Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:56:36.511261Z
Paper Citation Record · LEDGER
Geometric equivalence among smooth map germs
As of 16 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:1908.08232.
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 2026-08-16T06:30:59.297886+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
38 of 38 outbound references displayed
- verified exact0
- verified fuzzy19
- unresolved19
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 57ac7a3f-cd48-46fb-9834-a84b66e7a9ec · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.143340Z
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 72499822-2b08-4074-a996-98cbd505d71a · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.127652Z
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 4d82534d-2149-455d-906b-744675d75670 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.112788Z
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 fd1ac8e8-dedf-453e-b42d-c1f2d0b2e8ba · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.097155Z
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 7b0d8960-84fa-4c34-b80c-46b5b589a59e · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.080326Z
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 5c2609b9-bff0-44d2-97b0-48fdc00ec2eb · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.064469Z
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 2357c61c-33e4-4812-a4a0-ff0d80aaae6c · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.048874Z
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 bd42a682-01a6-4454-b003-5f2e07100f42 · outbound
This paper cites Damon, The unfolding and determinacy theorems for sub groups ofA andK.
Geometric equivalence among smooth map germs Damon, The unfolding and determinacy theorems for sub groups ofA andK
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:37.033790Z
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 739f52e3-694b-443b-b779-350e0bdc54f1 · outbound
This paper cites Domitrz and J.
Geometric equivalence among smooth map germs Domitrz and J
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:37.016440Z
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 581dd7a8-6cb4-458f-8e00-d0c65955ec04 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:37.000779Z
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 8a23d249-d168-4a26-8b54-ee7d386d7e6e · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.985736Z
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 38102d8a-47bb-4e19-83f8-1a0a92844ea1 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.969961Z
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 a9e9fb6a-1edd-4079-ba2a-dab60944d58e · outbound
This paper cites Fukui and M.
Geometric equivalence among smooth map germs Fukui and M
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.955137Z
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 6dac9161-46fb-4d14-a436-afb64932b5b5 · outbound
This paper cites Fukunaga and M.
Geometric equivalence among smooth map germs Fukunaga and M
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.939907Z
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 d0a3a21b-1676-42f4-9bab-f546c3444fec · outbound
This paper cites Fukunaga and M.
Geometric equivalence among smooth map germs Fukunaga and M
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T11:56:36.398268Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 756bcf84-3619-4aa0-97af-39c943309230 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.924852Z
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 396b996b-575e-4d41-8f4b-b1124255dbf6 · outbound
This paper cites Ishikawa, Families of functions dominated by distri butions ofC-classes of mappings.
Geometric equivalence among smooth map germs Ishikawa, Families of functions dominated by distri butions ofC-classes of mappings
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.909835Z
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 f1c9b9b9-e371-428e-afa8-f8d00326cee4 · outbound
This paper cites Ishikawa and S.
Geometric equivalence among smooth map germs Ishikawa and S
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.894010Z
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 1a4c10df-8a10-4c98-a793-3ed5fe8a218a · outbound
This paper cites Ishikawa, Singularities of frontals.
Geometric equivalence among smooth map germs Ishikawa, Singularities of frontals
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.878325Z
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 b725cd2d-e30c-4ab8-99b2-4b7c513931f0 · outbound
This paper cites Izumiya, M.
Geometric equivalence among smooth map germs Izumiya, M
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.862592Z
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 49901662-0810-4a31-a23d-6481c235d796 · outbound
This paper cites Malgrange, Ideals of differentiable functions.
Geometric equivalence among smooth map germs Malgrange, Ideals of differentiable functions
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.845538Z
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 2621b830-5fb6-4a2c-ab3c-c026bd0b8c42 · outbound
This paper cites Mancini and M.
Geometric equivalence among smooth map germs Mancini and M
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.830188Z
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 aa098233-12d6-4c46-b899-507e34c35551 · outbound
This paper cites Mancini, M.
Geometric equivalence among smooth map germs Mancini, M
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.815409Z
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 2d225d29-4b5b-49f5-8344-6e9a07371d13 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.799912Z
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 a160b631-9c14-4925-a909-5d67be1a678d · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.783527Z
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 e56f8a7a-ef18-43e9-b61c-2ab4b117e13c · outbound
This paper cites Martinet, Singularities of smooth Functions and Maps.
Geometric equivalence among smooth map germs Martinet, Singularities of smooth Functions and Maps
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.766926Z
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 df4e72ab-c5ea-4ade-8a25-9eac7895bbe0 · outbound
This paper cites Mather, Stability of C ∞-Mappings III.
Geometric equivalence among smooth map germs Mather, Stability of C ∞-Mappings III
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.750965Z
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 bb25769c-fa43-422f-a8c2-37f00181c2a1 · outbound
This paper cites Mather, Stability of C ∞-Mappings IV.
Geometric equivalence among smooth map germs Mather, Stability of C ∞-Mappings IV
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.735447Z
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 7dd257b7-21a1-441d-bcd1-0dc0a7ee2fcc · outbound
This paper cites Mather, Unpublished note on right equivalence.
Geometric equivalence among smooth map germs Mather, Unpublished note on right equivalence
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.719221Z
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 b4820803-a9e5-4365-bcbe-865e09be73c9 · outbound
This paper cites Nomizu and T.
Geometric equivalence among smooth map germs Nomizu and T
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.703583Z
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 6b19b894-3609-4901-995b-eb5c81d9a393 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.688062Z
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 5d8ff022-c99c-41ed-a1aa-f9fb0f913a01 · outbound
This paper cites Saji, Normal form of the swallowtail and its applicat ions.
Geometric equivalence among smooth map germs Saji, Normal form of the swallowtail and its applicat ions
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.668907Z
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 d183d8d0-8c27-4f76-a5c3-763c2bf97436 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.649264Z
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 cbc4ced7-8cf0-45ef-9419-1029cbd86d64 · outbound
This paper cites Teramoto, K.
Geometric equivalence among smooth map germs Teramoto, K
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.630092Z
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 7566d397-5e92-4f8c-890f-4d6d5ee7ebab · outbound
This paper cites Thom and H.
Geometric equivalence among smooth map germs Thom and H
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:56:36.612696Z
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 4df9d389-5435-4f9d-81d9-5eed11cd2bb4 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.595821Z
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 89797d39-2339-4f58-aec5-ffc857c0edcf · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.579283Z
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 57214af3-6c51-4066-8ab2-a4ce2e59f965 · outbound
This paper cites an unresolved cited work.
Geometric equivalence among smooth map germs Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:56:36.561987Z
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.
Pith citing papers
No inbound Pith citation observations are available.