We propose and evaluate a source-equals-detector search for the deexcitation of the long-lived isomer <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> in natural tantalum (Ta), using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray transition-edge-sensor (TES) array. Two capabilities absent in conventional high-purity germanium (HPGe) searches are exploited: (i) near-unity containment of low-energy secondaries [internal-conversion (IC) electrons and characteristic x-rays] and of the nuclear recoil, enabling a calorimetric, event-by-event measurement of the total deposited energy in the absorber; and (ii) a delayed-coincidence tag using the subsequent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn></mrow></mmultiscripts></mrow></math> electron-capture (EC) decay to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Hf</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn></mrow></mmultiscripts></mrow></math>. We evaluate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>σ</mi></math> discovery reach for IC and for dark-matter (DM)-induced deexcitation in two benchmark scenarios: a strongly interacting DM subcomponent and inelastic DM with off diagonal couplings. Using a background model based on intrinsic radioactivity in the Ta absorber and realistic detector performance, we show that arrays with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>TES</mi></mrow></msub><mo>=</mo><mn>256</mn></mrow></math> and 1,000 pixels can reach the theoretically expected IC half-life within 2.6 yr and 0.66 yr, respectively. For an array with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>TES</mi></msub><mo>=</mo><msup><mn>10</mn><mn>4</mn></msup></math> and a five-year exposure, the projected sensitivity to DM-induced de-excitation surpasses limits inferred from HPGe nonobservations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> and probes regions of parameter space not covered by current direct-detection experiments.

Japan

A. Gando

K. Ichimura

K. Ishidoshiro

T. Kikuchi

T. Kishimoto

A. Takeuchi

R. Sato

R. Smith

Probing internal conversion and dark-matter-induced deexcitation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray TES array

As double heavy quarkonia, charmonium and bottomonium are generally considered to have small relativistic corrections and can be treated using nonrelativistic models. However, this is not always the case. In this paper, we employ the relativistic Bethe-Salpeter (BS) equation method to calculate the electromagnetic (EM) radiative decays of heavy quarkonium where the $\textit{M}$1 transition provides the leading-order contribution. Compared to nonrelativistic method which only computes $\textit{M}$1 transition, our calculations include $\textit{M}$1 + $\textit{E}$2 + $\textit{M}$3 + $\textit{E}$4 transitions, where the higher-order multipoles, $\textit{E}$2, $\textit{M}$3, and $\textit{E}$4, account for relativistic corrections. The study finds that relativistic effects are large in such transitions even for bottomonium. For instance: the relativistic corrections in the decays $\textit{ψ}$($\textit{nS}$) → $\textit{γη}$ ($\textit{mS}$) ($\textit{n}$ ≥ $\textit{m}$) range from 68$\textit{.}$1% to 83$\textit{.}$2%, while those for ϒ($\textit{nS}$) → $\textit{γη}$ ($\textit{mS}$) range between 65$\textit{.}$9% and 75$\textit{.}$2%.

China

Su-Yan Pei

Wei Li

Wen-Yuan Ke

Yi-Yi Rui

Qiang Li

Guo-Li Wang

Large relativistic corrections to nonrelativistic $\textit{M}$1 transitions in heavy quarkonium

We derive decomposition formulas for supercharacters of quantum affine orthosymplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>. As a special case, our results provide explicit character formulas for a class of Kirillov-Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis.

Zengo Tsuboi

Character formulas for Kirillov-Reshetikhin modules via folding of supercharacters of <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory <math altimg='si3.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>T</mi><msub><mi>L</mi><mi>m</mi></msub></mrow></math>, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: <math altimg='si9.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si6.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>. We show that the extra <italic>&#945;TL<inf>m</inf></italic> term significantly alters the mass-radius relation of WDs, especially at high central densities <math altimg='si11.svg'><mrow><mo>(</mo><msub><mi>&#961;</mi><mi>c</mi></msub><mo>&#8819;</mo><msup><mn>10</mn><mn>8</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><msup><mn>10</mn><mn>9</mn></msup><mspace width='0.16em' /><mrow><mi mathvariant='normal'>g</mi></mrow><mo linebreak='goodbreak'>/</mo><mi>c</mi><msup><mi>m</mi><mn>3</mn></msup><mo>)</mo></mrow></math>, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter <italic>&#945;</italic>, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter <italic>&#945;</italic> for the two choices of the Lagrangian density <italic>L<inf>m</inf></italic>.

