Paper Citation Record · LEDGER

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions

As of 19 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2501.17518.

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

pith.paper-citation-record.v1
2501.17518 v3

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:14:13.117708Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:14:14.063685Z

Reference resolution

18 of 18 outbound references displayed

verified exact3
verified fuzzy10
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 081ff2ef-2647-4ff8-bb76-cb244f76e100 · outbound

This paper cites URLhttp://proceedings.mlr.press/v80/ganea18a.html.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions URLhttp://proceedings.mlr.press/v80/ganea18a.html

Reference 1

Resolution: verified exact; doi, observed 2026-05-23T04:42:33.150292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4a9f1554-6a14-461a-82a1-82fd6b1c4ae8 · outbound

This paper cites URLhttp://proceedings.mlr.press/v80/sala18a.html.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions URLhttp://proceedings.mlr.press/v80/sala18a.html

Reference 2

Resolution: verified exact; doi, observed 2026-05-23T04:42:33.143438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c2d412a7-598a-4f9e-b202-6f91644b3f4f · outbound

This paper cites Ivan Vendrov, Ryan Kiros, Sanja Fidler, and Raquel Urtasun.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Ivan Vendrov, Ryan Kiros, Sanja Fidler, and Raquel Urtasun

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.718586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 433c97db-a893-4ed8-8f17-47fbee94caa1 · outbound

This paper cites Order-Embeddings of Images and Language.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Order-Embeddings of Images and Language

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-05-23T04:42:33.138633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6c63d777-4541-47a5-8a55-87fe9a35061b · outbound

This paper cites For any ball ball(c′, r′)⊆ball(c 2, r2) withr ′ ≤0.5·r 1, we must have: ||c1 −c ′||p p +|r 1 −r ′|p >(0.5·r 1)p.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions For any ball ball(c′, r′)⊆ball(c 2, r2) withr ′ ≤0.5·r 1, we must have: ||c1 −c ′||p p +|r 1 −r ′|p >(0.5·r 1)p

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.751498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 24b23284-d635-4eba-a714-3a9b3d13511e · outbound

This paper cites For any n, M >0 , we can select n distinct vectors c1.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions For any n, M >0 , we can select n distinct vectors c1

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.759411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ceaf71bc-a101-47fd-bcff-73020e6781d9 · outbound

This paper cites Next, we focus on the cased bd(reg1,reg 2) = 0.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Next, we focus on the cased bd(reg1,reg 2) = 0

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.744587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9b63afde-534c-4a97-9ee1-df5eb25f9b2f · outbound

This paper cites Similarly, since x2 ⊆reg c 1 ⊆reg c 2 and x2 ∈reg 2, we also havex 2 ∈∂(reg 2).

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Similarly, since x2 ⊆reg c 1 ⊆reg c 2 and x2 ∈reg 2, we also havex 2 ∈∂(reg 2)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.721907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ba37616c-0e02-4269-bbfc-bb2e6e85bbe3 · outbound

This paper cites an unresolved cited work.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:25:27.724805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8cf5f45e-eca5-4225-83e7-e2bd57e94914 · outbound

This paper cites Sincereg ′ 2 ⊆reg 2, of course we have dbd(reg1,reg ′ 2)≤d bd(reg1,reg 2).

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Sincereg ′ 2 ⊆reg 2, of course we have dbd(reg1,reg ′ 2)≤d bd(reg1,reg 2)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.728303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b9c8d1e4-f3e2-4eaf-8072-8270eb097bf3 · outbound

This paper cites an unresolved cited work.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:25:27.734746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 69f57534-f896-48a4-802c-f5f40dd034ac · outbound

This paper cites regn ⊆reg such that for any distincti, j∈ {1.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions regn ⊆reg such that for any distincti, j∈ {1

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-23T04:42:35.056417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a010de0c-43cc-4752-b3b3-f7460e706c33 · outbound

This paper cites an unresolved cited work.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:25:27.731497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 68313875-cc09-4aa5-8716-265b21254083 · outbound

This paper cites SubclassOf.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions SubclassOf

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.737882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 44d596bb-9f30-4845-ae07-eab21b88dc48 · outbound

This paper cites The energy function is given by: E(u, v) =∥max{|c u −c v|+o v −o u,0}∥, where cu and cv denote the center vectors of the boxes, and ou and ov denote the offsets of the boxes.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions The energy function is given by: E(u, v) =∥max{|c u −c v|+o v −o u,0}∥, where cu and cv denote the center vectors of the boxes, and ou and ov denote the offsets of the boxes

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.741237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aefb2b9f-0be9-4646-b886-38d6a13d1369 · outbound

This paper cites The energy function is defined as: E(u, v) = max{∥cu −c v∥+r v −r u,0}, wherec u andc v represent the centers of the balls, andr u andr v represent their radii.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions The energy function is defined as: E(u, v) = max{∥cu −c v∥+r v −r u,0}, wherec u andc v represent the centers of the balls, andr u andr v represent their radii

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.748197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7276b95e-3a3c-4b26-aba9-4b7b67ee9b70 · outbound

This paper cites an unresolved cited work.

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-05-23T05:25:27.754584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ca69acb5-525c-499f-ae73-03784140a9bf · outbound

This paper cites This allows it to define box(A⊓B) as box(A)∩box(B).

RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions This allows it to define box(A⊓B) as box(A)∩box(B)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T05:25:27.757206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 38941f00-c28b-4cbc-af9e-ee6d43d2fc67 · inbound

Language Models as Ontology Encoders cites this paper.

Language Models as Ontology Encoders RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions

Reference 34

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T16:14:14.105057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.