Paper Citation Record · LEDGER

Universal lower bound on the axion decay constant from free streaming effects

As of 16 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 5 inbound Pith citation observations for arXiv:2507.01956.

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

pith.paper-citation-record.v1
2507.01956 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:54:54.809546Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:22:44.498614Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T21:04:21.858173Z

Reference resolution

51 of 51 outbound references displayed

verified exact5
verified fuzzy2
unresolved44
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a162eace-1f73-42f8-85fb-d49e913b20ae · outbound

This paper cites (23) and (28) become stronger.

Universal lower bound on the axion decay constant from free streaming effects (23) and (28) become stronger

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:54:55.790559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d80e6559-87c6-48a9-971f-8ed38f653042 · outbound

This paper cites an unresolved cited work.

Universal lower bound on the axion decay constant from free streaming effects Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:51.982491Z

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Observation 9374eda8-8df1-4327-968e-847adf6de308 · outbound

This paper cites Weinberg, Phys.

Universal lower bound on the axion decay constant from free streaming effects Weinberg, Phys

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.034276Z

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Observation 822ceffa-5c42-4b60-878f-e72894d2d187 · outbound

This paper cites Wilczek, Phys.

Universal lower bound on the axion decay constant from free streaming effects Wilczek, Phys

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.074784Z

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Observation 503f2ead-c1a7-46e9-b2f7-48d1e4b41f9b · outbound

This paper cites The Strong CP Problem and Axions.

Universal lower bound on the axion decay constant from free streaming effects The Strong CP Problem and Axions

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.128316Z

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Observation 56839726-d59a-40d0-bbf7-c1e31ce970fc · outbound

This paper cites Abbott and P.

Universal lower bound on the axion decay constant from free streaming effects Abbott and P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:54:55.762567Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b2dd1aa9-e65f-4dfb-8035-0e2b9edab158 · outbound

This paper cites Dine and W.

Universal lower bound on the axion decay constant from free streaming effects Dine and W

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.225568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ec661ea-9d6c-4267-8d2d-a5ebf80d6642 · outbound

This paper cites Preskill, M.

Universal lower bound on the axion decay constant from free streaming effects Preskill, M

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.262007Z

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Unavailable: canonical work link unavailable.

Observation 90cc202a-0454-401a-9db4-211e0462002f · outbound

This paper cites Axions In String Theory.

Universal lower bound on the axion decay constant from free streaming effects Axions In String Theory

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.305978Z

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Observation 06a04c4f-b925-4f1a-b485-cf45ea6eb6ec · outbound

This paper cites String Axiverse.

Universal lower bound on the axion decay constant from free streaming effects String Axiverse

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.344977Z

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Observation 9df562a4-52e7-49ce-9b6d-d4d434c8fa45 · outbound

This paper cites Axion cosmology with long-lived domain walls.

Universal lower bound on the axion decay constant from free streaming effects Axion cosmology with long-lived domain walls

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.392963Z

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Unavailable: canonical work link unavailable.

Observation 13172e55-3fb0-44bd-a012-9e0425d26dad · outbound

This paper cites QCD Axion Dark Matter with a Small Decay Constant.

Universal lower bound on the axion decay constant from free streaming effects QCD Axion Dark Matter with a Small Decay Constant

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.440562Z

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Observation dcb5ef20-b71e-46b8-8da9-d59c0ae2a0cb · outbound

This paper cites The Supercooled Universe.

Universal lower bound on the axion decay constant from free streaming effects The Supercooled Universe

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.490477Z

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Unavailable: canonical work link unavailable.

Observation 90420e8a-2275-439c-bff9-9d8a8c00cf1c · outbound

This paper cites Axion Kinetic Misalignment Mechanism.

Universal lower bound on the axion decay constant from free streaming effects Axion Kinetic Misalignment Mechanism

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.528237Z

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Unavailable: canonical work link unavailable.

Observation 0f681308-214d-4007-9be7-5a0d67a1f509 · outbound

This paper cites QCD Axion Dark Matter from a Late Time Phase Transition.

Universal lower bound on the axion decay constant from free streaming effects QCD Axion Dark Matter from a Late Time Phase Transition

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.565365Z

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Unavailable: canonical work link unavailable.

