Five positive point charges in R³ have at least 24 nondegenerate critical points, contradicting the proposed (5−1)² bound
Intake record · five gates mapped · no audit gate has run
Current record status
What this docket currently establishes
Intake record · five gates mapped · no audit gate has run. This docket identifies what has been checked and what remains open. It does not validate or reject the manuscript's headline claim beyond the explicitly stated scope.
- Claim
- Five positive point charges in R³ have at least 24 nondegenerate critical points, contradicting the proposed (5−1)² bound
- Source version
- arXiv 2607.27197v1 · arXiv v1
- Source SHA-256
4178ddc5a4efcdc11726bea6d6d20785575c55564095dbf53bfaa6d26055a958- Source locked
- Last material update
- Next open step
- Independently derive the exact rescaling, Taylor coefficients, and polynomial skeleton before testing the critical-point count
One-minute summary
The manuscript claims a configuration of five positive charges with at least 24 nondegenerate critical points of its Coulomb potential. Since (5−1)²=16, that would contradict the proposed Maxwell bound. The source is locked and five gates are mapped; no computation or mathematical audit has run in this lab.
Scope of this docket
The planned audit covers exact rescaling and Taylor coefficients, an exhaustive exact classification of 21 limiting critical points, persistence of 21 plus 3 branches, the Morse perturbation, and global finiteness.
Claim and dependency map
Exact rescaling and Taylor skeleton
Depends on: locked v1 source
Exhaustive exact classification of 21 limiting critical points
Depends on: G1
Persistence and separation of 21 plus 3 critical-point branches
Depends on: G2
Morse perturbation via transversality with positive charges
Depends on: G3
Global finiteness of the complete critical set
Depends on: G4
Evidence routes
- computational
- Planned: independent symbolic coefficient comparison, exact real-root isolation, and a separately implemented Hessian replay.
- expert
- Planned: specialist review of quantitative persistence, transversality, and global analytic bounds.
Findings and scope limits
No audit gate has run and no mathematical finding has been issued.
The intake target is five charges and at least 24 nondegenerate critical points, not a three-charge or five-equilibrium construction.
Open Steps—where expert eyes are needed
Can the displayed limiting polynomial and all 21 real critical points be derived and certified exactly from the locked source?
This is the first finite, falsifiable gate underneath the claimed 24-point configuration.
Source record and provenance
Nine-page arXiv v1 source. The locked record shows no journal reference or referee disposition.
Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case.
Retrieved .
Version and record history
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new docket
2026-07-29-maxwell-conjecture
arXiv v1 source locked and five audit gates mapped; no gate run
Statuses describe evidence collected for a defined scope. They are not peer-review decisions, publication recommendations, or certificates of mathematical truth.