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.gitattributes

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 # Video files - compressed
 *.mp4 filter=lfs diff=lfs merge=lfs -text
 *.webm filter=lfs diff=lfs merge=lfs -text
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README.md

@@ -0,0 +1,110 @@
+---
+pretty_name: MesoMathematics — Mathlib 4.33 proof-network artifacts
+license: apache-2.0
+language:
+- en
+tags:
+- lean
+- mathlib
+- theorem-proving
+- formal-mathematics
+- hypergraph
+- network-science
+configs:
+- config_name: mathlib-declarations-v4.33.0
+  data_files:
+  - split: train
+    path: raw/mathlib-v4.33.0/declarations-*.jsonl
+---
+
+# MesoMathematics
+
+Frozen data artifacts for the paper **“Mathematical Knowledge at the
+Mesoscale: Organization after the Formal Mathematics Revolution”** by Andrea
+E. V. Ferrari, Benjy Firester, Xinze Li, Simone Severini, and Patrick Shafto.
+The corresponding source code, exact commands, and manuscript live in the
+[`MathNetwork/MesoMathematics`](https://github.com/MathNetwork/MesoMathematics)
+repository.
+
+This release fixes Mathlib at `v4.33.0`, commit
+`db584cd6d46c92f209a44c0f1c829460d327499d`, with Lean `v4.33.0`.  The full
+commit, not the tag, identifies the corpus.  It also records the Section 3.4
+comparison against `metamath/set.mm` commit
+`057f4c461055d0b1ed78d9d333aa3de34d9771fa`.
+
+## What is here
+
+| path | contents |
+|---|---|
+| `raw/mathlib-v4.33.0/` | 569,189 Lean declarations in 57 JSONL shards, plus the extractor manifest |
+| `derived/mathlib-v4.33.0/primary-theorem-hypergraph.json` | primary theorem view: 251,416 vertices and 195,884 retained-proof hyperedges |
+| `derived/mathlib-v4.33.0/sensitivity-internal-only-theorem-hypergraph.json` | legacy-filter sensitivity view: 276,024 vertices and 200,602 hyperedges |
+| `results/` | claim-addressed outputs for Sections 3 and 4, including sensitivity results |
+| `labels/` | the reviewed 36-declaration Ahlfors target and its native Lean audit |
+| `spec/` | normative definitions of the corpus, statistics, and navigation experiment |
+| `verification/` | independent Metamath-adapter cross-check |
+| `metadata/claims.json` | paper-section-to-artifact registry |
+| `metadata/release.json` | frozen source revisions, counts, sizes, and release identity |
+| `SHA256SUMS` | SHA-256 digest for every published file except the checksum file itself |
+
+The raw declaration rows have the schema `mesomath-corpus-v2`.  Each row
+records its Lean name, defining module and namespace, declaration kind,
+reducibility, references appearing in its elaborated type and stored value,
+sharing-aware DAG sizes, definition height, and auto/private/internal-name
+flags.  Referenced declarations are not unfolded.
+
+The two hypergraph files have schema `mesomath-theorem-hypergraph-v2`.
+`vertices` stores a stable integer ID and theorem metadata.  An entry
+`{"inputs": [...], "output": i}` in `edges` represents the set of retained
+theorem premises consumed by the stored proof of vertex `i`.  Each theorem has
+one stored Lean proof; consequently every depth, reuse, and compression
+measurement is relative to that retained proof.
+
+## Which object supports which claim
+
+The authoritative map is [`metadata/claims.json`](metadata/claims.json):
+
+- `S3.1-depth-growth.json`: recorded depth and pairwise-closure controls;
+- `S3.2-namespace-depth.json`: namespace-level depth summaries;
+- `S3.3-compression-reuse.json`: compression–reuse association and bootstrap interval;
+- `S3.4-projection-geometry.json`: projection sensitivity, spectral dimension,
+  four-point hyperbolicity, and degree-preserving null ensembles;
+- `S3.4-metamath.json`: the pinned cross-library comparison;
+- `S4.1-navigation.json`: the reviewed Mathlib 4.33 complex-analysis ranking pilot.
+
+These files supersede the historical v4.30-era numerical artifacts.  They
+must not be mixed with numbers from an earlier Mathlib snapshot.
+
+## Reproduction and verification
+
+Start with [`docs/REPRODUCING.md`](docs/REPRODUCING.md).  It separates the
+native Lean export, graph-view materialization, statistical analyses,
+Metamath adapter, and navigation experiment.  The source repository pins the
+Lean toolchain and Python environment and contains the tests.  A complete
+second Section 4 run produced a byte-identical output file.
+
+To check this deposit after download:
+
+```bash
+shasum -a 256 -c SHA256SUMS
+```
+
+## Scope and limitations
+
+This is a trace of one formal library, language, community, snapshot, and one
+retained proof per theorem.  It is not a unique graph of mathematics.  The
+declaration graph used in Section 4 is a parallel view of the same exported
+corpus, not a projection of the theorem-only hypergraph.  Namespace regions
+are reproducible library partitions, not claims about intrinsic disciplinary
+boundaries.  Projection-dependent geometry is reported together with its
+comparison model rather than as an invariant of the corpus.
+
+## Licenses
+
+Mathlib-derived exports and graph artifacts are distributed under the Apache
+License 2.0; the upstream license text is included at
+`licenses/mathlib-APACHE-2.0.txt`.  The source `set.mm` database is not
+redistributed here: only aggregate comparison results are included.  Upstream
+`set.mm` is dedicated to the public domain under CC0; its license text is
+included at `licenses/set.mm-CC0.txt`.
+

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docs/REPRODUCING.md

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+# Reproducibility package
+
+This directory reproduces the empirical claims in Sections 3 and 4 of the
+paper.  It is intentionally separate from `../paper`: the paper is a readable
+article, while this directory fixes executable objects, parameters and result
+artifacts.
+
+## Frozen corpus
+
+| component | value |
+|---|---|
+| Mathlib release | `v4.33.0` |
+| Mathlib commit | `db584cd6d46c92f209a44c0f1c829460d327499d` |
+| Lean toolchain | `leanprover/lean4:v4.33.0` |
+| Raw schema | `mesomath-corpus-v2` |
+| set.mm commit | `057f4c461055d0b1ed78d9d333aa3de34d9771fa` |
+
+The tag is descriptive; the full commit is authoritative.
+
+## Paper claims and experiment IDs
+
+| ID | Paper claim | Inputs | Result artifact |
+|---|---|---|---|
+| `S3.1-depth-growth` | theorem graph is deep and sparse | primary theorem view | `results/S3.1-depth-growth.json` |
+| `S3.2-namespace-depth` | namespace depths differ by over an order of magnitude | primary theorem view | `results/S3.2-namespace-depth.json` |
+| `S3.3-compression-reuse` | proof-term/statement ratio is associated with reuse | primary theorem view | `results/S3.3-compression-reuse.json` |
+| `S3.4-projection-geometry` | measurements depend on projection, but detected geometry lies within degree-preserving nulls | primary theorem hypergraph | `results/S3.4-projection-geometry.json` |
+| `S3.4-metamath` | depth growth is similar across libraries but compression--reuse is not | Mathlib primary view and pinned `set.mm` | `results/S3.4-metamath.json` |
+| `S4.1-navigation` | structure ranks a reviewed target above random | v4.33 declaration view and reviewed labels | `results/S4.1-navigation.json` |
+
+`claims.json` is the machine-readable version of this table.  A result is not
+ready to enter the paper until it records the corpus manifest hash, analysis
+configuration and random seed where relevant.  Sections 3 and 4 have been
+rerun on v4.33.0.  Section 4's exact historical inputs remain as a regression
+fixture, while the paper result uses the reviewed current statements and a
+graph built entirely from the pinned v4.33.0 export.
+
+## Layout
+
+```text
+experiments/
+  claims.json              claim-to-artifact registry
+  spec/                    exact mathematical and computational objects
+  LEGACY_AUDIT.md          claim-by-claim audit of the old implementation
+  legacy/                  small immutable regression fixtures from old runs
+  lean/                    native Mathlib environment extractor
+  analysis/                statistical analysis and figure generation
+  labels/                  reviewed external labels (for Section 4)
+  data/raw/                Lean exports; generated, not committed
+  data/derived/            declared graph views; generated, not committed
+  results/                 reviewed machine-readable result manifests
+```
+
+## Reproduction stages
+
+1. Build and test the native extractor:
+
+   ```sh
+   cd lean
+   lake update
+   lake exe cache get
+   lake build
+   lake exe meso-extractor-tests
+   ```
+
+2. Export the Mathlib corpus:
+
+   ```sh
+   lake exe meso-extract --out ../data/raw/mathlib-v4.33.0
+   ```
+
+   A fast format smoke test may import one module explicitly; this is never a
+   substitute for the full command above:
+
+   ```sh
+   lake exe meso-extract \
+     --out /tmp/mesomath-smoke \
+     --import-module Mathlib.Data.Nat.ModEq \
+     --module-prefix Mathlib.Data.Nat.ModEq \
+     --limit 25
+   ```
+
+3. Materialize the paper's graph views and run analyses:
+
+   ```sh
+   cd ../analysis
+   uv run pytest
+   uv run mesomath-analysis views \
+     ../data/raw/mathlib-v4.33.0 ../data/derived/mathlib-v4.33.0
+   uv run mesomath-analysis run-s3 \
+     ../data/derived/mathlib-v4.33.0/primary-theorem-hypergraph.json \
+     ../results
+   uv run mesomath-analysis run-geometry \
+     ../data/derived/mathlib-v4.33.0/primary-theorem-hypergraph.json \
+     ../results/S3.4-projection-geometry.json
+   ```
+
+   The `views` command writes both the primary auto/private-filtered theorem
+   hypergraph and an internal-name-only sensitivity view matching the legacy
+   filter.  Section 3 commands use the primary file unless explicitly pointed
+   at the sensitivity file.
+
+4. Clone the exact Metamath Proof Explorer snapshot and run the independent
+   cross-library adapter:
+
+   ```sh
+   git clone https://github.com/metamath/set.mm ../data/raw/set.mm
+   git -C ../data/raw/set.mm checkout 057f4c461055d0b1ed78d9d333aa3de34d9771fa
+   uv run mesomath-analysis run-metamath \
+     ../data/raw/set.mm ../results/S3.4-metamath.json \
+     --revision 057f4c461055d0b1ed78d9d333aa3de34d9771fa \
+     --mathlib-depth-result ../results/S3.1-depth-growth.json \
+     --mathlib-compression-result ../results/S3.3-compression-reuse.json
+   ```
+
+   The parser's theorem count and selected reuse/proof-size values were
+   cross-checked against the official C verifier; the exact audit is recorded
+   in `verification/metamath-official-verifier.md`.
+
+5. Run the reviewed v4.33 declaration-graph experiment:
+
+   ```sh
+   uv run mesomath-analysis run-navigation \
+     ../data/raw/mathlib-v4.33.0 \
+     ../labels/ahlfors_positive_declarations_v4.33-review.csv \
+     ../results/S4.1-navigation.json
+   ```
+
+   A complete second run produced a byte-identical result file (SHA-256
+   `76c7510f933daa39b0ae2ba42bd8e1d1728c481948bf03811a4e40aed4a2e9f3`).
+
+The full-corpus commands are deliberately separate from unit tests: importing
+and traversing all of Mathlib is an experiment run, not a build step.

