Paper Citation Record · LEDGER

Families of Morse functions for manifolds with boundary

As of 13 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 3 inbound Pith citation observations for arXiv:2507.15847.

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

pith.paper-citation-record.v1
2507.15847 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:33:07.382673Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T11:56:30.989775Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T11:04:47.780418Z

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy7
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4531d96e-0eca-4a4c-86d1-78ce9b13973f · outbound

This paper cites auser Classics. Birkh\.

Families of Morse functions for manifolds with boundary auser Classics. Birkh\

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:09.869466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7cce8a0f-b006-4683-a30c-e6a597b60aa3 · outbound

This paper cites Merging boundary critical points of a M orse function.

Families of Morse functions for manifolds with boundary Merging boundary critical points of a M orse function

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:09.715857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 757e3382-9365-46c6-b6aa-45386812718e · outbound

This paper cites Morse theory for manifolds with boundary.

Families of Morse functions for manifolds with boundary Morse theory for manifolds with boundary

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:09.505720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8cfeb53e-9596-4199-8c8c-d64ab67e9fa8 · outbound

This paper cites Embedded M orse T heory and R elative S plitting of C obordisms of M anifolds.

Families of Morse functions for manifolds with boundary Embedded M orse T heory and R elative S plitting of C obordisms of M anifolds

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:09.323651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c7c25fdb-6d30-4069-bf4a-c266e9171b7a · outbound

This paper cites an unresolved cited work.

Families of Morse functions for manifolds with boundary Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:33:09.166532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9427fb52-135b-45b1-880a-5b22e2d8a4e8 · outbound

This paper cites an unresolved cited work.

Families of Morse functions for manifolds with boundary Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:33:09.008839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 62bd94c5-3cc8-4059-83bf-9ac505b1d189 · outbound

This paper cites Jankowski and R.

Families of Morse functions for manifolds with boundary Jankowski and R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:08.846631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8b40cd83-c0dc-4263-a049-e2fa4fc70ee8 · outbound

This paper cites Monopoles and three-manifolds , volume 10 of New Mathematical Monographs.

Families of Morse functions for manifolds with boundary Monopoles and three-manifolds , volume 10 of New Mathematical Monographs

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:08.642552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b55024e2-1175-4171-b088-7397d6b230db · outbound

This paper cites an unresolved cited work.

Families of Morse functions for manifolds with boundary Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:33:08.500641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 75b48c15-1eb3-4987-b7a1-184cd75313c4 · outbound

This paper cites an unresolved cited work.

Families of Morse functions for manifolds with boundary Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:33:08.307155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 65bbcc96-7bcb-46ce-a85a-6cca613a2b79 · outbound

This paper cites an unresolved cited work.

Families of Morse functions for manifolds with boundary Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:33:07.986538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d65156f7-9161-40bc-825a-a688d8f0ed5b · outbound

This paper cites Wasserman.

Families of Morse functions for manifolds with boundary Wasserman

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:33:07.702325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation 03ffaa3a-1968-4a12-9585-1ff901d24755 · inbound

Reidemeister and movie moves for involutive links cites this paper.

Reidemeister and movie moves for involutive links Families of Morse functions for manifolds with boundary

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-12T09:11:26.834462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4d738d87-fe6b-4a06-a231-fc5ed71b702b · inbound

Reidemeister and movie moves for involutive links cites this paper.

Reidemeister and movie moves for involutive links Families of Morse functions for manifolds with boundary

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-22T11:04:47.783325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3dd93659-acb1-4916-ba28-24f7cf459762 · inbound

Resolved Maxwell-Boundary Normal Forms and Exact Reentrant Scaling in Accelerating AdS Black Holes cites this paper.

Resolved Maxwell-Boundary Normal Forms and Exact Reentrant Scaling in Accelerating AdS Black Holes Families of Morse functions for manifolds with boundary

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-01T11:56:30.989775Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.