Brazil

Edson Otoniel

Juan M.Z. Pretel

Clésio E. Mota

César O.V. Flores

Victor B.T. Alves

Germany

Franciele M. da Silva

White dwarf structure in <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity: Beyond the Chandrasekhar mass limit

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

The nuclear modification factor <italic>R</italic> <inf>AA</inf> of charm jets, identified by the presence of a D 0 meson among the jet constituents, has been measured for the first time in Pb&#8211;Pb collisions at a centre-of-mass energy per nucleon pair <math altimg='si8.svg'><mrow><msqrt><msub><mi>s</mi><mtext>NN</mtext></msub></msqrt><mspace width='0.33em' /><mo linebreak='goodbreak'>=</mo><mspace width='0.33em' /><mn>5.02</mn></mrow></math> TeV with the ALICE detector at the LHC. The D 0 mesons and their charge conjugates are reconstructed from the hadronic decay D <math altimg='si9.svg'><mrow><msup><mrow /><mn>0</mn></msup><mo>&#8594;</mo><msup><mrow><mi mathvariant='normal'>K</mi></mrow><mo>&#8722;</mo></msup><msup><mi>&#960;</mi><mo>+</mo></msup></mrow></math>. Jets are reconstructed from D 0-meson candidates and charged particles using the anti- <italic>k</italic> <inf>T</inf> algorithm with jet resolution parameter <math altimg='si10.svg'><mrow><mi>R</mi><mspace width='0.33em' /><mo linebreak='goodbreak'>=</mo><mspace width='0.33em' /><mn>0.3</mn></mrow></math>, in the jet transverse momentum ( <italic>p</italic> <inf>T</inf>) range 5 <math altimg='si11.svg'><mrow><mo>&lt;</mo><msubsup><mi>p</mi><mrow><mi mathvariant='normal'>T</mi></mrow><mrow><mtext>ch</mtext><mspace width='0.33em' /><mtext>jet</mtext></mrow></msubsup><mo linebreak='goodbreak'>&lt;</mo></mrow></math> 50 GeV/ <italic>c</italic> and pseudorapidity | <italic>&#951;</italic> ch&#8201;jet|&#8239;&lt;&#8239;0.6. A hint of reduced suppression in the charm-jet <italic>R</italic> <inf>AA</inf> is observed in comparison to inclusive jets in central Pb&#8211;Pb collisions with a significance of about 2 <italic>&#963;</italic> in 20 <math altimg='si11.svg'><mrow><mo>&lt;</mo><msubsup><mi>p</mi><mrow><mi mathvariant='normal'>T</mi></mrow><mrow><mtext>ch</mtext><mspace width='0.33em' /><mtext>jet</mtext></mrow></msubsup><mo linebreak='goodbreak'>&lt;</mo></mrow></math> 50&#8239;GeV/ <italic>c</italic>, suggesting the in-medium energy loss to depend on both the difference between quark and gluon coupling strength (Casimir colour-charge effect) and quark mass (dead-cone effect). The data are compared with model calculations that include mass effects in the in-medium energy loss. Several state-of-the-art models are consistent with the data, with the LIDO model providing the best description of the data in the common kinematic range of inclusive and D 0-tagged jets, highlighting the role of mass effects in interpreting the results.