labels/ahlfors_positive_declarations_v4.33-audit.json

@@ -0,0 +1,1765 @@
+{"source_labels": "../labels/ahlfors_positive_declarations_v4.30.csv",
+ "schema": "mesomath-label-review-v1",
+ "records":
+ [{"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddCommGroup.toDivisionAddCommMonoid",
+    "AddCommMagma.toAdd",
+    "AddCommMonoid.toAddCommSemigroup",
+    "AddCommSemigroup.toAddCommMagma",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "Complex",
+    "Complex.I",
+    "Complex.addCommGroup",
+    "Complex.im",
+    "Complex.instAdd",
+    "Complex.instDenselyNormedField",
+    "Complex.instMul",
+    "Complex.instNormedField",
+    "Complex.instSemiring",
+    "Complex.ofReal",
+    "Complex.re",
+    "Complex.reProdIm",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HAdd.hAdd",
+    "HMul.hMul",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "MeasureTheory.MeasureSpace.volume",
+    "Module.toDistribMulAction",
+    "NegZeroClass.toZero",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.complexToReal",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.lattice",
+    "Real.measureSpace",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "Set.uIcc",
+    "SubNegMonoid.toAddMonoid",
+    "SubNegMonoid.toSub",
+    "SubNegZeroMonoid.toNegZeroClass",
+    "SubtractionCommMonoid.toSubtractionMonoid",
+    "SubtractionMonoid.toSubNegZeroMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "instHAdd",
+    "instHMul",
+    "instHSMul",
+    "instHSub",
+    "intervalIntegral"],
+   "statement_dag_size": 326,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (f : ℂ → E) (z w : ℂ),\n  DifferentiableOn ℂ f (Set.uIcc z.re w.re ×ℂ Set.uIcc z.im w.im) →\n    (((∫ (x : ℝ) in z.re..w.re, f (↑x + ↑z.im * Complex.I)) - ∫ (x : ℝ) in z.re..w.re, f (↑x + ↑w.im * Complex.I)) +\n          Complex.I • ∫ (y : ℝ) in z.im..w.im, f (↑w.re + ↑y * Complex.I)) -\n        Complex.I • ∫ (y : ℝ) in z.im..w.im, f (↑z.re + ↑y * Complex.I) =\n      0",
+   "present": true,
+   "name": "Complex.integral_boundary_rect_eq_zero_of_differentiableOn",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toDivisionAddCommMonoid",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "ContinuousOn",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableAt",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "LE.le",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.closedBall",
+    "NegZeroClass.toZero",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instLE",
+    "Real.instZero",
+    "SDiff.sdiff",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "Set.Countable",
+    "Set.instMembership",
+    "Set.instSDiff",
+    "SubNegZeroMonoid.toNegZeroClass",
+    "SubtractionCommMonoid.toSubtractionMonoid",
+    "SubtractionMonoid.toSubNegZeroMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "circleIntegral"],
+   "statement_dag_size": 211,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {R : ℝ},\n  0 ≤ R →\n    ∀ {f : ℂ → E} {c : ℂ} {s : Set ℂ},\n      s.Countable →\n        ContinuousOn f (Metric.closedBall c R) →\n          (∀ z ∈ Metric.ball c R \\ s, DifferentiableAt ℂ f z) → ∮ (z : ℂ) in C(c, R), f z = 0",
+   "present": true,
+   "name": "Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "CompleteSpace",
+    "Complex",
+    "Complex.I",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instDivInvMonoid",
+    "Complex.instMul",
+    "Complex.instNatCast",
+    "Complex.instNormedField",
+    "Complex.instOne",
+    "Complex.instSemiring",
+    "Complex.instSub",
+    "Complex.ofReal",
+    "ContinuousOn",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableAt",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivInvMonoid.toDiv",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HAdd.hAdd",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HPow.hPow",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "LT.lt",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.closedBall",
+    "Module.toDistribMulAction",
+    "Monoid.toNPow",
+    "NPow.toPow",
+    "Nat",
+    "Nat.cast",
+    "Nat.factorial",
+    "Nat.instAtLeastTwoHAddOfNat",
+    "Nat.instNeZeroSucc",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "One.toOfNat1",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instLT",
+    "Real.instZero",
+    "Real.pi",
+    "SDiff.sdiff",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "Set",
+    "Set.Countable",
+    "Set.instMembership",
+    "Set.instSDiff",
+    "SubNegMonoid.toAddMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "circleIntegral",
+    "instAddNat",
+    "instHAdd",
+    "instHDiv",
+    "instHMul",
+    "instHPow",
+    "instHSMul",
+    "instHSub",
+    "instOfNatAtLeastTwo",
+    "instOfNatNat",
+    "iteratedDeriv"],
+   "statement_dag_size": 419,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {R : ℝ} {f : ℂ → E} {c : ℂ}\n  {s : Set ℂ},\n  0 < R →\n    ∀ (n : ℕ),\n      s.Countable →\n        ContinuousOn f (Metric.closedBall c R) →\n          (∀ z ∈ Metric.ball c R \\ s, DifferentiableAt ℂ f z) →\n            ∮ (z : ℂ) in C(c, R), (1 / (z - c) ^ (n + 1)) • f z =\n              (2 * ↑Real.pi * Complex.I / ↑n.factorial) • iteratedDeriv n f c",
+   "present": true,
+   "name":
+   "Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["CompleteSpace",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "DivInvMonoid.toDiv",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HPow.hPow",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.sphere",
+    "Monoid.toNPow",
+    "NPow.toPow",
+    "Nat",
+    "Nat.cast",
+    "Nat.factorial",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.instDivInvMonoid",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMonoid",
+    "Real.instMul",
+    "Real.instNatCast",
+    "Real.instZero",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Set",
+    "Set.instMembership",
+    "Zero.toOfNat0",
+    "instHDiv",
+    "instHMul",
+    "instHPow",
+    "iteratedDeriv"],
+   "statement_dag_size": 210,
+   "statement":
+   "∀ {F : Type v} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℂ F] [CompleteSpace F] {c : ℂ} {R C : ℝ} {f : ℂ → F}\n  (n : ℕ),\n  0 < R →\n    DiffContOnCl ℂ f (Metric.ball c R) →\n      (∀ z ∈ Metric.sphere c R, ‖f z‖ ≤ C) → ‖iteratedDeriv n f c‖ ≤ ↑n.factorial * C / R ^ n",
+   "present": true,
+   "name": "Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le",
+   "module": "Mathlib.Analysis.Complex.Liouville",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Bornology.IsBounded",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "Differentiable",
+    "Eq",
+    "Exists",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toBornology",
+    "PseudoMetricSpace.toUniformSpace",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "Set.range",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 124,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {F : Type v} [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] {f : E → F},\n  Differentiable ℂ f → Bornology.IsBounded (Set.range f) → ∃ c, ∀ (z : E), f z = c",
+   "present": true,
+   "name": "Differentiable.exists_const_forall_eq_of_bounded",
+   "module": "Mathlib.Analysis.Complex.Liouville",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Bornology.IsBounded",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "Differentiable",
+    "Eq",
+    "Exists",
+    "Function.const",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toBornology",
+    "PseudoMetricSpace.toUniformSpace",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "Set.range",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 127,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {F : Type v} [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] {f : E → F},\n  Differentiable ℂ f → Bornology.IsBounded (Set.range f) → ∃ c, f = Function.const E c",
+   "present": true,
+   "name": "Differentiable.exists_eq_const_of_bounded",
+   "module": "Mathlib.Analysis.Complex.Liouville",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.instSemiring",
+    "Exists",
+    "LT.lt",
+    "MulZeroClass.toZero",
+    "Nat",
+    "Nat.instMulZeroClass",
+    "Nat.instPreorder",
+    "OfNat.ofNat",
+    "Polynomial",
+    "Polynomial.IsRoot",
+    "Polynomial.degree",
+    "Preorder.toLT",
+    "WithBot",
+    "WithBot.instPreorder",
+    "WithBot.zero",
