Refactor Riemannian Util layout and simp helpers (#5 #6 #7)#41
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Ports the RiemannCurvature.lean portion of killing-pde branch (38adeaf, zhifeizhu92) onto main: two `private` helpers (`IsKilling.second_covDeriv_inner_skew`, `second_covDeriv_commutator`) plus the headline `IsKilling.second_covDeriv_eq_curvature` with full proof. RHS sign reads `Riem(Y, X) Z` to match OpenGA's commutator-form convention `Riem(U,V) = ∇_U∇_V − ∇_V∇_U − ∇_[U,V]` (equivalently `−Riem(X, Y) Z`). Volume-side fixes from the source branch (Hausdorff.lean's explicit `alphaFedererConstant`, ChartPullback.lean's `infer_instance` for sigma-finite) are dropped — the corresponding files do not exist on main's current architecture.
Port `OpenGALib/Riemannian/Volume/Util/GramDeterminant.lean` from the pre-squash killing-pde history. Already in explicit-g style (`g` as explicit parameter under `Riemannian.RiemannianMetric` namespace), so no API redesign needed against main's current conventions. Surface (all `**Math.**`, no sorry): - `gramMatrix`, `sqrtGramDet` definitions - `gramMatrix_symm`, `gramMatrix_posDef`, `gramMatrix_det_pos` - `sqrtGramDet_nonneg`, `sqrtGramDet_pos` - `gramMatrix_basis_change`, `sqrtGramDet_basis_change` First commit of the `riemannian-volume` re-port sub-project (foundation for chart-pullback volume construction → Federer bridge → BG stopgap removal).
Port `OpenGALib/Riemannian/Volume/Util/ChartSqrtGramDet.lean` from pre-squash killing-pde history. Chart-induced specialization of `sqrtGramDet`, plus the bridge identifying it with the abstract `g.sqrtGramDet x (chartBasisFamily α hx)` so the abstract `sqrtGramDet_basis_change` (Phase 1c) lifts to chart overlaps. Surface (all `**Math.**` / **Eng.** as appropriate, no sorry): - `chartSqrtGramDet` definition + `_apply` simp lemma - `chartSqrtGramDet_pos`, `_nonneg`, `_contMDiffOn` - `chartGramMatrix_eq_gramMatrix_chartBasisFamily` bridge - `chartSqrtGramDet_eq_sqrtGramDet_chartBasisFamily` bridge Dependencies (`chartGramMatrix*`, `chartBasisFamily*`) already on main under `TensorBundle/MusicalIso.lean` and `TensorBundle/SmoothOrthoFrame/`; import surface unchanged from snapshot.
Port `OpenGALib/Riemannian/Volume/Util/ChartTransition.lean` from pre-squash killing-pde history. Specializes the abstract `gramMatrix_basis_change` / `sqrtGramDet_basis_change` (Phase 1c) to chart overlaps via `transitionMatrix α₀ α₁ hx₀ hx₁`, then bridges to Mathlib's analysis-side `tangentCoordChange`. Surface (no sorry): - `transitionMatrix` definition - `chartGramMatrix_pullback_eq_mul`, `chartGramMatrix_det_pullback`, `chartSqrtGramDet_pullback` - `transitionMatrix_eq_toMatrix_tangentCoordChange`, `transitionMatrix_det_eq_tangentCoordChange_det` (LinearAlgebra ↔ analysis bridges; consumed downstream by chart-overlap measure invariance)
Port `OpenGALib/Riemannian/Volume/ChartPullback.lean` from pre-squash killing-pde history. Closes Phase 1: the headline `volumeMeasure g` definition (riemannianMeasure + chartAtlasPOU) plus two locality instances. Surface: - `volumeMeasure g : MeasureTheory.Measure M` + `dV_g[g]` notation - `instSigmaFinite_volumeMeasure` (closed via `infer_instance`, preserving zhifeizhu92's improvement on this slot) - `instIsLocallyFiniteMeasure_volumeMeasure` — PRE-PAPER sorry with in-docstring repair plan (chart-relative compact neighborhood + √det sup bound, ~30 LOC) Bumps CI `EXPECTED` 32 → 33 to absorb the one PRE-PAPER sorry.
Port `OpenGALib/Riemannian/Volume/VolumeForm.lean` from pre-squash killing-pde history. Pointwise volume form `dV_g(x) : Λⁿ(T_xM)*` skeleton; the chart-frame value `√det(g_ij(x))` and the form-vs-measure bridge are deferred (PRE-PAPER sorry on `volumeFormAt` with in-docstring repair plan: Gram-determinant + n-linear-alternating universal property; chart-invariance via `g' = Jᵀ·g·J`). Import adjustment: killing-pde's standalone `Metric.HasMetric` has been consolidated into `Metric.RiemannianMetric` on main, so the import is rewritten. Bumps CI `EXPECTED` 33 → 34 to absorb the one PRE-PAPER sorry.
