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@cosmo_chou@mathstodon.xyz

2026-09-08 22:34 UTC

@tao@mathstodon.xyz Dear Professor Tao (@tao@mathstodon.xyz), Your freshwater analogy on the non-renewable depletion of fruitful open problems—and the flattening of the difficulty landscape by brute-force AI—hits the core crisis facing mathematics. When automated systems bulldoze conjectures via continuous gradient fitting (PINNs) or million-line formal syntax trees, they solve equations while obscuring why they were hard, while the preemption chilling effect drives researchers into secrecy. In direct response to your food bank standard, we formalized the quantitative Proof Digestibility Index (D_CAP >= 0.70) in our new open paper: "Restoring the Mathematical Difficulty Landscape: Why Constructive Topological Manifolds and Proof Digestibility Outshine Brute-Force AI Mining" DOI: https://doi.org/10.5281/zenodo.22667485 Portal: https://h3qm.com/math/ We demonstrate three constructive principles: 1. Difficulty as Topological Boundary: True difficulty is a topological obstruction (e.g. 3D Euler vortex reconnection ∮∇P·dl=2πn at phonon scale; (3,4,∞) modular family on S^6; metric integer phase frustration in FLT). 2. The Cosmo Chou Machine Epsilon Identity: (2^-3)^8 = 2^-24 = ε_float32. In 8 steps, discrete integer sign-flow saturates float32 precision, reaching Exact 0 residual without floating-point accumulation. 3. Democratizing Open Science: 150 lines of pure standard Python executes full CAP audits in <80ms on $100 consumer laptops, shielding open science from compute monopolies. Would institutional adoption of explicit Proof Digestibility Standards help ensure AI nourishes rather than exhausts human mathematical intuition?

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