Paper Citation Record · LEDGER

Differentiable structures on a union of two open sets

As of 23 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2507.05156.

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

pith.paper-citation-record.v1
2507.05156 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:47:10.203559Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

20 of 20 outbound references displayed

verified exact7
verified fuzzy3
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b58914c3-e51e-4fd7-90e7-e4e9c0cc3bfe · outbound

This paper cites Exotic structures on smooth four-manifolds.

Differentiable structures on a union of two open sets Exotic structures on smooth four-manifolds

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T19:47:10.323562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 18590ec4-a371-41e6-97cf-d705e0914044 · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 2

Resolution: verified exact; doi, observed 2026-08-06T19:47:10.313884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 91cf480b-bf2b-4ba7-8fd5-99e156d3e4cd · outbound

This paper cites Cosmic censorship of smooth structures.Comm.

Differentiable structures on a union of two open sets Cosmic censorship of smooth structures.Comm

Reference 3

Resolution: verified exact; doi, observed 2026-08-06T19:47:10.302920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3a1aefa4-3d8e-4c23-9406-6075725f4676 · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-06T19:47:10.292831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7f8c1de5-2d72-4a4e-88eb-516fbf2c4910 · outbound

This paper cites Freed and Karen K.

Differentiable structures on a union of two open sets Freed and Karen K

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:47:10.694276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f0dc85e4-85bb-41c8-9fd4-c404cd476ba8 · outbound

This paper cites The topology of four-dimensional manifolds.

Differentiable structures on a union of two open sets The topology of four-dimensional manifolds

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.139060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7591e305-6039-48e3-8a53-687ed2deafb4 · outbound

This paper cites Springer, Singapore, 2014.doi:10.1007/978-981-287-257-9.

Differentiable structures on a union of two open sets Springer, Singapore, 2014.doi:10.1007/978-981-287-257-9

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.149538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d16bc58c-e5b1-4676-9174-a7f4c499f98f · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.156575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da5ff02-9a31-4f4b-8a35-dbd4f2ed9976 · outbound

This paper cites Vari´ et´ es (non s´ epar´ ees) ` a une dimension et structures feuillet´ ees du plan.

Differentiable structures on a union of two open sets Vari´ et´ es (non s´ epar´ ees) ` a une dimension et structures feuillet´ ees du plan

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.162227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b37b7d1-26b5-451e-b3af-5d6b83928e07 · outbound

This paper cites Foundational essays on topological manifolds, smoothings, and triangulations.

Differentiable structures on a union of two open sets Foundational essays on topological manifolds, smoothings, and triangulations

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:47:10.678582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 490d1f39-2667-4462-a06d-f64c857bc75f · outbound

This paper cites Classification of differentiable structures on the non-Hausdorff line with two origins.

Differentiable structures on a union of two open sets Classification of differentiable structures on the non-Hausdorff line with two origins

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:47:10.276778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2aa2c378-a3da-4c79-ae2d-847d19b0808c · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.173981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbfd68dc-3c96-4f81-a347-d7f011b8fa86 · outbound

This paper cites Obstructions to the smoothing of piecewise-differentiable homeomorphisms.Ann.

Differentiable structures on a union of two open sets Obstructions to the smoothing of piecewise-differentiable homeomorphisms.Ann

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.177668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30e05052-d86f-4148-93c6-b665e84586a3 · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 15

Resolution: verified exact; raw_fallback, observed 2026-08-06T19:47:10.461882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a38e4f5e-2ac0-4269-a28a-d8cbd5575291 · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.184992Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2b22ff6-f1ba-494e-970f-bc0f2bb2f950 · outbound

This paper cites The piecewise-linear structure of Euclidean space.Proc.

Differentiable structures on a union of two open sets The piecewise-linear structure of Euclidean space.Proc

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:47:10.668654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 51796b4e-6c3c-4eb4-a0ab-865ef5edd532 · outbound

This paper cites Gauge theory on asymptotically periodic 4-manifolds.

Differentiable structures on a union of two open sets Gauge theory on asymptotically periodic 4-manifolds

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.192432Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90966595-64c8-4053-8af6-884638bf9afa · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T19:47:10.195900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33b11394-cde9-42d9-8210-980c25a31408 · outbound

This paper cites an unresolved cited work.

Differentiable structures on a union of two open sets Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:47:10.659157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a87da27b-049e-4bcc-bd06-135b1290e267 · outbound

This paper cites Department of Algebra and Topology, Institute of Mathematics of NAS of Ukraine, Tereshchenkivska str.

Differentiable structures on a union of two open sets Department of Algebra and Topology, Institute of Mathematics of NAS of Ukraine, Tereshchenkivska str

Reference 1961

Resolution: verified exact; doi, observed 2026-08-06T19:47:10.233871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.