Paper Citation Record · LEDGER

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs

As of 10 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.05973.

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

pith.paper-citation-record.v1
2606.05973 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T11:05:00.463771Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact3
verified fuzzy27
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 11c0efb6-942c-4dc9-a50b-565e72873bd1 · outbound

This paper cites Gradient Flows in Metric Spaces and in the Space of Probability Measures , edition =.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Gradient Flows in Metric Spaces and in the Space of Probability Measures , edition =

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.883539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0694b962-c2ec-4d67-b4b2-d1b1af875cb0 · outbound

This paper cites 2001 , doi =.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2001 , doi =

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.881426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b130ef9-30f5-445d-bb10-08fac6de6ea5 · outbound

This paper cites 2018 , doi =.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2018 , doi =

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.863711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation efcfcd50-c68b-452d-9953-608a8e7584fa · outbound

This paper cites Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-06-30T11:54:38.848050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a8867d58-6ec2-44a1-bd26-d69376027861 · outbound

This paper cites Reports on mathematical physics , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Reports on mathematical physics , volume=

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.859922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1df9041a-c466-4cd3-96d0-9c535a232455 · outbound

This paper cites Quantum scattering theory on graphs with tails.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Quantum scattering theory on graphs with tails

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-06-30T11:54:38.850674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b29c8137-0e9a-4cd8-aa65-2de37ad391a5 · outbound

This paper cites 2024 , eprint =.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2024 , eprint =

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.849732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5244e2f5-6d2b-420c-81e7-9f7f257747b2 · outbound

This paper cites Journal of mathematical physics , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Journal of mathematical physics , volume=

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.857690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a1a878a4-8203-4868-9241-8364c9b83601 · outbound

This paper cites Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-07T02:18:23.387196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dea0bebf-379f-4986-9a7e-92eb964d50af · outbound

This paper cites 2013 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2013 , publisher=

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.851553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f8778577-5157-4cdd-aaf0-110835b7e505 · outbound

This paper cites an unresolved cited work.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-07-09T11:56:12.885187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bc6b271e-d0cb-481b-8207-30c9f6b8657e · outbound

This paper cites Some basic structures , author=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Some basic structures , author=

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.861885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 85a7da87-a290-41df-b894-980f8f92e4eb · outbound

This paper cites 2013 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2013 , publisher=

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.897348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5e9d2559-dd16-42ca-97ff-4f33f52d3fd5 · outbound

This paper cites Annals of Physics , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Annals of Physics , volume=

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.894141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c4064c8b-e883-4bda-8a9c-7dbc400f47d6 · outbound

This paper cites Advances in Physics , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Advances in Physics , volume=

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.865430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 03cd543f-aeae-4c01-8365-ccaa866c61e5 · outbound

This paper cites Journal of Physics A: Mathematical and General , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Journal of Physics A: Mathematical and General , volume=

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.875450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 194ea095-3c5a-45e0-bee9-1185faa58c28 · outbound

This paper cites Journal of Physics A: Mathematical and General , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Journal of Physics A: Mathematical and General , volume=

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.889476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fd25d924-c23c-41ca-b156-b9719934c505 · outbound

This paper cites Opuscula Mathematica , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Opuscula Mathematica , volume=

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.895796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2abe6e1d-a909-4350-8406-2ade08ecbfa5 · outbound

This paper cites Nuclear physics B , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Nuclear physics B , volume=

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.873014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a96c4a1d-2c71-4875-89ea-2569c774e15c · outbound

This paper cites SIAM Journal on Applied Dynamical Systems , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs SIAM Journal on Applied Dynamical Systems , volume=

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.867444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 30e824c1-d6b3-4952-a52e-fcd6f682b8e1 · outbound

This paper cites Nonlinearity , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Nonlinearity , volume=

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.853258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e943d447-84da-4d48-9cb6-c079d0df6767 · outbound

This paper cites Hamiltonian Systems: Dynamics, Analysis, Applications , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Hamiltonian Systems: Dynamics, Analysis, Applications , volume=

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.906321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3620d0e8-c88b-4824-afe3-cd3ed8ef890e · outbound

This paper cites 1991 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 1991 , publisher=

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.908325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 81bd2c75-5afb-498c-b899-fc24037eadda · outbound

This paper cites 2005 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2005 , publisher=

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.882692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cec53ae2-d27a-4c4b-8bc0-ee8da1900077 · outbound

This paper cites 2006 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2006 , publisher=

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.877235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 663db262-5a70-4acc-9957-c58f519892c9 · outbound

This paper cites Communications in Mathematical Physics , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Communications in Mathematical Physics , volume=

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.902707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bc60e7f1-cf2c-4d2b-a368-ccb2788219a7 · outbound

This paper cites 1989 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 1989 , publisher=

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.904582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b7cf4ac2-f1da-442d-b05a-9ce14558199b · outbound

This paper cites 2008 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2008 , publisher=

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.910095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 275d0bee-eedf-4246-adce-d98e03121f56 · outbound

This paper cites 2012 , publisher=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs 2012 , publisher=

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.900923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b5a31bb3-bc1a-4529-b24e-3ec95ddf7aa0 · outbound

This paper cites Physical Review E , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Physical Review E , volume=

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.887311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e2de7f44-0c22-4f3b-9756-2a67c6909b08 · outbound

This paper cites Physical review E , volume=.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Physical review E , volume=

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T11:56:12.899217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bdbe277e-9191-423c-9b31-cb7a1321e5d1 · outbound

This paper cites Journal of Physics A: Mathematical and Theoretical , abstract =.

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs Journal of Physics A: Mathematical and Theoretical , abstract =

Reference 32

Resolution: verified exact; doi, observed 2026-06-30T11:14:37.251854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

No inbound Pith citation observations are available.