Paper Citation Record · LEDGER

Large and small hierarchies from finite modular symmetries

As of 11 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 2 inbound Pith citation observations for arXiv:2412.18435.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.18435 v1

Coverage vector

measured 66 of 66 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:52:20.569351Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T10:45:52.684568Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T10:56:52.116242Z

Reference resolution

66 of 66 outbound references displayed

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External citation measurements

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Outbound references

Observation ce764fee-aeaf-4b50-ae50-d204fcb0cf3e · outbound

This paper cites Are neutrino masses modular forms?.

Large and small hierarchies from finite modular symmetries Are neutrino masses modular forms?

Reference 1

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Observation e30a181d-0933-4319-af65-54bdcfbf37f5 · outbound

This paper cites Discrete Flavor Symmetries and Models of Neutrino Mixing.

Large and small hierarchies from finite modular symmetries Discrete Flavor Symmetries and Models of Neutrino Mixing

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.329398Z

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Observation acbb99c1-0650-4ad7-b279-13e03caffed2 · outbound

This paper cites Non-Abelian Discrete Symmetries in Particle Physics.

Large and small hierarchies from finite modular symmetries Non-Abelian Discrete Symmetries in Particle Physics

Reference 3

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Observation 3dcdd5e7-c0ca-4e9c-bd23-f7200f72efba · outbound

This paper cites Lepton mixing and discrete symmetries.

Large and small hierarchies from finite modular symmetries Lepton mixing and discrete symmetries

Reference 4

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Observation c3ec32e0-830c-42fb-8099-563451cc6585 · outbound

This paper cites Neutrino Mass and Mixing with Discrete Symmetry.

Large and small hierarchies from finite modular symmetries Neutrino Mass and Mixing with Discrete Symmetry

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.341602Z

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Observation 598138be-cab7-44bc-9f4e-68bb21294507 · outbound

This paper cites Kobayashi, H.

Large and small hierarchies from finite modular symmetries Kobayashi, H

Reference 6

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Observation a12adca1-8853-4158-bb92-2814b3015c33 · outbound

This paper cites Neutrino mixing from finite modular groups.

Large and small hierarchies from finite modular symmetries Neutrino mixing from finite modular groups

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.349571Z

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Observation 50318703-7c23-4f95-a4ea-5b368d3f8024 · outbound

This paper cites Lepton Masses and Mixing from Modular $S_4$ Symmetry.

Large and small hierarchies from finite modular symmetries Lepton Masses and Mixing from Modular $S_4$ Symmetry

Reference 8

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Observation 51e1c029-4efd-4213-aa78-38e69de516b4 · outbound

This paper cites Modular $A_5$ Symmetry for Flavour Model Building.

Large and small hierarchies from finite modular symmetries Modular $A_5$ Symmetry for Flavour Model Building

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.357298Z

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Observation de6ab320-8590-4218-89c2-d8d1ee89b409 · outbound

This paper cites Modular symmetry at level 6 and a new route towards finite modular groups.

Large and small hierarchies from finite modular symmetries Modular symmetry at level 6 and a new route towards finite modular groups

Reference 10

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Observation fbf7d987-5f19-4cdf-a29d-209a10818e10 · outbound

This paper cites Neutrino Masses and Mixing from Double Covering of Finite Modular Groups.

Large and small hierarchies from finite modular symmetries Neutrino Masses and Mixing from Double Covering of Finite Modular Groups

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.364532Z

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Observation b030ba73-f809-4d50-a567-937d1b3e20c5 · outbound

This paper cites Double Cover of Modular $S_4$ for Flavour Model Building.

Large and small hierarchies from finite modular symmetries Double Cover of Modular $S_4$ for Flavour Model Building

Reference 12

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Observation 99a87bbb-6747-4b1b-a289-d11355ecc446 · outbound

This paper cites Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group.

Large and small hierarchies from finite modular symmetries Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.371783Z

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Observation b1c8fbc5-c468-4046-9088-91a287003188 · outbound

This paper cites Double Covering of the Modular $A^{}_5$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model.

Large and small hierarchies from finite modular symmetries Double Covering of the Modular $A^{}_5$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.375130Z

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Observation 6ad39a9a-6bc2-4339-9815-738a487fa1bb · outbound

This paper cites Modular flavor symmetric models.

Large and small hierarchies from finite modular symmetries Modular flavor symmetric models

Reference 15

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Observation 9f71d59a-2983-4c29-a5f2-c287c67a36b9 · outbound

This paper cites Neutrino Mass and Mixing with Modular Symmetry.

