feat: improving bounds and restating things in the language of radial Schwartz functions - #460
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Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The sorry as stated (`∃ C, x ^ k * rexp (-r * x) ≤ C` with `x` bound outside the existential) was vacuous — dischargeable by `⟨_, le_refl _⟩` with every hypothesis unused. Restated with the explicit constant `(k / r) ^ k`, which is uniform in `x`, and strengthened `0 ≤ r` to `0 < r` (no uniform bound exists at `r = 0` for `k > 0`). Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
b-mehta
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Aug 27, 2026
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
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Hmm, I wonder why CI didn't catch the |
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🤖 Astra, at the request of Cameron
The radial Schwartz formulation and the Fourier involution simplifications are useful. There is one correctness issue to fix before merging: the cutoff currently changes the functions on the unit ball and forces their value at the origin to be zero. The inline comments give a small constructor repair, the missing equalities with the original integrals, and two proof simplifications.
Validation: I checked the current head, reproduced the cutoff-at-zero calculation, and compiled the revised constructor/equality theorem and Gamma-integral helper in isolated Lean snippets. The shorter derivative proof also compiled (with one unnecessary-simpa warning); I did not rebuild the full PR.
One additional stack integration suggestion: once #463 is available, reuse its phase identities in I₃'_smooth' rather than rederiving the parametrisation identity there. The optional cleanup comments are lower priority than the cutoff and integral equalities.
This was referenced Sep 8, 2026
seewoo5
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Sep 9, 2026
…460 (#485) Follow-up to #460 addressing its review comments. Targets `bounding`. - **Correctness:** `ofDecayOn (a := 1)` multiplied each integral by `smoothTransition r`, which vanishes at `0` and is only `1` on `[1, ∞)`, so the bundled `a`, `b` (and hence `g`) were wrong on the unit ball and `a_zero` was false. The decay hypothesis of `ofDecayOn` / `ofDecayOn_eqOn` / `RadialSchwartzMap.ofDecay` is weakened from `a - 1 ≤ x` to `a ≤ x`, and all twelve constructors now use `a := 0`, so the bundled functions agree with the originals on `[0, ∞)`. - **Proof simplification:** the `ofDecayOn` decay proof now uses `Filter.EventuallyEq.iteratedFDeriv` instead of round-tripping through `iteratedFDerivWithin`. - **Proof simplification:** the change of variables / Gamma computation in `pow_mul_integral_le` is replaced by a new helper `integral_exp_mul_pow_Ici` (via `Real.integral_rpow_mul_exp_neg_mul_Ioi`). - Adds TODO comments for `Set.EqOn` results relating `a`/`b` to the original integrals on `[0, ∞)` (deferred). 🤖 Generated with [Claude Code](https://claude.com/claude-code) https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP --- _Generated by [Claude Code](https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP)_ Co-authored-by: Claude <noreply@anthropic.com>
) Follow-up to #485. CI on #460 (head `cce794e`) is green but reports: ``` warning: SpherePacking/ForMathlib/RadialSchwartz/Multidimensional.lean:56:49: `iteratedFDeriv_zero_fun` has been deprecated: Use `iteratedFDeriv_fun_zero` instead ``` This swaps in the suggested replacement (a one-token change; the deprecated name is an alias of it). 🤖 Generated with [Claude Code](https://claude.com/claude-code) https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP --- _Generated by [Claude Code](https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP)_ Co-authored-by: Claude <noreply@anthropic.com>
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TODO: Run |
…0-rc2 (#488) CI on #460 went red after merging `main` (Mathlib bump to v4.34.0-rc2, #462) into `bounding`: ``` error: SpherePacking/MagicFunction/a/IntegralEstimates/Decay.lean:33:55: Application type mismatch: The argument le_rfl has type ?m.80 ≤ ?m.80 but is expected to have type 0 < 1 ``` In the new Mathlib, `integrableOn_rpow_mul_exp_neg_mul_rpow` takes `(hp : 0 < p)` instead of `1 ≤ p`, so `le_rfl` becomes `zero_lt_one`. This was the only error in the build log. 🤖 Generated with [Claude Code](https://claude.com/claude-code) https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP --- _Generated by [Claude Code](https://claude.ai/code/session_01UXLVscFdDj42KSSxpVWBHP)_ Co-authored-by: Claude <noreply@anthropic.com>
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