Paper Citation Record · LEDGER

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse

As of 13 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2607.05695.

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

pith.paper-citation-record.v1
2607.05695 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T03:37:30.216735Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T01:02:38.468388Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-13T06:15:01.053796Z

Reference resolution

32 of 32 outbound references displayed

verified exact1
verified fuzzy22
unresolved8
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2f47f160-1797-4aca-b0af-54f5509a3cdf · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 1

Resolution: malformed identifier; raw_fallback, observed 2026-07-11T03:37:48.415698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 142715e9-bba4-4818-a7db-4300a0bc61de · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.393074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c1f9332f-033d-4001-9d2e-563701e8887a · outbound

This paper cites The values are in normalised cost units and are not directly comparable in absolute magnitude to the Roman-period values, which useorbisdenarius units.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse The values are in normalised cost units and are not directly comparable in absolute magnitude to the Roman-period values, which useorbisdenarius units

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.778201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ac8c132d-e304-4d87-a712-c6ff18b595de · outbound

This paper cites The administrative, commercial, and geographic cycle structures deform at the same rate.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse The administrative, commercial, and geographic cycle structures deform at the same rate

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.589510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ea6fb456-9cd9-4295-aaaa-92e4976aa184 · outbound

This paper cites Three patterns emerge.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Three patterns emerge

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.564035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d5891c82-f107-40dd-b1c3-6c9064571979 · outbound

This paper cites Topological Signatures of Imperial Stress: Persistent Homology of the Eastern Mediterranean Trade Network, 0--400 CE.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Topological Signatures of Imperial Stress: Persistent Homology of the Eastern Mediterranean Trade Network, 0--400 CE

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-07-11T03:37:46.678454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 09900376-28e7-4d8a-aa35-03f1e8d0b286 · outbound

This paper cites Meeks and R.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Meeks and R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.820098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cab99d04-b030-4571-9d02-2048d7f35684 · outbound

This paper cites Scheidel and E.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Scheidel and E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.846842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0bf88a58-beb4-45ff-b262-2672fa1e80e3 · outbound

This paper cites Scheidel, I.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Scheidel, I

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.669469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b9ed5b83-85f6-4090-8443-351b275accae · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.683379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0bab44f8-99ce-4003-8efe-7fd4c1e5cf9c · outbound

This paper cites McCormicket al., Digital atlas of Roman and Medieval civilizations (DARMC), Harvard University, Mapping Past Societies (2013).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse McCormicket al., Digital atlas of Roman and Medieval civilizations (DARMC), Harvard University, Mapping Past Societies (2013)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.739323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation da2bfd20-e422-4e01-9d85-31c2168345e6 · outbound

This paper cites ˚Ahlfeldt, Digital atlas of the Roman empire (DARE), Digital Atlas of the Roman Empire (2013).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse ˚Ahlfeldt, Digital atlas of the Roman empire (DARE), Digital Atlas of the Roman Empire (2013)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.375403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 86049cdd-b312-474f-a209-74487b5effce · outbound

This paper cites Wickham,Framing the Early Middle Ages: Europe and the Mediterranean, 400–800(Oxford University Press, Oxford, 2005).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Wickham,Framing the Early Middle Ages: Europe and the Mediterranean, 400–800(Oxford University Press, Oxford, 2005)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.615046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bc38c394-267c-4e9b-b824-99af78edcdc7 · outbound

This paper cites Heather,The Fall of the Roman Empire: A New History of Rome and the Barbarians(Pan Books, London, 2006).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Heather,The Fall of the Roman Empire: A New History of Rome and the Barbarians(Pan Books, London, 2006)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.655220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2cb937a0-b251-4071-9137-9563bf620926 · outbound

This paper cites Ward-Perkins,The Fall of Rome and the End of Civilization(Oxford University Press, Oxford, 2005).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Ward-Perkins,The Fall of Rome and the End of Civilization(Oxford University Press, Oxford, 2005)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.801344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c9f53694-791c-4765-82b6-b9f586a52351 · outbound

This paper cites McCormick,Origins of the European Economy: Communications and Commerce, A.D.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse McCormick,Origins of the European Economy: Communications and Commerce, A.D

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.577071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d3704bd8-5034-457c-ba49-967f4e149574 · outbound

This paper cites Harper,The Fate of Rome: Climate, Disease, and the End of an Empire(Princeton University Press, Princeton, 2017).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Harper,The Fate of Rome: Climate, Disease, and the End of an Empire(Princeton University Press, Princeton, 2017)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.203044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 970633ac-8c1f-4fb2-a6d6-0cda8b4d268d · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.240012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 68b64c35-29e3-48d2-be95-6b28d1837a4a · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.762008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 00aba5af-c735-4add-a4ae-c44701f90727 · outbound

This paper cites Edelsbrunner, D.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Edelsbrunner, D

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.539967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 91638b90-de37-4fc9-bf0b-6e2bac84bf91 · outbound

This paper cites Kerber, D.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Kerber, D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.283769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 561222d0-35d0-473f-8308-f0c268b25bae · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.641184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1e92f76d-b735-49b1-b5e3-b6d2723731ba · outbound

This paper cites Naismith, R.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Naismith, R

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.730799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 78a5c74f-371d-4b99-811b-acc13f42b1f3 · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.754589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ac554093-7ab0-41b9-a333-31c549a658bf · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.701232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d803c203-0ad0-47bb-b516-750fcd2c04cf · outbound

This paper cites Kennedy,The Prophet and the Age of the Caliphates: The Islamic Near East from the Sixth to the Eleventh Century (Longman, London and New York, 1986).

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Kennedy,The Prophet and the Age of the Caliphates: The Islamic Near East from the Sixth to the Eleventh Century (Longman, London and New York, 1986)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.327797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2b803425-eef9-4ca8-a66b-143ec2a12bba · outbound

This paper cites Rucco, F.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Rucco, F

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.350381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 99f430b3-c45d-4269-801d-43a4e4d2ee67 · outbound

This paper cites Their absolute magnitudes are therefore not directly comparable.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Their absolute magnitudes are therefore not directly comparable

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.628622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 50a96e20-6247-4b76-a8d4-4d219e95ed51 · outbound

This paper cites B”untgen, V.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse B”untgen, V

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.206967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7735d786-303b-4400-9095-f9915bc72ad1 · outbound

This paper cites Mordechai, M.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Mordechai, M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.344831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6a9f6495-3db3-4a57-bc98-e2b69ca86c77 · outbound

This paper cites 443 for Hispania and 141 for Africa Occidentalis), reflecting the incompleteness of the Pleiades coverage for northern Gaul.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse 443 for Hispania and 141 for Africa Occidentalis), reflecting the incompleteness of the Pleiades coverage for northern Gaul

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-11T03:37:48.601754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a57ce4b9-3b17-4436-a183-0ce0d78e7a9c · outbound

This paper cites an unresolved cited work.

Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-07-11T03:37:48.486778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation 28629ba5-f771-46a7-8de9-f040b48139a2 · inbound

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) cites this paper.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-07-13T01:09:13.400342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.