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Lean evidence record

Power-Law Phase Gap for Multiples of log₂ 3: Lean evidence

This technical record binds the exact theorem statement to its commit-pinned Lean source, checker results, assumptions, and publication-review status.

Read theorem page
Lean buildpassed
Unfinished proof stepsNone
Publication reviewsAccepted

Line counts exclude blank lines; comments and documentation count. The total is the commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded.

Exact formal proposition

Hypotheses and conclusion

This is the exact recorded theorem statement, followed by the source definitions that give its named predicates and quantities their full meaning.

theorem existsPhaseGapRhin : ∃ c : ℝ, PhaseGap c (143 / 10 : ℝ)
Definitions used in this proposition

PhaseGap

structure PhaseGap (c kappa : ℝ) : Prop where
  c_pos : 0 < c
  c_le_one : c ≤ 1
  two_lt_kappa : 2 < kappa
  gap : ∀ q : ℕ, 0 < q →
    c * Real.rpow (q : ℝ) (1 - kappa) ≤
      nearestIntegerNorm ((q : ℝ) * logTwoThree)
Open main Lean file

Technical evidence record

Source identity, checker results, and assumptions

Main Lean declaration
existsPhaseGapRhin
Source commit
a7e937d2c870

Mechanical evidence

How Lean checked the proof

These fields support the exact Lean declaration, not a broader informal claim.

Artifact ID
artifact.known-rhin-phase-gap.exists.v001
Declarations covered by recorded evidence
Erdos1135.ND.existsPhaseGapRhin
Lean build
passed
Recorded build time
1.3 s one machine-dependent evidence run, not a benchmark
Evidence collected
· clean-source provenance recorded
Unfinished proof check
passed
Lean toolchain
leanprover/lean4:v4.30.0-rc2
Recorded source commit
a7e937d2c87047b2275323c5f186e6e8bdefceb3
Source SHA-256
sha256:223b9cc07b21fbfd22d0bf53683f76b2a046ed083b1986210478c3f36c5e360e
Statement alignment
accepted

Lean foundations

Standard foundations used by the proof

Lean reports the logical foundations below through Mathlib. They are standard proof-system foundations, not conjectural mathematical assumptions about this theorem. The recorded closure stays within the approved classical_mathlib_standard profile, with no unexpected axiom or unfinished-proof placeholder.

  • Classical.choice
  • Quot.sound
  • propext

Files and machine-readable evidence

Reproduce or inspect the recorded check

Use the complete first-party source bundle for reconstruction, or inspect the exact main file and checker evidence separately. Mathlib and other third-party dependencies are identified but not rebundled.

Checked source + agent continuation package · 40 Lean files · 1 evidence record · Download ZIPBrowse counted source onlineDownload main Lean fileDownload checker evidence (JSON)Download Apache-2.0 license

Review bindings

Publication reviews accepted

All four required publication-review gates are accepted for the retained presentation of this exact theorem. The review bindings are recorded separately from the Lean build and do not broaden the formal statement.

Read the publication-review details