+    "Zero.toOfNat0"],
+   "statement_dag_size": 52,
+   "statement": "∀ {f : Polynomial ℂ}, 0 < f.degree → ∃ z, f.IsRoot z",
+   "present": true,
+   "name": "Complex.exists_root",
+   "module": "Mathlib.Analysis.Complex.Polynomial.Basic",
+   "kind": "theorem"},
+  {"type_refs": ["Complex", "Complex.instField", "IsAlgClosed"],
+   "statement_dag_size": 5,
+   "statement": "IsAlgClosed ℂ",
+   "present": true,
+   "name": "Complex.isAlgClosed",
+   "module": "Mathlib.Analysis.Complex.Polynomial.Basic",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AnalyticAt",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableAt",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Filter.Eventually",
+    "Iff",
+    "InnerProductSpace.toNormedSpace",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "UniformSpace.toTopologicalSpace",
+    "nhds"],
+   "statement_dag_size": 147,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {c : ℂ},\n  AnalyticAt ℂ f c ↔ ∀ᶠ (z : ℂ) in nhds c, DifferentiableAt ℂ f z",
+   "present": true,
+   "name": "Complex.analyticAt_iff_eventually_differentiableAt",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AnalyticAt",
+    "Compl.compl",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "ContinuousAt",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableAt",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Filter.Eventually",
+    "InnerProductSpace.toNormedSpace",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "Set.instCompl",
+    "Set.instSingletonSet",
+    "Singleton.singleton",
+    "UniformSpace.toTopologicalSpace",
+    "nhdsWithin"],
+   "statement_dag_size": 170,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {c : ℂ},\n  (∀ᶠ (z : ℂ) in nhdsWithin c {c}ᶜ, DifferentiableAt ℂ f z) → ContinuousAt f c → AnalyticAt ℂ f c",
+   "present": true,
+   "name":
+   "Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt",
+   "module": "Mathlib.Analysis.Complex.RemovableSingularity",
+   "kind": "theorem"},
+  {"type_refs":
+   ["And",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "ContinuousAt",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Filter",
+    "Filter.instMembership",
+    "Iff",
+    "Membership.mem",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "SDiff.sdiff",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "Set.instSDiff",
+    "Set.instSingletonSet",
+    "Singleton.singleton",
+    "UniformSpace.toTopologicalSpace",
+    "nhds"],
+   "statement_dag_size": 157,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {s : Set ℂ}\n  {c : ℂ}, s ∈ nhds c → (DifferentiableOn ℂ f (s \\ {c}) ∧ ContinuousAt f c ↔ DifferentiableOn ℂ f s)",
+   "present": true,
+   "name": "Complex.differentiableOn_compl_singleton_and_continuousAt_iff",
+   "module": "Mathlib.Analysis.Complex.RemovableSingularity",
+   "kind": "theorem"},
+  {"type_refs":
+   ["CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Filter",
+    "Filter.Eventually",
+    "Filter.NeBot",
+    "IsOpen",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "TendstoLocallyUniformlyOn",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 177,
+   "statement":
+   "∀ {E : Type u_1} {ι : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {U : Set ℂ} {φ : Filter ι}\n  {F : ι → ℂ → E} {f : ℂ → E} [CompleteSpace E] [φ.NeBot],\n  TendstoLocallyUniformlyOn F f φ U → (∀ᶠ (n : ι) in φ, DifferentiableOn ℂ (F n) U) → IsOpen U → DifferentiableOn ℂ f U",
+   "present": true,
+   "name": "TendstoLocallyUniformlyOn.differentiableOn",
+   "module": "Mathlib.Analysis.Complex.LocallyUniformLimit",
+   "kind": "theorem"},
+  {"type_refs":
+   ["And",
+    "Asymptotics.IsBigO",
+    "Complex",
+    "Complex.im",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "Complex.re",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "DivInvMonoid.toDiv",
+    "Eq",
+    "Exists",
+    "Filter",
+    "Filter.atTop",
+    "Filter.comap",
+    "Filter.instInf",
+    "Filter.principal",
+    "Function.comp",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HSub.hSub",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Min.min",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.exp",
+    "Real.instAddGroup",
+    "Real.instDivInvMonoid",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMul",
+    "Real.instPreorder",
+    "Real.instSub",
+    "Real.lattice",
+    "Real.norm",
+    "Real.pi",
+    "Set.Ioo",
+    "Set.preimage",
+    "abs",
+    "instHDiv",
+    "instHMul",
+    "instHSub"],
+   "statement_dag_size": 237,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {a b C : ℝ} {f : ℂ → E} {z : ℂ},\n  DiffContOnCl ℂ f (Complex.im ⁻¹' Set.Ioo a b) →\n    (∃ c < Real.pi / (b - a),\n        ∃ B,\n          f =O[Filter.comap (abs ∘ Complex.re) Filter.atTop ⊓ Filter.principal (Complex.im ⁻¹' Set.Ioo a b)] fun z =>\n            Real.exp (B * Real.exp (c * |z.re|))) →\n      (∀ (z : ℂ), z.im = a → ‖f z‖ ≤ C) → (∀ (z : ℂ), z.im = b → ‖f z‖ ≤ C) → a ≤ z.im → z.im ≤ b → ‖f z‖ ≤ C",
+   "present": true,
+   "name": "PhragmenLindelof.horizontal_strip",
+   "module": "Mathlib.Analysis.Complex.PhragmenLindelof",
+   "kind": "theorem"},
+  {"type_refs":
+   ["And",
+    "Asymptotics.IsBigO",
+    "Complex",
+    "Complex.im",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "Complex.re",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "DivInvMonoid.toDiv",
+    "Eq",
+    "Exists",
+    "Filter",
+    "Filter.atTop",
+    "Filter.comap",
+    "Filter.instInf",
+    "Filter.principal",
+    "Function.comp",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HSub.hSub",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Min.min",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.exp",
+    "Real.instAddGroup",
+    "Real.instDivInvMonoid",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMul",
+    "Real.instPreorder",
+    "Real.instSub",
+    "Real.lattice",
+    "Real.norm",
+    "Real.pi",
+    "Set.Ioo",
+    "Set.preimage",
+    "abs",
+    "instHDiv",
+    "instHMul",
+    "instHSub"],
+   "statement_dag_size": 237,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {a b C : ℝ} {f : ℂ → E} {z : ℂ},\n  DiffContOnCl ℂ f (Complex.re ⁻¹' Set.Ioo a b) →\n    (∃ c < Real.pi / (b - a),\n        ∃ B,\n          f =O[Filter.comap (abs ∘ Complex.im) Filter.atTop ⊓ Filter.principal (Complex.re ⁻¹' Set.Ioo a b)] fun z =>\n            Real.exp (B * Real.exp (c * |z.im|))) →\n      (∀ (z : ℂ), z.re = a → ‖f z‖ ≤ C) → (∀ (z : ℂ), z.re = b → ‖f z‖ ≤ C) → a ≤ z.re → z.re ≤ b → ‖f z‖ ≤ C",
+   "present": true,
+   "name": "PhragmenLindelof.vertical_strip",
+   "module": "Mathlib.Analysis.Complex.PhragmenLindelof",
+   "kind": "theorem"},
+  {"type_refs":
+   ["CompleteSpace",
+    "Complex",
+    "Complex.IsExactOn",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Metric.ball",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 127,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {c : ℂ} {r : ℝ} {f : ℂ → E} [CompleteSpace E],\n  DifferentiableOn ℂ f (Metric.ball c r) → Complex.IsExactOn f (Metric.ball c r)",
+   "present": true,
+   "name": "DifferentiableOn.isExactOn_ball",
+   "module": "Mathlib.Analysis.Complex.HasPrimitives",
+   "kind": "theorem"},
+  {"type_refs":
+   ["CompleteSpace",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "Eq",
+    "InnerProductSpace.toNormedSpace",
+    "Metric.ball",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.complexToReal",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.circleAverage",
+    "Real.instAddGroup",
+    "Real.lattice",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "abs"],
+   "statement_dag_size": 113,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {R : ℝ} {c : ℂ},\n  DiffContOnCl ℂ f (Metric.ball c |R|) → Real.circleAverage f c R = f c",
+   "present": true,
+   "name": "circleAverage_of_differentiable_on",
+   "module": "Mathlib.Analysis.Complex.MeanValue",
+   "kind": "theorem"},
+  {"type_refs":
+   ["CompleteSpace",
+    "Complex",
+    "Complex.instFiniteDimensionalReal",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Eq",
+    "InnerProductSpace.HarmonicOnNhd",
+    "Metric.closedBall",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.circleAverage",
+    "Real.instAddGroup",
+    "Real.lattice",
+    "Real.normedField",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "abs",
+    "instInnerProductSpaceRealComplex"],