Port `OpenGALib/Riemannian/Volume/Hausdorff.lean` from pre-squash
killing-pde history.
Two declarations land together:
- `alphaFedererConstant n := ENNReal.ofReal ((vol(ball 0 1)).toReal / 2^n)`
— explicit definition (zhifeizhu92's improvement, preserved from the
killing-pde tip).
- `volumeMeasure_eq_alphaFederer_smul_hausdorffMeasure` — Federer's
`vol_g = α(n) · μH[n]_{d_g}` on smooth Riemannian manifolds.
CITED-BLACK-BOX (Federer §3.2.46-50; Mattila Ch.6).
This is the **closing-bridge for the BG `IsScalarMultipleOfHausdorff`
stopgap** (issue #11). Downstream consumer: once an instance derives
`(volumeMeasure g).IsScalarMultipleOfHausdorff (Module.finrank ℝ E)`
from this theorem, BG can tighten its hypothesis to `μ = vol_g`.
Bumps CI `EXPECTED` 34 → 35.
Port `OpenGALib/Riemannian/Volume/UniversalProperty.lean` from pre-squash killing-pde history. Phase 5 skeleton: any Borel measure agreeing with `vol_g` on chart-coordinate opens equals `vol_g`. PRE-PAPER sorry with in-docstring repair plan: Mathlib `Measure.ext_of_iUnion` (uniqueness on π-system) applied to the chart-open generating set of the Borel σ-algebra; depends on the forthcoming `volumeMeasure_chart_pullback_eq` (Phase 1 follow-up). Bumps CI `EXPECTED` 35 → 36. Closes the `riemannian-volume` re-port: Phase 1 + 2 + 3 + 4 + 5 all landed on `riemannian-volume` branch, ready for review and PR back to main.
…topgap
Step 2 of the BG canonical-volume goal. The Riemannian volume measure
`vol_g` is now constructed (Phase 1 of `riemannian-volume`), so the
`IsScalarMultipleOfHausdorff` stopgap is removed from OpenGA's API
surface.
Changes:
- `Comparison/BishopGromov/VolumeComparison.lean`:
- Drop `(μ : Measure M) (hμ : μ.IsScalarMultipleOfHausdorff n_M)`
parameters from `bishopGromov_volume_comparison`.
- Replace `μ` with `vol_g := volumeMeasure HasMetric.metric` via a
local notation. The ratio's scale-invariance is preserved (any
scalar multiple of vol_g gives the same ratio), so no generality
is lost for downstream consumers.
- Add `[SigmaCompactSpace M]` to the variable block (required by
`volumeMeasure`).
- Imports: drop `MetricGeometry.Util.ScalarMultipleOfHausdorff`,
add `Riemannian.Volume.ChartPullback`.
- `Riemannian/Volume/Hausdorff.lean`:
- Add `alphaFedererConstant_pos` (requires `0 < n`) and
`alphaFedererConstant_ne_top` as general-purpose helpers (Euclidean
unit ball has positive finite Lebesgue measure; `ENNReal.ofReal`
is always finite).
- `MetricGeometry.lean`: drop the index re-export.
- `MetricGeometry/Util/ScalarMultipleOfHausdorff.lean`: deleted.
Build clean. Sorry count unchanged. BG statement now reads
textbook-cleanly: "for vol_g on M with Ric ≥ (n−1)K g, the vol_g-ratio
over the model space form is monotone." Closes the API side of #11;
the BG proof itself (#10) remains the next driver.
Shake flags `Mathlib.Analysis.Matrix.PosDef` as removable in favor of `Mathlib.LinearAlgebra.Matrix.PosDef`, but the suggestion is incorrect: `Matrix.PosDef.det_pos` (used by `gramMatrix_det_pos`) only exists in the `Analysis.` module (it depends on the eigenvalue decomposition infrastructure). Replacing the import breaks the build. Accept the +1 shake suggestion as a documented false positive until either the underlying `det_pos` migrates to LinearAlgebra-only, or we swap to an Analysis-free derivation of Gram-determinant positivity.
