State of Proof

2026-07-29-maxwell-conjecture · Potential theory

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

  1. G1 · claim mapped

    Exact rescaling and Taylor skeleton

    Depends on: locked v1 source

  2. G2 · claim mapped

    Exhaustive exact classification of 21 limiting critical points

    Depends on: G1

  3. G3 · claim mapped

    Persistence and separation of 21 plus 3 critical-point branches

    Depends on: G2

  4. G4 · claim mapped

    Morse perturbation via transversality with positive charges

    Depends on: G3

  5. G5 · claim mapped

    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

  1. No audit gate has run and no mathematical finding has been issued.

  2. 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

Potential theory and exact real algebra · audit not started

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

  1. 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.