Paper Citation Record · LEDGER

Geometric equivalence among smooth map germs

As of 19 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.

pith.paper-citation-record.v1
1908.08232 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:56:36.511261Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.