Paper Citation Record · LEDGER

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

As of 8 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 5 inbound Pith citation observations for arXiv:2505.15507.

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

pith.paper-citation-record.v1
2505.15507 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:23:34.371185Z

measured 29 of 29 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 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:28:26.062143Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-25T04:45:20.322782Z

Reference resolution

24 of 24 outbound references displayed

verified exact1
verified fuzzy12
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 169ec391-eba8-4998-8ac1-1ffd11fda108 · outbound

This paper cites Mac Lane.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Mac Lane

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:39.417558Z

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 d6acc554-12a8-44d3-9176-391d6cfd6528 · outbound

This paper cites Mitchell and M.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Mitchell and M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:39.204051Z

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 62fda000-0372-44ea-a3fa-7ed0e84c6457 · outbound

This paper cites Sabour, N.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Sabour, N

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:39.033706Z

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 53a09cdf-6592-46bc-8325-6a74a23f4e55 · outbound

This paper cites Gilmer, S.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Gilmer, S

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:38.788912Z

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 d7caaca9-9ed3-471f-8979-5b2ff73f5a82 · outbound

This paper cites Coecke, M.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Coecke, M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:38.483863Z

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 2112df82-4d81-400c-83a2-73a0532b7a9e · outbound

This paper cites Baroni and R.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Baroni and R

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:38.161331Z

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 af5f5cd0-37e5-414e-9380-3e12b7bf175b · outbound

This paper cites Rudolph and E.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Rudolph and E

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:37.860004Z

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 3e2019f2-3245-463b-aa71-66767c44f072 · outbound

This paper cites Socher, B.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Socher, B

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:37.555877Z

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 55b52bb0-d3b6-42db-84c3-9542e8e72968 · outbound

This paper cites V aswani, N.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning V aswani, N

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:37.160483Z

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 7a467c97-4c7e-4cf6-a5c9-c67fdad4363f · outbound

This paper cites an unresolved cited work.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:23:36.885955Z

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 b90e8319-3ce7-43f4-8a65-476fd5b713cb · outbound

This paper cites an unresolved cited work.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:23:36.615267Z

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 70259861-069e-412b-b531-6084f86eaf7d · outbound

This paper cites Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:32.655174Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85bbe20f-c6b7-472b-914d-35e1b4a16d5f · outbound

This paper cites Aguiar and S.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Aguiar and S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:36.216311Z

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 e34019b8-d9ba-40f0-a4ad-93ed65d5aa46 · outbound

This paper cites an unresolved cited work.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:23:35.906851Z

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 fae5d155-19a5-48a2-a24c-b6e12fed6ff7 · outbound

This paper cites Balteanu, Z.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Balteanu, Z

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:35.582689Z

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 cc7b863c-515f-42fd-b7ed-c7d7ba7b3912 · outbound

This paper cites Cichocki, N.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Cichocki, N

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:23:35.287382Z

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 815400c3-384c-445b-b7d7-a56b01cfb48b · outbound

This paper cites RoFormer: Enhanced Transformer with Rotary Position Embedding.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning RoFormer: Enhanced Transformer with Rotary Position Embedding

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:33.390015Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8843e37b-8c22-4118-ba7c-26ceab61d659 · outbound

This paper cites Rotary Position Embedding for Vision Transformer.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Rotary Position Embedding for Vision Transformer

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:33.614694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14e2d092-5ddd-48b9-86b6-7ee05dc72463 · outbound

This paper cites DeBERTa: Decoding-enhanced BERT with Disentangled Attention.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning DeBERTa: Decoding-enhanced BERT with Disentangled Attention

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:33.742269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eac20ea5-6869-4e26-9879-491a42618d25 · outbound

This paper cites Neelakantan, K.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Neelakantan, K

Reference 20

Resolution: verified exact; raw_fallback, observed 2026-08-07T15:23:34.895926Z

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 460733f2-f682-4b7b-910c-74f9ecd56756 · outbound

This paper cites Efficiently Modeling Long Sequences with Structured State Spaces.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Efficiently Modeling Long Sequences with Structured State Spaces

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:33.992490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 996648a7-754d-4887-a0b5-ec61406fcea1 · outbound

This paper cites Hyena Hierarchy: Towards Larger Convolutional Language Models.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Hyena Hierarchy: Towards Larger Convolutional Language Models

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:34.109068Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9998e6ce-5f45-445a-9187-5e56665e4be0 · outbound

This paper cites Mamba: Linear-Time Sequence Modeling with Selective State Spaces.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:34.223253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5592d445-b953-4432-9af4-55e3ef3ac710 · outbound

This paper cites Operadic categories and 2-Segal sets.

Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning Operadic categories and 2-Segal sets

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T15:23:34.371185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation c88c17f0-29ea-40d7-98ae-e24f309d1f41 · inbound

Directional Non-Commutative Monoidal Structures with Interchange Law via Commutative Generators cites this paper.

Directional Non-Commutative Monoidal Structures with Interchange Law via Commutative Generators Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T12:28:26.062143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6405777f-400b-4db7-b120-71e46f7bd831 · inbound

Directional Non-Commutative Monoidal Embeddings for MNIST cites this paper.

Directional Non-Commutative Monoidal Embeddings for MNIST Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T11:07:46.645351Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6bf5e5e2-cc82-420c-bfcb-58335dcb54c9 · inbound

JoFormer (Journey-based Transformer): Theory and Empirical Analysis on the Tiny Shakespeare Dataset cites this paper.

JoFormer (Journey-based Transformer): Theory and Empirical Analysis on the Tiny Shakespeare Dataset Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T05:10:50.642197Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d433bafd-1fbb-49bb-8054-9c5956afa970 · inbound

Commutator-Induced Uncertainty in VAEs cites this paper.

Commutator-Induced Uncertainty in VAEs Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

Reference 58

Resolution: verified exact; arxiv_id, observed 2026-05-25T04:45:20.325909Z

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 ccb0602b-dcb4-4802-93b5-9f6737157389 · inbound

Journey Operators for Structured Multi-Axis Composition cites this paper.

Journey Operators for Structured Multi-Axis Composition Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-30T21:28:26.173311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.