Observation 6fd9e072-80ab-418e-8049-900e6bf29505 · outbound

This paper cites Axion Kinetic Misalignment and Parametric Resonance from Inflation.

Universal lower bound on the axion decay constant from free streaming effects Axion Kinetic Misalignment and Parametric Resonance from Inflation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.602289Z

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Observation 4864b13e-5b42-4e91-b48e-e04b4a4c7b06 · outbound

This paper cites ALP Dark Matter from Kinetic Fragmentation: Opening up the Parameter Window.

Universal lower bound on the axion decay constant from free streaming effects ALP Dark Matter from Kinetic Fragmentation: Opening up the Parameter Window

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.645013Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a702cba9-aef9-4379-8cc4-cef916561494 · outbound

This paper cites The meso-inflationary QCD axion.

Universal lower bound on the axion decay constant from free streaming effects The meso-inflationary QCD axion

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.697436Z

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Unavailable: canonical work link unavailable.

Observation f1843aac-1394-4461-baa1-fed841d4fc89 · outbound

This paper cites More axions from diluted domain walls.

Universal lower bound on the axion decay constant from free streaming effects More axions from diluted domain walls

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:54:55.611794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cec581ea-3a7b-4d6c-a822-9f9f361d63c6 · outbound

This paper cites Model implementations of axion dark matter from kinetic misalignment.

Universal lower bound on the axion decay constant from free streaming effects Model implementations of axion dark matter from kinetic misalignment

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.781062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c12e57d-7193-407d-a1f3-2e4191354354 · outbound

This paper cites Er¨ oncel, Y.

Universal lower bound on the axion decay constant from free streaming effects Er¨ oncel, Y

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.825848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17f5eb3c-128d-4e37-afe3-9f308657921d · outbound

This paper cites Bodas, R.

Universal lower bound on the axion decay constant from free streaming effects Bodas, R

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.872168Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6dc09a0-d1be-4af1-a3b7-83a65baf430f · outbound

This paper cites Scalars Gliding Through an Expanding Universe.

Universal lower bound on the axion decay constant from free streaming effects Scalars Gliding Through an Expanding Universe

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:54:55.429223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e20f2e08-d49a-41d1-9cff-9b3feeee1c20 · outbound

This paper cites Dark matter from an even lighter QCD axion: trapped misalignment.

Universal lower bound on the axion decay constant from free streaming effects Dark matter from an even lighter QCD axion: trapped misalignment

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.948808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69f23c3a-929a-46ac-acd2-04f8fa30e729 · outbound

This paper cites Cosmological effects of Peccei-Quinn symmetry breaking on QCD axion dark matter.

Universal lower bound on the axion decay constant from free streaming effects Cosmological effects of Peccei-Quinn symmetry breaking on QCD axion dark matter

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:52.998660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2c66c34-fcab-4756-9541-8481c4f3dbdb · outbound

This paper cites Axion dark matter from frictional misalignment.

Universal lower bound on the axion decay constant from free streaming effects Axion dark matter from frictional misalignment

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.033531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d6d001b-4614-4b72-a56e-f16ed7b68668 · outbound

This paper cites Axion production via trapped misalignment from Peccei-Quinn symmetry breaking.

Universal lower bound on the axion decay constant from free streaming effects Axion production via trapped misalignment from Peccei-Quinn symmetry breaking

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.070820Z

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Unavailable: canonical work link unavailable.

Observation f370e8e8-4ba1-4506-92d4-0218a7e7ce4b · outbound

This paper cites an unresolved cited work.

Universal lower bound on the axion decay constant from free streaming effects Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:54:55.740905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0b9ca253-ee39-4068-ac50-6f4bb613ba1e · outbound

This paper cites Anharmonic Evolution of the Cosmic Axion Density Spectrum.

Universal lower bound on the axion decay constant from free streaming effects Anharmonic Evolution of the Cosmic Axion Density Spectrum

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.133533Z

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Unavailable: canonical work link unavailable.

Observation 369f38f4-9730-4b49-9474-cf2c51e851de · outbound

This paper cites Axion Misalignment Driven to the Hilltop.