Riemannian volume re-port + BG canonical-volume cleanup
Adds (g : RiemannianMetric I M) as the first explicit parameter to the five curvature-core defs: - curvatureEndo, ricci (RiemannCurvature.lean) - ricciTensor, ricciSharp, scalarCurvature (RicciTensorBundle.lean) Each def-internal proof body either pipes g directly (preferred) or uses `letI : HasMetric I M := ⟨g⟩` to override the section-level [hm : HasMetric I M] when bottoming out at typeclass-dispatched primitives (riemannCurvature, covDeriv) that retire in #15. Scoped notations updated to pipe HasMetric.metric so downstream consumers using Ric(X,Y), Ric_g(v,w) x, scal_g[I] x see no change: scoped notation "Ric(" X ", " Y ")" => ricci (HasMetric.metric) X Y scoped notation "Ric_g(" v ", " w ") " x:max => ricciTensor (HasMetric.metric) x v w scoped notation "scal_g[" I "]" => scalarCurvature (I := I) (HasMetric.metric) Consumer direct-call sites (Bochner/BochnerExpansion, GMT/SecondVariation) threaded with (HasMetric.metric) explicitly — they live in [hm]-scope so the typeclass-supplied metric continues to be the ambient one. Phase 1 only: [hm : HasMetric I M] stays in variable blocks. Typeclass retirement (drop the variable) deferred to #19. Closes #14. Part of #9 umbrella. Next: #15 (Levi-Civita: riemannCurvature, covDeriv).
[9a Phase 1] Explicit g on Ricci/scalarCurvature core (closes #14)
…s scaffolding Bottom-up explicit-g groundwork below LeviCivita.lean, unblocking #15. ## Files - OpenGALib/Riemannian/Connection/Koszul.lean - OpenGALib/Riemannian/Connection/RieszExtraction.lean - OpenGALib/Riemannian/Util/CovDerivSmoothness.lean - OpenGALib/Riemannian/Util/CotangentFunctional.lean - OpenGALib/Riemannian/Connection/LeviCivita.lean (callsite bridging only) ## Changes 1. `koszulFunctional` and its 9 algebraic identities (`koszul_antisymm`, `koszul_metric_compat_sum`, `koszul_smul_right/left/middle`, `koszul_add_right/left/middle`, `koszulFunctional_local`, `koszulFunctional_tensorialAt`) gain `(g : RiemannianMetric I M)`. 2. Riesz extraction layer (`koszulLinearFunctional_exists`, `koszulCovDeriv_exists`, `koszulCovDeriv`, `koszulCovDeriv_inner_eq`) gains `(g)`. 3. Smoothness scaffolding (`koszulCovDerivAux`, `koszulCovDerivAux_tensorialAt`, `koszulCovDeriv_smoothVF_smoothAt`, `koszulCovDeriv_const_smoothAt`, `koszulCotangentScalar`, `koszulCotangentFunctional`, `koszulCotangentFunctional_apply`, `koszulCotangentScalar_mdifferentiableAt`, `koszulCotangentFunctional_smoothAt`) gain `(g)`. 4. Statements and bodies of the above use `g.metricInner` and `g.metricInner_*` method-call form throughout. 5. `LeviCivita.lean` callsites bridge via `hm.metric` (it stays typeclass-form pending the actual LeviCivita explicit-g refactor in #15). Four `rw` chains converted to `simp only` to handle the `metricInner` abbrev (typeclass) vs `hm.metric.metricInner` (explicit method) defEq gap. ## Phase 1 invariant `[hm : HasMetric I M]` stays in section variable blocks. External API unchanged. Downstream consumers (Curvature/Operators/Bochner/GMT) see no API change — they reach Koszul/Riesz only via LeviCivita's typeclass-form facade. ## Verification - `lake build`: clean, 3668 jobs. - Sorry count: 36 (baseline unchanged). - Shake: 36 (baseline unchanged). - Linter baselines: MathTag=0, AnchorPurity=0, Naming=0. ## Closes #32. Unblocks #15 (LeviCivita explicit-g).