Large and small hierarchies from finite modular symmetries Neutrino Mass and Mixing with Modular Symmetry

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.382303Z

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Observation e8059014-0ff7-4841-ad06-17663538fc57 · outbound

This paper cites Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau = i$.

Large and small hierarchies from finite modular symmetries Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau = i$

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.385869Z

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Observation 30690757-0a01-4a4d-a89b-8d15086610ee · outbound

This paper cites Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries.

Large and small hierarchies from finite modular symmetries Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.389501Z

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Observation e896aa86-cfc7-445c-a2aa-6657d56e81c3 · outbound

This paper cites $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau = \omega$.

Large and small hierarchies from finite modular symmetries $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau = \omega$

Reference 19

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Observation 6b28f645-dc55-4e77-9fda-6f919c2fb3ba · outbound

This paper cites Quark hierarchical structures in modular symmetric flavor models at level 6.

Large and small hierarchies from finite modular symmetries Quark hierarchical structures in modular symmetric flavor models at level 6

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.396531Z

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Observation 0ef096f0-aa8d-4640-96d4-ed90264f42bf · outbound

This paper cites Quark masses and CKM hierarchies from $S_4^\prime$ modular flavor symmetry.

Large and small hierarchies from finite modular symmetries Quark masses and CKM hierarchies from $S_4^\prime$ modular flavor symmetry

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.400045Z

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Observation e61870ce-69d8-4c4f-bb50-41b16a1d4526 · outbound

This paper cites Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models.

Large and small hierarchies from finite modular symmetries Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models

Reference 22

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Observation 382bc7bf-d8a8-451b-990e-bfa5cdcfc56a · outbound

This paper cites Quark and lepton hierarchies from $S_4^\prime$ modular flavor symmetry.

Large and small hierarchies from finite modular symmetries Quark and lepton hierarchies from $S_4^\prime$ modular flavor symmetry

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.407090Z

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Observation 6cae424e-45bc-40d0-ab33-788c5f929270 · outbound

This paper cites $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau = i\infty$.

Large and small hierarchies from finite modular symmetries $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau = i\infty$

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.410455Z

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Observation 19af20a5-c336-48eb-8d36-b5fb65e6ce61 · outbound

This paper cites Fermion Hierarchies in $SU(5)$ Grand Unification from $\Gamma_6^\prime$ Modular Flavor Symmetry.

Large and small hierarchies from finite modular symmetries Fermion Hierarchies in $SU(5)$ Grand Unification from $\Gamma_6^\prime$ Modular Flavor Symmetry

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.414145Z

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Observation 50aec203-9583-4842-9304-8e6db7059aa4 · outbound

This paper cites Quarks at the modular $S_4$ cusp.

Large and small hierarchies from finite modular symmetries Quarks at the modular $S_4$ cusp

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.417565Z

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Observation d37702e8-e55e-4b69-a1cd-e16907a0df99 · outbound

This paper cites $Sp(6,Z)$ modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $\widetilde{\Delta}(96)$.

Large and small hierarchies from finite modular symmetries $Sp(6,Z)$ modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $\widetilde{\Delta}(96)$

Reference 27

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Observation f8efdd86-eb02-4390-9e8d-7451215855b2 · outbound

This paper cites CP phase in modular flavor models and discrete Froggatt-Nielsen models.

Large and small hierarchies from finite modular symmetries CP phase in modular flavor models and discrete Froggatt-Nielsen models

Reference 28

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Observation fc2fa115-4d41-4672-9ed1-3d691d9901a2 · outbound

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Large and small hierarchies from finite modular symmetries Unresolved cited work

Reference 29

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Observation ea2d2c4a-c4b1-42de-abc1-98f995f35617 · outbound

This paper cites Ferrara, N.

Large and small hierarchies from finite modular symmetries Ferrara, N

Reference 30

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Observation 32788bbf-521c-4ba8-b0fe-426050118ea0 · outbound

This paper cites Cvetic, A.

Large and small hierarchies from finite modular symmetries Cvetic, A

Reference 31

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Observation 28422fe4-c96c-426b-a34f-770ec4dd0b3e · outbound

This paper cites $A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry.

Large and small hierarchies from finite modular symmetries $A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry

Reference 32

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Observation a015764f-141c-432a-8766-ebb365ec4ce6 · outbound

This paper cites $CP$ violation in modular invariant flavor models.

