Paper Citation Record · LEDGER

Regions represented as foliated forms and natural smooth maps onto them

As of 13 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2607.17180.

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

pith.paper-citation-record.v1
2607.17180 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T18:58:37.350850Z

measured 31 of 31 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:16.975440Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T00:54:17.255244Z

Reference resolution

30 of 30 outbound references displayed

verified exact0
verified fuzzy0
unresolved28
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 155e32c1-b454-42a2-a417-321657c18eb7 · outbound

This paper cites an unresolved cited work.

Regions represented as foliated forms and natural smooth maps onto them Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:33.387291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b95c29ad-065e-4ca6-ba71-966c0dfd15f3 · outbound

This paper cites Burlet and G.

Regions represented as foliated forms and natural smooth maps onto them Burlet and G

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:33.501248Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 248f1b41-e981-4292-909d-8cf0dd1edc30 · outbound

This paper cites Eliashberg, On singularities of folding type , Math.

Regions represented as foliated forms and natural smooth maps onto them Eliashberg, On singularities of folding type , Math

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:33.597036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16fdd3da-cb2a-4dd1-ace6-7c86243b8329 · outbound

This paper cites Eliashberg, Surgery of singularities of smooth mappings , Math.

Regions represented as foliated forms and natural smooth maps onto them Eliashberg, Surgery of singularities of smooth mappings , Math

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:33.805424Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0efe6c52-3906-4802-b5ee-80cd5e8be3d4 · outbound

This paper cites an unresolved cited work.

Regions represented as foliated forms and natural smooth maps onto them Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:33.964199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16db8194-fb2b-4cd9-a823-95884c75ebe6 · outbound

This paper cites Gelbukh, A ﬁnite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018.

Regions represented as foliated forms and natural smooth maps onto them Gelbukh, A ﬁnite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018

Reference 6

Resolution: malformed identifier; doi_truncated, observed 2026-08-01T19:03:29.506227Z

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 483254df-f65e-4edd-84e0-0ce07adecf7d · outbound

This paper cites Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ.

Regions represented as foliated forms and natural smooth maps onto them Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ

Reference 7

Resolution: malformed identifier; no resolver link, observed 2026-08-01T18:58:34.198358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a46f6577-34b9-4c5a-a0e4-ca39fcdc89ff · outbound

This paper cites Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–.

Regions represented as foliated forms and natural smooth maps onto them Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:34.353802Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c32eae17-b4a9-435d-9d73-08befe156795 · outbound

This paper cites Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024.

Regions represented as foliated forms and natural smooth maps onto them Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:34.541864Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8e7c155-257e-499b-9e68-f2e46ad96eb2 · outbound

This paper cites Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17.

Regions represented as foliated forms and natural smooth maps onto them Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:34.662042Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4897cac8-5107-49a7-96d4-14a24b2e021f · outbound

This paper cites On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values.

Regions represented as foliated forms and natural smooth maps onto them On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:34.787122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 946b64b2-bdde-40cf-a1c7-71c084a563f1 · outbound

This paper cites On Reeb graphs induced from smooth functions on closed or open manifolds.

Regions represented as foliated forms and natural smooth maps onto them On Reeb graphs induced from smooth functions on closed or open manifolds

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:34.939137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7695997-8aed-40e1-9ad2-1203a0f00f01 · outbound

This paper cites Real algebraic functions on closed manifolds whose Reeb spaces are given graphs.

Regions represented as foliated forms and natural smooth maps onto them Real algebraic functions on closed manifolds whose Reeb spaces are given graphs

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.070793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99e94745-ffe6-43c7-acd4-7efcce6bd589 · outbound

This paper cites Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages.

Regions represented as foliated forms and natural smooth maps onto them Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.191467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85896afb-be26-4d25-9c26-ec98efc35389 · outbound

This paper cites Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space.

Regions represented as foliated forms and natural smooth maps onto them Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.299919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5bdd1cb-771c-4d7a-9ec0-6ada92e9c3af · outbound

This paper cites Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres.