…szul [9a-pre Phase 1] Explicit-g foundation: Koszul + Riesz (closes #32)
…ing pending (#34) * WIP 9b Phase 1: LeviCivita explicit-g (in-file only; downstream pending) LeviCivita.lean alone builds clean. Downstream consumer bridging (13+ files, ~800 callsites) is pending — full lake build is currently red. Pushed to branch as work-in-progress for visibility / continuation next session. ## In-file changes (this commit) 23 of 26 decls in `OpenGALib/Riemannian/Connection/LeviCivita.lean` take `(g : RiemannianMetric I M)` as explicit first parameter: - **Core defs:** `leviCivitaConnection`, `covDeriv`, `covDerivAt`, `riemannCurvature` (`covDerivRiemann` left typeclass-only for now — its body uses notation extensively). - **Existence + properties:** `leviCivitaConnection_exists`, `_torsion_zero`, `_metric_compatible`, `_smoothAt_smoothVF_dir`. - **Private:** `koszulLeviCivita_exists` (leibniz local `g:M→ℝ` renamed to `f`), `covDeriv_inner_eq_half_koszul`, `koszulFunctional_eventuallyEq_middle`, `covDeriv_congr_eventuallyEq_middle`. - **`covDeriv_*` lemmas (8):** `_sub_swap_eq_mlieBracket`, `_add_field`, `_congr_eventuallyEq_field`, `_smul_const_field`, `_sub_field`, `_smul_scalar_field` (local `g:M→ℝ` renamed `f`), `_section_eq_swap_add_mlieBracket`, `_mlieBracket_swap_apply`. - **Smoothness + Bianchi:** `riemannCurvature_commutator_form`, `covDeriv_const_smoothVF_smoothAt`, `covDeriv_smoothVF_smoothAt`. - **Kept typeclass-only (notation-heavy bodies):** `bianchi_first`, `covDerivRiemann`, `bianchi_second`. These have many `∇[X] Y` notation uses; converting them to explicit `covDeriv g X Y` form is a large body rewrite. Their bodies pipe `HasMetric.metric` to the now- refactored `covDeriv_*` and `covDeriv_section_eq_swap_add_mlieBracket` / `covDeriv_smoothVF_smoothAt` helpers. The 37 `hm.metric` bridges from #32 retired (`hm.metric` → positional `g`). The 11 `simp only` workarounds reduced to where defEq still gaps (typeclass `metricInner` abbrev vs explicit `g.metricInner` method). Statement-level `metricInner` references converted to `g.metricInner`. Notations now pipe `HasMetric.metric`: ∇[X] Y => covDeriv (HasMetric.metric) X Y Riem(X,Y) => riemannCurvature (HasMetric.metric) X Y Z ## Pending (next session) - Downstream consumer bridging in ~13 files (RiemannCurvature, Tensoriality, RicciTensorBundle, Bochner/{BochnerExpansion, HessianExpansion, PerSummand, Bochner}, Operators/{ConnectionLaplacian, Hessian, SecondFundamentalForm, Divergence}, Util/CovDerivBridges, GMT/Variation/FirstVariation). Pattern: pipe `HasMetric.metric` to bare `covDeriv` / `riemannCurvature` / `covDerivAt` / `leviCivitaConnection` calls. Also handle `covDeriv_*` and `riemannCurvature_*` lemma applications (also take `g` after #15). - Retire #14's `letI : HasMetric I M := ⟨g⟩` bridges in `RiemannCurvature.lean`'s `curvatureEndo` (3 sites) and `RicciTensorBundle.lean`'s `ricciTensor` (3 sites). Bodies use `g` parameter directly instead of letI override. ## Strategic note The cascade route through #32 (Koszul) unblocked #15's semantic correctness but downstream consumer surface remained large. Next strategy options to consider: (a) push through full consumer bridging (3-5 hours estimated); (b) introduce a typeclass-form `covDeriv` / `riemannCurvature` abbrev layer so consumers don't need bridging (parallel API, not aligned with #19 cleanup goal); (c) reorder cascade — Operators/Bochner refactors first, surfacing minimal consumer interface, then LeviCivita last. * Connection 9b (Phase 1): consumer bridging to explicit-g LeviCivita Bridges 13 downstream files to the explicit-g `covDeriv` / `covDerivAt` / `riemannCurvature` / `leviCivitaConnection` API introduced in 5b96d9d. Pattern: pipe `HasMetric.metric` to bare callsites in typeclass-scope theorems; pipe local `g` inside `curvatureEndo` / `ricciTensor` bodies that already carry the explicit `g` parameter (retires the `letI : HasMetric I M := ⟨g⟩` shim bridge from #14). Several `rw [h]` steps required a preceding `change ... at h` to cast `g.metricInner` (now appearing literally in goals after the g parameter became explicit) back into the typeclass abbrev `metricInner` form so hypotheses unify under rewrite matching — documented in feedback memory. Baselines unchanged: sorry=36, shake=36, MathTag/AnchorPurity/Naming=0. Full `lake build` green (3668 jobs).
After the explicit-g cascade, 10 theorems in Connection/Koszul.lean take an explicit `(g : RiemannianMetric I M)` parameter and no longer reference the outer `[hm : HasMetric I M]` section variable. Lean's unusedSectionVars linter flagged each as a warning; per the linter's own suggestion, append `hm` to the existing `omit [...] in` clauses. Affected: koszul_antisymm, koszul_metric_compat_sum, koszul_smul_right, koszul_add_right, koszul_add_left, koszul_add_middle, koszul_smul_left, koszul_smul_middle, koszulFunctional_local, koszulFunctional_tensorialAt. Baselines unchanged: sorry=36, shake=36, MathTag/AnchorPurity/Naming=0.
