Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-21T10:21:52.137491Z
Paper Citation Record · LEDGER
Multidimensional cost geometry
As of 12 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2604.06957.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-27T21:21:08.965514Z
Reference resolution
22 of 22 outbound references displayed
- verified exact3
- verified fuzzy13
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation c1781d8a-0116-4103-9605-66793a40fd52 · outbound
This paper cites Acz´ el,Lectures on Functional Equations and Their Applications, Academic Press.
Multidimensional cost geometry Acz´ el,Lectures on Functional Equations and Their Applications, Academic Press
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.087620Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2db672d2-a380-4784-bc53-cc927edfb9f2 · outbound
This paper cites Acz´ el and J.
Multidimensional cost geometry Acz´ el and J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.108433Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2ab9617a-26ff-4c99-a8f0-6ff98c969674 · outbound
This paper cites Amari,Differential-geometrical methods in statistics,Springer Lecture Notes in Statistics 28.
Multidimensional cost geometry Amari,Differential-geometrical methods in statistics,Springer Lecture Notes in Statistics 28
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.097089Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2378c93d-6f8a-4cfa-b459-ad2b5456608d · outbound
This paper cites Amari,Information Geometry and Its Applications,Springer.
Multidimensional cost geometry Amari,Information Geometry and Its Applications,Springer
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.096517Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 64f5db1f-8da9-45a0-8710-bea7ca9d14c1 · outbound
This paper cites Barrab` es, W.
Multidimensional cost geometry Barrab` es, W
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.113067Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation a393bd21-32db-414a-8153-f9a9a22c69d3 · outbound
This paper cites Foundations of Carrollian Geometry.
Multidimensional cost geometry Foundations of Carrollian Geometry
Reference 6
- Resolution
- verified exact
- arxiv_id, observed 2026-06-09T03:08:02.159860Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4b71a096-dd55-47dc-8b30-abe712ccc570 · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.111270Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation be5d878d-37bb-4f9b-8686-40c65a95b631 · outbound
This paper cites Itakura and S.
Multidimensional cost geometry Itakura and S
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.091250Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 0e6c32c4-440b-4d67-9836-051d9ccc395a · outbound
This paper cites Li,Transport information Bregman divergences, Information Geometry, 4 (2021), 435–470.
Multidimensional cost geometry Li,Transport information Bregman divergences, Information Geometry, 4 (2021), 435–470
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.110436Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 75312cbf-6c5a-4ed0-bd36-b8359c7f07dc · outbound
This paper cites Mikeˇ s, E.
Multidimensional cost geometry Mikeˇ s, E
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.103121Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f229124b-375e-4309-bae2-a566cb84788a · outbound
This paper cites O’Neill,Semi-Riemannian Geometry with Applications to Relativity, Academic Press.
Multidimensional cost geometry O’Neill,Semi-Riemannian Geometry with Applications to Relativity, Academic Press
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.099412Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 71eda3ae-94b1-4669-bba1-e2f605299a9c · outbound
This paper cites Coherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics.
Multidimensional cost geometry Coherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-05-21T10:24:06.871878Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation cfdfafdc-f1a6-411e-a798-c116808403f2 · outbound
This paper cites Poisson,A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press.
Multidimensional cost geometry Poisson,A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.112534Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 44c706be-3571-4517-be9c-772e9e8a9c72 · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.114341Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c4bfa448-44a8-4c70-8e11-e46b6f79af60 · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.106582Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation af6f1df0-7345-4cd5-9a8e-2481bdb06d56 · outbound
This paper cites Shima,The Geometry of Hessian Structures, World Scientific.
Multidimensional cost geometry Shima,The Geometry of Hessian Structures, World Scientific
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.107415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4cd0b92b-6a32-45f5-950f-4f07f028286c · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.125624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 32af0730-ecb6-474e-8c38-078d9910d8ae · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.118534Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation cbb47454-b31b-4b0b-b21d-192b109c31f6 · outbound
This paper cites Washburn and M.
Multidimensional cost geometry Washburn and M
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.116263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation fc7f00e1-6e69-4ef8-b046-1e9bafbcbfce · outbound
This paper cites The d'Alembert Inevitability Theorem.
Multidimensional cost geometry The d'Alembert Inevitability Theorem
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-05-21T10:24:06.877954Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d6f8f98e-f6bd-4a95-aa37-2e6b3d367eff · outbound
This paper cites Yano,Differential Geometry on Complex and Almost Complex Spaces, Oxford, London–New York– Paris–Frankfurt.
Multidimensional cost geometry Yano,Differential Geometry on Complex and Almost Complex Spaces, Oxford, London–New York– Paris–Frankfurt
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-21T10:24:07.124740Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 3b06dee4-5728-4925-99cb-fb7c33e379c7 · outbound
This paper cites an unresolved cited work.
Multidimensional cost geometry Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-05-21T10:24:07.123501Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Pith citing papers
No inbound Pith citation observations are available.