The Census of Charge: Every Mechanism That Quantizes Charge, Its Price, and the One Number None of Them Derives

A census of every mechanism in the literature by which electric charge is quantized, built under the discipline of the factor census (paper D1, DOI 10.5281/zenodo.23734950): the candidate set closed in advance, each entry given its producing test and its price, the two halves of the phenomenon - quantization of ratios versus the value of the unit - graded separately for every entry. The question is the one The Pair Derives Charge (DOI 10.5281/zenodo.23768419) left standing: charge universality now has a conditional derivation in this program, while the value of e is derived by no one. Six entries: (1) minimal coupling alone - no quantization; each species' charge is a coupling written in by hand (the null baseline). (2) The Dirac monopole - genuine derivation of commensurability from topology; the unit's size is set by the monopole's own charge, which the argument does not fix. Price: one unobserved entity. (3) Kaluza-Klein compactification - charge as momentum around a compact circle, quantized by single-valuedness; the unit is set by the circle's radius, which the mechanism does not derive. Price: an unobserved geometry with an unset scale. (4) Grand-unified embedding - SU(5) tracelessness over the 5-bar forces 3 x (+1/3) + (-1) + 0 = 0, so the quark fractions are derived, the strongest first-half result in the table; the unit's size is the unified coupling delivered by running from measured inputs. Price: an unobserved unification. (5) Anomaly cancellation - the cancellation equations fix the observed charge assignments up to one overall normalization, given the representation content. Price: the representation content itself, taken from observation. (6) Pair cancellation (this program, Paper 29) - derives sameness (universality, |q_p| = |q_e| conditionally, vacuum charge density identically zero) from exactly-two pairing; Paper 29's own grade for the value of e is MISSING and this census does not improve it. Price: one labeled postulate - exactly-two-ness - the only entry whose price is a counting postulate rather than an unobserved particle or a geometric scale. THE CENSUS'S RESULT IS A CLASS STATEMENT: no known mechanism derives the value of e unconditionally; every entry either quantizes ratios only or buys its unit with something unobserved or unset. The g-2 toll (pre-registered: the residue must move one floor or the paper prints that it could not) is paid by printing the failure: a_e = 0.00115965218059(13) (Fan et al. 2023) is an alpha-delivery device - its theory value takes alpha as an input, and the two best independent alpha determinations (caesium recoil alpha^-1 = 137.035999046, rubidium recoil 137.035999206) disagree by 1.60 x 10^-7, more than either uncertainty, so the residue tracks the alpha input. Floor unmoved. THE VALUE OF e IS NOT DERIVED - by this program, or, per this census, by anyone.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23774106
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

The Census of Charge: Every Mechanism That Quantizes Charge, Its Price, and the One Number None of Them Derives

William Alexander Aldred
5 links
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

The Census of Charge: Every Mechanism That Quantizes Charge, Its Price, and the One Number None of Them Derives

William Alexander Aldred
preprint en

Abstract

A census of every mechanism in the literature by which electric charge is quantized, built under the discipline of the factor census (paper D1, DOI 10.5281/zenodo.23734950): the candidate set closed in advance, each entry given its producing test and its price, the two halves of the phenomenon - quantization of ratios versus the value of the unit - graded separately for every entry. The question is the one The Pair Derives Charge (DOI 10.5281/zenodo.23768419) left standing: charge universality now has a conditional derivation in this program, while the value of e is derived by no one. Six entries: (1) minimal coupling alone - no quantization; each species' charge is a coupling written in by hand (the null baseline). (2) The Dirac monopole - genuine derivation of commensurability from topology; the unit's size is set by the monopole's own charge, which the argument does not fix. Price: one unobserved entity. (3) Kaluza-Klein compactification - charge as momentum around a compact circle, quantized by single-valuedness; the unit is set by the circle's radius, which the mechanism does not derive. Price: an unobserved geometry with an unset scale. (4) Grand-unified embedding - SU(5) tracelessness over the 5-bar forces 3 x (+1/3) + (-1) + 0 = 0, so the quark fractions are derived, the strongest first-half result in the table; the unit's size is the unified coupling delivered by running from measured inputs. Price: an unobserved unification. (5) Anomaly cancellation - the cancellation equations fix the observed charge assignments up to one overall normalization, given the representation content. Price: the representation content itself, taken from observation. (6) Pair cancellation (this program, Paper 29) - derives sameness (universality, |q_p| = |q_e| conditionally, vacuum charge density identically zero) from exactly-two pairing; Paper 29's own grade for the value of e is MISSING and this census does not improve it. Price: one labeled postulate - exactly-two-ness - the only entry whose price is a counting postulate rather than an unobserved particle or a geometric scale. THE CENSUS'S RESULT IS A CLASS STATEMENT: no known mechanism derives the value of e unconditionally; every entry either quantizes ratios only or buys its unit with something unobserved or unset. The g-2 toll (pre-registered: the residue must move one floor or the paper prints that it could not) is paid by printing the failure: a_e = 0.00115965218059(13) (Fan et al. 2023) is an alpha-delivery device - its theory value takes alpha as an input, and the two best independent alpha determinations (caesium recoil alpha^-1 = 137.035999046, rubidium recoil 137.035999206) disagree by 1.60 x 10^-7, more than either uncertainty, so the residue tracks the alpha input. Floor unmoved. THE VALUE OF e IS NOT DERIVED - by this program, or, per this census, by anyone.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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