Universal lower bound on the axion decay constant from free streaming effects Axion Misalignment Driven to the Hilltop

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.170855Z

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Unavailable: canonical work link unavailable.

Observation 8ab20c55-6f2a-43a7-b14c-032761b41a4c · outbound

This paper cites QCD Axion on Hilltop by a Phase Shift of $\pi$.

Universal lower bound on the axion decay constant from free streaming effects QCD Axion on Hilltop by a Phase Shift of $\pi$

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.216274Z

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Unavailable: canonical work link unavailable.

Observation ac35bee4-8679-48fa-87ec-74fe7c475c05 · outbound

This paper cites The Large-Misalignment Mechanism for the Formation of Compact Axion Structures: Signatures from the QCD Axion to Fuzzy Dark Matter.

Universal lower bound on the axion decay constant from free streaming effects The Large-Misalignment Mechanism for the Formation of Compact Axion Structures: Signatures from the QCD Axion to Fuzzy Dark Matter

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.254977Z

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Unavailable: canonical work link unavailable.

Observation 63208913-3d4d-4298-bd01-ab22ab9e12eb · outbound

This paper cites Maximal axion misalignment from a minimal model.

Universal lower bound on the axion decay constant from free streaming effects Maximal axion misalignment from a minimal model

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:54:55.342690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e0c7edc5-ba36-455d-a779-af37d798d6ea · outbound

This paper cites A lower bound on dark matter mass.

Universal lower bound on the axion decay constant from free streaming effects A lower bound on dark matter mass

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.336863Z

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Unavailable: canonical work link unavailable.

Observation cb95e10e-9f0d-4a67-9e9c-c9720007cbad · outbound

This paper cites Warm and Fuzzy Dark Matter: Free Streaming of Wave Dark Matter.

Universal lower bound on the axion decay constant from free streaming effects Warm and Fuzzy Dark Matter: Free Streaming of Wave Dark Matter

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.357007Z

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Unavailable: canonical work link unavailable.

Observation 73565dc4-efff-4ec6-92b8-b78cd3dd0d6d · outbound

This paper cites Free Streaming in Warm Wave Dark Matter.

Universal lower bound on the axion decay constant from free streaming effects Free Streaming in Warm Wave Dark Matter

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.381146Z

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Observation 634724f2-74f6-4ef0-be2a-eba4b6fee805 · outbound

This paper cites Free streaming of warm wave dark matter in modified expansion histories.

Universal lower bound on the axion decay constant from free streaming effects Free streaming of warm wave dark matter in modified expansion histories

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.479439Z

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Unavailable: canonical work link unavailable.

Observation 63ef7ac2-7cb3-410f-8459-52ec0aba4cad · outbound

This paper cites Interference with Gravitational Instability: Hot and Fuzzy Dark Matter.

Universal lower bound on the axion decay constant from free streaming effects Interference with Gravitational Instability: Hot and Fuzzy Dark Matter

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.624469Z

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Unavailable: canonical work link unavailable.

Observation 62a53249-8d66-4aa0-b6b9-c00c315c6b4b · outbound

This paper cites First constraints on fuzzy dark matter from Lyman-$\alpha$ forest data and hydrodynamical simulations.

Universal lower bound on the axion decay constant from free streaming effects First constraints on fuzzy dark matter from Lyman-$\alpha$ forest data and hydrodynamical simulations

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.753239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 198883b9-f302-43eb-965b-68334ea7146c · outbound

This paper cites Strong bound on canonical ultra-light axion dark matter from the Lyman-alpha forest.

Universal lower bound on the axion decay constant from free streaming effects Strong bound on canonical ultra-light axion dark matter from the Lyman-alpha forest

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:53.896051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d23a99f3-f873-4905-9618-d656c8849f40 · outbound

This paper cites Early Structure Formation Constraints on the Ultra-Light Axion in the Post-Inflation Scenario.

Universal lower bound on the axion decay constant from free streaming effects Early Structure Formation Constraints on the Ultra-Light Axion in the Post-Inflation Scenario

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.054811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2670f6d7-0c5d-4af6-af53-a32c79f69f06 · outbound

This paper cites Evolution of String-Wall Networks and Axionic Domain Wall Problem.