+   "statement_dag_size": 92,
+   "statement":
+   "∀ {F : Type u_1} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] [CompleteSpace F] {f : ℂ → F} {c : ℂ} {R : ℝ},\n  InnerProductSpace.HarmonicOnNhd f (Metric.closedBall c |R|) → Real.circleAverage f c R = f c",
+   "present": true,
+   "name": "HarmonicOnNhd.circleAverage_eq",
+   "module": "Mathlib.Analysis.Complex.Harmonic.MeanValue",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instInv",
+    "Complex.instNatCast",
+    "Complex.instNormedField",
+    "Complex.instSemiring",
+    "Complex.instSub",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HPow.hPow",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "Inv.inv",
+    "Membership.mem",
+    "Metric.ball",
+    "Module.toDistribMulAction",
+    "Monoid.toNPow",
+    "NPow.toPow",
+    "Nat",
+    "Nat.cast",
+    "Nat.factorial",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "Set",
+    "Set.instMembership",
+    "SubNegMonoid.toAddMonoid",
+    "SummationFilter.unconditional",
+    "UniformSpace.toTopologicalSpace",
+    "instHPow",
+    "instHSMul",
+    "instHSub",
+    "iteratedDeriv",
+    "tsum"],
+   "statement_dag_size": 280,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] ⦃f : ℂ → E⦄ ⦃c : ℂ⦄ ⦃r : ℝ⦄,\n  DifferentiableOn ℂ f (Metric.ball c r) →\n    ∀ ⦃z : ℂ⦄, z ∈ Metric.ball c r → ∑' (n : ℕ), (↑n.factorial)⁻¹ • (z - c) ^ n • iteratedDeriv n f c = f z",
+   "present": true,
+   "name": "Complex.taylorSeries_eq_on_ball",
+   "module": "Mathlib.Analysis.Complex.TaylorSeries",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableAt",
+    "Eq",
+    "Filter.Eventually",
+    "Function.comp",
+    "IsLocalMax",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "NormedSpace.complexToReal",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instPreorder",
+    "Real.normedField",
+    "Real.partialOrder",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "StrictConvexSpace",
+    "UniformSpace.toTopologicalSpace",
+    "nhds"],
+   "statement_dag_size": 178,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {F : Type v} [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] [StrictConvexSpace ℝ F] {f : E → F} {c : E},\n  (∀ᶠ (z : E) in nhds c, DifferentiableAt ℂ f z) → IsLocalMax (Norm.norm ∘ f) c → ∀ᶠ (y : E) in nhds c, f y = f c",
+   "present": true,
+   "name": "Complex.eventually_eq_of_isLocalMax_norm",
+   "module": "Mathlib.Analysis.Complex.AbsMax",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toDivisionAddCommMonoid",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "Function.comp",
+    "Function.const",
+    "IsMaxOn",
+    "Membership.mem",
+    "Metric.ball",
+    "NegZeroClass.toZero",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "NormedSpace.complexToReal",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instPreorder",
+    "Real.normedField",
+    "Real.partialOrder",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "Set",
+    "Set.EqOn",
+    "Set.instMembership",
+    "StrictConvexSpace",
+    "SubNegZeroMonoid.toNegZeroClass",
+    "SubtractionCommMonoid.toSubtractionMonoid",
+    "SubtractionMonoid.toSubNegZeroMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0"],
+   "statement_dag_size": 268,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {F : Type v} [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] [StrictConvexSpace ℝ F] {f : E → F} {b : ℝ},\n  DifferentiableOn ℂ f (Metric.ball 0 b) →\n    ∀ {v : E},\n      v ∈ Metric.ball 0 b →\n        IsMaxOn (Norm.norm ∘ f) (Metric.ball 0 b) v → Set.EqOn f (Function.const E (f v)) (Metric.ball 0 b)",
+   "present": true,
+   "name": "Complex.eq_const_of_exists_max",
+   "module": "Mathlib.Analysis.Complex.AbsMax",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNorm",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "Complex.instSub",
+    "DFunLike.coe",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "Eq",
+    "Function.locallyFinsuppWithin",
+    "Function.locallyFinsuppWithin.instFunLike",
+    "HAdd.hAdd",
+    "HMul.hMul",
+    "HSub.hSub",
+    "InnerProductSpace.toNormedSpace",
+    "Int",
+    "Int.cast",
+    "Int.instSemiring",
+    "Inv.inv",
+    "MeromorphicOn",
+    "MeromorphicOn.divisor",
+    "Metric.closedBall",
+    "MulZeroClass.toZero",
+    "Ne",
+    "NontriviallyNormedField.toNormedField",
+    "Norm.norm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "RCLike.toInnerProductSpaceReal",
+    "Real",
+    "Real.circleAverage",
+    "Real.instAdd",
+    "Real.instAddCommMonoid",
+    "Real.instAddGroup",
+    "Real.instIntCast",
+    "Real.instInv",
+    "Real.instMul",
+    "Real.instRCLike",
+    "Real.instZero",
+    "Real.lattice",
+    "Real.log",
+    "Real.normedAddCommGroup",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "abs",
+    "finsum",
+    "instHAdd",
+    "instHMul",
+    "instHSub",
+    "instMulZeroClassOfSemiring",
+    "meromorphicTrailingCoeffAt"],
+   "statement_dag_size": 249,
+   "statement":
+   "∀ {c : ℂ} {R : ℝ} {f : ℂ → ℂ},\n  R ≠ 0 →\n    MeromorphicOn f (Metric.closedBall c |R|) →\n      Real.circleAverage (fun x => Real.log ‖f x‖) c R =\n        ∑ᶠ (u : ℂ), ↑((MeromorphicOn.divisor f (Metric.closedBall c |R|)) u) * Real.log (R * ‖c - u‖⁻¹) +\n            ↑((MeromorphicOn.divisor f (Metric.closedBall c |R|)) c) * Real.log R +\n          Real.log ‖meromorphicTrailingCoeffAt f c‖",
+   "present": true,
+   "name": "MeromorphicOn.circleAverage_log_norm",
+   "module": "Mathlib.Analysis.Complex.JensenFormula",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.instAddCommMonoid",
+    "Complex.instMul",
+    "Complex.instNormedField",
+    "Complex.instOne",
+    "Complex.instSemiring",
+    "Complex.stolzSet",
+    "Filter.Tendsto",
+    "Filter.atTop",
+    "Finset.range",
+    "Finset.sum",
+    "HMul.hMul",
+    "HPow.hPow",
+    "Monoid.toNPow",
+    "NPow.toPow",
+    "Nat",
+    "Nat.instPreorder",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "OfNat.ofNat",
+    "One.toOfNat1",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toMonoid",
+    "SummationFilter.unconditional",
+    "UniformSpace.toTopologicalSpace",
+    "instHMul",
+    "instHPow",
+    "nhds",
+    "nhdsWithin",
+    "tsum"],
+   "statement_dag_size": 124,
+   "statement":
+   "∀ {f : ℕ → ℂ} {l : ℂ},\n  Filter.Tendsto (fun n => ∑ i ∈ Finset.range n, f i) Filter.atTop (nhds l) →\n    ∀ {M : ℝ}, Filter.Tendsto (fun z => ∑' (n : ℕ), f n * z ^ n) (nhdsWithin 1 (Complex.stolzSet M)) (nhds l)",
+   "present": true,
+   "name": "Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet",
+   "module": "Mathlib.Analysis.Complex.AbelLimit",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.exp",
+    "Complex.exp_ne_zero",
+    "Complex.instNormedField",
+    "Complex.instZero",
+    "IsCoveringMap",
+    "Ne",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Subtype",
+    "Subtype.mk",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "instTopologicalSpaceSubtype"],
+   "statement_dag_size": 58,
+   "statement": "IsCoveringMap fun z => ⟨Complex.exp z, ⋯⟩",
+   "present": true,
+   "name": "Complex.isCoveringMap_exp",
+   "module": "Mathlib.Analysis.Complex.CoveringMap",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "Dist.dist",
+    "LE.le",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.closedBall",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toDist",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instLE",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "Set",
+    "Set.MapsTo",
+    "Set.instMembership",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 188,
+   "statement":
+   "∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] {R : ℝ} {f : E → F} {c z : E},\n  DifferentiableOn ℂ f (Metric.ball c R) →\n    Set.MapsTo f (Metric.ball c R) (Metric.closedBall (f c) R) →\n      z ∈ Metric.ball c R → Dist.dist (f z) (f c) ≤ Dist.dist z c",
+   "present": true,
+   "name": "Complex.dist_le_dist_of_mapsTo_ball_self",
+   "module": "Mathlib.Analysis.Complex.Schwarz",
+   "kind": "theorem"},
+  {"type_refs":
+   ["And",
+    "Asymptotics.IsBigO",
+    "Bornology.cobounded",
+    "Complex",
+    "Complex.I",
+    "Complex.instDenselyNormedField",
+    "Complex.instMul",
+    "Complex.instNorm",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "Complex.ofReal",
