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We show that the prime terms in the explicit formula are forced by geometry: they arise as closed orbit lengths of the
𝐺
𝐿
1
GL
1
scale flow on adeles. From this geometric trace, a Weil-type formula for an operator-built entire function
𝐷
D emerges, with the Archimedean part derived from the heat kernel of
𝐴
0
A
0
. A direct identity of determinants links
𝐷
D to a self-adjoint ratio determinant and, through a zero-measure equality based on Paley–Wiener/Cartwright/de Branges, yields
𝐷
≡
Ξ
D≡Ξ and the Riemann Hypothesis. No Euler product is used in the construction.
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Title Geometric Adelic Trace and Prime Closed Orbits: An Operator-Theoretic Proof of the Riemann Hypothesis
We show that the prime terms in the explicit formula are forced by geometry: they arise as closed orbit lengths of the
𝐺
𝐿
1
GL
1
scale flow on adeles. From this geometric trace, a Weil-type formula for an operator-built entire function
𝐷
D emerges, with the Archimedean part derived from the heat kernel of
𝐴
0
A
0
. A direct identity of determinants links
𝐷
D to a self-adjoint ratio determinant and, through a zero-measure equality based on Paley–Wiener/Cartwright/de Branges, yields
𝐷
≡
Ξ
D≡Ξ and the Riemann Hypothesis. No Euler product is used in the construction.
Work type Education, Informative
Tags the riemann hypothesis in full
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Registry info in Safe Creative
Identifier 2509123050391
Entry date Sep 12, 2025, 6:23 PM UTC
License All rights reserved
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Copyright registered declarations
Author 100.00 %. Holder JOSE MANUEL MOTA BURRUEZO. Date Sep 12, 2025.
Information available at https://www.safecreative.org/work/2509123050391-geometric-adelic-trace-and-prime-closed-orbits-an-operator-theoretic-proof-of-the-riemann-hypothesis
/
Registration: 2509123050391