France

S. Acharya

India

A. Agarwal

Switzerland

G. Aglieri Rinella

Italy

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

South Korea

S.U. Ahn

Slovakia

I. Ahuja

A. Akindinov

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H.M. Alfanda

Mexico

R. Alfaro Molina

B. Ali

A. Alici

United States

N. Alizadehvandchali

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A.R. Altamura

I. Altsybeev

J.R. Alvarado

M.N. Anaam

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

L. Aphecetche

H. Appelshäuser

C. Arata

S. Arcelli

R. Arnaldi

J.G.M.C.A. Arneiro

I.C. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

D. Averyanov

M.D. Azmi

H. Baba

A. Badalà

J. Bae

Y.W. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

A. Balbino

A. Baldisseri

Poland

B. Balis

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G.G. Barnaföldi

L.S. Barnby

E. Barreau

V. Barret

L. Barreto

C. Bartels

K. Barth

E. Bartsch

N. Bastid

Sweden

S. Basu

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J.L. Bazo Alba

Denmark

I.G. Bearden

C. Beattie

P. Becht

D. Behera

I. Belikov

A.D.C. Bell Hechavarria

F. Bellini

R. Bellwied

S. Belokurova

L.G.E. Beltran

Y.A.V. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

M.G. Besoiu

L. Betev

P.P. Bhaduri

Investigating charm quark energy loss in medium with the nuclear modification factor of D <bold>0</bold>-tagged jets

We consider near-extremal membranes embedded in M-theory, consistently truncated to gauged $$ \mathcal{N} $$ = 2 supergravity in four dimensions on the coset space $\textit{M}$ . These are holographically dual to 2+1 dimensional superconformal gauge theory with U(1) × U(1) global symmetry. Turning on the chemical potential to either the $\textit{R}$-symmetry or the baryonic symmetry gives access to the quantum critical regime of the boundary gauge theory. We study perturbative stability of the extremal limit, and demonstrate that membranes with topological (baryonic) charge are free from all known instabilities. $\textit{R}$-charged membranes are free from the superconducting instabilities, but have unstable charge transport and instabilities associated with the condensation of the axions.

Canada

Alex Buchel

Ruben Monten

Near-extremal membranes in M-theory

Motivated by recent progress in the spurion analysis of non-invertible selection rules (NISRs) arising from near-group fusion algebras, we further generalize the framework to a class of NISRs obtained from $\textit{ℤ}$ orbifolding of a $\textit{ℤ}$ symmetry, denoted as $\textit{ℤ}$ /$\textit{ℤ}$ . Many structural features are carried over: for instance, our labeling scheme enables systematic tracking of all couplings when constructing composite amplitudes from simpler building blocks at arbitrary loop orders in perturbation theory. Our analysis provides a transparent understanding of both low-order and all-order zeros of couplings under radiative corrections. Furthermore, we examine the fate of low-order zeros when the fusion algebra is not faithfully realized — a situation not captured by the vanilla argument of “loop-induced groupification” — and formulate a conjecture on the related aspects of particle decoupling and effective theory. Finally, we discuss the low-order versus all-order zeros in Yukawa textures from the perspective of spurion analysis.

Motoo Suzuki

Ling-Xiao Xu

Spurion analysis of $\textit{ℤ}$ $\textit{M}$ /$\textit{ℤ}$ 2 non-invertible selection rules: low-order versus all-order zeros

