator—is developed in the companion papers. Keywords: paradoxes, Canvas Temporal Mathematics, CTM, ZFC, Boolean equality, completed infinity, continuum, axiom of choice, static truth, local realism, spectral equality, asymptotic infinity, discrete spacetime, Steering dynamics, non-local canvas, dissolution, Russell, Cantor, Banach–Tarski, Zeno, Liar, EPR, Bell, measurement problem