Universal lower bound on the axion decay constant from free streaming effects Evolution of String-Wall Networks and Axionic Domain Wall Problem

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.166653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd28b137-a3bb-4951-9972-57bf29fb01bf · outbound

This paper cites Axion dark matter from topological defects.

Universal lower bound on the axion decay constant from free streaming effects Axion dark matter from topological defects

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.312926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e9a097a-0cf3-4f4c-8478-51fed8745a62 · outbound

This paper cites an unresolved cited work.

Universal lower bound on the axion decay constant from free streaming effects Unresolved cited work

Reference 44

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:54:55.198657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1da4203b-d42b-49c1-9f5a-4798dd3a1504 · outbound

This paper cites New Constraints on Warm Dark Matter from the Lyman-$\alpha$ Forest Power Spectrum.

Universal lower bound on the axion decay constant from free streaming effects New Constraints on Warm Dark Matter from the Lyman-$\alpha$ Forest Power Spectrum

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.533686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04faac55-9bd4-4760-84cf-07ffd6d7bdf2 · outbound

This paper cites Simulations of axion-like particles in the post-inflationary scenario.

Universal lower bound on the axion decay constant from free streaming effects Simulations of axion-like particles in the post-inflationary scenario

Reference 46

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:54:54.987456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a17207ab-739a-46b4-8e1e-bb55d8815b1e · outbound

This paper cites Early Growth of Structure in Warm Wave Dark Matter.

Universal lower bound on the axion decay constant from free streaming effects Early Growth of Structure in Warm Wave Dark Matter

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.682763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 902c852b-efd8-49af-bfe9-723623d8c330 · outbound

This paper cites On Effective Degrees of Freedom in the Early Universe.

Universal lower bound on the axion decay constant from free streaming effects On Effective Degrees of Freedom in the Early Universe

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.693933Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5cf5ec1a-5ea8-42fd-a541-443bc0610944 · outbound

This paper cites Resolving the Hubble Tension with New Early Dark Energy.

Universal lower bound on the axion decay constant from free streaming effects Resolving the Hubble Tension with New Early Dark Energy

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.700651Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab65ff60-1fa3-4041-9e74-35a1fce0a2eb · outbound

This paper cites O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020).

Universal lower bound on the axion decay constant from free streaming effects O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020)

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.723398Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 051b9797-eba4-4312-b99d-bf9fde52a463 · outbound

This paper cites an unresolved cited work.

Universal lower bound on the axion decay constant from free streaming effects Unresolved cited work

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-06T20:54:54.809546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 24314efe-cc4a-4f74-bb1f-fbd13c48a0ea · inbound

Multi-species Dark Matter with Warmth and Randomness cites this paper.

Multi-species Dark Matter with Warmth and Randomness Universal lower bound on the axion decay constant from free streaming effects

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:04:21.859806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0572b8a4-1928-42be-9e02-d4ef11de150b · inbound

Growth of Structure in Multi-species Wave Dark Matter cites this paper.

Growth of Structure in Multi-species Wave Dark Matter Universal lower bound on the axion decay constant from free streaming effects

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:00:38.144295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4cecf24d-fd54-46b2-b6ab-abdde20d59cb · inbound

Dark Matter and Baryon Asymmetry from Monopole-Axion Interactions cites this paper.

Dark Matter and Baryon Asymmetry from Monopole-Axion Interactions Universal lower bound on the axion decay constant from free streaming effects

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-03T22:31:04.583095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da18109-f0d2-483c-ba51-32a5b0edfa13 · inbound

Echoes of Global Cosmic Strings cites this paper.

Echoes of Global Cosmic Strings Universal lower bound on the axion decay constant from free streaming effects

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-10T11:00:04.602120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8f607de4-b274-4683-9904-b570841ff9ed · inbound

Inflationary Axion Isocurvature in the CMB across All Ultralight Masses cites this paper.

Inflationary Axion Isocurvature in the CMB across All Ultralight Masses Universal lower bound on the axion decay constant from free streaming effects

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-11T04:22:44.498614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.