The concepts at eleven parameters: the primary, the secondary and the optional, their hierarchy and their graph
Abstract
The unified theory at eleven parameters counted its concepts, six, and their bits, twentytwo, against the two hundred and eighty-three bits of the thirty-four numbers it locates. This paper takes the count apart. It sorts every concept the series names into three lists, ranks the first two by dependence and the third by cost. The primary concepts are the six inputs that are not numbers, the eleven, the finite algebra, the gauging, the Higgs doublet, the compensator and the line. Their dependence graph has two roots and three levels, and each is tied to facts that the theory would lose without it, from one, for the line, to seven, for the compensator. The secondary concepts are the fifteen the theory inherits, seven mathematical and eight physical, from the Lie algebra to renormalisation; their graph has two roots and five levels, every physical concept resting on a mathematical one and every primary concept using at least two of them. The optional concepts are ten names the series gives to its own theorems and readings, from the two readings to the amalgamated sum, and nothing in the first two lists depends on them. Their cost is measured as the number of the thirty-one articles whose abstract presupposes each, from twelve for the readings to none for the amalgamated sum. The paper says which optional concepts can be dropped at the cost of readability alone and which carry a ledger or a reading with them, and it draws the three graphs. Mass, spin, space, time and the fermion content are not concepts in this currency; the paper says why. Nothing here changes the theory; what it adds is the map of its vocabulary, with the depth at which each word sits.
Related
- Quantifying Information Hierarchy for Neutrino Oscillation Parameters at JUNO
- Structural signatures of primary and secondary relaxation during physical aging of a metallic glass
- Synthesis and properties of (FeSnPbSb)S quinary sulphides: Bridging mechanochemical and high-entropy concepts
- How Quantum Is Light? Concepts, Measures, and Applications of Optical Quantumness
- Fundamental concepts of thermal phonon coherence
BibTeX
@misc{reynaud2026concepts,
title = {{The concepts at eleven parameters: the primary, the secondary and the optional, their hierarchy and their graph}},
author = {Patrick B. Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05769941v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The concepts at eleven parameters: the primary, the secondary and the optional, their hierarchy and their graph
AU - Patrick B. Reynaud
PY - 2026
DA - 2026/09/29
PB - HAL
UR - https://hal.science/hal-05769941v2
AB - The unified theory at eleven parameters counted its concepts, six, and their bits, twentytwo, against the two hundred and eighty-three bits of the thirty-four numbers it locates. This paper takes the count apart. It sorts every concept the series names into three lists, ranks the first two by dependence and the third by cost. The primary concepts are the six inputs that are not numbers, the eleven, the finite algebra, the gauging, the Higgs doublet, the compensator and the line. Their dependence graph has two roots and three levels, and each is tied to facts that the theory would lose without it, from one, for the line, to seven, for the compensator. The secondary concepts are the fifteen the theory inherits, seven mathematical and eight physical, from the Lie algebra to renormalisation; their graph has two roots and five levels, every physical concept resting on a mathematical one and every primary concept using at least two of them. The optional concepts are ten names the series gives to its own theorems and readings, from the two readings to the amalgamated sum, and nothing in the first two lists depends on them. Their cost is measured as the number of the thirty-one articles whose abstract presupposes each, from twelve for the readings to none for the amalgamated sum. The paper says which optional concepts can be dropped at the cost of readability alone and which carry a ledger or a reading with them, and it draws the three graphs. Mass, spin, space, time and the fermion content are not concepts in this currency; the paper says why. Nothing here changes the theory; what it adds is the map of its vocabulary, with the depth at which each word sits.
ER -