+    "Complex.re",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "Exists",
+    "Filter",
+    "Filter.IsBoundedUnder",
+    "Filter.atTop",
+    "Filter.instInf",
+    "Filter.principal",
+    "HMul.hMul",
+    "HPow.hPow",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Min.min",
+    "Nat",
+    "Nat.instAtLeastTwoHAddOfNat",
+    "Nat.instNeZeroSucc",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toBornology",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.exp",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMul",
+    "Real.instNatCast",
+    "Real.instPow",
+    "Real.instPreorder",
+    "Real.instZero",
+    "Real.norm",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Set.ofPred",
+    "Zero.toOfNat0",
+    "instHMul",
+    "instHPow",
+    "instOfNatAtLeastTwo",
+    "instOfNatNat"],
+   "statement_dag_size": 252,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {C : ℝ} {f : ℂ → E} {z : ℂ},\n  DiffContOnCl ℂ f {z | 0 < z.re} →\n    (∃ c < 2, ∃ B, f =O[Bornology.cobounded ℂ ⊓ Filter.principal {z | 0 < z.re}] fun z => Real.exp (B * ‖z‖ ^ c)) →\n      (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) Filter.atTop fun x => ‖f ↑x‖) →\n        (∀ (x : ℝ), ‖f (↑x * Complex.I)‖ ≤ C) → 0 ≤ z.re → ‖f z‖ ≤ C",
+   "present": true,
+   "name": "PhragmenLindelof.right_half_plane_of_bounded_on_real",
+   "module": "Mathlib.Analysis.Complex.PhragmenLindelof",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AnalyticOnNhd",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "Eq",
+    "Exists",
+    "InnerProductSpace.toNormedSpace",
+    "IsOpenMap",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "Or",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Set.univ",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 104,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {g : E → ℂ},\n  AnalyticOnNhd ℂ g Set.univ → (∃ w, ∀ (z : E), g z = w) ∨ IsOpenMap g",
+   "present": true,
+   "name": "AnalyticOnNhd.is_constant_or_isOpenMap",
+   "module": "Mathlib.Analysis.Complex.OpenMapping",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddCommMagma.toAdd",
+    "AddCommMonoid.toAddCommSemigroup",
+    "AddCommSemigroup.toAddCommMagma",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "Complex.instSemiring",
+    "Complex.instSub",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivInvMonoid.toDiv",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HAdd.hAdd",
+    "HDiv.hDiv",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.closedBall",
+    "Module.toDistribMulAction",
+    "NontriviallyNormedField.toNormedField",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.complexToReal",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instDivInvMonoid",
+    "Real.normedField",
+    "Real.partialOrder",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "Set",
+    "Set.EqOn",
+    "Set.MapsTo",
+    "Set.instMembership",
+    "StrictConvexSpace",
+    "SubNegMonoid.toAddMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "dslope",
+    "instHAdd",
+    "instHDiv",
+    "instHSMul",
+    "instHSub"],
+   "statement_dag_size": 313,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {R₁ R₂ : ℝ} {f : ℂ → E} {c z₀ : ℂ}\n  [StrictConvexSpace ℝ E],\n  DifferentiableOn ℂ f (Metric.ball c R₁) →\n    Set.MapsTo f (Metric.ball c R₁) (Metric.closedBall (f c) R₂) →\n      z₀ ∈ Metric.ball c R₁ →\n        ‖dslope f c z₀‖ = R₂ / R₁ → Set.EqOn f (fun z => f c + (z - c) • dslope f c z₀) (Metric.ball c R₁)",
+   "present": true,
+   "name": "Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div",
+   "module": "Mathlib.Analysis.Complex.Schwarz",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "Complex",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedField",
+    "ContinuousLinearMap",
+    "ContinuousLinearMap.hasOpNorm",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "LE.le",
+    "LT.lt",
+    "Metric.ball",
+    "Metric.closedBall",
+    "NontriviallyNormedField.toNormedField",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedField.toField",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "One.toOfNat1",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instOne",
+    "Real.instZero",
+    "RingHom.id",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "Semiring.toNonAssocSemiring",
+    "Set.MapsTo",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "fderiv"],
+   "statement_dag_size": 262,
+   "statement":
+   "∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [inst_2 : NormedAddCommGroup F]\n  [inst_3 : NormedSpace ℂ F] {R : ℝ} {f : E → F} {c : E},\n  DifferentiableOn ℂ f (Metric.ball c R) →\n    Set.MapsTo f (Metric.ball c R) (Metric.closedBall (f c) R) → 0 < R → ‖fderiv ℂ f c‖ ≤ 1",
+   "present": true,
+   "name": "Complex.norm_fderiv_le_one_of_mapsTo_ball",
+   "module": "Mathlib.Analysis.Complex.Schwarz",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AnalyticOn",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "InnerProductSpace.toNormedSpace",
+    "IsOpen",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 144,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {s : Set ℂ} {f : ℂ → E},\n  DifferentiableOn ℂ f s → IsOpen s → AnalyticOn ℂ f s",
+   "present": true,
+   "name": "DifferentiableOn.analyticOn",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Algebra.id",
+    "ChainCompletePartialOrder.instOfCompleteLattice",
+    "ChainCompletePartialOrder.toPartialOrder",
+    "ClosureOperator",
+    "ClosureOperator.instFunLike",
+    "CommRing.toCommSemiring",
+    "CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
+    "CompleteBooleanAlgebra.toCompleteLattice",
+    "Complex",
+    "Complex.commRing",
+    "Complex.instAddCommMonoid",
+    "Complex.instField",
+    "Complex.instNormedField",
+    "Complex.instSemiring",
+    "DFunLike.coe",
+    "Field.toSemifield",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "LinearMap",
+    "LinearMap.instFunLike",
+    "MulZeroClass.toZero",
+    "Nat",
+    "Nat.instMulZeroClass",
+    "Nat.instPreorder",
+    "NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing",
+    "NonUnitalSeminormedRing.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toNormedCommRing",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "PartialOrder.toPreorder",
+    "Polynomial",
+    "Polynomial.degree",
+    "Polynomial.derivative",
+    "Polynomial.module",
+    "Polynomial.rootSet",
+    "Polynomial.semiring",
+    "Preorder.toLT",
+    "Real",
+    "Real.instRCLike",
+    "Real.normedField",
+    "Real.partialOrder",
+    "Real.semiring",
+    "RingHom.id",
+    "SeminormedCommRing.toNonUnitalSeminormedCommRing",
+    "Semiring.toAddCommMonoid",
+    "Semiring.toModule",
+    "Semiring.toNonAssocSemiring",
+    "Set",
+    "Set.instCompleteAtomicBooleanAlgebra",
+    "Set.instLE",
+    "WithBot",
+    "WithBot.instPreorder",
+    "WithBot.zero",
+    "Zero.toOfNat0",
+    "convexHull",
+    "instInnerProductSpaceRealComplex",
+    "instIsDomain"],
+   "statement_dag_size": 207,
+   "statement":
+   "∀ {P : Polynomial ℂ}, 0 < P.degree → (Polynomial.derivative P).rootSet ℂ ⊆ (convexHull ℝ) (P.rootSet ℂ)",
+   "present": true,
+   "name": "Polynomial.rootSet_derivative_subset_convexHull_rootSet",
+   "module": "Mathlib.Analysis.Complex.Polynomial.GaussLucas",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AnalyticOn",
+    "CompleteSpace",
+    "Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "Iff",
+    "InnerProductSpace.toNormedSpace",
+    "IsOpen",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "PseudoMetricSpace.toUniformSpace",
+    "RCLike.innerProductSpace",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "UniformSpace.toTopologicalSpace"],
+   "statement_dag_size": 144,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {s : Set ℂ},\n  IsOpen s → (AnalyticOn ℂ f s ↔ DifferentiableOn ℂ f s)",
+   "present": true,
+   "name": "Complex.analyticOn_iff_differentiableOn",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["Complex",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instNorm",
+    "Complex.instNormedField",
+    "Complex.instZero",
+    "Complex.re",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DivInvMonoid.toDiv",
+    "DivisionSemiring.toSemiring",
+    "Field.toSemifield",
+    "HAdd.hAdd",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HSub.hSub",