Large and small hierarchies from finite modular symmetries $CP$ violation in modular invariant flavor models

Reference 33

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Observation 3f05d656-92b7-4b6a-b663-15b9a553bacf · outbound

This paper cites Modular Flavour Symmetries and Modulus Stabilisation.

Large and small hierarchies from finite modular symmetries Modular Flavour Symmetries and Modulus Stabilisation

Reference 34

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Observation a31108bb-ae31-4b8a-bb78-d4ace6c0bf33 · outbound

This paper cites Matter matters in moduli fixing and modular flavor symmetries.

Large and small hierarchies from finite modular symmetries Matter matters in moduli fixing and modular flavor symmetries

Reference 35

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Observation f8f0b0bb-064c-4905-8944-b222894f88e9 · outbound

This paper cites Modulus stabilisation in the multiple-modulus framework.

Large and small hierarchies from finite modular symmetries Modulus stabilisation in the multiple-modulus framework

Reference 36

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Observation 5e938633-0c82-4fef-8de6-212e959b4b15 · outbound

This paper cites Heterotic de Sitter Beyond Modular Symmetry.

Large and small hierarchies from finite modular symmetries Heterotic de Sitter Beyond Modular Symmetry

Reference 37

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This paper cites Moduli stabilization in finite modular symmetric models.

Large and small hierarchies from finite modular symmetries Moduli stabilization in finite modular symmetric models

Reference 38

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This paper cites Spontaneous CP violation and partially broken modular flavor symmetries.

Large and small hierarchies from finite modular symmetries Spontaneous CP violation and partially broken modular flavor symmetries

Reference 39

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Observation ac6e5168-483b-4c4a-9278-1e960d913ade · outbound

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Large and small hierarchies from finite modular symmetries Unresolved cited work

Reference 40

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Observation 3d24c798-82a6-436c-ac07-3892ae26e801 · outbound

This paper cites CFT's From Calabi-Yau Four-folds.

Large and small hierarchies from finite modular symmetries CFT's From Calabi-Yau Four-folds

Reference 41

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Observation bc16c938-9916-465a-a25a-76c251ca97c4 · outbound

This paper cites Landscape of Modular Symmetric Flavor Models.

Large and small hierarchies from finite modular symmetries Landscape of Modular Symmetric Flavor Models

Reference 42

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Observation 15cca2af-dfd5-4ce2-af25-1f44ec04b889 · outbound

This paper cites Residual flavor symmetry breaking in the landscape of modular flavor models.

Large and small hierarchies from finite modular symmetries Residual flavor symmetry breaking in the landscape of modular flavor models

Reference 43

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Observation 78f5720f-0a0f-4b77-9bc4-67e44feb9f2b · outbound

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Large and small hierarchies from finite modular symmetries Modular invariant inflation

Reference 44

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Observation c2096e55-6d88-42c5-a84d-9c7101e1be31 · outbound

This paper cites Moduli inflation from modular flavor symmetries.

Large and small hierarchies from finite modular symmetries Moduli inflation from modular flavor symmetries

Reference 45

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Observation 44fd3a16-3e6b-4bb7-a990-2a54d16d8d64 · outbound

This paper cites Modular Invariant Slow Roll Inflation.

Large and small hierarchies from finite modular symmetries Modular Invariant Slow Roll Inflation

Reference 46

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This paper cites Modular Invariant Hilltop Inflation.

Large and small hierarchies from finite modular symmetries Modular Invariant Hilltop Inflation

Reference 47

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This paper cites Modular Invariant Starobinsky Inflation and the Species Scale.

Large and small hierarchies from finite modular symmetries Modular Invariant Starobinsky Inflation and the Species Scale

Reference 48

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Large and small hierarchies from finite modular symmetries Moduli trapping mechanism in modular flavor symmetric models

Reference 49

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Observation bae81dc6-a8f7-473a-a764-31f062752f9f · outbound

This paper cites Radiative correction on moduli stabilization in modular flavor symmetric models.

Large and small hierarchies from finite modular symmetries Radiative correction on moduli stabilization in modular flavor symmetric models

Reference 50

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Observation c9586ace-2aa9-402f-a214-4b4068c11a19 · outbound

This paper cites Finite modular axion and radiative moduli stabilization.

Large and small hierarchies from finite modular symmetries Finite modular axion and radiative moduli stabilization

Reference 51

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Observation 6cfd57ef-1cd3-4e20-9411-aad1269c7f61 · outbound

This paper cites Finite modular majoron.

