Paper Citation Record · LEDGER

Advancing Geometry with AI: Multi-agent Generation of Polytopes

As of 10 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 7 inbound Pith citation observations for arXiv:2502.05199.

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

pith.paper-citation-record.v1
2502.05199 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T22:49:48.971136Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:45:47.269752Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T09:59:45.510337Z

Reference resolution

34 of 34 outbound references displayed

verified exact1
verified fuzzy23
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d96482e4-622c-434b-a309-2f66c36283df · outbound

This paper cites Deformed products and maximal shadows of polytopes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Deformed products and maximal shadows of polytopes

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.326573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 675f91d7-8fb0-4c2f-8907-9c467551289c · outbound

This paper cites Polytopes and Machine Learning.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Polytopes and Machine Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.855572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01b2ef8b-6a97-4f9f-bf79-a359c5b8cd33 · outbound

This paper cites The simplex method: a probabilistic analysis.

Advancing Geometry with AI: Multi-agent Generation of Polytopes The simplex method: a probabilistic analysis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.316879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b2555108-3fb3-42cc-b416-a7faaf784195 · outbound

This paper cites Reverb: A Framework For Experience Replay.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Reverb: A Framework For Experience Replay

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.863354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4b658eb-9de2-4356-9f81-8e8a7159e446 · outbound

This paper cites Machine learning: The di- mension of a polytope.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Machine learning: The di- mension of a polytope

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.307406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dbe8a2dc-1d66-420f-afde-191078dc8b3b · outbound

This paper cites Linear programming and extensions.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Linear programming and extensions

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.297475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ace8166b-5b31-4763-8f14-ba8ccd7af770 · outbound

This paper cites Advancing mathematics by guiding human intuition with AI.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Advancing mathematics by guiding human intuition with AI

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.288076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 355ad0fd-b005-4a28-be1a-1ad730c06e6d · outbound

This paper cites an unresolved cited work.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:49:49.278617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5da2da08-b260-4e8b-be92-95d0ef6d87a8 · outbound

This paper cites Neighbourly polytopes with few vertices.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Neighbourly polytopes with few vertices

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.269035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation add18001-0681-4554-98c1-9c19777a1f6a · outbound

This paper cites Discovering faster matrix multiplication algorithms with reinforcement learning.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Discovering faster matrix multiplication algorithms with reinforcement learning

Reference 10

Resolution: malformed identifier; no resolver link, observed 2026-08-09T22:49:48.884272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c848386-37a7-475d-b57d-f7f44ece184e · outbound

This paper cites Combinatorial face enumeration in convex polytopes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Combinatorial face enumeration in convex polytopes

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.259641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0230a2a5-a3ac-454b-9378-71335d2aba8c · outbound

This paper cites Neighborly and cyclic polytopes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Neighborly and cyclic polytopes

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.249727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 82e47866-2c6e-42c7-b3ac-06b263ce37be · outbound

This paper cites Polymake: a framework for analyzing convex poly- topes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Polymake: a framework for analyzing convex poly- topes

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.239858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 10a57e71-1111-4086-8105-ad38cbb34bc8 · outbound

This paper cites Machine-learning mathematical structures.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Machine-learning mathematical structures

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.230284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a2d0976e-bd85-4d01-943d-828f77c00a2d · outbound

This paper cites Machine Learning in Physics and Geometry.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Machine Learning in Physics and Geometry

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.901163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6ab19f8-6d10-4fc9-8588-9e1a47884743 · outbound

This paper cites Gaussian Error Linear Units (GELUs).

Advancing Geometry with AI: Multi-agent Generation of Polytopes Gaussian Error Linear Units (GELUs)

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.905065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0326f3e-3f40-440c-8f35-45cbc40363b0 · outbound

This paper cites A quasi-polynomial bound for the diameter of graphs of polyhedra.

Advancing Geometry with AI: Multi-agent Generation of Polytopes A quasi-polynomial bound for the diameter of graphs of polyhedra

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.220357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0c979ca5-1879-40b1-9803-3aa9d07e4f2f · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Adam: A Method for Stochastic Optimization

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.912356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58479359-f6fd-4743-9de0-c9d9332a624d · outbound

This paper cites How good is the simplex algorithm.

Advancing Geometry with AI: Multi-agent Generation of Polytopes How good is the simplex algorithm

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.210633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4f08d784-48bf-48d4-8d58-0584ff1a454e · outbound

This paper cites The width of five-dimensional prismatoids.

Advancing Geometry with AI: Multi-agent Generation of Polytopes The width of five-dimensional prismatoids

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.200654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6037b6c5-14f5-4d9e-bec4-5998c2891426 · outbound

This paper cites polyDB: a database for polytopes and related objects.

