Paper Citation Record · LEDGER

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2506.08858.

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

pith.paper-citation-record.v1
2506.08858 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:11:58.445619Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

37 of 37 outbound references displayed

verified exact1
verified fuzzy25
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d114f5c4-dba4-4dfb-a6eb-29f3312b9ce3 · outbound

This paper cites τ -tilting theory.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences τ -tilting theory

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.858187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 23c07a78-afad-4098-b91a-71cc2f4f051d · outbound

This paper cites Lattice theory of the poset of regions.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Lattice theory of the poset of regions

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.666774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6d297fba-a99d-4934-8007-610bd62f84ff · outbound

This paper cites Maximal green sequences for cluster-tilted algebras of finite representation type.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Maximal green sequences for cluster-tilted algebras of finite representation type

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.767037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f4e2778f-6f91-4e8e-bc92-ab65bfda71c0 · outbound

This paper cites Higher Bruhat orders of types B and C.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Higher Bruhat orders of types B and C

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:11:58.543305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e57ad832-d44a-4f13-b8c5-0ca273545f2e · outbound

This paper cites Shard modules.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Shard modules

Reference 13

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T05:11:58.527868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 64b6a4f5-e1b6-4a24-b786-92fc1e9ba385 · outbound

This paper cites Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.375632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2455ffc-2bd5-4c6d-8d56-c935fd6dbf7c · outbound

This paper cites an unresolved cited work.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:11:58.707808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1cb34aba-3ec0-45d1-8b46-329fe83cc5c9 · outbound

This paper cites On the module categories of generalized preprojective algebras of Dynkin type.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences On the module categories of generalized preprojective algebras of Dynkin type

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.687654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 06672056-368b-4f17-b725-5c3552580078 · outbound

This paper cites Higher Bruhat orders in type B.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Higher Bruhat orders in type B

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.655323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 52418646-0d9e-4d6b-a9cc-886fdca4eae0 · outbound

This paper cites Classifying τ -tilting modules over preprojective algebras of Dynkin type.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Classifying τ -tilting modules over preprojective algebras of Dynkin type

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.717510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c37e0bbf-d30d-4830-9375-f1f7b4acc399 · outbound

This paper cites Pro-species of algebras I: Basic properties.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Pro-species of algebras I: Basic properties

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.737516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2dbf23b3-34f2-4578-9445-3afddae589fb · outbound

This paper cites A survey of congruences and quotients of partially ordered sets.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences A survey of congruences and quotients of partially ordered sets

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.602858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 013b0ed0-7684-4fa1-9336-a38299d3c4bf · outbound

This paper cites Cambridge University Press, Cambridge, 2006, pp.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Cambridge University Press, Cambridge, 2006, pp

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.847417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c1cb7372-5b9a-4f66-8149-81ec0169ae44 · outbound

This paper cites Unzerlegbare Darstellungen. I.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Unzerlegbare Darstellungen. I

Reference 127

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.797212Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 67bd2e47-0eb8-4d6c-a364-8a71509229a0 · outbound

This paper cites Heaps of pieces. I. Basic definitions and combinatorial lemmas.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Heaps of pieces. I. Basic definitions and combinatorial lemmas

Reference 202

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.644747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cd7865c7-90c5-4f18-b3ba-0248d51bbaee · outbound

This paper cites Minimal inclusions of torsion classes.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Minimal inclusions of torsion classes

Reference 231

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.837425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e16d4b70-fe98-4467-91ae-411d70ca062d · outbound

This paper cites Cambrian lattices.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Cambrian lattices

Reference 273

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.677166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation eb0ae30f-15aa-4cc1-bb89-811e7d4ddda8 · outbound

This paper cites On algebras of finite representation type.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences On algebras of finite representation type

Reference 299

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.817211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f4c6f12e-6b87-4fd8-9e55-f5ebfa265d12 · outbound

This paper cites Torsion pairs for quivers and the Weyl groups.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Torsion pairs for quivers and the Weyl groups

Reference 308

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.697380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b0e49bdd-8b4c-4b8f-9cfd-ae655aa13807 · outbound