Large and small hierarchies from finite modular symmetries Finite modular majoron

Reference 52

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Observation 0d342ab5-2369-47c1-86b4-54ea51826ef4 · outbound

This paper cites Common origin of the strong CP and CKM phases in string compactifications.

Large and small hierarchies from finite modular symmetries Common origin of the strong CP and CKM phases in string compactifications

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-08-11T04:52:20.749371Z

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Observation 0216e505-6c93-4a72-b296-62b9fc005923 · outbound

This paper cites Modular invariance and the QCD angle.

Large and small hierarchies from finite modular symmetries Modular invariance and the QCD angle

Reference 54

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This paper cites $A_4$ modular invariance and the strong CP problem.

Large and small hierarchies from finite modular symmetries $A_4$ modular invariance and the strong CP problem

Reference 55

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Observation 51ae9aed-b87c-411e-92c0-a640d36f0020 · outbound

This paper cites Finite modular symmetries and the strong CP problem.

Large and small hierarchies from finite modular symmetries Finite modular symmetries and the strong CP problem

Reference 56

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Observation 4adb1631-abba-4039-a7b8-5cf0c44b2d9c · outbound

This paper cites Solving the strong CP problem without axions.

Large and small hierarchies from finite modular symmetries Solving the strong CP problem without axions

Reference 57

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Observation 610a54ad-fd77-49af-82e2-edbc06850b91 · outbound

This paper cites CPon Dark Matter.

Large and small hierarchies from finite modular symmetries CPon Dark Matter

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.536229Z

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Observation 829c2591-e9d1-4081-8581-921e200e4ba9 · outbound

This paper cites Modular symmetry in magnetized $T^{2g}$ torus and orbifold models.

Large and small hierarchies from finite modular symmetries Modular symmetry in magnetized $T^{2g}$ torus and orbifold models

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.540108Z

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Observation 8e6dc896-d67f-4712-9f71-466a177618a6 · outbound

This paper cites Automorphic Forms and Fermion Masses.

Large and small hierarchies from finite modular symmetries Automorphic Forms and Fermion Masses

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-11T04:52:20.543870Z

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Observation feab5d0c-eb84-483f-b903-e1aa510664e8 · outbound

This paper cites CP Symmetry and Symplectic Modular Invariance.

Large and small hierarchies from finite modular symmetries CP Symmetry and Symplectic Modular Invariance

Reference 61

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Observation 9216bed4-2c93-4e98-b7cd-99e59a56799c · outbound

This paper cites Neutrino Masses and Higher Degree Siegel Modular Forms.

Large and small hierarchies from finite modular symmetries Neutrino Masses and Higher Degree Siegel Modular Forms

Reference 62

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Observation e7d14ff7-3c2a-4fde-bcbd-350eb4675c15 · outbound

This paper cites Universal predictions of Siegel modular invariant theories near the fixed points.

Large and small hierarchies from finite modular symmetries Universal predictions of Siegel modular invariant theories near the fixed points

Reference 63

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Observation 2341cc37-b47e-4568-a4b1-352b27974581 · outbound

This paper cites Moduli stabilization and light axion by Siegel modular forms.

Large and small hierarchies from finite modular symmetries Moduli stabilization and light axion by Siegel modular forms

Reference 64

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Observation a39ccd10-1c09-484a-9cb3-ac66d327b87a · outbound

This paper cites Modular symmetry of soft supersymmetry breaking terms.

Large and small hierarchies from finite modular symmetries Modular symmetry of soft supersymmetry breaking terms

Reference 65

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Observation 096fa529-8c2b-4c45-abe7-b85d5ec1038b · outbound

This paper cites Measurement of the permanent electric dipole moment of the neutron.

Large and small hierarchies from finite modular symmetries Measurement of the permanent electric dipole moment of the neutron

Reference 66

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Observation e8ae669a-dac4-4640-9b52-e3a2d6f6f5e4 · inbound

Modulus stabilization of modular flavor models in Jordan frame supergravity cites this paper.

Modulus stabilization of modular flavor models in Jordan frame supergravity Large and small hierarchies from finite modular symmetries

Reference 55

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Observation 7de443ad-b10a-45d4-9c34-de0b42788aa2 · inbound

Finite modular Coleman-Weinberg inflation cites this paper.

Finite modular Coleman-Weinberg inflation Large and small hierarchies from finite modular symmetries

Reference 50

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