Row 8: no monopoles of our sector

Row 8 predicts that no magnetic monopole of our own electromagnetism, an isolated magnetic north or south pole, will ever be detected. Many theories that unify the forces predict such monopoles, and searches have found none [T]. The program’s first explanation of that absence, that monopoles live in the conjugate sector, died in the checkpoint’s monopole audit: the duality that relates magnetic to electric charge is the electric–magnetic one, not Born reciprocity, and inflation already accounts for the absence. The row now keeps the null with the standard explanation and adds one laboratory analog: monopoles of Berry curvature in momentum space, found in crystals called Weyl semimetals. A direct detection of a monopole of our sector would kill the row.

Status: Alive (#11 §13 row 8) — the row carries no tag; the audit behind it is [D], its account of the absence is inflationary dilution [T], and the Weyl-semimetal analog is a memory citation [16†] (#11 §11.1) — not machine-checked. The lab notebook’s rationale for the null, “p-polarized solitons”, is dead (its obituary).

The row#

Checkpoint #11 §13, row 8:

“Ours” restricts the row to monopoles that carry magnetic charge under our own electromagnetism, the electromagnetic U(1) of the Standard Model. Monopoles of a hidden or conjugate gauge sector are not covered by it.

The observable [T]#

A magnetic monopole is a particle that carries magnetic charge alone (magnetic monopoles). Dirac showed that a single monopole anywhere would require every electric charge to be a multiple of a basic unit, and that the magnetic charge is then large, inversely proportional to the electric one (Dirac quantization and the DSZ pairing, DSZ being Dirac–Schwinger–Zwanziger). Grand unified theories, in which the forces of the Standard Model merge at high energy, contain monopoles as solitons of the gauge and Higgs fields, with masses set by the unification scale (the ’t Hooft–Polyakov monopole).

Two kinds of observation bear on them (monopole flux bounds):

• Direct searches. A monopole passing through a superconducting loop changes the current in the loop by a fixed step, whatever its speed; a fast monopole passing through matter ionizes it far more strongly than a singly charged particle [T]. Detectors built on these effects count monopoles crossing them.
• Astrophysical bounds. Monopoles moving through the Galaxy’s magnetic field would gain energy from it and drain it; the field’s survival caps their flux (the Parker bound) [T].

The standard expectation#

“Model-dependent” (#11 §13). Whether monopoles of our sector should be found depends on the theory and the cosmology [T]. A symmetry-breaking transition that can produce monopoles produces at least about one per causally connected region (the Kibble mechanism); for superheavy monopoles that is far too many, and annihilation does not remove enough of them. A period of inflation after they form dilutes them to an unobservable density. This is the monopole problem and its standard remedy (inflation, reheating and entropy dilution). Whether any monopoles remain to be found then depends on when they formed relative to inflation and on their mass [T].

#11 §11.2 adds, from the literature, why magnetic states are hard to see in general [T]: “Non-observation is structural: Dirac’s condition e·g ~ 2π pins the magnetic coupling near 4π/e² ≈ 34 — the magnetic world is our strong-coupling mirror, heavy and bound.” review/wiki-build-flags.md item 28 records that the number is right and the formula beside it is not: “With α = e²/4π, 4π/e² = 1/α ≈ 137; e·g = 2π gives g²/4π = π/e² = 1/(4α) ≈ 34.26.” The flag awaits Paul’s ruling, and this page quotes #11 as written (the magnetic mirror-family).

The Broken-Born requirement#

A null with the standard explanation#

The checkpoint’s monopole audit (#11 §11.1, “The monopole audit, revised [D]”):

As an explanation of the null result: dead — the relevant duality is electric–magnetic (E↔B, g → 1/g), not x↔p, and inflationary dilution already accounts for absence [T]. As ontology: alive and consequence-bearing — by P4, conjugate-sector solitons gravitate; “true but irrelevant” is the empty set (a correction supplied by P.R.).

The first sentence gives the row its footing. #11 gives the null no rationale of its own: its account of the absence of our monopoles is inflationary dilution, which is established physics [T] and does not depend on Born reciprocity. The row’s content is the commitment itself: a permanent null, with a direct detection as its kill condition.

The rationale that died#

The null was first the lab notebook’s: “Permanent null (p-polarized solitons)” (#1 §9 row 8). It rested on founding supposition 5, “Monopoles live in conjugate space, explaining non-detection”: monopoles would belong to the p-polarized sector, which our detectors cannot register because “gauge forces do not cross polarizations” (#11 §4, P4). The audit killed that explanation on two independent grounds:

• The wrong duality. Electric–magnetic duality exchanges electric and magnetic fields and charges, and with Dirac’s condition weak and strong coupling (S-duality and Montonen–Olive). Born reciprocity ρ: (x, p) → (p, −x) acts on phase space (Born reciprocity). Whether a particle is magnetically charged is a question about the first symmetry, not the second.
• Inflation suffices. The absence is expected without any conjugate sector, so it gives no support to one.

#11 App. A item 5 records the supposition as “split: as explanation, dead (wrong duality; inflation suffices); as ontology, alive and consequence-bearing”. The full record is Obituary: conjugate monopoles explain the null result.

Not a statement about conjugate monopoles#

The surviving half of the supposition concerns monopoles of the conjugate sector, which row 8 does not cover. If they exist, they gravitate, because P4 couples both sectors of matter to the same geometry (conjugate monopoles as ontology). They would interact with our matter only through gravity, so the flux searches below do not test them (our sector’s monopoles).

