Paper Citation Record · LEDGER

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings

As of 11 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.07319.

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

pith.paper-citation-record.v1
2607.07319 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-09T14:43:27.288339Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

28 of 28 outbound references displayed

verified exact15
verified fuzzy2
unresolved3
parse uncertain0
malformed identifier7
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c75efd38-a3e8-4ece-bb4f-970224e607b0 · outbound

This paper cites Banaschewski, Another look at the localic Tychonoff theorem, Comment.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Banaschewski, Another look at the localic Tychonoff theorem, Comment

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T14:46:17.750123Z

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 b87fcc4d-7e34-4207-9742-b01f9bdf8aa3 · outbound

This paper cites Biswas, S.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Biswas, S

Reference 2

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.564971Z

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 f5472c02-5cf3-4800-a95b-fbb7f1fb2324 · outbound

This paper cites Biswas, S.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Biswas, S

Reference 3

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.551619Z

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 4f7fd859-6cb3-406f-9a16-dd89903e6f43 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 4

Resolution: malformed identifier; raw_fallback, observed 2026-07-09T14:46:17.753642Z

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 2cebbb53-c6c1-4db4-b377-b23dba738c5e · outbound

This paper cites Cambridge University Press.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Cambridge University Press

Reference 5

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.570879Z

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 d89229ae-2575-40cb-bfc7-be50294e9b30 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-07-09T14:46:17.747215Z

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 f90733ae-1093-4df0-a770-aa766211c9ec · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 7

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.579444Z

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 56896025-207c-42b9-9fc4-8f81aed2ecd2 · outbound

This paper cites Gillman and M.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Gillman and M

Reference 8

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.586025Z

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 363b3b69-26a8-4b40-b31b-44c85cda5d3f · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 9

Resolution: malformed identifier; raw_fallback, observed 2026-07-09T14:46:17.739514Z

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 cfc16799-e971-46d0-a471-bc3efee96fed · outbound

This paper cites Goswami, Onz-ideals andz-closure operations of semirings, I, Quaest.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Goswami, Onz-ideals andz-closure operations of semirings, I, Quaest

Reference 10

Resolution: malformed identifier; arxiv_id, observed 2026-07-09T14:46:17.596490Z

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 8f297cd7-0835-4112-a39d-8c3140d58697 · outbound

This paper cites Goswami and T.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Goswami and T

Reference 11

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.583286Z

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 eb9e219d-31b6-4e71-81ae-947d3932cda9 · outbound

This paper cites Goswami and T.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Goswami and T

Reference 12

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.583525Z

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 26a08706-63f7-4071-b2f3-f883cd1068cd · outbound

This paper cites Goswami and A.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Goswami and A

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-07-09T14:46:17.572614Z

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 eb38dcdb-c119-4838-a7ae-9e674360bb65 · outbound

This paper cites Grothendieck,Éléments de géométrie algébrique.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Grothendieck,Éléments de géométrie algébrique

Reference 14

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.563124Z

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 535bb190-b674-4efc-81c1-63b26c316430 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-07-09T14:46:17.755291Z

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 2c47b890-d20c-460f-8461-48df29e47134 · outbound

This paper cites Hebisch and H.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Hebisch and H

Reference 16

Resolution: malformed identifier; doi_truncated, observed 2026-07-09T14:46:17.581234Z

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 5d80e3c0-bbb1-4cb3-8c4a-c55f2790b743 · outbound

This paper cites Hochster, Prime ideal structure in commutative rings, Trans.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Hochster, Prime ideal structure in commutative rings, Trans

Reference 17

Resolution: malformed identifier; raw_fallback, observed 2026-07-09T14:46:17.751989Z

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 a43ad892-52a9-4d79-bcf5-e695430b86bc · outbound

This paper cites Ighedo and W.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Ighedo and W

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-09T14:46:17.577321Z

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 c15d7888-9c8f-4959-a3d3-f061f2726f43 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.586295Z

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 eb83928a-3cfb-4f97-8cde-d6ba6835b81c · outbound

This paper cites Masset, R.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Masset, R

Reference 20

Resolution: malformed identifier; doi_truncated, observed 2026-07-09T14:46:17.581548Z

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 77024490-4d8f-486f-8024-e4ccc4cb40a3 · outbound

This paper cites Lombardi and C.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Lombardi and C

Reference 21

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.574302Z

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 29308b46-5ade-4afa-aaa8-573daa1f7296 · outbound

This paper cites Mason,z-ideals and prime ideals, J.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Mason,z-ideals and prime ideals, J

Reference 22

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.572956Z

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 3f97ada7-0698-4ab5-a7f4-aa8d507ed7f4 · outbound

This paper cites Mason, Primez-ideals ofC(X)and related rings, Canad.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Mason, Primez-ideals ofC(X)and related rings, Canad

Reference 23

Resolution: malformed identifier; raw_fallback, observed 2026-07-09T14:46:17.744400Z

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 d2893e93-a4a5-4547-8d57-e8631a363c7f · outbound

This paper cites Nachbin, Une propriété caractéristique des algèbres booléiennes, Portugal.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Nachbin, Une propriété caractéristique des algèbres booléiennes, Portugal

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T14:46:17.746493Z

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 268d3dcd-0c83-4d53-a92b-74d784cc8657 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-07-09T14:46:17.748374Z

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 f74e7ed8-043f-4a9a-bca5-448ec7287cd0 · outbound

This paper cites an unresolved cited work.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Unresolved cited work

Reference 26

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.566959Z

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 03c766ee-463f-4dfa-90e8-82afd48923aa · outbound

This paper cites Sengupta, A.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Sengupta, A

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-07-09T14:46:17.556760Z

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 05123630-e8f1-4730-9121-83b39a6cbd9a · outbound

This paper cites Subramanian, V on Neumann regularity in semirings, Math.

Maximal-Hull $z$-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings Subramanian, V on Neumann regularity in semirings, Math

Reference 28

Resolution: verified exact; doi, observed 2026-07-09T14:46:17.562138Z

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.