Paper Citation Record · LEDGER

A simplex-based measure of symmetry

As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2607.03815.

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

pith.paper-citation-record.v1
2607.03815 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T23:46:19.952850Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T12:57:39.424144Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

verified exact0
verified fuzzy0
unresolved26
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malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cccd0a59-a150-464f-951f-80694eb1c0e7 · outbound

This paper cites Understanding deep neural networks with rectified linear units.

A simplex-based measure of symmetry Understanding deep neural networks with rectified linear units

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e06faad1-3805-4162-8777-5aa37593a523 · outbound

This paper cites On the expressiveness of rational ReLU neural networks with bounded depth.

A simplex-based measure of symmetry On the expressiveness of rational ReLU neural networks with bounded depth

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ccae670-4c6e-42de-80f7-6f1a4e5d0349 · outbound

This paper cites Kadets-type theorems for partitions of a convex body.

A simplex-based measure of symmetry Kadets-type theorems for partitions of a convex body

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

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Observation 8f6dd9ca-5cdb-4137-89bd-3236555e3779 · outbound

This paper cites Zico Kolter.

A simplex-based measure of symmetry Zico Kolter

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05235bb3-0b5d-4fce-a5a4-e464288935d4 · outbound

This paper cites On the Depth of Monotone ReLU Neural Networks and ICNNs.

A simplex-based measure of symmetry On the Depth of Monotone ReLU Neural Networks and ICNNs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e3236267-9a96-48d1-af1f-b2b7e4b584bd · outbound

This paper cites Better neural network expressivity: Subdividing the simplex.

A simplex-based measure of symmetry Better neural network expressivity: Subdividing the simplex

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

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Observation 20289ab7-7d27-4ded-91d1-2fc9d293466c · outbound

This paper cites Around the Rogers--Shephard inequality.

A simplex-based measure of symmetry Around the Rogers--Shephard inequality

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4df508ac-9b3f-4fa4-82bc-a9c08e2dbdea · outbound

This paper cites Approximation of general smooth convex bodies.

A simplex-based measure of symmetry Approximation of general smooth convex bodies

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c0b7871-e9b7-40f1-b08f-693b231f78d6 · outbound

This paper cites The stability of the Rogers--Shephard inequality and some related inequalities.

A simplex-based measure of symmetry The stability of the Rogers--Shephard inequality and some related inequalities

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edc074f1-fe09-440d-a642-29eb67fd68a5 · outbound

This paper cites Firey and Branko Gr \"u nbaum.

A simplex-based measure of symmetry Firey and Branko Gr \"u nbaum

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1fe2c1b-4326-48dc-b8de-86102b87a615 · outbound

This paper cites Measures of symmetry for convex sets.

A simplex-based measure of symmetry Measures of symmetry for convex sets

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92022db4-5b65-47c8-824f-cf430f426b62 · outbound

This paper cites an unresolved cited work.

A simplex-based measure of symmetry Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 622652eb-b782-416a-99de-0e22da4b692b · outbound

This paper cites Convex Polytopes.

A simplex-based measure of symmetry Convex Polytopes

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 307cb021-bbb6-4eb3-961d-b3e6aa18a3c6 · outbound

This paper cites Stability of the Minkowski measure of asymmetry for convex bodies.

A simplex-based measure of symmetry Stability of the Minkowski measure of asymmetry for convex bodies

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f67e3683-7863-4c15-8138-160a736b26ba · outbound

This paper cites Towards lower bounds on the depth of ReLU neural networks.

A simplex-based measure of symmetry Towards lower bounds on the depth of ReLU neural networks

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0dfc4bf-68a1-432e-9df1-198f11422065 · outbound

This paper cites Lower bounds on the depth of integral ReLU neural networks via lattice polytopes.

A simplex-based measure of symmetry Lower bounds on the depth of integral ReLU neural networks via lattice polytopes

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

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Observation f3e6cf44-b726-4fad-9ab6-4667cbc8d7ae · outbound

This paper cites Indecomposable polytopes.

A simplex-based measure of symmetry Indecomposable polytopes

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71201e23-87ac-47b9-ace8-2fa7393f5a48 · outbound

This paper cites an unresolved cited work.

A simplex-based measure of symmetry Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f8efb37-8970-4389-aae8-a0602a4bf9a2 · outbound

This paper cites Stability for some extremal properties of the simplex.

A simplex-based measure of symmetry Stability for some extremal properties of the simplex

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 741eee92-fb62-4aed-aec2-ffb4dd2c0b0d · outbound

This paper cites Convex bodies: the Brunn--Minkowski theory , volume 151.

A simplex-based measure of symmetry Convex bodies: the Brunn--Minkowski theory , volume 151

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6621a6e-28e6-4835-ada0-5884250dc996 · outbound

This paper cites Shephard.

A simplex-based measure of symmetry Shephard

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

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Observation 4c8e2002-dba9-4816-9c59-b1d47ca124ac · outbound

This paper cites Shephard.

A simplex-based measure of symmetry Shephard

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9699717-2444-4b39-940b-4d782cf04251 · outbound

This paper cites Notes on Schneider ’s stability estimates for convex sets.

A simplex-based measure of symmetry Notes on Schneider ’s stability estimates for convex sets

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36fc7ec2-67b7-4513-bd1a-e1e025498aa7 · outbound

This paper cites Measures of symmetry for convex sets and stability , volume 776.

A simplex-based measure of symmetry Measures of symmetry for convex sets and stability , volume 776

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bec7f941-1929-4365-91c9-fc538eee57b9 · outbound

This paper cites an unresolved cited work.

A simplex-based measure of symmetry Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2f1ef02-8554-40a1-8598-e225b8275a9c · outbound

This paper cites Generalization of hinging hyperplanes.

A simplex-based measure of symmetry Generalization of hinging hyperplanes

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-11T23:46:19.952850Z

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Pith citing papers

Observation 8419c82d-680d-4efd-b879-4884a6997863 · inbound

Tight Stability Estimates Near the Simplex and Improved Bounds for the Diameter of the Banach-Mazur Compactum in Fixed Dimensions cites this paper.

Tight Stability Estimates Near the Simplex and Improved Bounds for the Diameter of the Banach-Mazur Compactum in Fixed Dimensions A simplex-based measure of symmetry

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-30T12:57:39.424144Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.