Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:56:22.513837Z
Paper Citation Record · LEDGER
Regularity Conditions for Critical Point Convergence
As of 22 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.01854.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
32 of 32 outbound references displayed
- verified exact2
- verified fuzzy21
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 9714bb8b-dee3-4e6b-a128-773579adb52f · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.784893Z
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 b1df0c1a-d589-498c-a862-eb3b57533576 · outbound
This paper cites Multiple testing of local maxima for detection of peaks in random fields.
Regularity Conditions for Critical Point Convergence Multiple testing of local maxima for detection of peaks in random fields
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.778341Z
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 17ae5d0b-df27-41e8-a5c0-bb8bc358154c · outbound
This paper cites Nichols, and Armin Schwarzman.
Regularity Conditions for Critical Point Convergence Nichols, and Armin Schwarzman
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.771627Z
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 5b286d7a-0aaf-4b14-b48c-f8fee60c9764 · outbound
This paper cites Coleman and Luciano Pietronero.
Regularity Conditions for Critical Point Convergence Coleman and Luciano Pietronero
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.763996Z
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 c770a48b-7b9f-4b82-b0ba-8eef7af6c07d · outbound
This paper cites de Gouveia dal Pino, Annibal Hetem, Jorge E.
Regularity Conditions for Critical Point Convergence de Gouveia dal Pino, Annibal Hetem, Jorge E
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.756026Z
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 ebe89bfa-4433-4e2b-b2b6-90ec8101217a · outbound
This paper cites Friston, Keith J.
Regularity Conditions for Critical Point Convergence Friston, Keith J
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.748539Z
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 5cac7112-242b-4c25-b9a5-533353933eb7 · outbound
This paper cites Topological fdr for neuroimaging.
Regularity Conditions for Critical Point Convergence Topological fdr for neuroimaging
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.741864Z
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 e9f8c78c-79fe-4b9c-9c4b-eae125ffcd4d · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.735059Z
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 0589d208-cbda-4c18-8499-66f9eb08afb2 · outbound
This paper cites Adler and Jonathan E.
Regularity Conditions for Critical Point Convergence Adler and Jonathan E
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.727167Z
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 c7fc689c-450f-4aea-88a4-083448b0f6e9 · outbound
This paper cites Object detection under the linear subspace model with application to cryo-EM images.
Regularity Conditions for Critical Point Convergence Object detection under the linear subspace model with application to cryo-EM images
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T20:56:22.443921Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 255d506c-2fef-4354-9aed-bb83ab23df46 · outbound
This paper cites A generalized Poincar\'e-Hopf index theorem.
Regularity Conditions for Critical Point Convergence A generalized Poincar\'e-Hopf index theorem
Reference 11
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:56:22.555866Z
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 2365d884-ae51-4056-8969-b1e76190e93e · outbound
This paper cites The Mountain Pass Theorem: Variants, Generalizations and Some Appli- cations.
Regularity Conditions for Critical Point Convergence The Mountain Pass Theorem: Variants, Generalizations and Some Appli- cations
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.720086Z
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 a217d148-a5c9-4aca-a832-af3988f631ba · outbound
This paper cites Arnold, Alexander Varchenko, and Sabir M.
Regularity Conditions for Critical Point Convergence Arnold, Alexander Varchenko, and Sabir M
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.713649Z
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 7cf2bae1-74af-4ea8-9619-c5b534ee6751 · outbound
This paper cites Parametric Morse lemmas for C1,1-functions.
Regularity Conditions for Critical Point Convergence Parametric Morse lemmas for C1,1-functions
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.706347Z
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 1273cb8b-f078-4337-9899-8bf7c018ded3 · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.699750Z
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 6238da7d-040f-47f3-8833-41bb6fa9b795 · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.691839Z
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 fa06782f-8759-4ff6-bbd3-d45847e9bb2e · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.685069Z
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 b9869924-d730-4433-a942-a4a7f1b18af0 · outbound
This paper cites Differential Topology.
Regularity Conditions for Critical Point Convergence Differential Topology
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.677132Z
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 fa91a226-8288-4104-831f-f14bf04b1771 · outbound
This paper cites M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle (i).Journal de Math´ ematiques Pures et Appliqu´ ees, 7:375–422, 1881.
Regularity Conditions for Critical Point Convergence M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle (i).Journal de Math´ ematiques Pures et Appliqu´ ees, 7:375–422, 1881
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.669407Z
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 5d86837e-acb2-4a8a-9cd8-a5208ddffc11 · outbound
This paper cites Vektorfelder in n-dimensionalen-mannigfaltigkeiten.
Regularity Conditions for Critical Point Convergence Vektorfelder in n-dimensionalen-mannigfaltigkeiten
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.660778Z
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 e120c4b6-8c2a-429d-9f2b-685555beeb70 · outbound
This paper cites Morse Theory.
Regularity Conditions for Critical Point Convergence Morse Theory
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.653509Z
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 5f9252e0-7fdc-46fc-91bb-f8b98e20d9c4 · outbound
This paper cites Topics in Nonlinear Functional Analysis: Notes by R.
Regularity Conditions for Critical Point Convergence Topics in Nonlinear Functional Analysis: Notes by R
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.645043Z
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 1bd84fa8-3520-4325-806a-d55cd830b89b · outbound
This paper cites Introduction to Random Fields.
Regularity Conditions for Critical Point Convergence Introduction to Random Fields
Reference 23
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:56:22.541508Z
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 827dc09e-737d-4b55-9727-641946643874 · outbound
This paper cites An Invitation to Morse Theory.
Regularity Conditions for Critical Point Convergence An Invitation to Morse Theory
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.636588Z
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 a4059742-b6b3-4733-994d-c7139e0cd7d4 · outbound
This paper cites An introduction to transversality.
Regularity Conditions for Critical Point Convergence An introduction to transversality
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.627437Z
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 bab48d35-48a7-4afd-a99b-e3b7bff75caa · outbound
This paper cites Mountain pass on a closed convex set.
Regularity Conditions for Critical Point Convergence Mountain pass on a closed convex set
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.619216Z
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 439e8fde-4df3-459a-9b02-a5d4d7ea07f7 · outbound
This paper cites Hirsch, Stephen Smale, and Robert L.
Regularity Conditions for Critical Point Convergence Hirsch, Stephen Smale, and Robert L
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.611516Z
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 dc5b3a94-251e-436e-be87-979345e02443 · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.603723Z
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 4754879c-c149-43a2-af0e-c18eea4848c2 · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.596120Z
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 123c1683-8d8b-4ad7-8719-3e439c93a339 · outbound
This paper cites As f is a homeomorphism we have that t∗ 2 = t∗.
Regularity Conditions for Critical Point Convergence As f is a homeomorphism we have that t∗ 2 = t∗
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.588412Z
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 c6ae719e-2178-48b7-ad5d-96d4eac7f5de · outbound
This paper cites an unresolved cited work.
Regularity Conditions for Critical Point Convergence Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:56:22.580960Z
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 d9d1d149-c6f4-4f1e-896f-6b0887c40d86 · outbound
This paper cites It now follows from the definition of κ that, for n large enough, ( fn(B1)) κ 2 ⊂ fn(B2).
Regularity Conditions for Critical Point Convergence It now follows from the definition of κ that, for n large enough, ( fn(B1)) κ 2 ⊂ fn(B2)
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:56:22.572113Z
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.