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Paper Citation Record · LEDGER

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians

As of 8 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2507.21906.

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

pith.paper-citation-record.v1
2507.21906 v2

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:33:57.668642Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:42:45.308061Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T13:42:46.677252Z

Reference resolution

14 of 14 outbound references displayed

  • verified exact2
  • verified fuzzy6
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 17c451be-09f0-4699-8eaa-afd7c4cd1946 · outbound

This paper cites The Carrollian Kaleidoscope.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians The Carrollian Kaleidoscope

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-06T12:33:57.610013Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T12:33:57.610013Z digest=sha256:1750fc78ca6b8cbf12d7db0c8c882327b2ff9482c85d67b9b8b83d5eddd948f0

Observation 072e3a03-1194-4130-bc0e-7fff9621de2b · outbound

This paper cites Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-06T12:33:57.726733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.615745Z digest=sha256:bed181338d5b48e4b42a4e5000f80ada0c50370cc614472a297e8aeaf2f848a6

Observation bced0525-10cd-4a5b-b4ce-4c9b8991d8ae · outbound

This paper cites Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Carrollian $\mathbb{R}^\times$-bundles II: Sigma Models on Event Horizons

Reference 3

Resolution
verified exact
local_arxiv, observed 2026-08-06T12:33:57.707126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.620669Z digest=sha256:fd0913d5601d8e87c87f13b764402335df81252b57908ffd219eb1724d8219fd

Observation 134f41d1-5431-452b-a12d-4e69c03b0685 · outbound

This paper cites & Horvathy, P.A., Conformal Carroll groups,J.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians & Horvathy, P.A., Conformal Carroll groups,J

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.890515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.625391Z digest=sha256:9fc050b97335d0ea111d8a6e3406cb5546aa65e25b408786ff3e9b25aa715b5a

Observation ab371a71-3e68-48ba-9f10-48ae1e4104a7 · outbound

This paper cites & Horvathy, P.A., Conformal Carroll groups and BMS symmetry,Class.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians & Horvathy, P.A., Conformal Carroll groups and BMS symmetry,Class

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.877181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.629619Z digest=sha256:4f383f8a050689962363e418e0cdfb984c2fc5ab7bec4a910dc70a7b658fe977

Observation 2261203e-21df-4bb4-8490-9ec8803b7e76 · outbound

This paper cites & Zhang, P.M., Carroll versus Newton and Galilei: Two Dual Non-Einsteinian Concepts of Time,Class.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians & Zhang, P.M., Carroll versus Newton and Galilei: Two Dual Non-Einsteinian Concepts of Time,Class

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.863909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.635539Z digest=sha256:782bb762f1f0ae34ae59adea46c2d466f499ca1db73da82f85dab722e16ca539

Observation ec07ea62-d4c3-4a84-9041-0088fe2e3a3a · outbound

This paper cites an unresolved cited work.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:33:57.849658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.639909Z digest=sha256:7d777fc17842b6bc5767500bf7cd77f819e4b261269ead7a317ad41d79522d4b

Observation a4de7d2b-2978-4851-abd7-969dc4be2519 · outbound

This paper cites an unresolved cited work.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:33:57.836703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.644025Z digest=sha256:25246ff6530196966163c30333388faeb8067752481a945e9e8a4d98658f72d5

Observation f3d2e8de-f4f3-49af-aaf4-109c884da30e · outbound

This paper cites an unresolved cited work.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:33:57.822916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.648108Z digest=sha256:b9692d9f8819dc67ed4a8dcfb5788e30e8d50b472c588e7b31d518997296fe32

Observation 58d5973c-e9b7-4738-bd5e-449fb76f39a9 · outbound

This paper cites An introduction, 3rd ed., Cambridge: Cambridge University Press, Volume lxii, 686 p.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians An introduction, 3rd ed., Cambridge: Cambridge University Press, Volume lxii, 686 p

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.808469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.652664Z digest=sha256:86f904a0e9752fc9f89878b0b7a85582dce8ce7aecc2f832d690833bb0e264c8

Observation 3f9f3b48-24e5-4cef-81c9-41611e9f5115 · outbound

This paper cites an unresolved cited work.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:33:57.795210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.656656Z digest=sha256:38c8e74f495daedce2574fd03d83a4d3779fea650a3465ec42352c91af88b54f

Observation 6da1a1f2-52da-4f0a-badb-6d982d39325d · outbound

This paper cites an unresolved cited work.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:33:57.781576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.660518Z digest=sha256:e0b2ddf067d90831ab9dc974009d60d39c06b1e0db60dcbe5029d94747f4fc32

Observation 02fc7609-fd20-4dad-95f4-0e7b3e0c0ef1 · outbound

This paper cites Bristol: Institute of Physics (IOP) xxii, 573 p.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Bristol: Institute of Physics (IOP) xxii, 573 p

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.768123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.664603Z digest=sha256:d53d0c0da9b10173a87b0f8e9ef74c166fece95388dc8f2d907aa5de4fd64ec7

Observation 5cb59198-237d-42cd-bd1b-78d42219a15f · outbound

This paper cites Email address:andrewjamesbruce@googlemail.com.

Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians Email address:andrewjamesbruce@googlemail.com

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:33:57.754436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T12:33:57.668642Z digest=sha256:2fd69485570d41b4975f9f55068fc0e942620809ea8d37ca883910fabb0c18fa

Pith citing papers

Observation 0853bd3b-6436-4e89-9230-c8239dbb0b0c · inbound

Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond cites this paper.

Carrollian $\mathbb{R}^\times$-bundles: Connections and Beyond Carrollian $\mathbb{R}^\times$-bundles III: The Hodge Star and Hodge--de Rham Laplacians

Reference 6

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:42:46.744600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:42:45.308061Z digest=sha256:5491300b745479b731cc1a0f8ff19177576a0f4b74943311702906873e96f4c7