Their candidacy as the dark matter is dead. Superheavy monopoles of a hidden SU(2) → U(1) sector were developed as the standalone proposal #14 and retired on 2026-10-19, after round 3 of blind review found their abundance estimate misnormalized (#11 §12; Obituary: superheavy conjugate solitons). #14 had used the flux bounds only counterfactually, to show that its monopoles could not have carried our magnetic charge: “Not monopoles of our U(1). If these objects carried magnetic charge under our electromagnetism, they would be classic monopoles and excluded.” (#14 §4; a counterfactual for the soliton candidate).

The only shadow: Berry-curvature monopoles#

#11 §11.1 ends the audit with an analog in condensed matter: “Their laboratory shadow is real: Weyl semimetals host catalogued families of momentum-space Berry-curvature monopoles [16†] — right geometry, different flux.”

In a crystal, an electron’s quantum state in each energy band depends on its crystal momentum, and the way the state’s phase turns as the momentum changes defines a field over momentum space, the Berry curvature [T]. In a Weyl semimetal two bands touch at isolated points of momentum space, and each touching point is a source or a sink of Berry curvature with a quantized total flux: a monopole in momentum space [T]. In the wiki’s reading, “right geometry” refers to the location, momentum space, the space toward which the program’s conjugate sector is polarized. “Different flux” says what the monopole is a source of: Berry curvature, a property of electron states, not a magnetic field (the laboratory shadow).

Reference [16]† is S.-Y. Xu et al., “Discovery of a Weyl fermion semimetal,” Science 349, 613 (2015), and B. Q. Lv et al., Phys. Rev. X 5, 031013 (2015). Both are cited from model memory and await the † literature battery.

The row calls these monopoles “the only shadow”. The documents do not say what the phrase commits the program to. In the wiki’s reading it names the one realized system with monopoles in momentum space, an analog rather than a test: their existence neither supports nor threatens the null for monopoles of our sector.

What kills it#

“Direct detection” (#11 §13): a confirmed monopole of our electromagnetism, registered for instance by the current step it induces in a superconducting loop or by its ionization track [T]. The lab notebook’s wording was “Direct monopole detection” (#1 §9).

In the wiki’s reading, since #11 attributes the absence to inflation, a detection would refute the program’s commitment to a permanent null rather than a mechanism of its own. The documents do not say what else it would bear on.

The data situation#

No monopole of our sector has been detected [T]. The flux limits the record quotes come from the review of #14, where the round-3 referee checked each against its source (review/round3/referee/audit-notes.md, Step 1):

[20] PDG 2024 (Milstead & Weinberg), eq. (95.9): Parker F < 1e-15 cm^-2 sr^-1 s^-1 for M <~ 1e17 GeV. SUPPORTS.
[21] MACRO final: Table 2: "<= 2.8e-16 for m >~ 1e10 GeV, beta > 1e-4"; global 1.4e-16. SUPPORTS the 2.8e-16 figure exactly.

PDG is the Particle Data Group; MACRO, the Monopole, Astrophysics and Cosmic Ray Observatory, was an underground detector built for monopole searches. F is the flux of monopoles per unit area, time and solid angle, and β the speed in units of c. The v3 worklog adds how to cite the first: “For the 10⁻¹⁵ Parker value, cite PDG 2024 or Turner–Parker–Bogdan, PRD 26, 1296 (1982), not Parker 1970 alone” (‘Verified references for v3’). The bounds, their derivation and the extended Parker bound are on monopole flux bounds.

These limits are consistent with the row and cannot confirm it. #11 §15 names rows 1, 4 and 7 as the program’s near-term falsification exposure; row 8 is not among them.

History of the row#

The parenthesis “(p-polarized solitons)” was the dead explanation. v1 dropped it and carried the row without any section on monopoles. #11 v2.0 added the charge-lattice section 11 with the audit, and changed the observable from “Magnetic monopoles” to “Magnetic monopoles (ours)”; the same version proposed conjugate monopoles as a dark-matter candidate, which the qualifier leaves outside the row (the history of the predictions table).

The handoff listed the explanation among the dead claims: “Conjugate monopoles as the explanation of our monopole non-detection (wrong duality; inflation suffices). As ontology they’re alive (the soliton candidate).” (HANDOFF.md §2). Since 2026-10-19 the soliton candidate is retired as well. The repository’s one-line description, “Physics hypothesis explaining dark matter and missing magnetic monopoles” (README.md), still states the dead explanation and is stale on the monopole point; see flag 37 in review/wiki-build-flags.md (CLAUDE.md and the README).

Sources#

• papers/broken-born-checkpoint-v2.md §13 row 8 — the row; §11.1 — the audit [D], inflationary dilution [T] and the Weyl-semimetal shadow; §11.2 — non-observation of magnetic states [T]; §4 — P4; §12 — the soliton obituary; §15 — the near-term rows; ref [16†]; App. A item 5 — the split founding supposition
• review/round3/referee/audit-notes.md Step 1, citations [20] and [21] — the Parker and MACRO limits, checked against their sources
• review/v3-worklog.md ‘Verified references for v3’ — how to cite the Parker value
• review/wiki-build-flags.md item 28 — the formula beside “≈ 34” in §11.2; item 37 — the stale README
• notes/knot-dark-matter-standalone.md §4 — the counterfactual use of the bounds (withdrawn manuscript)
• notes/broken-born-theory.md §9 — v0.1’s row 8 and its dead rationale
• notes/broken-born-program-v1.md §9 — v1’s row 8
• HANDOFF.md §2 — the explanation among the dead claims
• README.md — the stale tagline