+    "LE.le",
+    "LT.lt",
+    "Membership.mem",
+    "Metric.ball",
+    "Nat",
+    "Nat.instAtLeastTwoHAddOfNat",
+    "Nat.instNeZeroSucc",
+    "NontriviallyNormedField.toNormedField",
+    "Norm.norm",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instAdd",
+    "Real.instDivInvMonoid",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMul",
+    "Real.instNatCast",
+    "Real.instSub",
+    "Real.instZero",
+    "Semifield.toDivisionSemiring",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Set",
+    "Set.MapsTo",
+    "Set.instMembership",
+    "Set.ofPred",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "instHAdd",
+    "instHDiv",
+    "instHMul",
+    "instHSub",
+    "instOfNatAtLeastTwo",
+    "instOfNatNat"],
+   "statement_dag_size": 222,
+   "statement":
+   "∀ {f : ℂ → ℂ} {M R : ℝ} {z : ℂ},\n  0 < M →\n    DifferentiableOn ℂ f (Metric.ball 0 R) →\n      Set.MapsTo f (Metric.ball 0 R) {z | z.re ≤ M} →\n        0 < R → z ∈ Metric.ball 0 R → ‖f z‖ ≤ 2 * M * ‖z‖ / (R - ‖z‖) + ‖f 0‖ * (R + ‖z‖) / (R - ‖z‖)",
+   "present": true,
+   "name": "Complex.borelCaratheodory",
+   "module": "Mathlib.Analysis.Complex.BorelCaratheodory",
+   "kind": "theorem"},
+  {"type_refs":
+   ["BddAbove",
+    "Complex",
+    "Complex.HadamardThreeLines.verticalClosedStrip",
+    "Complex.HadamardThreeLines.verticalStrip",
+    "Complex.instDenselyNormedField",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "Complex.re",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "DivInvMonoid.toDiv",
+    "Function.comp",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HPow.hPow",
+    "HSub.hSub",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Membership.mem",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "OfNat.ofNat",
+    "One.toOfNat1",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.instDivInvMonoid",
+    "Real.instLE",
+    "Real.instLT",
+    "Real.instMul",
+    "Real.instOne",
+    "Real.instPow",
+    "Real.instSub",
+    "Set",
+    "Set.image",
+    "Set.instMembership",
+    "Set.instSingletonSet",
+    "Set.preimage",
+    "Singleton.singleton",
+    "instHDiv",
+    "instHMul",
+    "instHPow",
+    "instHSub"],
+   "statement_dag_size": 228,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} {z : ℂ} {a b l u : ℝ},\n  l < u →\n    z ∈ Complex.HadamardThreeLines.verticalClosedStrip l u →\n      DiffContOnCl ℂ f (Complex.HadamardThreeLines.verticalStrip l u) →\n        BddAbove (Norm.norm ∘ f '' Complex.HadamardThreeLines.verticalClosedStrip l u) →\n          (∀ z ∈ Complex.re ⁻¹' {l}, ‖f z‖ ≤ a) →\n            (∀ z ∈ Complex.re ⁻¹' {u}, ‖f z‖ ≤ b) → ‖f z‖ ≤ a ^ (1 - (z.re - l) / (u - l)) * b ^ ((z.re - l) / (u - l))",
+   "present": true,
+   "name":
+   "Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip'",
+   "module": "Mathlib.Analysis.Complex.Hadamard",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "CompleteSpace",
+    "Complex",
+    "Complex.I",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instInv",
+    "Complex.instMul",
+    "Complex.instNatCast",
+    "Complex.instNormedField",
+    "Complex.instSemiring",
+    "Complex.instSub",
+    "Complex.ofReal",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HMul.hMul",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "Inv.inv",
+    "Membership.mem",
+    "Metric.ball",
+    "Metric.closedBall",
+    "Module.toDistribMulAction",
+    "Nat",
+    "Nat.instAtLeastTwoHAddOfNat",
+    "Nat.instNeZeroSucc",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.pi",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "Set",
+    "Set.instMembership",
+    "SubNegMonoid.toAddMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "circleIntegral",
+    "instHMul",
+    "instHSMul",
+    "instHSub",
+    "instOfNatAtLeastTwo",
+    "instOfNatNat"],
+   "statement_dag_size": 322,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {R : ℝ} {c w : ℂ} {f : ℂ → E},\n  DifferentiableOn ℂ f (Metric.closedBall c R) →\n    w ∈ Metric.ball c R → ∮ (z : ℂ) in C(c, R), (z - w)⁻¹ • f z = (2 * ↑Real.pi * Complex.I) • f w",
+   "present": true,
+   "name": "DifferentiableOn.circleIntegral_sub_inv_smul",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"},
+  {"type_refs":
+   ["BddAbove",
+    "Complex",
+    "Complex.HadamardThreeLines.interpStrip'",
+    "Complex.HadamardThreeLines.verticalClosedStrip",
+    "Complex.HadamardThreeLines.verticalStrip",
+    "Complex.instDenselyNormedField",
+    "Complex.instNorm",
+    "Complex.instNormedAddCommGroup",
+    "Complex.instNormedField",
+    "Complex.instRCLike",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DiffContOnCl",
+    "Function.comp",
+    "InnerProductSpace.toNormedSpace",
+    "LE.le",
+    "LT.lt",
+    "Membership.mem",
+    "Norm.norm",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toNorm",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedSpace",
+    "RCLike.innerProductSpace",
+    "Real",
+    "Real.instLE",
+    "Real.instLT",
+    "Set",
+    "Set.image",
+    "Set.instMembership"],
+   "statement_dag_size": 135,
+   "statement":
+   "∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {l u : ℝ},\n  l < u →\n    ∀ {f : ℂ → E} {z : ℂ},\n      z ∈ Complex.HadamardThreeLines.verticalClosedStrip l u →\n        DiffContOnCl ℂ f (Complex.HadamardThreeLines.verticalStrip l u) →\n          BddAbove (Norm.norm ∘ f '' Complex.HadamardThreeLines.verticalClosedStrip l u) →\n            ‖f z‖ ≤ ‖Complex.HadamardThreeLines.interpStrip' f l u z‖",
+   "present": true,
+   "name":
+   "Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip",
+   "module": "Mathlib.Analysis.Complex.Hadamard",
+   "kind": "theorem"},
+  {"type_refs":
+   ["AddCommGroup.toAddCommMonoid",
+    "AddCommGroup.toAddGroup",
+    "AddGroup.toSubNegMonoid",
+    "AddMonoid.toAddZeroClass",
+    "AddZero.toZero",
+    "AddZeroClass.toAddZero",
+    "CompleteSpace",
+    "Complex",
+    "Complex.I",
+    "Complex.addCommGroup",
+    "Complex.instDenselyNormedField",
+    "Complex.instDivInvMonoid",
+    "Complex.instMul",
+    "Complex.instNatCast",
+    "Complex.instNormedField",
+    "Complex.instOne",
+    "Complex.instSemiring",
+    "Complex.instSub",
+    "Complex.ofReal",
+    "DenselyNormedField.toNontriviallyNormedField",
+    "DifferentiableOn",
+    "DistribMulAction.toDistribSMul",
+    "DistribSMul.toSMulZeroClass",
+    "DivInvMonoid.toDiv",
+    "DivisionSemiring.toSemiring",
+    "Eq",
+    "Field.toSemifield",
+    "HDiv.hDiv",
+    "HMul.hMul",
+    "HPow.hPow",
+    "HSMul.hSMul",
+    "HSub.hSub",
+    "LT.lt",
+    "Metric.closedBall",
+    "Module.toDistribMulAction",
+    "Monoid.toNPow",
+    "NPow.toPow",
+    "Nat",
+    "Nat.instAtLeastTwoHAddOfNat",
+    "Nat.instNeZeroSucc",
+    "NontriviallyNormedField.toNormedField",
+    "NormedAddCommGroup",
+    "NormedAddCommGroup.toAddCommGroup",
+    "NormedAddCommGroup.toSeminormedAddCommGroup",
+    "NormedCommRing.toSeminormedCommRing",
+    "NormedField.toField",
+    "NormedField.toNormedCommRing",
+    "NormedSpace",
+    "NormedSpace.toModule",
+    "OfNat.ofNat",
+    "One.toOfNat1",
+    "PseudoMetricSpace.toUniformSpace",
+    "Real",
+    "Real.instLT",
+    "Real.instZero",
+    "Real.pi",
+    "SMulZeroClass.toSMul",
+    "Semifield.toDivisionSemiring",
+    "SeminormedAddCommGroup.toPseudoMetricSpace",
+    "SeminormedCommRing.toSeminormedRing",
+    "SeminormedRing.toPseudoMetricSpace",
+    "Semiring.toModule",
+    "Semiring.toMonoid",
+    "SubNegMonoid.toAddMonoid",
+    "UniformSpace.toTopologicalSpace",
+    "Zero.toOfNat0",
+    "circleIntegral",
+    "deriv",
+    "instHDiv",
+    "instHMul",
+    "instHPow",
+    "instHSMul",
+    "instHSub",
+    "instOfNatAtLeastTwo",
+    "instOfNatNat"],
+   "statement_dag_size": 367,
+   "statement":
+   "∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {R : ℝ} {f : ℂ → E} {c : ℂ},\n  0 < R →\n    DifferentiableOn ℂ f (Metric.closedBall c R) →\n      ∮ (z : ℂ) in C(c, R), (1 / (z - c) ^ 2) • f z = (2 * ↑Real.pi * Complex.I) • deriv f c",
+   "present": true,
+   "name": "DifferentiableOn.deriv_eq_smul_circleIntegral",
+   "module": "Mathlib.Analysis.Complex.CauchyIntegral",
+   "kind": "theorem"}],
+ "record_count": 36,
+ "mathlib_revision": "db584cd6d46c92f209a44c0f1c829460d327499d",
+ "lean_version": "4.33.0"}