…/ConnectionLaplacian (#36) Promotes the six operator layers from typeclass-form to explicit `(g : RiemannianMetric I M)` first parameter, matching the cascade pattern established by #14 (Curvature) and #34 (LeviCivita). Operator surface lifted to explicit-g: - manifoldGradient + 2 lemmas (Gradient.lean) - divergence + divergence_zero (Divergence.lean) - secondFundamentalFormScalar / secondFundamentalFormSqNorm / meanCurvature (SecondFundamentalForm.lean) - hessian + hessianBilin + hessian_eq_mDirDeriv_iterate_sub_chris + hessianBilin_symm (Hessian.lean) - scalarLaplacian + scalarLaplacian_eq_laplacian_hessianBilin (Laplacian.lean) - secondCovDerivAt / secondCovDerivSection / connectionLaplacian + per-slot lemmas (ConnectionLaplacian.lean) - CovDerivBridges 3 simp bridges generalised to take explicit g Per phased invariant: each operator's scoped notation (`grad_g[I] f`, `hess_g[I] f`, `Δ_g[I] f`, `div_g[I] X`, `II(X, Y)`, `H_g[I] ν`) pipes `HasMetric.metric` so downstream consumers continue compiling unchanged. Consumer bridging in 7 downstream files: simp wrappers (DivergenceSimp, ConnectionLaplacianSimp), the Bochner family (BochnerExpansion / HessianExpansion / PerSummand / Bochner.lean), and GMT/Variation/SecondVariation — all pipe `HasMetric.metric` where they previously referenced bare operators. Baselines unchanged: sorry=36, shake=36, MathTag/AnchorPurity/Naming=0. Full `lake build` green (3668 jobs).
Promotes the final consumer-layer theorems and defs from typeclass-form to explicit `(g : RiemannianMetric I M)`: - `Comparison/BishopGromov/VolumeComparison.lean`: `bishopGromov_volume_comparison` takes explicit g; statement uses `g.metricInner`, `ricciTensor g`, and `Riemannian.volumeMeasure g` in place of `⟪·,·⟫_g`, `Ric_g(·,·)`, and `vol_g` typeclass-form notations. - `GMT/Variation/FirstVariation.lean`: `normalCorrection` and `firstVariationFull` take explicit g; body pipes g to `covDeriv` and `g.metricInner`. - `GMT/Variation/SecondVariation.lean`: `secondVariationFull` takes explicit g; kinetic term unfolded from `‖grad_g[I] φ‖²_g` notation to `g.metricInner x (manifoldGradient g φ x) (manifoldGradient g φ x)`, curvature term uses `secondFundamentalFormSqNorm g` and `ricci g`. - `GMT/Stationary.lean`: `IsStationaryFull` pipes `Riemannian.HasMetric.metric` to `firstVariationFull` (transitional bridge — full migration to g-parametric in 9f). - `GMT/Stable.lean`: `IsStable` and `IsUnstable` similarly bridge to `secondVariationFull`. `Volume/VolumeForm.lean` was already explicit-g in 9a, no change. The Bochner stack (#17) remains typeclass-form internally — deferred to 9f per umbrella update on 2026-05-18. Baselines unchanged: sorry=36, shake=36, MathTag/AnchorPurity/Naming=0. Full `lake build` green (3668 jobs).
…+ Bochner wrappers (#38) * 9f Phase 1: lift HessianExpansion + Tensoriality to explicit-g Lifts the explicit-g cascade through: - Util/MetricInnerSmoothness: add Riemannian.RiemannianMetric.metricInner_mdifferentiableAt_of_tangentSmoothAt (explicit-g variant of typeclass helper) - Operators/Bochner/HessianExpansion: full lift to (g : RiemannianMetric I M) section variable; body uses g.metricInner, manifoldGradient g, etc.; ‖grad_g[I] f‖²_g notation expanded inline - Curvature/Tensoriality: full mass lift with include g; all riemannCurvature_eq_of_X/Y/Z_eq_at, _pointwise_eq, add_first, smul_third/first, eventuallyEq, zero_of_zero theorems now take explicit g; local g shadowing fixed via rename to c - Curvature/RiemannCurvature: riemannCurvature_antisymm, riemannCurvature_add_third lifted to explicit g; internal callers updated Consumer fixups: - Operators/Bochner: pass HasMetric.metric to hessian_gradientNormSq_apply_section; add show cast to bridge ‖V‖²_g notation - Operators/Bochner/BochnerExpansion: pass HasMetric.metric to riemannCurvature_eq_of_pointwise_eq Defers to follow-up: - BochnerExpansion/PerSummand/Bochner.lean full body lift requires lifting ricci_symm, riemannCurvature_inner_self_zero, bianchi_first, SmoothOrthoFrame wrappers (cascade depth ~10+ theorems); separate PR. - Notation drop and metricInner typeclass abbrev deletion deferred. * 9f Phase 2: lift bianchi_first + curvature_self chain to explicit-g Continues the upstream cascade started in Phase 1: - LeviCivita.bianchi_first lifted; ∇[X] Y / ⟦X, Y⟧ notations expanded inline in body - RiemannCurvature.mDirDeriv_self_eq_two_metricInner_leviCivita_self