Paper Citation Record · LEDGER

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height

As of 22 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2412.12319.

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

pith.paper-citation-record.v1
2412.12319 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T14:23:12.204116Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

verified exact3
verified fuzzy16
unresolved3
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 156e786d-1857-4140-b82f-3a6c3699f39f · outbound

This paper cites Probability distributions on cladograms.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Probability distributions on cladograms

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.872726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 52fc0eda-009a-4ca3-bc67-58bd2d17e8c2 · outbound

This paper cites The Critical Beta-splitting Random Tree II: Overview and Open Problems.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height The Critical Beta-splitting Random Tree II: Overview and Open Problems

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T14:23:12.065396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9fa6d0c-4b99-4a33-a042-52c1774db0ec · outbound

This paper cites The critical beta-split ting random tree III: The exchangeable partition representation and the fringe tree.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height The critical beta-split ting random tree III: The exchangeable partition representation and the fringe tree

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.853695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e0b88d1f-ba46-4460-8bdb-81271cde8add · outbound

This paper cites The harmoni c descent chain.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height The harmoni c descent chain

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.834547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 11c2a8c8-9c36-452f-be7f-fd0971ecf1b7 · outbound

This paper cites The Critical Beta-splitting Random Tree: Heights and Related Results.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height The Critical Beta-splitting Random Tree: Heights and Related Results

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-11T14:23:12.471623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3d1423ff-4372-4ee4-beb2-2ca063ed51c0 · outbound

This paper cites Random Fragmentation and Coagulation Processes , volume 102 of Cambridge Studies in Advanced Mathematics.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Random Fragmentation and Coagulation Processes , volume 102 of Cambridge Studies in Advanced Mathematics

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.807654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3b302d2b-cbea-478f-a2f8-96048085a596 · outbound

This paper cites Large Deviation Techniques and Applications, 2nd ed.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Large Deviation Techniques and Applications, 2nd ed

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.788270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e407d6d1-9335-4f8d-afe0-a8b343aba9b6 · outbound

This paper cites Analytic Information Theory.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Analytic Information Theory

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.768626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a34d4ffc-d705-4778-9cc7-ea5ad2c3fc03 · outbound

This paper cites Mellin transforms and asymptotics: harmonic sums.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Mellin transforms and asymptotics: harmonic sums

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.745373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b519fd2d-a143-4dee-b3e4-5c42938bd96e · outbound

This paper cites Analytic Combinatorics.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Analytic Combinatorics

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.719816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e894391d-4a70-4369-81ee-a7574869f706 · outbound

This paper cites Regenerative compositions in the case of slow vari- ation: a renewal theory approach.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Regenerative compositions in the case of slow vari- ation: a renewal theory approach

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.700418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5e62a407-7ead-4363-9629-d9f67d7ff7cb · outbound

This paper cites Continuum tree asymptotics of discrete fragmentations and applications t o phylogenetic models.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Continuum tree asymptotics of discrete fragmentations and applications t o phylogenetic models

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.679427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e430e514-c0ac-401f-af0d-dd3ec7a09078 · outbound

This paper cites The genealogyof self-similar fragmentations with neg- ative index as a continuum random tree.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height The genealogyof self-similar fragmentations with neg- ative index as a continuum random tree

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.658838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7717f3c9-ff78-4d7e-b30e-1ee27fdc314f · outbound

This paper cites Handelsman and John S.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Handelsman and John S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.639829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 84027926-8f45-4a72-98cf-b43856c18909 · outbound

This paper cites A comment on `The harmonic descent chain' by D.J. Aldous, S. Janson and X. Li.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height A comment on `The harmonic descent chain' by D.J. Aldous, S. Janson and X. Li

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-11T14:23:12.443781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5f1a89f7-fc33-4a6f-896d-4c7fa507712b · outbound

This paper cites Another proof of CLT for critical be ta-splitting tree.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Another proof of CLT for critical be ta-splitting tree

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.615771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e576fba9-65c2-4a2c-b418-0e0da1fe6ceb · outbound

This paper cites An Introduction to Harmonic Analysis.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height An Introduction to Harmonic Analysis

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.594662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 146d87b6-aa7d-433c-b0ab-871f78cdc1f4 · outbound

This paper cites Critical beta-splitting, via contrac tion.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Critical beta-splitting, via contrac tion

Reference 18

Resolution: verified exact; raw_fallback, observed 2026-08-11T14:23:12.414950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a47f2a6e-7568-48ee-8d7b-04d161f4c1dc · outbound

This paper cites an unresolved cited work.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T14:23:12.575322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 52418415-e04c-410f-9e14-3b338cd5ee7c · outbound

This paper cites On the contra ction method with degenerate limit equation.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height On the contra ction method with degenerate limit equation

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.554597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c6e21789-7ae3-4251-88f9-6d7bda304a1c · outbound

This paper cites Asymptotics an d Mellin–Barnes integrals.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Asymptotics an d Mellin–Barnes integrals

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:23:12.532505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b7532d44-7e29-43c0-875f-1fd7d60ba2a3 · outbound

This paper cites an unresolved cited work.

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T14:23:12.512737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.