Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) | Paper Citation Record

Observation 669a71fc-18fc-4f71-b34f-e547fbc0e1de · outbound

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

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Observation c9e2bee0-ae31-4a0e-9043-ddb0791fb5ec · outbound

This paper cites HGeo increaseswhile HAdmin collapses, with the divergence ∆H(t) = HGeo(t) −H Admin(t) rising from zero at 180 CE to +3 .065 at the end of the period.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) HGeo increaseswhile HAdmin collapses, with the divergence ∆H(t) = HGeo(t) −H Admin(t) rising from zero at 180 CE to +3 .065 at the end of the period

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Observation 3cab1194-28f3-4382-b197-9121d0ec769c · outbound

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

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

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Observation e65fc2bc-62bd-46f2-bf59-ff62f92183ca · outbound

This paper cites HTrade is stable across all 420 years suggesting that long-distance trade circuits constitute a topological pattern invariant to the political systems that facilitate them.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) HTrade is stable across all 420 years suggesting that long-distance trade circuits constitute a topological pattern invariant to the political systems that facilitate them

Reference 4

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Observation d24b4d09-b261-4369-8fbb-9ba606980ac6 · outbound

This paper cites The log-normal form preserves strict positivity and is the natural model for multiplicative noise on a cost variable [27].

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) The log-normal form preserves strict positivity and is the natural model for multiplicative noise on a cost variable [27]

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Observation 87e2162a-caec-431c-98c5-db74f8105dd0 · outbound

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

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Observation ec0c0ee0-74f2-4199-8706-b1255baa697a · outbound

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

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Observation 563e863a-9fc9-47b0-9d7f-e5ccd5da8fb9 · outbound

This paper cites Its purpose is to model the progressive severance of inter-regional connectivity after the Yellow Turban Rebellion as a cost penalty.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Its purpose is to model the progressive severance of inter-regional connectivity after the Yellow Turban Rebellion as a cost penalty

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Observation 74a051fb-26b8-4798-ac6c-7253d351f272 · outbound

This paper cites Two phases show statistically significant trends: Phase B (Wu Di expansion, −141to −50BCE): ˆβ1 = +0.0132 yr −1, R2 = 0.674, p = 0.004.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Two phases show statistically significant trends: Phase B (Wu Di expansion, −141to −50BCE): ˆβ1 = +0.0132 yr −1, R2 = 0.674, p = 0.004

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

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Observation 7d195c0d-e71d-4173-a6ab-ce9f55de4380 · outbound

This paper cites A large W2 signals a substantial reorganization of the cycle structure; a small W2 signals near-stability.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) A large W2 signals a substantial reorganization of the cycle structure; a small W2 signals near-stability

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Observation a199448d-9a1d-4d89-a84f-72832ba5f2d6 · outbound

This paper cites W×(d) measures the full geometric distance between the two barcodes: it is zero when the two networks are topologically identical and grows as they differ.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) W×(d) measures the full geometric distance between the two barcodes: it is zero when the two networks are topologically identical and grows as they differ

Reference 12

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Observation e7e73acb-49bf-4f31-9b90-0deb2479574f · outbound

This paper cites A large ξ means loops appear at many different spatial scales during the same decade — the network has structure at both local and long-range levels.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) A large ξ means loops appear at many different spatial scales during the same decade — the network has structure at both local and long-range levels

Reference 13

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Observation 59452941-9636-4fa8-ba68-f730eadef4f1 · outbound

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

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Observation 886d7ee0-7f2a-4803-b0d6-2ebe40007c6d · outbound

This paper cites This is50 years before the formal dissolution(220 CE) and14 years before the Yellow Turban Rebellion(184 CE).

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) This is50 years before the formal dissolution(220 CE) and14 years before the Yellow Turban Rebellion(184 CE)

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Observation ec7bb600-2568-49a8-b309-e47d5b68418c · outbound

This paper cites This coincides with the decade after Yellow Turban activation, and with the onset of the Admin–Geo divergence ( W× = 737, ∆H = +1.35).

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) This coincides with the decade after Yellow Turban activation, and with the onset of the Admin–Geo divergence ( W× = 737, ∆H = +1.35)

Reference 16

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

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

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Observation 891646d8-386f-4560-a422-2ae3bd55c7b3 · outbound

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

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Observation e5bcd55b-ec63-41ef-9064-aed7bc8fa84a · outbound

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

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

Reference 21

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Observation 3649e24c-0ed7-47b0-b1e5-f50cde5eaea6 · outbound

This paper cites HAdmin, HGeo, and HTrade are topologically irreducible observables giving us information on complementary properties of the Han empire.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) HAdmin, HGeo, and HTrade are topologically irreducible observables giving us information on complementary properties of the Han empire

Reference 22

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Observation 2898a308-0b59-4e8a-ab51-6d835917505a · outbound

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

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Observation 4319393c-94ec-4b9b-b70f-c3e6dddb1741 · outbound

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

Reference 24

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Observation 81959929-cf53-4ba8-af93-706388721f51 · outbound

This paper cites This suggests that TDA can recover politically meaningful geographic domains when topographic structure and historically motivated friction channels are incorporated.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) This suggests that TDA can recover politically meaningful geographic domains when topographic structure and historically motivated friction channels are incorporated

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Observation d739b034-28a6-415d-9df6-784e0b6edb9a · outbound

This paper cites HTrade shows no significant structural breaks at any of the eight historical breakpoints (0/8), including the final dissolution.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) HTrade shows no significant structural breaks at any of the eight historical breakpoints (0/8), including the final dissolution

Reference 26

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Observation 5d34d599-7d47-4246-8213-03da1842e1b8 · outbound

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

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Topological Signatures of Imperial Stress: Persistent Homology of the Eastern Mediterranean Trade Network, 0--400 CE

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

This paper cites 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 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

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Observation c6f87d88-d3ce-45da-a940-ca335bf485e6 · outbound

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

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Observation ecafbd3d-af3b-45b1-a0eb-bc9acc1ecf67 · outbound

This paper cites Turchin,Historical Dynamics: Why States Rise and Fall(Princeton University Press, Princeton, 2003).

