Paper Citation Record · LEDGER

Unexpected shape of the primordial black hole mass function

As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 3 inbound Pith citation observations for arXiv:2412.07709.

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

pith.paper-citation-record.v1
2412.07709 v3

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:43:04.568152Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T07:53:10.117303Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T21:38:59.166135Z

Reference resolution

27 of 27 outbound references displayed

verified exact1
verified fuzzy3
unresolved20
parse uncertain0
malformed identifier2
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c9d936c2-0da2-49bb-8e78-c7760e0d5971 · outbound

This paper cites 1 Note that we are not assuming a window function in (3).

Unexpected shape of the primordial black hole mass function 1 Note that we are not assuming a window function in (3)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:43:05.405239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2797d08e-cb8a-4af5-9901-8c0b2fd3d3d1 · outbound

This paper cites v(rm) ≡ rm∂rg(rm; ⃗ x0) = 0 (5) and w ≡ −r2 m∂2 r g(rm; ⃗ x0) ≥ 0.

Unexpected shape of the primordial black hole mass function v(rm) ≡ rm∂rg(rm; ⃗ x0) = 0 (5) and w ≡ −r2 m∂2 r g(rm; ⃗ x0) ≥ 0

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:43:05.386692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 68674901-6ad3-41cf-8198-53acbc2c4621 · outbound

This paper cites The threshold gc depends significantly on the radial pro- file of the perturbation.

Unexpected shape of the primordial black hole mass function The threshold gc depends significantly on the radial pro- file of the perturbation

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:43:05.363986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation aba882de-91b6-4666-8d7c-85948ccdaa96 · outbound

This paper cites an unresolved cited work.

Unexpected shape of the primordial black hole mass function Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.418653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f8bb374-c04a-4248-8267-0c2cce3a04a2 · outbound

This paper cites an unresolved cited work.

Unexpected shape of the primordial black hole mass function Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.426716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33488c6f-0248-4179-9f51-43fb699f0e9c · outbound

This paper cites Ivanov, P.

Unexpected shape of the primordial black hole mass function Ivanov, P

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.436220Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation effbfb43-007c-45f8-b8d2-c1dd912c9c0c · outbound

This paper cites Primordial Black Holes.

Unexpected shape of the primordial black hole mass function Primordial Black Holes

Reference 7

Resolution: malformed identifier; no resolver link, observed 2026-08-11T18:43:04.442794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70c7194f-45aa-41ec-b50a-4914e44fa540 · outbound

This paper cites Planck 2018 results. X. Constraints on inflation.

Unexpected shape of the primordial black hole mass function Planck 2018 results. X. Constraints on inflation

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.450383Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f18dcd8-f448-45f8-8b50-0cef7cd7a2ee · outbound

This paper cites an unresolved cited work.

Unexpected shape of the primordial black hole mass function Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.457412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75d7247b-84e2-4cd5-91ff-2fce068708c8 · outbound

This paper cites Shibata and M.

Unexpected shape of the primordial black hole mass function Shibata and M

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-11T18:43:05.287408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ab9db8d7-cb07-4e83-96a1-eb45230fdc79 · outbound

This paper cites an unresolved cited work.

Unexpected shape of the primordial black hole mass function Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.467027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5139ac40-22de-438f-8e21-7fbe4ee9af91 · outbound

This paper cites Cosmological long-wavelength solutions and primordial black hole formation.

Unexpected shape of the primordial black hole mass function Cosmological long-wavelength solutions and primordial black hole formation

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.472821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fd05bdb-203c-4594-85ca-81cc91af8ca6 · outbound

This paper cites Application of peaks theory to the abundance of primordial black holes.

Unexpected shape of the primordial black hole mass function Application of peaks theory to the abundance of primordial black holes

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.478331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40e9036c-3bc5-474a-a39a-230fa9684935 · outbound

This paper cites The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription.

Unexpected shape of the primordial black hole mass function The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.484091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae19113f-08cf-4798-86e9-e31bc8d4e8a6 · outbound

This paper cites Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations.

