Paper Citation Record · LEDGER

Geometry of the Atomic Condition

As of 7 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.22782.

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

pith.paper-citation-record.v1
2607.22782 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T05:40:06.146213Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

28 of 28 outbound references displayed

verified exact1
verified fuzzy0
unresolved27
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 49517e95-6752-4336-bb33-3e703f78c52e · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.076331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b87cbe7-df80-46f2-bf3d-fb667874c664 · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.149626Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1bb339b-35ae-4383-a338-349f1601632e · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.207575Z

Source-reported events for the cited work

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Observation d9cc3cbd-8395-4d68-8efb-a6c4846bddfe · outbound

This paper cites Dimensional estimates and rectifiability for measures satisfying linear PDE constraints.

Geometry of the Atomic Condition Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.275314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 239cf3d4-7575-45ee-b502-406106d8120a · outbound

This paper cites Burago and S.

Geometry of the Atomic Condition Burago and S

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.321481Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3b6312b-aaec-468b-9766-5b4b1d223994 · outbound

This paper cites Busemann and E.

Geometry of the Atomic Condition Busemann and E

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.371247Z

Source-reported events for the cited work

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Observation 07e741fb-d5cc-48b5-9d32-8a481a4c028c · outbound

This paper cites Convexity on G rassmann manifolds.

Geometry of the Atomic Condition Convexity on G rassmann manifolds

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.434588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f9c83be-7ca5-4af5-a93b-4ddf036ddf85 · outbound

This paper cites Geometry of B anach spaces, duality mappings and nonlinear problems , volume 62 of Mathematics and its Applications.

Geometry of the Atomic Condition Geometry of B anach spaces, duality mappings and nonlinear problems , volume 62 of Mathematics and its Applications

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.497446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 704a3520-2a5d-40d2-8e7b-8dfe6a35ddda · outbound

This paper cites Tensor norms and operator ideals , volume 176 of North-Holland Mathematics Studies.

Geometry of the Atomic Condition Tensor norms and operator ideals , volume 176 of North-Holland Mathematics Studies

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.580485Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de981402-79b3-4c7b-86d0-2d3391c384ec · outbound

This paper cites Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies.

Geometry of the Atomic Condition Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.666251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 657e0592-d1b0-41dd-9b96-6d56284f1421 · outbound

This paper cites Michael-simon inequality for anisotropic energies close to the area via multilinear kakeya-type bounds.

Geometry of the Atomic Condition Michael-simon inequality for anisotropic energies close to the area via multilinear kakeya-type bounds

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.739537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f3bb166-db27-4362-95cc-4262f8806a2b · outbound

This paper cites Equivalence of the ellipticity conditions for geometric variational problems.

Geometry of the Atomic Condition Equivalence of the ellipticity conditions for geometric variational problems

Reference 12

Resolution: verified exact; doi, observed 2026-08-01T05:44:12.732995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation abc3c10b-99ff-477a-8c18-b24c1c154f87 · outbound

This paper cites Construction of F illings with P rescribed G aussian I mage and A pplications.

Geometry of the Atomic Condition Construction of F illings with P rescribed G aussian I mage and A pplications

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:04.929513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 402cb0c9-cfc3-4a4e-93cd-3a30af918b65 · outbound

This paper cites Regularity for graphs with bounded anisotropic mean curvature.

Geometry of the Atomic Condition Regularity for graphs with bounded anisotropic mean curvature

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.004222Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f85ac98d-2eab-4318-b5f3-a0ebf434b93b · outbound

This paper cites Topology: a geometric approach , volume 4 of Sigma Series in Pure Mathematics.

Geometry of the Atomic Condition Topology: a geometric approach , volume 4 of Sigma Series in Pure Mathematics

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.097618Z

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Observation ffef6e76-3c9d-4b17-817e-209eb4262809 · outbound

This paper cites Geometric measure theory.

Geometry of the Atomic Condition Geometric measure theory

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.206599Z

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Observation ccf6c173-5198-45a1-96ac-5f1c77c13a44 · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.344858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 27f40faa-e8e7-45ba-935e-178a65b48527 · outbound

This paper cites Existence of solutions to a general geometric elliptic variational problem.

Geometry of the Atomic Condition Existence of solutions to a general geometric elliptic variational problem

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.420138Z

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Unavailable: canonical work link unavailable.

Observation 15afa60a-6395-4ae1-8eec-9d9d8cab4d78 · outbound

This paper cites Strictly convex submanifolds and hypersurfaces of positive curvature.

Geometry of the Atomic Condition Strictly convex submanifolds and hypersurfaces of positive curvature

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.448331Z

Source-reported events for the cited work

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Observation 87953325-2879-4f41-a0b6-c1f6cf667392 · outbound

This paper cites Grothendieck.

Geometry of the Atomic Condition Grothendieck

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.546607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d37c7565-ea98-4296-abc6-7cf76fc962a9 · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.630057Z

Source-reported events for the cited work

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Observation b7835015-b6c9-40c5-9eca-3e1cb7fe8b68 · outbound

This paper cites The joint spectral radius , volume 385 of Lecture Notes in Control and Information Sciences.

Geometry of the Atomic Condition The joint spectral radius , volume 385 of Lecture Notes in Control and Information Sciences

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.715467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce183f90-478d-4f89-9c3a-562e7261a298 · outbound

This paper cites On polyconvexity and A lmgren uniform ellipticity with respect to polyhedral test pairs.

Geometry of the Atomic Condition On polyconvexity and A lmgren uniform ellipticity with respect to polyhedral test pairs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.785821Z

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Observation 0a9178e8-6617-45f3-b669-cafb2c6c599c · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.869895Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4c6baa7-eddc-4283-ae16-79b690ee4b09 · outbound

This paper cites an unresolved cited work.

Geometry of the Atomic Condition Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:05.941347Z

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Observation e3bb2215-f53d-4b13-b8bd-6304e347d5ee · outbound

This paper cites Tyrrell Rockafellar.

Geometry of the Atomic Condition Tyrrell Rockafellar

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:06.008726Z

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Observation c70344e7-2425-4eaa-88ea-5d00b1828a56 · outbound

This paper cites A T heory of C ross- S paces , volume No.

Geometry of the Atomic Condition A T heory of C ross- S paces , volume No

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:06.079502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 622ee5de-6560-47ca-a269-fc1ad87846e3 · outbound

This paper cites On general minimax theorems.

Geometry of the Atomic Condition On general minimax theorems

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T05:40:06.146213Z

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Pith citing papers

No inbound Pith citation observations are available.