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Mathematics
The Claim Before the Proof
Definitions and Assumptions
What Counts as Proof?
Mathematical Models and Physical Theories
Counterexamples
Uncertainty Without Confidence Theatre
AI as Proposer, Not Authority
Provenance and Reproducibility
Symbolic Algebra with SymPy
Adversarial Math From First Principles
Constraints and Models with Z3
Lean 4 and Mathlib
Rocq as an Independent Kernel
Isabelle/HOL and Countermodels
SageMath and Scientific Computation
The Cross-System Claim Contract
The Investigation Engine
Events and Reference Frames
The Postulates and Their Roles
The Lorentz Transformation
The Invariant Interval
Time Dilation and Length Contraction
Velocity, Light Cones, and Causality
Anatomy of a Challenge
Hidden-Assumption Audits
From a Source Page to a Checked Theorem
Alternative Formulations
Repairing a Refuted Claim
The `sorry` That Wasn't the Proof
Independent Reproduction
What We Can Conclude