Paper Citation Record · LEDGER

Disproof of the tree product conjecture via the Heisenberg group

As of 14 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2607.03041.

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

pith.paper-citation-record.v1
2607.03041 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T05:16:24.888605Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:49:33.547702Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T19:49:34.323064Z

Reference resolution

30 of 30 outbound references displayed

verified exact19
verified fuzzy0
unresolved8
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0a11be0c-7da6-488b-b6bb-14c22800d3e6 · outbound

This paper cites Angel (2003).

Disproof of the tree product conjecture via the Heisenberg group Angel (2003)

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71d05013-ad88-4fd5-aa8f-4fe196706ce2 · outbound

This paper cites Pascal Gollin , Kevin Hendrey , Robert Hickingbotham , Tony Huynh , Freddie Illingworth , Youri Tamitegama , Jane Tan , and David R.

Disproof of the tree product conjecture via the Heisenberg group Pascal Gollin , Kevin Hendrey , Robert Hickingbotham , Tony Huynh , Freddie Illingworth , Youri Tamitegama , Jane Tan , and David R

Reference 2

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.408205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4297699a-adb8-4a8f-902b-e999d3017c5c · outbound

This paper cites Pascal Gollin , Daniel J.

Disproof of the tree product conjecture via the Heisenberg group Pascal Gollin , Daniel J

Reference 3

Resolution: malformed identifier; doi_truncated, observed 2026-07-12T05:18:34.457305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f66dc1c1-73e7-4667-ab49-f38289d2cdf2 · outbound

This paper cites https://doi.org/10.1007/s11511-012-0071-9 Compression bounds for L ipschitz maps from the H eisenberg group to L_1.

Disproof of the tree product conjecture via the Heisenberg group https://doi.org/10.1007/s11511-012-0071-9 Compression bounds for L ipschitz maps from the H eisenberg group to L_1

Reference 4

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.403785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 97205c0c-e06f-46aa-95ac-4fd5262ea944 · outbound

This paper cites Seweryn , and David R.

Disproof of the tree product conjecture via the Heisenberg group Seweryn , and David R

Reference 5

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.380021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b028a457-17f9-42c2-865a-c6ebb9b403ce · outbound

This paper cites Wood (2022).

Disproof of the tree product conjecture via the Heisenberg group Wood (2022)

Reference 6

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.464856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3ca1c973-b3a0-4699-969b-bd63cd063d01 · outbound

This paper cites Seweryn , and David R.

Disproof of the tree product conjecture via the Heisenberg group Seweryn , and David R

Reference 7

Resolution: malformed identifier; doi_truncated, observed 2026-07-12T05:18:34.439079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f7ab4ec3-2bac-431a-9905-d61f4f24a413 · outbound

This paper cites Wood (2020).

Disproof of the tree product conjecture via the Heisenberg group Wood (2020)

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4754d592-e511-45a2-a735-dcba69e832fa · outbound

This paper cites https://doi.org/10.1002/rsa.70059 Size- R amsey numbers of structurally sparse graphs.

Disproof of the tree product conjecture via the Heisenberg group https://doi.org/10.1002/rsa.70059 Size- R amsey numbers of structurally sparse graphs

Reference 9

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.412023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 082e316a-46d9-47f9-bec2-2bcfc79a8e50 · outbound

This paper cites Wood (2023).

Disproof of the tree product conjecture via the Heisenberg group Wood (2023)

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab237ea3-6437-4994-932c-a16a11133ddb · outbound

This paper cites Wood (2025).

Disproof of the tree product conjecture via the Heisenberg group Wood (2025)

Reference 11

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.424916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ca1fd8fb-4920-471d-87fd-535f4687e3c9 · outbound

This paper cites Lee (2021).

Disproof of the tree product conjecture via the Heisenberg group Lee (2021)

Reference 12

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.399739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 02fc023f-7875-40c6-85cd-e9b8e34236c3 · outbound

This paper cites Grigorchuk and P.

Disproof of the tree product conjecture via the Heisenberg group Grigorchuk and P

Reference 13

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.395005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 686045dd-e2be-4561-be86-3a374bd5166b · outbound

This paper cites Godsil , Wilfried Imrich , Norbert Seifter , Mark E.

