Book 6: seed differential-equations library (heat equation + helix to… - #24
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TOTOGT wants to merge 5 commits into
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Book 6: seed differential-equations library (heat equation + helix to…#24TOTOGT wants to merge 5 commits into
TOTOGT wants to merge 5 commits into
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…y model scaffolds)
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new version of this paper was added to folder PAPERS on AXLE |
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Seeds the Book 6 differential-equations library with two honest-scaffold Lean companions, per each paper's own sorry/axiom ledger. No lake build attempted yet.
HeatEquation_Step1.lean (new):
H10 (H^1_0(0,1)) and the bilinear form a_tau are axiom-backed placeholders, matching the monograph's own Remark 1.1/2.1. a_coercive, a_bounded, weak_solution_exists_unique are sorry (Part I). Ah is a real, concrete tridiagonal matrix, no placeholder needed; Ah_isSymm is proved outright. truncation_error, energy_stability, lax_equivalence_specialized are sorry (Part II). discreteLaplacian_eigenpairs, conditioning_bound are sorry (Part III). H_heat_deriv and H_heat_strictly_decreasing are proved outright with no H10 needed, since it is a concrete check on the exact solution matching the monograph's Remark 20.2. compression_not_injective is proved outright from an axiomatized kernel element, matching the monograph's Remark 21.7 which calls it close to mechanical.
HelixToyModel.lean (added as-is): already a complete file with real proofs (neutral-line sign trichotomy, Hopf-degeneracy identity) plus three tagged sorries, issues H1 through H3, for the closed-form ODE check, the Lyapunov limit, and the no-go divergence argument.
differential-equations/ contains the paper sources: heat-equation/heat_equation_monograph.pdf and helix-toy-model/ with the tex, pdf, py, and figure files.
lakefile.toml gets two new lean_lib targets: HeatEquationStep1 and HelixToyModel.
Nothing here has been compiled against Mathlib. Every sorry is tagged with an issue ID in the file header, mirroring the AXLE tracker convention used for TribonacciRatioConvergence.lean.