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Turchin,Historical Dynamics: Why States Rise and Fall(Princeton University Press, Princeton, 2003)

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Observation 9c0fb95a-7b75-4b73-93c5-98ee9ebda033 · outbound

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

Reference 31

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Observation 99cfb8a1-447c-4155-8d63-b7f040a6c1c1 · outbound

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

Reference 32

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Observation 5001968a-295b-4089-a34b-c76fc67f902f · outbound

This paper cites Ruccoet al., A new topological entropy-based approach for measuring similarities among piecewise linear functions, in Proceedings of ECCS 2014(Springer, Cham, 2017), p.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Ruccoet al., A new topological entropy-based approach for measuring similarities among piecewise linear functions, in Proceedings of ECCS 2014(Springer, Cham, 2017), p

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Observation 6250ff37-32d9-4a1c-adc6-cba14f0869d9 · outbound

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

Reference 34

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

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

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

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

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Observation 272063ce-1ab1-4367-847f-3b06d4415722 · outbound

This paper cites van der Waltet al., scikit-image: image processing in Python, PeerJ2, e453 (2014), doi:10.7717/peerj.453.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) van der Waltet al., scikit-image: image processing in Python, PeerJ2, e453 (2014), doi:10.7717/peerj.453

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Observation a5be5469-95e7-4564-b3cc-178766d42e0e · outbound

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

Reference 42

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

Reference 43

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Observation d1d45c91-7811-4fb9-a673-3d00851c26a7 · outbound

This paper cites Verhagen and T.

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

Reference 44

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

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

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

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Observation 09e96fe5-af45-4313-8cc7-5fe8b826d3c5 · outbound

This paper cites de Crespigny,A Biographical Dictionary of Later Han to the Three Kingdoms (23–220 AD)(Brill, Leiden, 2007), doi:10.1163/ej.9789004156050.i-1311.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) de Crespigny,A Biographical Dictionary of Later Han to the Three Kingdoms (23–220 AD)(Brill, Leiden, 2007), doi:10.1163/ej.9789004156050.i-1311

Reference 48

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This paper cites de Crespigny,Imperial Warlord: A Biography of Cao Cao, 155–220 AD(Brill, Leiden, 2010), doi:10.1163/ej.9789004185227.i-554.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) de Crespigny,Imperial Warlord: A Biography of Cao Cao, 155–220 AD(Brill, Leiden, 2010), doi:10.1163/ej.9789004185227.i-554

Reference 49

Resolution: verified exact; doi, observed 2026-07-13T01:09:13.387729Z

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 143fd42f-d776-4480-a883-ee92d4144900 · outbound

This paper cites Bollob´ as,Random Graphs, 2nd ed.

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Bollob´ as,Random Graphs, 2nd ed

Reference 50

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b131c2ec-9b4f-4d2b-b2bc-92448caa6dc0 · outbound

This paper cites Albert, H.

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

Reference 51

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a049ab96-cff2-4d25-9d19-2baab5122246 · outbound

This paper cites an unresolved cited work.

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

Reference 52

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebfaeaf9-4ee9-4cfc-aae9-bef92193284d · outbound

This paper cites Limpert, W.

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

Reference 53

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb2e0777-e304-46a4-9524-bd2d6a4e85ba · outbound

This paper cites an unresolved cited work.

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

Reference 54

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation faf4a1de-5aa3-4f67-9350-7667b8ba9cec · outbound

This paper cites an unresolved cited work.

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

Reference 55

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cd1f725-bd20-4eac-bac5-4303efc47801 · outbound

This paper cites Scheidel and E.

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

Reference 56

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5fb03cfa-3e9a-4a52-aaab-16ef31f87469 · outbound

This paper cites de Crespigny,Northern Frontier: The Policies and Strategy of the Later Han Empire(Australian National University, Canberra, 1984).

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) de Crespigny,Northern Frontier: The Policies and Strategy of the Later Han Empire(Australian National University, Canberra, 1984)

Reference 57

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9fd879a-d6fb-458a-bd4d-5a49bf70f10e · outbound

This paper cites Scheffer,Critical Transitions in Nature and Society(Princeton University Press, Princeton, 2009).

Topological Signatures of Imperial Collapse and Fragmentation: Administrative Dissolution, Territorial Reorganization and Early-Warning Observables in the Han Dynasty Network (206~BCE\,--\,220~CE) Scheffer,Critical Transitions in Nature and Society(Princeton University Press, Princeton, 2009)

Reference 58

Resolution: unresolved; no resolver link, observed 2026-07-13T01:02:38.468388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Outbound references

Pith citing papers