Paper Citation Record · LEDGER

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings

As of 4 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2605.09551.

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

pith.paper-citation-record.v1
2605.09551 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T03:16:23.636393Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+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 fuzzy26
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6eba55c7-f970-455a-8826-7ad81bac0447 · outbound

This paper cites Arithmetic Circuits.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Arithmetic Circuits

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.377573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 7027e15b-4a41-4f0e-be4c-c3262c941b7d · outbound

This paper cites arXiv preprint arXiv:2512.23121 , year=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings arXiv preprint arXiv:2512.23121 , year=

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:21:19.410284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 23445630-f4e4-46cf-946a-73c694169da3 · outbound

This paper cites SIAM Journal on Computing , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings SIAM Journal on Computing , volume=

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.528818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation a9814745-2bb5-40f1-94dc-66a4e0a5ad32 · outbound

This paper cites an unresolved cited work.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-12T20:21:50.524889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 7a818892-f3bd-48d5-bff6-24142e7ca1d7 · outbound

This paper cites Information and Computation , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Information and Computation , volume=

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.499595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation b3af1caa-385d-411c-b3f3-9bc4917371e5 · outbound

This paper cites 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) , pages=

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.364489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation b09fd8a3-6268-4508-87b9-5cf48c920230 · outbound

This paper cites Journal of Automata, Languages and Combinatorics , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Journal of Automata, Languages and Combinatorics , volume=

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.373586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 6a2484c5-d53d-4560-ac9d-cfeae83f7444 · outbound

This paper cites Proceedings of the eighteenth annual ACM symposium on Theory of computing , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Proceedings of the eighteenth annual ACM symposium on Theory of computing , pages=

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.453339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation b6c5d499-d8db-4c24-933b-5b1130a312a1 · outbound

This paper cites Proceedings of the London Mathematical Society Symposium on Boolean Function Complexity , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Proceedings of the London Mathematical Society Symposium on Boolean Function Complexity , pages=

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.482296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 8e77e5f0-f5fa-4dc7-a0d2-387151277dc9 · outbound

This paper cites International Journal of Advances in Engineering Sciences and Applied Mathematics , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings International Journal of Advances in Engineering Sciences and Applied Mathematics , volume=

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.360650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 559e0425-8a1a-49ee-8e6e-3d9b041ae3ad · outbound

This paper cites Theory of Computing , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Theory of Computing , volume=

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.384765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 6bec7716-5258-4f6b-abef-e224f3d5e82f · outbound

This paper cites Journal of the ACM (JACM) , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Journal of the ACM (JACM) , volume=

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.369601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 090b8c90-a324-4cb2-a595-26487fdfb2ff · outbound

This paper cites an unresolved cited work.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-12T20:21:50.489347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 390c6195-fcf3-4836-90f4-629c001d8eb9 · outbound

This paper cites Proceedings of the eleventh annual ACM symposium on Theory of computing , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Proceedings of the eleventh annual ACM symposium on Theory of computing , pages=

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.494525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation eca9bce5-12b7-47bb-bb7b-539045c77fda · outbound

This paper cites Journal of the ACM (JACM) , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Journal of the ACM (JACM) , volume=

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.411088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation ac76b6bb-3b16-40aa-8a85-09ad97cf7f38 · outbound

This paper cites Theory of Computing Systems , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Theory of Computing Systems , volume=

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.416150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 45f675d7-921f-4bad-b7e8-8e7e0cb65e9b · outbound

This paper cites On the optimality of.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings On the optimality of

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.433352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation a290c87a-9b41-41ec-9938-04091b366843 · outbound

This paper cites Journal of the ACM (JACM) , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Journal of the ACM (JACM) , volume=

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.467625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation f9d49a36-0c61-4bd1-a83a-430320915461 · outbound

This paper cites Discrete mathematics , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Discrete mathematics , volume=

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.459712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 15fe8804-3a67-4686-aee2-307bf157cd58 · outbound

This paper cites Proceedings of the American Mathematical society , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Proceedings of the American Mathematical society , volume=

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.438339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 4c4add8a-dd7b-44aa-ace6-94e6ac8a9138 · outbound

This paper cites The Bell System Technical Journal , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings The Bell System Technical Journal , volume=

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.446152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation d2f936b2-b986-4324-a750-18369782dfc3 · outbound

This paper cites Github survey , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Github survey , volume=

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.400555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 932383d8-ce46-41fb-b2ee-2d5a165c7931 · outbound

This paper cites Characterizing.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Characterizing

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.407436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation ed1e14a1-00d0-4490-b53b-03bb2c4182b4 · outbound

This paper cites Quarterly of applied mathematics , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Quarterly of applied mathematics , volume=

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.392585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 529b32d6-2de5-4e17-9ffb-116664881aca · outbound

This paper cites an unresolved cited work.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-12T20:21:50.396517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 0dd4959f-ea8a-4f0e-b2ab-52231e1bd84c · outbound

This paper cites Proceedings of the twentieth annual ACM symposium on Theory of computing , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Proceedings of the twentieth annual ACM symposium on Theory of computing , pages=

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.463995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 413e1212-86b9-4e69-aa40-b40635bcf93b · outbound

This paper cites computational complexity , volume=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings computational complexity , volume=

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.388705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation df5f0cdc-32c7-4014-a17c-877c00a2cb00 · outbound

This paper cites The Power of Depth 2 Circuits over Algebras , booktitle =.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings The Power of Depth 2 Circuits over Algebras , booktitle =

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:21:18.535935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation ae8e5c14-4f59-4799-9989-16f542221538 · outbound

This paper cites an unresolved cited work.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-05-12T03:21:18.537826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation dc03b8ca-dda6-41f7-93b6-16a3df2e622b · outbound

This paper cites Electron.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings Electron

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.478420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 2a17ee6f-9533-40e0-8b94-7878c2732c93 · outbound

This paper cites International symposium on mathematical foundations of computer science , pages=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings International symposium on mathematical foundations of computer science , pages=

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.381311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 2ae80ebd-b890-4e8e-b9b8-197f9ef64596 · outbound

This paper cites 2025 , school=.

VP, VNP and Algebraic Branching Programs over Min-Plus Semirings 2025 , school=

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:21:50.403637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Pith citing papers

No inbound Pith citation observations are available.