Pulsars, with their extreme densities and precise measurements, offer an exceptional probe of matter under intense gravity. We examined compact star structures within the extended <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity framework, incorporating the Ricci scalar, matter Lagrangian, and energy-momentum trace. Introducing coupling constants <italic>&#955;</italic> <inf>1</inf> and <italic>&#955;</italic> <inf>2</inf> enabled a realistic description beyond general relativity. Using the Durgapal-Bannerji-type metric, we derived modified field and TOV equations, obtaining expressions for energy density and anisotropic pressures. With the transformation <math altimg='si165.svg'><mrow><msup><mi>e</mi><mrow><mi mathvariant='script'>B</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup><mo linebreak='goodbreak'>=</mo><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math> and a chosen anisotropy function &#916;( <italic>r</italic>), regular stellar models were integrated and matched smoothly to the exterior Schwarzschild-de Sitter spacetime. All physical conditions are satisfied: density and pressures are positive and finite; &#916;( <italic>r</italic>)&#8239;&gt;&#8239;0 implies an outward-directed force; sound speeds remain subluminal; and the adiabatic index &#915;&#8239;&gt;&#8239;4/3 ensures dynamical stability. The generalized TOV equation confirms equilibrium among gravitational, hydrostatic, anisotropic, and curvature-matter coupling forces. The <math altimg='si166.svg'><mrow><mi>M</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>R</mi></mrow></math> relations exhibit clear trends. For <math altimg='si167.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>4</mn><mo>,</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0.4</mn></mrow></math>: PSR J2215+5135 (2.28, <italic>M</italic> <inf>&#8857;</inf>) has <math altimg='si168.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>13</mn><mo>.</mo><msubsup><mn>05</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.13</mn></mrow></msubsup></mrow></math> km (GR: 12.33&#8239;km); PSR J0740+6620 (2.08, <italic>M</italic> <inf>&#8857;</inf>): 12.68 &#8239;&#8594;&#8239; 13.32&#8239;km; PSR J0348+0432 (2.01, <italic>M</italic> <inf>&#8857;</inf>): 12.76 &#8239;&#8594;&#8239; 13.39&#8239;km; PSR J0030+0451 (1.44, <italic>M</italic> <inf>&#8857;</inf>): 13.19 &#8239;&#8594;&#8239; 13.77&#8239;km. Positive <italic>&#955;</italic> <inf>1</inf> compresses stars <math altimg='si169.svg'><mrow><mo>(</mo><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>11</mn><mo>.</mo><msup><mn>26</mn><mrow><mo>+</mo><mn>0.33</mn></mrow></msup></mrow></math> km for <math altimg='si170.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mrow><mo>=</mo><mn>5</mn><mo>)</mo></mrow></mrow></math>, while <math altimg='si171.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn></mrow></math> expands to <math altimg='si27.svg'><mrow><mn>13</mn><mo>.</mo><msubsup><mn>07</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.14</mn></mrow></msubsup></mrow></math> km. At <math altimg='si5.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mn>3</mn></mrow></math>, varying <italic>&#955;</italic> <inf>2</inf> shifts <italic>R</italic> from <math altimg='si86.svg'><mrow><mn>12</mn><mo>.</mo><msubsup><mn>32</mn><mrow><mo>&#8722;</mo><mn>0.29</mn></mrow><mrow><mo>+</mo><mn>0.18</mn></mrow></msubsup></mrow></math> km <math altimg='si172.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn><mo>)</mo></mrow></math> to <math altimg='si173.svg'><mrow><mn>11</mn><mo>.</mo><msup><mn>23</mn><mrow><mo>+</mo><mn>0.35</mn></mrow></msup></mrow></math> km <math altimg='si174.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>5</mn><mo>)</mo></mrow></math>. Overall, including <math altimg='si175.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> or <math altimg='si176.svg'><mi mathvariant='script'>T</mi></math> slightly enlarges radii, showing that tuning <italic>&#955;</italic> <inf>1</inf>,&#8201; <italic>&#955;</italic> <inf>2</inf> precisely controls compactness and maximum mass&#8212;consistent with observations and testable by future data.

Oman

S.K. Maurya

South Africa

Azerbaijan

A. Errehymy

K.N. Singh

Kuwait

O. Donmez

Uzbekistan

J. Rayimbaev

S. Otaboyev

Y. Turaev

Constraining <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity with millisecond pulsar observations

We present a non-singular, definition-level formulation of F-theory by replacing the traditional shrinking-fiber limit of M-theory with compactification on a tower-completed circle described using perfectoid geometry and condensed mathematics. This construction provides an intrinsic eleven-dimensional carrier for modular data and admits a canonical tilting and comparison procedure that yields elliptic geometry as an output rather than an auxiliary input. Using this framework, we establish a precise M-theory/Type IIB dictionary in the constant-coupling sector, showing how the physical axio-dilaton is fixed by eleven-dimensional geometric and topological data. The correspondence is tested at the level of the ten-dimensional bosonic effective action, including its topological couplings inherited from eleven dimensions. The tower-completed geometry naturally organizes global sectors in generalized cohomology, with charge data governed by K-theory and exhibiting a canonical prime-power torsion structure. We further show how this framework extends to varying-coupling backgrounds and duality defects, admits a natural adelic completion with prime-independence, and generalizes to higher-rank and U-duality geometries. We also discuss holographic aspects and the anomaly-refined extension of the duality group beyond the bosonic truncation. Together, these results provide a coherent, non-singular foundation for F-theory and its extensions.