Disproof of the tree product conjecture via the Heisenberg group Godsil , Wilfried Imrich , Norbert Seifter , Mark E

Reference 14

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.389976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d2974ef9-6ec2-48c3-b869-c7b7854ec793 · outbound

This paper cites Grigorchuk (1991).

Disproof of the tree product conjecture via the Heisenberg group Grigorchuk (1991)

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68751776-0ff8-4efd-bb2a-dd6870acb6dd · outbound

This paper cites an unresolved cited work.

Disproof of the tree product conjecture via the Heisenberg group Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 764d203e-44e0-4c15-bb75-a5a3271a2b44 · outbound

This paper cites Gromov (1987).

Disproof of the tree product conjecture via the Heisenberg group Gromov (1987)

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0617eaa-16aa-42fe-ac8a-a5cc8929e741 · outbound

This paper cites an unresolved cited work.

Disproof of the tree product conjecture via the Heisenberg group Unresolved cited work

Reference 18

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.368715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d6167b88-3fc6-480a-9e61-2d3af84e15ab · outbound

This paper cites Wood (2024).

Disproof of the tree product conjecture via the Heisenberg group Wood (2024)

Reference 19

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.432945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 087c0037-9c12-4190-b276-689103a8c483 · outbound

This paper cites A bound for groups of linear growth https://doi.org/10.1007/BF01189278.

Disproof of the tree product conjecture via the Heisenberg group A bound for groups of linear growth https://doi.org/10.1007/BF01189278

Reference 20

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.461415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 824aa647-c46a-41fb-8a33-914b997c9a06 · outbound

This paper cites Imrich and N.

Disproof of the tree product conjecture via the Heisenberg group Imrich and N

Reference 21

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.420272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e38a466c-9c68-4a87-bf5b-2817caf2c1c5 · outbound

This paper cites Imrich and N.

Disproof of the tree product conjecture via the Heisenberg group Imrich and N

Reference 22

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.444954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 70830743-24fb-436c-a14e-7483061eee9b · outbound

This paper cites Wood (2024).

Disproof of the tree product conjecture via the Heisenberg group Wood (2024)

Reference 23

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.428182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 636f1dbb-af86-47b8-8a3c-1a67ed411502 · outbound

This paper cites Lee (2007).

Disproof of the tree product conjecture via the Heisenberg group Lee (2007)

Reference 24

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.372679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a00efe6b-c771-4bc1-a13a-186a2ffc48f0 · outbound

This paper cites Lee and Assaf Naor (2005).

Disproof of the tree product conjecture via the Heisenberg group Lee and Assaf Naor (2005)

Reference 25

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.416740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c90eb75d-ec18-407f-b391-33b8d45480e2 · outbound

This paper cites an unresolved cited work.

Disproof of the tree product conjecture via the Heisenberg group Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2412b21a-a06f-4dbd-89bb-757d9f3b6a9b · outbound

This paper cites an unresolved cited work.

Disproof of the tree product conjecture via the Heisenberg group Unresolved cited work

Reference 27

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.475539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5f58148a-833f-4c5e-a26d-34ec036f1cba · outbound

This paper cites an unresolved cited work.

Disproof of the tree product conjecture via the Heisenberg group Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-07-12T05:18:34.483372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation aa8de1c2-4934-4287-9d3d-e4e0090f6295 · outbound

This paper cites Wood , and Wendy Yi (2022).

Disproof of the tree product conjecture via the Heisenberg group Wood , and Wendy Yi (2022)

Reference 29

Resolution: malformed identifier; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28080d37-de33-421b-b869-09d956917dd4 · outbound

This paper cites Wolf (Jan.

Disproof of the tree product conjecture via the Heisenberg group Wolf (Jan

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-12T05:16:24.888605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 7389a2d2-1c25-4d43-a094-0c37897672dd · inbound

Subdivided expanders and counterexamples to the Tree Product Conjecture cites this paper.

Subdivided expanders and counterexamples to the Tree Product Conjecture Disproof of the tree product conjecture via the Heisenberg group

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:49:34.481634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.