Regions represented as foliated forms and natural smooth maps onto them Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.462916Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d64b800b-c07c-4b79-bb10-e69d73f5dd3f · outbound

This paper cites an unresolved cited work.

Regions represented as foliated forms and natural smooth maps onto them Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.579331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce7bdaea-19db-43cd-ad0d-d43481f0ea22 · outbound

This paper cites Kitazawa, Fundamental examples of Reeb spaces of smooth functions deﬁ ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2.

Regions represented as foliated forms and natural smooth maps onto them Kitazawa, Fundamental examples of Reeb spaces of smooth functions deﬁ ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.682987Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5232ece3-bd6e-4e2f-aec7-3e54654cb873 · outbound

This paper cites Kitazawa, Reeb spaces of functions being analytic on dense subsets and their graph struc- tures, arXiv:2602.23380.

Regions represented as foliated forms and natural smooth maps onto them Kitazawa, Reeb spaces of functions being analytic on dense subsets and their graph struc- tures, arXiv:2602.23380

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.849513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a31663fd-a153-4b24-8272-800461c6302e · outbound

This paper cites Kitazawa, Reeb spaces of smooth functions associated to globally simi lar graphs of smooth functions, arXiv:2603.02791.

Regions represented as foliated forms and natural smooth maps onto them Kitazawa, Reeb spaces of smooth functions associated to globally simi lar graphs of smooth functions, arXiv:2603.02791

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:35.929109Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a3218b7-46bd-4037-aa13-2d1a6826bfe9 · outbound

This paper cites Masumoto and O.

Regions represented as foliated forms and natural smooth maps onto them Masumoto and O

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.047389Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 967873e8-70a7-4cbc-b3f4-7d1050100e11 · outbound

This paper cites Realization of a graph as the Reeb graph of a Morse function on a manifold.

Regions represented as foliated forms and natural smooth maps onto them Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.217443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc1ba694-f1d6-4582-aa4c-2a498f1c7397 · outbound

This paper cites Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1).

Regions represented as foliated forms and natural smooth maps onto them Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1)

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.315899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25b6ac64-9158-47d7-a1e5-d8933f7d4b5f · outbound

This paper cites Milnor, Lectures on the h-cobordism theorem , Math.

Regions represented as foliated forms and natural smooth maps onto them Milnor, Lectures on the h-cobordism theorem , Math

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.466931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f33a3a8f-8088-4d18-985e-8d4bf9c70245 · outbound

This paper cites an unresolved cited work.

Regions represented as foliated forms and natural smooth maps onto them Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.603457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 029071f8-5f80-4632-a900-ea6a6788faed · outbound

This paper cites Saeki, Notes on the topology of folds , J.

Regions represented as foliated forms and natural smooth maps onto them Saeki, Notes on the topology of folds , J

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.796481Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 112ff211-6ecc-4da6-b9c4-aecca3c7c0d1 · outbound

This paper cites Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl.

Regions represented as foliated forms and natural smooth maps onto them Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:36.929792Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea6f76a2-1908-43a8-85f2-c81ea384ea22 · outbound

This paper cites Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396.

Regions represented as foliated forms and natural smooth maps onto them Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:37.048310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ed4a136-71d0-41a4-9efb-2b8ae2436a06 · outbound

This paper cites Thom, Les singularites des applications diﬀerentiables , Ann.

Regions represented as foliated forms and natural smooth maps onto them Thom, Les singularites des applications diﬀerentiables , Ann

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:37.183397Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0eca82a-49b5-46c7-8bea-a30a27b00840 · outbound

This paper cites Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann.

Regions represented as foliated forms and natural smooth maps onto them Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T18:58:37.350850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation c3ca4fb5-96b6-464e-9652-3f411e29625f · inbound

Fundamental examples of height functions on closed manifolds and their 1st derivatives cites this paper.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Regions represented as foliated forms and natural smooth maps onto them

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-05T00:54:17.259564Z

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.