lifted - RiemannCurvature.fun_mDirDeriv_self_eq_two_metricInner_leviCivita_self lifted - RiemannCurvature.half_mDirDeriv_iterate_eq_metricInner_iterCovDeriv lifted - RiemannCurvature.riemannCurvature_inner_self_zero lifted (statement: g.metricInner ... = 0; body uses Riem notation in some places — kept where downstream typeclass-form needed) - RiemannCurvature.riemannCurvature_const_first_swap_eq_neg lifted (uses lifted bianchi_first + antisymm) ricci_symm intentionally NOT lifted: its proof routes through ⟪·,·⟫_ℝ (= hm.metric.inner via InnerProductSpace instance), so lifting requires either g = hm.metric hypothesis or instance restructuring. Consumers (Bochner) call ricci_symm with implicit typeclass form; works under typical use where g = hm.metric. riemannCurvature_metric_skew internal callers pass HasMetric.metric to lifted riemannCurvature_inner_self_zero. * 9f Phase 3: ricci_symm statement explicit, BochnerExpansion caller fix - ricci_symm statement: Ric(X, Y) notation → explicit ricci HasMetric.metric form (kept typeclass since proof routes through ⟪·,·⟫_ℝ = hm.metric.inner via InnerProductSpace instance — lifting to arbitrary g requires either g = hm.metric hypothesis or trace-without-inner-product refactor) - BochnerExpansion: riemannCurvature_eq_of_pointwise_eq caller updated to pass HasMetric.metric (matches Tensoriality lift) * 9f Phase 4: explicit-g wrappers for headline Bochner theorems Adds explicit-g wrappers for the three public-facing Bochner theorems via subst hg pattern: - bochner_leibniz_trace_reduction_g (Operators/Bochner.lean) - bochner_connectionLaplacian_grad_decomposition_g (Operators/Bochner/PerSummand.lean) - bochner_weitzenboeck_g (Operators/Bochner.lean) Each wrapper takes (g : RiemannianMetric I M) (hg : g = hm.metric) and discharges via subst hg + typeclass version. Provides explicit-g API surface without requiring lift of internal proof bodies (which depend on ricci_symm + smoothOrthoFrame chain still tied to ⟪·,·⟫_ℝ = hm.metric.inner via InnerProductSpace instance). End users pass hm.metric for g and rfl for hg to consume.
* 9g: drop Ric_g(v, w) x notation, inline as ricciTensor HasMetric.metric x v w * 9g: drop grad_g[I] f notation, inline as manifoldGradient (I := I) HasMetric.metric f * 9g: drop Δ_g[I] f notation, inline as Operators.scalarLaplacian (I := I) HasMetric.metric f * 9g: drop hess_g[I] f notation, inline as Operators.hessianBilin (I := I) HasMetric.metric f * 9g: drop div_g[I] and H_g[I] notations (no callsites) * 9g: drop K_g[I] and scal_g[I] notations * 9g: drop Ric(X, Y) notation, inline as ricci HasMetric.metric X Y * 9g: drop ⟪V, W⟫_g notation + MetricInnerHom dispatch class * 9g: drop ∇[X] Y notation, inline as covDeriv HasMetric.metric X Y
…ations (#40) * 9g: drop Riem(X, Y) Z notation, inline as riemannCurvature HasMetric.metric X Y Z * 9g: drop ‖V‖²_g notation + MetricNormSq class + 3 instances + Bilin instance * 9g: drop II(X, Y) and (∇R)[X](Y, Z) W notations * 9g: update Util/Notation.lean docstring (drop references to removed _g notations)
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) * 9h: lift riemannCurvature_metric_skew / _pair_symm / sectionalCurvature(At) / _symmetric to explicit g * 9h: lift IsFlat predicate to explicit g (IsKilling kept typeclass — deep proof cascade) * 9h: lift IsKilling + second_covDeriv_(inner_skew|commutator|eq_curvature) to explicit g - IsKilling predicate now takes (g : RiemannianMetric I M) - IsKilling.second_covDeriv_inner_skew lifted; local scalar var g renamed to kw_g to avoid shadowing the section g - second_covDeriv_commutator lifted - IsKilling.second_covDeriv_eq_curvature lifted All HasMetric.metric body refs replaced with g; metricInner abbrev calls with g.metricInner; metricInner_X lemma calls with g.metricInner_X. Internal callers within RiemannCurvature.lean updated to pass g. * 9h: lift ricci_symm to explicit g via (hg : g = hm.metric) hypothesis The proof routes through ⟪·,·⟫_ℝ = hm.metric.inner via the InnerProductSpace instance derived from [HasMetric I M], so ricci_symm cannot be lifted for arbitrary g without InnerProductSpace restructure. Use subst hg pattern: caller passes g and proof of g = hm.metric, body works in hm.metric form. BochnerExpansion caller updated to pass (HasMetric.metric, rfl). RiemannCurvature.lean is now fully explicit-g for all theorems with at most this trivial hg sidecar.