Advancing Geometry with AI: Multi-agent Generation of Polytopes polyDB: a database for polytopes and related objects

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.189915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0ab262c2-6702-48d2-bbe5-9813ed8e75f5 · outbound

This paper cites On the monotone upper bound problem.

Advancing Geometry with AI: Multi-agent Generation of Polytopes On the monotone upper bound problem

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.180194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0853e1ec-461d-4213-b841-eb349f98a6b4 · outbound

This paper cites A counterexample to the Hirsch conjecture.

Advancing Geometry with AI: Multi-agent Generation of Polytopes A counterexample to the Hirsch conjecture

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.170109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f6a996b8-90a2-4ef7-82e1-41d76079ca84 · outbound

This paper cites Recent progress on the combinatorial diameter of polytopes and simplicial complexes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Recent progress on the combinatorial diameter of polytopes and simplicial complexes

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.160161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7e7cb927-1b18-44a6-a29b-8572b9507241 · outbound

This paper cites Neighborly polytopes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Neighborly polytopes

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.150045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0021634e-820f-44ed-8dc2-ef1a724ef20d · outbound

This paper cites Techniques for investigating neighborly polytopes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Techniques for investigating neighborly polytopes

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.139144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b4c92fc-83de-4750-9e88-0951fc36fa8f · outbound

This paper cites An asymptotically improved upper bound on the diameter of polyhe- dra.

Advancing Geometry with AI: Multi-agent Generation of Polytopes An asymptotically improved upper bound on the diameter of polyhe- dra

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.128493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5dadd83c-fcca-4785-9e53-3f276d28ad2f · outbound

This paper cites An improved Kalai–Kleitman bound for the diameter of a polyhedron.

Advancing Geometry with AI: Multi-agent Generation of Polytopes An improved Kalai–Kleitman bound for the diameter of a polyhedron

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.118079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c58e6506-3f74-43dc-8e65-331f984b23cf · outbound

This paper cites Attention Is All You Need.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Attention Is All You Need

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.952846Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce3dc1e6-999f-4c38-9a99-59b6d1da92c6 · outbound

This paper cites Constructions in combinatorics via neural networks.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Constructions in combinatorics via neural networks

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.956768Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c354466-48eb-4aad-9bd4-3fcae1fd5986 · outbound

This paper cites Generalized cross entropy loss for training deep neural networks with noisy labels.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Generalized cross entropy loss for training deep neural networks with noisy labels

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.107532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 422fd71b-a001-4ee2-98be-d4a25e097cec · outbound

This paper cites Convex polytopes: extremal constructions and f -vector shapes.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Convex polytopes: extremal constructions and f -vector shapes

Reference 32

Resolution: verified exact; doi, observed 2026-08-09T22:49:49.011744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fea7825e-273d-450b-a995-8aa678a4e0a2 · outbound

This paper cites an unresolved cited work.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-09T22:49:48.967503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5af7cd18-7245-4735-b72b-1e5a99ca3a5a · outbound

This paper cites Polymath 3: Polynomial Hirsch Conjecture.

Advancing Geometry with AI: Multi-agent Generation of Polytopes Polymath 3: Polynomial Hirsch Conjecture

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:49:49.096887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation da1dde70-0fa3-4a5c-8cea-a2b5559ecacd · inbound

Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems cites this paper.

Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-07T12:45:47.269752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 763f1a7d-4aa1-4840-9091-6d5c3023b29d · inbound

Mathematical exploration and discovery at scale cites this paper.

Mathematical exploration and discovery at scale Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 276

Resolution: verified exact; arxiv_id, observed 2026-05-18T01:20:34.498510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f21490c1-faac-4fd4-a1fb-04b70825103a · inbound

AI for Mathematics: Progress, Challenges, and Prospects cites this paper.

AI for Mathematics: Progress, Challenges, and Prospects Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 132

Resolution: verified exact; arxiv_id, observed 2026-05-16T13:27:55.627049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 12d76a2a-525c-497f-87ef-0e7ec7388a70 · inbound

Improved Upper Bounds for Slicing the Hypercube cites this paper.

Improved Upper Bounds for Slicing the Hypercube Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:17.404619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fb0ee5e-2374-497f-aa6e-34b4584ec2d3 · inbound

Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra cites this paper.

Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T09:59:45.511842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d61d4a90-d487-410c-a391-dca048c0e1be · inbound

A ChatGPT-assisted Triangle Characterization of Affine Permutation Inversion Graphs cites this paper.

A ChatGPT-assisted Triangle Characterization of Affine Permutation Inversion Graphs Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-13T05:42:29.726060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37ce9808-6799-40f6-bb51-c03e1ec9c157 · inbound

LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesis cites this paper.

LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesis Advancing Geometry with AI: Multi-agent Generation of Polytopes

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T00:54:45.290298Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.