ProofAtlas

First-party checked source

Source for Tao’s Almost-Bounded Collatz Orbits

This pinned Lean source formalizes the following mathematical result: For every real-valued threshold function f on ℕ that tends to infinity, the positive starting values N whose standard Collatz orbit minimum is strictly below f(N) have logarithmic density one. Download the complete checked closure, open the endpoint, or browse its supporting modules to study the proof or develop an extension.

Immutable source commit: d53c8de00056fb05999e44589f2399d7efa026e4

Checked source + agent continuation package · 397 Lean files · 1 evidence record · Download ZIP

Each ZIP contains the checked first-party local Lean import closure, exact statements and boundaries, license, notice, evidence, a source-footprint manifest, and an agent continuation file. Mathlib and other third-party dependencies are not bundled; this is not a portable whole-repository release.

Formalization at a glance

What is checked—and how much source supports it

Browse the counted source
Declarations covered by evidence
2
First-party Lean files
397
Lean source lines
124,019
Main recorded file
110 lines

How counting works: Line counts exclude blank lines; comments and documentation count. The total is the deduplicated, commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded. Declaration count means names covered by the artifact's recorded evidence; it is not a count of every declaration in the source. Source footprint is not a difficulty or proof-quality score.

Exact theorem evidence

Tao’s Almost-Bounded Collatz Orbits

Erdos1135.Tao.taoAlmostBoundedColMin_checked, Erdos1135.Tao.taoAlmostBounded_checked

This is the hash-matched main Lean file. Its complete tracked local Lean import closure is browsable once below; checker evidence remains separate for this exact theorem.

Commit
d53c8de00056fb05999e44589f2399d7efa026e4
Main Lean file
Erdos1135/Tao/AlmostBounded.lean
Main-file footprint
110 lines
File SHA-256
sha256:ca16df30d1c105812c238360a63fa27d3ef1933631713aa4f6cced71b9f9267d
Complete Lean closure
397 files · 124,019 lines
Toolchain
leanprover/lean4:v4.30.0-rc2
Open main Lean file Download main Lean fileDownload checker evidence (JSON)Download Apache-2.0 licenseDownload Advameg, Inc. notice

Deduplicated checked source

Complete Lean import closure

This closure supports the theorem evidence record above.

Complete checked Lean closure

397 Lean files are available here

Start with the principal theorem and proof-architecture files below, or search the complete commit-pinned closure.

397Lean files
Search and browse all 397 checked Lean files

Every listed file is read from the same pinned Git commit. File links open raw source in a new tab; use the ZIP download for the complete package. External Mathlib modules are dependency-locked but are not copied into this first-party source tree.

Showing all 397 files

Erdos11358 files · 288 lines
Erdos1135/Tao5 files · 1,196 lines
Erdos1135/Tao/Density5 files · 1,205 lines
Erdos1135/Tao/Fourier32 files · 9,968 lines
Erdos1135/Tao/Probability37 files · 8,159 lines
Erdos1135/Tao/Renewal167 files · 75,780 lines
Erdos1135/Tao/Section312 files · 2,805 lines
Erdos1135/Tao/Section554 files · 10,399 lines
Erdos1135/Tao/Section639 files · 7,300 lines
Erdos1135/Tao/Syracuse34 files · 6,000 lines
Erdos1135/Terras/Core1 file · 58 lines
Erdos1135/Terras/Density1 file · 358 lines
Erdos1135/Terras/Parity2 files · 503 lines
Source hashMatches checked record
Lean buildPassed in recorded evidence
LicenseApache-2.0 · Advameg, Inc.

Provenance and reproducibility

Exact checked source, with reuse terms

The endpoint and every listed local import come from the exact recorded Git commit, and the endpoint matches the stored source hash byte for byte. The locally authored package material is licensed under Apache-2.0 by Advameg, Inc.; Mathlib and cited third-party material remain under their own terms. Machine-readable checker evidence is included.