Paper Citation Record · LEDGER

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

As of 17 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 4 inbound Pith citation observations for arXiv:2412.19324.

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

pith.paper-citation-record.v1
2412.19324 v4

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:53:46.925948Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:12:32.726376Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T10:56:52.087189Z

Reference resolution

29 of 29 outbound references displayed

verified exact1
verified fuzzy6
unresolved22
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8b7553b2-e25a-48ea-af38-1eb50ff4c8db · outbound

This paper cites $SL(2,\mathbb{Z})$ Cosmological Attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology $SL(2,\mathbb{Z})$ Cosmological Attractors

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.776134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42f7c4a9-9fd1-42be-9c5a-eff971340956 · outbound

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

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Modular Invariant Starobinsky Inflation and the Species Scale

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.781989Z

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Unavailable: canonical work link unavailable.

Observation 22ddd9eb-6aa2-4e99-a041-f1a563ca45ce · outbound

This paper cites Large and small field inflation from hyperbolic sigma models.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Large and small field inflation from hyperbolic sigma models

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.787373Z

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Observation 02dc5adc-0cf2-4bc7-905a-f4603347fd93 · outbound

This paper cites Landscape of Modular Cosmology.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Landscape of Modular Cosmology

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.792802Z

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Observation 81872343-f08c-4bd3-8860-b3a9c7d337e4 · outbound

This paper cites Universality of multi-field $\alpha$-attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Universality of multi-field $\alpha$-attractors

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.798028Z

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Observation b9f3f6ba-d273-41e4-b1cf-824637eae2a1 · outbound

This paper cites Hypernatural inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Hypernatural inflation

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:53:47.344171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d90d417f-5fec-4a8c-adc8-dac2fd5464cb · outbound

This paper cites Superconformal Inflationary $\alpha$-Attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Superconformal Inflationary $\alpha$-Attractors

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.809317Z

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Observation 13c97b75-1cf6-49f5-a83b-f567dfda3469 · outbound

This paper cites The Unity of Cosmological Attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology The Unity of Cosmological Attractors

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.814587Z

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Observation 3d347700-e154-4de9-a1d7-0fcaa47f262f · outbound

This paper cites The Hyperbolic Geometry of Cosmological Attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology The Hyperbolic Geometry of Cosmological Attractors

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.819629Z

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Observation 165f8115-6836-4b7e-8327-e25980277058 · outbound

This paper cites BICEP/Keck and Cosmological Attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology BICEP/Keck and Cosmological Attractors

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.824990Z

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Observation f5849e68-7f68-43a8-9c5d-409bafd863ef · outbound

This paper cites Escher in the Sky.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Escher in the Sky

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.830117Z

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Observation c53df00f-abc4-4245-a505-57b8b4fcd148 · outbound

This paper cites Petersson, ¨Uber die Entwicklungskoeffizienten der automorphen Formen , Acta Math.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Petersson, ¨Uber die Entwicklungskoeffizienten der automorphen Formen , Acta Math

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.520044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation db9dd119-fe56-44f6-b055-5667ba7b21ba · outbound

This paper cites Brisebarre and G.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Brisebarre and G

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.502920Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ca4d1637-736b-46c2-8397-7e349375136e · outbound

This paper cites Fibre Inflation: Observable Gravity Waves from IIB String Compactifications.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.845641Z

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Observation 2db9daab-ce14-4aa9-80b8-bff35f2d563e · outbound

This paper cites On the choice of entropy variables in multifield inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology On the choice of entropy variables in multifield inflation

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.851423Z

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Observation 24bf3a77-d007-4c13-94ca-783c539f1dc3 · outbound

This paper cites A Fake Instability in String Inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology A Fake Instability in String Inflation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.856491Z

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Observation 7e9f6306-0b1f-4c07-952e-7c0019eec3f4 · outbound

This paper cites Fibre Inflation and $\alpha$-attractors.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Fibre Inflation and $\alpha$-attractors

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.862493Z

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Observation cdec0c0a-61f5-4af0-93de-c54447e14496 · outbound

This paper cites Chiral global embedding of Fibre Inflation with $\overline{\rm D3}$ uplift.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Chiral global embedding of Fibre Inflation with $\overline{\rm D3}$ uplift

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.867383Z

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Observation d559210b-ec86-4448-8846-6caf0a7d9049 · outbound

This paper cites Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.872802Z

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Observation f4e8f8fe-c68b-4a76-9d34-6d13bbbd013e · outbound

This paper cites A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.878222Z

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Unavailable: canonical work link unavailable.

Observation 81108d9e-ec6d-4037-a40d-6ea5b42173b7 · outbound

This paper cites Mukhanov, Gravitational Instability of the Universe Filled with a Scalar Field , Formen, Acta Math.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Mukhanov, Gravitational Instability of the Universe Filled with a Scalar Field , Formen, Acta Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.486436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f5658717-be71-41e0-bf80-44270e69d906 · outbound

This paper cites Sasaki, Large Scale Quantum Fluctuations in the Inflationary Universe , Prog.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Sasaki, Large Scale Quantum Fluctuations in the Inflationary Universe , Prog

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.470356Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f9349a8f-159a-4617-a50f-ae51bcbac6d3 · outbound

This paper cites Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations , Sov.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations , Sov

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.454296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9aa7aeee-69e6-4b53-8186-d6e19fb4b061 · outbound

This paper cites Testing Two-Field Inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Testing Two-Field Inflation

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.898422Z

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Observation 6b01fed6-24f8-4101-8992-6bc640d920ed · outbound

This paper cites Perturbations in generalized multi-field inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Perturbations in generalized multi-field inflation

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.904382Z

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Observation 982865a2-6611-4b6d-818d-6af571574765 · outbound

This paper cites Particle Physics and Inflationary Cosmology.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Particle Physics and Inflationary Cosmology

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.909327Z

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Observation b854dc5e-e991-4ad5-ad1e-e385ceeb2781 · outbound

This paper cites Super-Horizon Scale Dynamics of Multi-Scalar Inflation.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Super-Horizon Scale Dynamics of Multi-Scalar Inflation

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.915296Z

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Observation 508b2e0f-1696-440f-883b-04c60dfdd3b5 · outbound

This paper cites Carrasco, R.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Carrasco, R

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:53:47.438225Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8349a7c6-c8e3-4292-8d2a-412c0956f02c · outbound

This paper cites Axion Stabilization in Modular Cosmology.

Double Exponents in $SL(2,\mathbb{Z})$ Cosmology Axion Stabilization in Modular Cosmology

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T00:53:46.925948Z

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Pith citing papers

Observation 49d82e45-0d82-4497-a64c-16fb0f7e46a8 · inbound

Post-inflationary enhancement of adiabatic perturbations in modular cosmology cites this paper.

Post-inflationary enhancement of adiabatic perturbations in modular cosmology Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:12:32.726376Z

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Observation 8ef10036-c56b-43ce-b9bf-4120a45019fe · inbound

Ultra slow-turn inflation cites this paper.

Ultra slow-turn inflation Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T19:14:20.199919Z

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Observation eb36ebc6-cb10-4439-8bca-99e3d5eba5cf · inbound

Some Properties and Uses of the Species Scale cites this paper.

Some Properties and Uses of the Species Scale Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-05-12T10:21:30.761976Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f166eef2-a803-4f69-848b-9b932562d6bb · inbound

Finite modular Coleman-Weinberg inflation cites this paper.

Finite modular Coleman-Weinberg inflation Double Exponents in $SL(2,\mathbb{Z})$ Cosmology

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:56:52.088574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.