Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T18:50:05.454131Z
Paper Citation Record · LEDGER
Approximation Depth of Convex Polytopes
As of 12 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.07779.
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 2026-08-12T06:34:41.77262+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
22 of 22 outbound references displayed
- verified exact1
- verified fuzzy9
- unresolved11
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 10fc8a0c-18c8-4d0d-80c1-fc4720cab427 · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.759453Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation be8f424a-4b0a-4e21-8076-ea05008c9ac3 · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.750773Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4a927e7d-103a-428c-9faf-2307da924be7 · outbound
This paper cites On the Depth of Monotone ReLU Neural Networks and ICNNs.
Approximation Depth of Convex Polytopes On the Depth of Monotone ReLU Neural Networks and ICNNs
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T18:50:04.167571Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6287391d-3b3d-449f-9c23-69ae891a47c8 · outbound
This paper cites 2, 325–341.
Approximation Depth of Convex Polytopes 2, 325–341
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.742396Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4804c12e-6db2-4f40-80b5-c39eef3eb07c · outbound
This paper cites 6, 906–917.
Approximation Depth of Convex Polytopes 6, 906–917
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.733839Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 20b441f7-7786-40eb-9944-86ebd5e6d23a · outbound
This paper cites 2, 91–100.
Approximation Depth of Convex Polytopes 2, 91–100
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.724888Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 56a56d04-ed0a-41fa-8a7a-a903435cd58e · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.715783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a44791da-5f10-40e9-ae77-b1ea93e0efe5 · outbound
This paper cites Grunbaum, Convex polytopes, Springer-Verlag, New York, 2003.
Approximation Depth of Convex Polytopes Grunbaum, Convex polytopes, Springer-Verlag, New York, 2003
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.706257Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4630f54c-41a5-48be-bbe2-81928b8c20e9 · outbound
This paper cites Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes.
Approximation Depth of Convex Polytopes Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes
Reference 9
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T18:50:05.570627Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 16b61f5c-0617-47af-841b-e1c05cb3c659 · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.697238Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2bacb692-2dfc-43a8-836d-d747f1b97d2b · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.688578Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 24dd081b-f597-438e-a351-ca95db2c516b · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.678603Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a529c40d-5244-4ba7-b808-de71270de292 · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.669397Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5b9f7aea-0e76-4f72-9868-1a7503f96eb7 · outbound
This paper cites 28, Princeton university press, 1997.
Approximation Depth of Convex Polytopes 28, Princeton university press, 1997
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.659947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 22b6950c-6588-4aee-9433-0c0042a71aea · outbound
This paper cites 151, Cambridge university press, 2013.
Approximation Depth of Convex Polytopes 151, Cambridge university press, 2013
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.648866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 529531a3-c1e5-4228-bd9c-98e1c00c6ddd · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.639431Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ff00bed8-a918-47b5-aea2-09d76b5897a5 · outbound
This paper cites Shephard, Decomposable convex polyhedra, Mathematika 10 (1963), no.
Approximation Depth of Convex Polytopes Shephard, Decomposable convex polyhedra, Mathematika 10 (1963), no
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.629464Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 3dd4354d-c47f-48f2-9d0a-bc77f54272d2 · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.619589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7f038d7f-11f4-4e72-a01e-5d39341a90db · outbound
This paper cites an unresolved cited work.
Approximation Depth of Convex Polytopes Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T18:50:05.609748Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2123ccd8-19e9-431d-a645-ddcd690710c1 · outbound
This paper cites 1, 287–295.
Approximation Depth of Convex Polytopes 1, 287–295
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.600412Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a88d18b0-3459-4cb4-b327-586792636a05 · outbound
This paper cites Valerdi, On minimal depth in neural networks , arXiv:2402.15315 (2024).
Approximation Depth of Convex Polytopes Valerdi, On minimal depth in neural networks , arXiv:2402.15315 (2024)
Reference 21
- Resolution
- verified exact
- raw_fallback, observed 2026-08-06T18:50:05.555345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation af6a3eb2-e01a-459a-b4a9-b3846f3b143b · outbound
This paper cites 12, 4425–4431.
Approximation Depth of Convex Polytopes 12, 4425–4431
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:50:05.590754Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
No inbound Pith citation observations are available.