A Duality Between Spacetime-Gauge-Incidence Actions and Matter Multiplicity
Abstract
We establish an exact action-multiplicity duality for finite gravity-matter systems in which spacetime, internal symmetry, and matter incidence are represented on a common carrier. The algebra generated by the complete spacetime-gauge-incidence action and the residual matter multiplicity determine one another as mutual commutants. The duality remains exact for singular and rank-deficient incidence maps and admits support-polar and multiplicity-quiver formulations, together with a positive rigidity certificate and a regulator-stable cofinal extension. On a certified structural branch, the residual multiplicity reconstructs the internal algebra of three-by-three and two-by-two complex matrices along with two copies of the complex numbers, while a canonical determinant incidence selects the special unitary gauge group S(U(3) x U(2)), which is isomorphic to the Standard Model gauge group SU(3) x SU(2) x U(1) modulo Z6. Anomaly cancellation fixes the hypercharge ratios, a distinct rank-three residual supplies the generation carrier, and a single grading-odd operator contains the finite Yukawa and Majorana sectors. Renewal Geometry provides one realization of the required joint carrier; the finite operator-algebraic results are otherwise independent of its microscopic construction.
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BibTeX
@misc{pelissier2026duality,
title = {{A Duality Between Spacetime-Gauge-Incidence Actions and Matter Multiplicity}},
author = {Aurelien Pelissier},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05755429v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Duality Between Spacetime-Gauge-Incidence Actions and Matter Multiplicity
AU - Aurelien Pelissier
PY - 2026
DA - 2026/09/19
PB - HAL
UR - https://hal.science/hal-05755429v1
AB - We establish an exact action-multiplicity duality for finite gravity-matter systems in which spacetime, internal symmetry, and matter incidence are represented on a common carrier. The algebra generated by the complete spacetime-gauge-incidence action and the residual matter multiplicity determine one another as mutual commutants. The duality remains exact for singular and rank-deficient incidence maps and admits support-polar and multiplicity-quiver formulations, together with a positive rigidity certificate and a regulator-stable cofinal extension. On a certified structural branch, the residual multiplicity reconstructs the internal algebra of three-by-three and two-by-two complex matrices along with two copies of the complex numbers, while a canonical determinant incidence selects the special unitary gauge group S(U(3) x U(2)), which is isomorphic to the Standard Model gauge group SU(3) x SU(2) x U(1) modulo Z6. Anomaly cancellation fixes the hypercharge ratios, a distinct rank-three residual supplies the generation carrier, and a single grading-odd operator contains the finite Yukawa and Majorana sectors. Renewal Geometry provides one realization of the required joint carrier; the finite operator-algebraic results are otherwise independent of its microscopic construction.
ER -