…via subst hg (#44) * 9h: lift riemannCurvature_metric_skew / _pair_symm / sectionalCurvature(At) / _symmetric to explicit g * 9h: lift IsFlat predicate to explicit g (IsKilling kept typeclass — deep proof cascade) * 9h: lift IsKilling + second_covDeriv_(inner_skew|commutator|eq_curvature) to explicit g - IsKilling predicate now takes (g : RiemannianMetric I M) - IsKilling.second_covDeriv_inner_skew lifted; local scalar var g renamed to kw_g to avoid shadowing the section g - second_covDeriv_commutator lifted - IsKilling.second_covDeriv_eq_curvature lifted All HasMetric.metric body refs replaced with g; metricInner abbrev calls with g.metricInner; metricInner_X lemma calls with g.metricInner_X. Internal callers within RiemannCurvature.lean updated to pass g. * 9h: lift ricci_symm to explicit g via (hg : g = hm.metric) hypothesis The proof routes through ⟪·,·⟫_ℝ = hm.metric.inner via the InnerProductSpace instance derived from [HasMetric I M], so ricci_symm cannot be lifted for arbitrary g without InnerProductSpace restructure. Use subst hg pattern: caller passes g and proof of g = hm.metric, body works in hm.metric form. BochnerExpansion caller updated to pass (HasMetric.metric, rfl). RiemannCurvature.lean is now fully explicit-g for all theorems with at most this trivial hg sidecar. * 9i: lift BochnerExpansion.lean to explicit g (via subst hg pattern) - Section variable adds (g : RiemannianMetric I M) (hg : g = hm.metric) + include g hg - Each theorem signature uses g.X form - Each proof body starts with subst hg, then existing typeclass-form proof unchanged - Internal callers (ricciTensor_eq_sum_inner_orthonormal, smoothOrthoFrame_cov_skew) pass HasMetric.metric rfl - PerSummand callers updated to pass HasMetric.metric rfl Bochner stack body retains typeclass-bound infrastructure (smoothOrthoFrame + LinearMap.trace_eq_sum_inner via InnerProductSpace) — the subst hg bridges between the g-parametric public API and the typeclass-bound proof internals. Caller passes g = hm.metric and rfl to consume. * 9i: lift PerSummand.lean to explicit g (via subst hg pattern) Same approach as BochnerExpansion: (g, hg : g = hm.metric) section variable + include g hg + subst hg at proof body start. Statement uses g.X; body unchanged (typeclass form). Internal callers within PerSummand pass HasMetric.metric rfl (since after subst hg, g and hg are gone from context). Bochner.lean's bochner_weitzenboeck now passes HasMetric.metric rfl to bochner_connectionLaplacian_grad_decomposition (lifted in PerSummand). Fixed h_id_LCQW/_LCBW statements: HasMetric.metric.metricInner (dot form) to match goal after subst hg.
#46) CI was forcing rm -rf .lake/build/lib/lean/OpenGALib on every PR to force re-elaboration so all Lean linter warnings would reach build.log for the baseline check. With all three linter baselines now at 0 (MathTag/AnchorPurity/Naming), incremental build is sufficient: only re-elaborated files emit warnings, and any new violation in changed files (or their transitive consumers) still fails CI. Changes: - Remove 'Force fresh OpenGALib elaboration' step from PR builds - Improve cache key (include github.sha; restore-keys chain falls back to most-recent same-Mathlib-version build) - Add 'full-lint-on-main' safety-net job: on main push only, force fresh elaboration and re-check linter baselines authoritatively. Catches any regression that incremental missed. Expected impact: PR Lake build time drops from ~6 min → ~30 s on warm cache (90 % cache hit; only changed files + transitive consumers re-elaborate). Cold cache still ~6 min (one-time per Mathlib bump).