Unexpected shape of the primordial black hole mass function Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.489683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ba0897d-da88-4772-a270-9b45bc7652bc · outbound

This paper cites Non-linear statistics of primordial black holes from gaussian curvature perturbations.

Unexpected shape of the primordial black hole mass function Non-linear statistics of primordial black holes from gaussian curvature perturbations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.495006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8398a329-7cb0-4401-8b13-43e50f1e6efb · outbound

This paper cites The statistics of primordial black holes in a radiation dominated Universe -- recent and new results.

Unexpected shape of the primordial black hole mass function The statistics of primordial black holes in a radiation dominated Universe -- recent and new results

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.500907Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 404390d0-9f48-4e6d-9c2d-da2ed7e7aa3c · outbound

This paper cites A universal threshold for primordial black hole formation.

Unexpected shape of the primordial black hole mass function A universal threshold for primordial black hole formation

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.506267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e9d8c55-cb5b-45ee-96dc-2b3b1cebf2df · outbound

This paper cites Escriv` a, Phys.

Unexpected shape of the primordial black hole mass function Escriv` a, Phys

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.512302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a27ec87e-b8ea-4dba-803e-afb76cef6e01 · outbound

This paper cites Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse.

Unexpected shape of the primordial black hole mass function Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse

Reference 20

Resolution: malformed identifier; no resolver link, observed 2026-08-11T18:43:04.519726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f90b080c-4600-4cfb-a36f-b9992e267154 · outbound

This paper cites an unresolved cited work.

Unexpected shape of the primordial black hole mass function Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.527467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd9fe4c7-d14d-44c4-803a-5b1773b0aacb · outbound

This paper cites The Primordial Black Hole Abundance: The Broader, the Better.

Unexpected shape of the primordial black hole mass function The Primordial Black Hole Abundance: The Broader, the Better

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.534547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5f89920-0a1b-4205-9e71-358aa1d1cd7b · outbound

This paper cites The abundance of primordial black holes depends on the shape of the inflationary power spectrum.

Unexpected shape of the primordial black hole mass function The abundance of primordial black holes depends on the shape of the inflationary power spectrum

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.542029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48e6e53e-3626-4c01-8129-ef977cbf12e9 · outbound

This paper cites Primordial black holes with an accurate QCD equation of state.

Unexpected shape of the primordial black hole mass function Primordial black holes with an accurate QCD equation of state

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.548366Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5cd7ac76-3ca2-4079-bb15-7ab7c23930e8 · outbound

This paper cites De Luca, G.

Unexpected shape of the primordial black hole mass function De Luca, G

Reference 25

Resolution: metadata mismatch; raw_fallback, observed 2026-08-11T18:43:04.882929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 472f435d-5e02-49f0-9aee-b584ec83c6c0 · outbound

This paper cites Uehara, A.

Unexpected shape of the primordial black hole mass function Uehara, A

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.560538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5171efbf-ae85-494e-bd0d-df43c37ac7dd · outbound

This paper cites Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation.

Unexpected shape of the primordial black hole mass function Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T18:43:04.568152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 078b5cff-5cdd-47a7-9b37-542cf1a46e1b · inbound

Synergy between CSST and future gravitational-wave detectors: Probing primordial black holes by cross-correlating dark sirens with galaxies cites this paper.

Synergy between CSST and future gravitational-wave detectors: Probing primordial black holes by cross-correlating dark sirens with galaxies Unexpected shape of the primordial black hole mass function

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:38:59.167495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3c68a291-e718-44ae-ac88-42e405eaf34b · inbound

Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes cites this paper.

Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes Unexpected shape of the primordial black hole mass function

Reference 81

Resolution: verified exact; arxiv_id, observed 2026-06-30T14:24:45.665645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 69317880-504d-4537-9f9f-a6305b03c784 · inbound

The statistics of curvature-profile dispersion in primordial black hole formation cites this paper.

The statistics of curvature-profile dispersion in primordial black hole formation Unexpected shape of the primordial black hole mass function

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-02T07:53:10.117303Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.