labels/ahlfors_positive_declarations_v4.33-review.csv

@@ -0,0 +1,37 @@
+name,importance_label,ahlfors_textbook_match,mathlib_revision,review_status,reviewer,review_date,notes
+Complex.integral_boundary_rect_eq_zero_of_differentiableOn,Cauchy's theorem (rectangle boundary),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable,Cauchy's theorem (circle integral),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable,Higher-derivative Cauchy formula,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le,Cauchy derivative estimate,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Differentiable.exists_const_forall_eq_of_bounded,Liouville's theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Differentiable.exists_eq_const_of_bounded,Liouville's theorem (constant-function form),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.exists_root,Fundamental theorem of algebra (root existence),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.isAlgClosed,Algebraic closure of the complex numbers,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.analyticAt_iff_eventually_differentiableAt,Local holomorphic-analytic equivalence,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt,Removable singularity theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.differentiableOn_compl_singleton_and_continuousAt_iff,Removable singularity criterion,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+TendstoLocallyUniformlyOn.differentiableOn,Locally uniform limits preserve holomorphicity,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+PhragmenLindelof.horizontal_strip,Phragmen-Lindelof principle (horizontal strip),no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+PhragmenLindelof.vertical_strip,Phragmen-Lindelof principle (vertical strip),no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+DifferentiableOn.isExactOn_ball,Existence of primitives on balls,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+circleAverage_of_differentiable_on,Mean-value theorem for holomorphic functions,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+HarmonicOnNhd.circleAverage_eq,Mean-value theorem for harmonic functions,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.taylorSeries_eq_on_ball,Taylor expansion theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.eventually_eq_of_isLocalMax_norm,Maximum modulus principle (local form),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.eq_const_of_exists_max,Maximum modulus principle (global form),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+MeromorphicOn.circleAverage_log_norm,Jensen's formula,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet,Abel's limit theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.isCoveringMap_exp,Complex exponential as a covering map,partial,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.dist_le_dist_of_mapsTo_ball_self,Schwarz lemma (distance form),yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+PhragmenLindelof.right_half_plane_of_bounded_on_real,Phragmen-Lindelof principle (half-plane),no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+AnalyticOnNhd.is_constant_or_isOpenMap,Open mapping theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div,Equality case of Schwarz lemma,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.norm_fderiv_le_one_of_mapsTo_ball,Schwarz lemma,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+DifferentiableOn.analyticOn,Holomorphic functions are analytic,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Polynomial.rootSet_derivative_subset_convexHull_rootSet,Gauss-Lucas theorem,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.analyticOn_iff_differentiableOn,Holomorphic-analytic equivalence,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.borelCaratheodory,Borel-Caratheodory theorem,no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip',Hadamard three-lines theorem (interpolation form),no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+DifferentiableOn.circleIntegral_sub_inv_smul,Cauchy integral formula,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip,Hadamard three-lines theorem,no,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label
+DifferentiableOn.deriv_eq_smul_circleIntegral,Cauchy differentiation formula,yes,db584cd6d46c92f209a44c0f1c829460d327499d,approved,MesoMathematics statement audit,2026-08-22,Pinned v4.33 statement matches the named-result label

labels/v4.33-statement-review.md

@@ -0,0 +1,39 @@
+# Mathlib 4.33 statement review
+
+Review date: 2026-08-22
+Mathlib commit: `db584cd6d46c92f209a44c0f1c829460d327499d`
+
+## Question
+
+Do the 36 declaration names recovered from the historical Section 4 pilot
+still denote the named complex-analysis results in the pinned Mathlib 4.33
+snapshot?
+
+## Evidence reviewed
+
+`ahlfors_positive_declarations_v4.33-audit.json` was exported by Lean from the
+pinned snapshot.  For every candidate it records presence, declaration kind,
+defining module, pretty-printed current statement, and referenced constants.
+The review compared that current statement with the named-result label in
+`ahlfors_positive_declarations_v4.33-review.csv`.
+
+## Decision
+
+All 36 candidates are present in the frozen complex-analysis slice, and each
+current statement matches its named-result label closely enough to retain it
+as a positive target.  The review file therefore marks all 36 rows
+`approved`.
+
+Approval here has a deliberately narrow meaning: the old name has been
+migrated to a checked v4.33 statement for this experiment.  It is not a claim
+that Ahlfors supplies a universal standard of mathematical importance.  The
+separate `ahlfors_textbook_match` column records whether the corresponding
+result is explicit, partial, or absent in the chosen textbook inventory; it
+does not determine the binary target.
+
+## Reproducibility boundary
+
+The candidate list came from the preregistered historical pilot, but all graph
+features, statements, modules, and declarations used by the new run come from
+the pinned Mathlib 4.33 snapshot.  Changing the Mathlib commit invalidates this
+approval file and requires a new statement export and review.

licenses/mathlib-APACHE-2.0.txt

@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
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+
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+      and distribution as defined by Sections 1 through 9 of this document.
+
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+
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licenses/set.mm-CC0.txt

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+Creative Commons Legal Code
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results/S3.4-projection-geometry.json

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+    "intercept": 0.03250680489480651,
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+  "maximum_recorded_depth": 167,
+  "num_hyperedges": 200602,
+  "num_vertices": 276024,
+  "pairwise_closure_controls": [
+    {
+      "depth": 4,
+      "growth_fit": {
+        "included_depths": [
+          0,
+          1,
+          2,
+          3
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+        "sample_count": 4,
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+        3,
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+        756030
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+      "seed_width": 3
+    },
+    {
+      "depth": 3,
+      "growth_fit": {
+        "included_depths": [
+          0,
+          1,
+          2
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+        "sample_count": 3,
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+      },
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+        3,
+        6,
+        30,
+        870
+      ],
+      "seed_width": 3
+    }
+  ],
+  "vertex_filter": "exclude-internal-name-only"
+}

results/sensitivity-internal-only/S3.2-namespace-depth.json

@@ -0,0 +1,22 @@
+{
+  "corpus_manifest_sha256": "d76ecf19cf968bcd8acee8cc64d504c2e98263849fafd2e88fc16c9205e587ab",
+  "num_hyperedges": 200602,
+  "num_vertices": 276024,
+  "regions": [
+    {
+      "count": 9264,
+      "maximum": 161,
+      "mean": 49.08538428324698,
+      "median": 51.0,
+      "prefix": "MeasureTheory"
+    },
+    {
+      "count": 36500,
+      "maximum": 50,
+      "mean": 3.2687397260273974,
+      "median": 1.0,
+      "prefix": "CategoryTheory"
+    }
+  ],
+  "vertex_filter": "exclude-internal-name-only"
+}

results/sensitivity-internal-only/S3.3-compression-reuse.json

@@ -0,0 +1,19 @@
+{
+  "bootstrap": {
+    "replicates": 200,
+    "sample_size": 30000,
+    "seed": 20260701
+  },
+  "corpus_manifest_sha256": "d76ecf19cf968bcd8acee8cc64d504c2e98263849fafd2e88fc16c9205e587ab",
+  "num_hyperedges": 200602,
+  "num_vertices": 276024,
+  "proof_size_vs_reuse_spearman": 0.10562270505343581,
+  "ratio_vs_reuse_ci95": [
+    0.24086072324474173,
+    0.26081427007426095
+  ],
+  "ratio_vs_reuse_spearman": 0.251072773378494,
+  "row_count": 276024,
+  "statement_size_vs_reuse_spearman": -0.12809023157564453,
+  "vertex_filter": "exclude-internal-name-only"
+}