This paper cites Freely braided elements of Coxeter groups.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Freely braided elements of Coxeter groups

Reference 309

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.786932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6990ab36-603b-4a02-af23-acce7a495745 · outbound

This paper cites Quivers with relations for symmetrizable Cartan matrices I: Foundations.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Quivers with relations for symmetrizable Cartan matrices I: Foundations

Reference 348

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.777068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0157cdc8-2677-48f3-8359-be44931da162 · outbound

This paper cites Singularities of toric varieties associated with finite distributive lattices.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Singularities of toric varieties associated with finite distributive lattices

Reference 350

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.624358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c33da095-4ff6-442f-a6ee-859f45e2597b · outbound

This paper cites On cluster theory and quantum dilogarithm identities.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences On cluster theory and quantum dilogarithm identities

Reference 758

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.747687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a33adb3f-5ae3-4791-9df7-5a6f3c01e81b · outbound

This paper cites Springer, Berlin, 1980, pp.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Springer, Berlin, 1980, pp

Reference 832

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.806786Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9b090f05-4458-4dcf-a87f-916b18e45910 · outbound

This paper cites On commutation classes of reduced words in Weyl groups.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences On commutation classes of reduced words in Weyl groups

Reference 901

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.827785Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation de5070c8-4c4e-4f3d-b0c8-31f170a648db · outbound

This paper cites Springer, Berlin, 1986, pp.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Springer, Berlin, 1986, pp

Reference 1234

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.634173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d4563a4c-d1f5-47c2-8332-910cb761a216 · outbound

This paper cites Maximal chain descent orders.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Maximal chain descent orders

Reference 1238

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T05:11:58.495414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e09e1d0b-27c5-4bda-8920-64689d38536a · outbound

This paper cites Order structure on the algebra of permutations and of planar binary trees.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Order structure on the algebra of permutations and of planar binary trees

Reference 1763

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.727679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9e67b26f-6180-4547-af5e-27274d848c53 · outbound

This paper cites Maps between higher Bruhat orders and higher Stasheff-Tamari posets.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Maps between higher Bruhat orders and higher Stasheff-Tamari posets

Reference 2002

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T05:11:58.481137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2bbd36f6-12b5-441f-ac6d-a4867fb33e3f · outbound

This paper cites Braids, Walls, and Mirrors.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Braids, Walls, and Mirrors

Reference 2011

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.341359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0412dcc8-6244-452c-81f9-bbfe4b0fae6b · outbound

This paper cites New interpretations of the higher Stasheff–Tamari orders.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences New interpretations of the higher Stasheff–Tamari orders

Reference 2020

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.613707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation afcedd51-6293-4996-b493-7205fdc40f2e · outbound

This paper cites Extending higher Bruhat orders to non-longest words in $S_n$.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Extending higher Bruhat orders to non-longest words in $S_n$

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.379108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1dacf24-c99c-4e2c-b1e1-b94d2c3a053a · outbound

This paper cites Directed hereditary species and decomposition spaces.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Directed hereditary species and decomposition spaces

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.345452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b38884ac-e53a-4cf0-ad0f-5d36689b6064 · outbound

This paper cites Demazure weaves for reduced plabic graphs (with a proof that Muller-Speyer twist is Donaldson-Thomas).

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Demazure weaves for reduced plabic graphs (with a proof that Muller-Speyer twist is Donaldson-Thomas)

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.337295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfc9c1b7-1c76-4e7d-8612-5a4eaeef4e82 · outbound

This paper cites Fans and polytopes in tilting theory I: Foundations.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Fans and polytopes in tilting theory I: Foundations

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.319048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fd008cf-545c-42a7-918c-592c4669d540 · outbound

This paper cites A categorification of combinatorial Auslander-Reiten quivers.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences A categorification of combinatorial Auslander-Reiten quivers

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-07T05:11:58.333540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d88a7c8e-e9c6-4e79-8551-998c81b392ce · outbound

This paper cites Infinite root systems, representations of graphs and invariant theory. II.

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences Infinite root systems, representations of graphs and invariant theory. II

Reference 7237

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:11:58.757225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.