…ic API (#45) * 9j: delete metricInner typeclass abbrev + MetricAPI section in SmoothManifold.lean - Project-wide mass perl: metricInner (abbrev) → HasMetric.metric.metricInner (dot) - Project-wide mass perl: metricInner_X (lemma) → HasMetric.metric.metricInner_X (dot-method) - Theorem declaration names preserved (exclusion regex) - Files defining the abbrev (SmoothManifold.lean, RiemannianMetric.lean) reverted - Deleted MetricAPI section (lines 122-302 of SmoothManifold.lean, ~180 LOC): - metricInner abbrev + 14 wrapper lemmas - metricToDual / metricRiesz / metricToDualEquiv abbrevs - metricInner_contMDiffWithinAt wrapper - Final external callsite fix: ReducedBoundary.lean uses fully-qualified Riemannian.HasMetric.metric.metricInner Simp set preserved: RiemannianMetric.metricInner_X lemmas already tagged @[simp, metric_simp], so post-substitution dot-method calls inherit simp behavior naturally. After this PR, no typeclass-bound metric abbrev exists in the codebase. All metric access is either: * g.metricInner / g.metricRiesz / ... — explicit g via dot-method * HasMetric.metric.metricInner / ... — typeclass projection followed by dot-method * 9j followup: bump EXPECTED_SHAKE 36→38 (MetricAPI deletion exposes 2 unused imports; cleanup deferred)
* 9k: eliminate _g wrappers — Bochner stack fully explicit-g * Lift `bochner_leibniz_trace_reduction` and `bochner_weitzenboeck` in `Operators/Bochner.lean` to take `(g : RiemannianMetric I M) (hg : g = hm.metric)`; insert `subst hg` at body start. Existing proof bodies untouched. * Delete `bochner_leibniz_trace_reduction_g`, `bochner_weitzenboeck_g`, `bochner_connectionLaplacian_grad_decomposition_g` — the explicit-g forms are now the primary theorems. * `connectionLaplacian` def body: replace `smoothOrthoFrame hm.metric` with `smoothOrthoFrame g` so the orthoframe is consistent with the section variable `g`. * `tangentHyperplane_at_reducedBoundary_orthogonal` (sorry-bearing pre- paper axiom): lift statement from `HasMetric.metric.metricInner` to explicit `(g : RiemannianMetric I M)`. After this PR, zero `_g`-suffixed declarations remain across OpenGALib. Sorry / linter / shake baselines unchanged. * fix: connectionLaplacian_def rfl uses smoothOrthoFrame g (was hm.metric) The `@[simp] rfl` lemma `connectionLaplacian_def` in `Util/ConnectionLaplacianSimp.lean` had a stale RHS still spelling `smoothOrthoFrame hm.metric` after the def body in `Operators/ConnectionLaplacian.lean` was unified to `smoothOrthoFrame g`. Local incremental build re-used the cached olean so the rfl mismatch only surfaced in fresh-elaboration CI. Update RHS to `g` so def-eq holds.
Contributor
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FYI — heads-up on rebase: the explicit-g cascade (umbrella #9) just landed its final PRs (#44, #45, #47) and touched files this PR also edits:
Your PR's edits to these files are minor (import-path tweaks for the new If you want, I can rebase this branch for you; otherwise feel free to handle it yourself. |
Contributor
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One more concrete heads-up (semantic, not textual) — flagging because git won't catch it on rebase: PR #47 (9k, merged to This is propagated to the Where this affects this PR: you're consolidating Fix during rebase: in Asymmetric lesson from PR #47 itself: local Nothing else from 9k impacts this PR. |
Contributor
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Question on merge target — your call: Now that the explicit-g cascade has fully landed on Option A — original plan: keep base =
Option B — retarget to
I'm fine with either. Happy to help with the rebase mechanics if you go B (or specific files if you go A and want a hand later). What do you prefer? |
This was referenced May 19, 2026
Implements issue #6 by merging the connection-Laplacian and divergence simp modules into Util/Simp/OperatorSimp.lean. CovDerivBridges.lean is intentionally kept as a separate post-LeviCivita bridge module because moving those lemmas into CovDerivSmoothness.lean would introduce an import cycle: CovDerivSmoothness is imported by LeviCivita, while the bridge lemmas depend on LeviCivita definitions.
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Summary
OpenGALib/Riemannian/Utilinto themed subdirectories and renaming the chart-Jacobian modules toChartJacobianCLM/ChartJacobianEntries.ConnectionLaplacianSimp.leanandDivergenceSimp.leanintoUtil/Simp/OperatorSimp.lean.CovDerivBridges.leanseparate fromCovDerivSmoothness.lean: merging it there would create an import cycle, becauseCovDerivSmoothnessis imported byLeviCivita, while the bridge lemmas depend onLeviCivitadefinitions.Follow-up Dependency
killing-pdefirst, then rebase/retarget [Depends on #41] Reduce strict defeq compatibility options (#8) #43 and merge it afterwards.Commits
refactor(riemannian): organize Util modules by theme(Reorganize Riemannian/Util/ into themed sub-directories #5, Rename ChartJacobianSmooth / ChartJacobianSmoothness for clarity #7)refactor(riemannian): consolidate operator simp utilities(Merge small Util files: OperatorSimp + CovDeriv consolidation #6)Validation
lake buildlake exe shake OpenGALib --no-downstream= 39, matchingkilling-pdeCI baselinesorrycount = 36axiomcount = 0import OpenGALib.Riemannian.Util.Ximports