spec/navigation.md

@@ -0,0 +1,57 @@
+# Section 4 navigation view
+
+Status: **computational object and v4.33.0 statement labels frozen**.
+
+## Declaration graph
+
+The whole-library vertex set contains non-auto/private raw declarations whose
+kind is theorem, definition or abbrev.  A directed edge `source -> target`
+means that `source` consumes `target`: the target occurs as a constant in the
+source type, stored value, or both.  Self references are removed and repeated
+occurrences are collapsed, while the type/value provenance bits are retained.
+
+The complex-analysis test set is the induced vertex set whose **defining
+module** equals `Mathlib.Analysis.Complex` or begins with that dotted prefix.
+This is not a filter on declaration names.
+
+## Features
+
+The six global features are log in-degree, log out-degree, log PageRank, log
+sampled directed betweenness, DAG layer and kernel definition height.  PageRank
+uses damping 0.85.  Betweenness uses 500 seeded source vertices with seed 42.
+
+The seventeen internal features are the induced graph's in/out edge and
+neighbor counts, total and reciprocal neighbors, two-hop in/out neighborhoods,
+clustering, component size, type-reference in/out ratios, forward and reverse
+PageRank, HITS hub and authority scores, and an isolation indicator.  Count and
+centrality transforms are fixed in `navigation/features.py`.
+
+The old pilot used two `lean-training-data` explicit-premise ratios instead of
+the new native type-reference ratios.  Consequently, the v4.33 result is a
+new pre-registered replication, not a byte-for-byte rerun of the old 23-column
+matrix.
+
+Within each split, missing values are imputed by training medians and every
+column is standardized by its training mean and population standard deviation.
+No name, module, declaration kind or text feature enters a model.
+
+## Labels and validation
+
+The external target must be a statement-level reviewed v4.33 file and must
+pass exact-name validation against the module slice.  The two recovered v4.30
+files remain historical evidence only: the old pilot used 36 positive nodes,
+whereas the recovered theorem-to-declaration mapping names 34 unique nodes,
+with a symmetric difference of 28 names.  Exact-name survival in v4.33 is a
+necessary check, not a replacement for reviewing the corresponding statements.
+
+Run 25 stratified 80/20 splits with seeds `20260804 + 1000 + repeat`.  Fit
+class-balanced logistic regression with an unpenalized intercept and L2
+coefficient 0.1.  Average precision is primary; the random reference for each
+split is its validation prevalence.  All split indices, transformations and
+first-split coefficients are written into the result.
+
+The earlier 1,549-declaration/36-positive pilot supplied the preregistered
+candidate names, not the analyzed graph.  The current statements for all 36
+names were reviewed against their labels and approved at the pinned v4.33
+commit; the evidence and decision rule are recorded in
+`labels/v4.33-statement-review.md`.

spec/objects.md

@@ -0,0 +1,76 @@
+# Frozen experimental objects
+
+This file is normative for the v4.33.0 reproduction.  Code and prose must be
+changed together whenever one of these choices changes.
+
+## Raw corpus
+
+The Lean extractor imports the umbrella module `Mathlib` at the pinned commit
+and visits kernel declarations whose defining module is `Mathlib` or begins
+with `Mathlib.`.  For every such declaration it records:
+
+- fully qualified name, defining module, namespace and declaration kind;
+- whether the name satisfies Lean's `Name.isInternal` predicate;
+- whether Lean classifies the name as automatically generated or private;
+- direct constants occurring in the elaborated type;
+- direct constants occurring in the retained value, when one exists;
+- the number of structurally distinct `Expr` subterms in the type and value.
+
+The raw export is not filtered into a research graph.  In particular, a
+reference to a constant outside the Mathlib-module corpus remains present as
+provenance even though it cannot become an internal graph edge.
+
+## Primary theorem view
+
+A vertex is a raw declaration satisfying all of the following:
+
+1. its `kind` is `theorem` (`ConstantInfo.thmInfo`);
+2. `is_auto_or_private` is false;
+3. it belongs to a Mathlib module by the raw-corpus rule above.
+
+For every retained theorem `T`, intersect its `value_refs` with this vertex
+set.  If the intersection is nonempty it yields one directed hyperedge
+
+```text
+{retained theorem constants in T's stored proof} -> T.
+```
+
+Inputs are a set and are serialized in name order.  Their occurrence order,
+multiplicity, inference rules, intermediate proof terms and alternative proofs
+are not represented.  A theorem with no retained in-view premise remains an
+isolated root and contributes no hyperedge.
+
+The diagnostic sensitivity view changes only condition 2: it excludes names
+for which `Name.isInternal` is true, reproducing the old extractor's narrower
+filter on the same v4.33.0 corpus.  It is not the paper's primary object.
+
+## Depth and reuse
+
+- Edge direction is premise to conclusion.
+- Recorded depth is the longest directed path ending at a vertex, with roots
+  at depth zero.
+- Direct reuse is the number of retained hyperedges in which a theorem occurs
+  as an input; repeated occurrences within one proof count once.
+
+These are properties of the induced view.  A root may have dependencies that
+were outside the view.
+
+## Expression-size proxy
+
+Statement size is the number of structurally distinct `Expr` subterms in the
+elaborated theorem type.  Proof-term size is the same count for its retained
+proof value.  Referenced declarations remain leaf constants: their bodies are
+not unfolded.  The Section 3.3 ratio is
+
+```text
+proof_term_dag_size / statement_dag_size.
+```
+
+It is therefore an elaborated-term proxy, not an expanded proof length and not
+the length of a shortest proof.
+
+## Declaration view for Section 4
+
+Section 4 is a parallel graph, not a projection of the primary theorem
+hypergraph.  Its exact inclusion rule, edge rule and frozen Ahlfors mapping are
+versioned separately in `navigation.md` before the v4.33.0 result is promoted.

spec/statistics.md

@@ -0,0 +1,85 @@
+# Statistical contracts
+
+## S3.1 depth growth
+
+Let `n_t` be the number of primary-view vertices at recorded depth `t`.
+Report the ordinary least-squares slope in
+
+```text
+log(n_(t+1)) = alpha + beta * log(n_t) + error
+```
+
+using adjacent nonzero layers only.  Report the included layer indices and
+sample count alongside the slope.  Pairwise-closure controls use the identical
+estimator.
+
+## S3.2 namespace depth
+
+The namespace of `A.B.c` is `A.B`.  The paper's named regions are prefix
+regions: `MeasureTheory` contains all vertices whose names begin with
+`MeasureTheory.`, and similarly for `CategoryTheory`.  Report count, mean,
+median and maximum depth for every requested prefix.
+
+## S3.3 compression and reuse
+
+Compute Spearman rank correlation with average ranks for ties.  Report three
+correlations: ratio--reuse, proof-size--reuse and statement-size--reuse.
+The confidence interval for ratio--reuse is a percentile bootstrap with the
+sample size, replicate count and pseudorandom seed recorded in the result.
+
+## S3.4 projection geometry
+
+The distance-sensitivity diagnostic compares precisely two metrics on theorem
+vertices: half the unweighted bipartite-incidence distance, and weighted
+two-section distance with clique-edge weight `1 / (arity - 1)`.  It reports
+both the fraction of all seeded draws and the fraction among comparable,
+nonidentical pairs.  The latter metric is evaluated on an exactly equivalent
+sparse directed incidence carrier rather than materializing the clique.  A
+fixed seeded set of uniformly sampled sources is paired with uniformly sampled
+targets; the source count and every source id are recorded.
+
+Spectral dimension and four-point hyperbolicity are separate diagnostics on
+the full unweighted bipartite incidence graph and the unweighted unit
+two-section.  The incidence null uses bipartite double-edge swaps and preserves
+the theorem-side and hyperedge-side degree sequences separately.  The unit
+two-section null uses ordinary simple-graph double-edge swaps.  Every result
+records projection, null algorithm, seed and ensemble size and retains every
+null value rather than only a range.  Each null requests four successful swaps
+per edge and records requested swaps, completed swaps and attempts.
+
+Four-point hyperbolicity is a landmark-sampled finite-graph diagnostic, not an
+exact graph constant.  Twenty-four theorem landmarks are sampled uniformly
+from the largest theorem-containing component, one BFS is cached per
+landmark, and 150 quadruples are drawn from the frozen landmark set.  The
+result reports the sampled maximum delta and its ratio to the maximum
+landmark eccentricity, along with all landmark ids.  The identical sampling
+contract is applied independently to every real and null projection.
+
+## S4.1 navigation
+
+All Ahlfors labels are reviewed declaration names tied to the frozen snapshot.
+Names, modules, declaration kinds and prose metadata are excluded from model
+features.  Every split records its indices and seed.  Average precision is the
+primary score; the random-ranking reference is the positive fraction of each
+validation split, not a hard-coded constant.
+
+## S3.4 Metamath comparison
+
+The input is `set.mm` at commit
+`057f4c461055d0b1ed78d9d333aa3de34d9771fa`.  Vertices are all `$p`
+statements.  One proof hyperedge joins the distinct earlier `$p` statements
+invoked directly by a decoded proof to its conclusion.  Depth and the
+adjacent-layer growth fit use the same contracts as S3.1.
+
+Statement size is the serialized token count of the conclusion and mandatory
+`$f`/`$e` hypotheses.  Proof size counts logical nodes in the decoded
+compressed-proof DAG: syntax nodes are suppressed, and explicit `Z`-saved
+subproof references share nodes, while independently reconstructed equal
+expressions remain distinct.  Direct reuse counts later proofs that invoke a
+theorem directly.  The compression--reuse statistics then use the same
+Spearman and bootstrap contracts as S3.3.
+
+These are language-native analogues, not shared units: Metamath tokens and
+decoded logical steps are not Lean expression-DAG nodes.  Cross-library
+comparisons therefore concern the sign and reproducibility of an association,
+not the absolute values of the ratios.