Paper Citation Record · LEDGER

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations

As of 15 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2506.23404.

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

pith.paper-citation-record.v1
2506.23404 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:53:02.514185Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

33 of 33 outbound references displayed

verified exact0
verified fuzzy23
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5f3c383f-581b-4b8b-95cc-d52403e86220 · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:08.491509Z

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 9d9d6a38-b497-4b54-b0ac-8df9f0fc1e95 · outbound

This paper cites Antonelli, A.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Antonelli, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:08.344697Z

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 9d9d1009-c1fb-42c3-bc78-48e8b8f19d2a · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:08.151921Z

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 c438b29d-361a-4b49-a110-f9e77110c691 · outbound

This paper cites Barrington, N.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Barrington, N

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:08.004498Z

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 7dc81c4d-0042-4551-9155-f58c997f08a9 · outbound

This paper cites Bellantoni and S.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Bellantoni and S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:07.821912Z

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 0c32cd89-47b3-4085-b9e3-10546102a502 · outbound

This paper cites Blanc and O.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Blanc and O

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:07.673703Z

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 f8f5eed8-5d4b-498d-84a1-83cc0d0c3445 · outbound

This paper cites Blanc and O.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Blanc and O

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:07.463709Z

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 eea521e8-60a7-473f-904b-8db8df279c9d · outbound

This paper cites Bonfante, R.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Bonfante, R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:07.134325Z

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 840b475d-3a47-4a00-8ec6-038472a0a318 · outbound

This paper cites Bournez and A.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Bournez and A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:06.791546Z

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 459a650d-a833-4703-9db3-518532d72d8c · outbound

This paper cites Bournez and A.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Bournez and A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:06.518675Z

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 0fc7bf3b-94a5-498d-b5c8-9a96ddbddd1e · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T21:53:00.644657Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fda36f0e-679a-4e58-af6c-e558bcd54928 · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:06.182588Z

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 c6f751a9-6ff7-4e50-9b9d-7469418e4348 · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:05.894284Z

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 4a150e43-b6da-4f08-b2c4-18f7347a9fb1 · outbound

This paper cites Clote and E.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Clote and E

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:05.706132Z

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 c4c6dd33-3716-4d5f-b06d-0eac9ad3358e · outbound

This paper cites Clote and G.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Clote and G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:05.526788Z

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 5da65edf-c58a-4113-b807-51d31e2ca87d · outbound

This paper cites Clote and G.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Clote and G

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:05.267768Z

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 8a9f0891-f3d6-49f3-9204-5a1c9f286545 · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:04.929865Z

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 6c24e841-9268-4a5e-ba6e-bb9d0887e492 · outbound

This paper cites Compton and C.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Compton and C

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:04.649509Z

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 46e6194c-573c-4310-8aca-765a366a0790 · outbound

This paper cites Cook and T.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Cook and T

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T21:53:01.348788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7523d09f-1e0c-4291-8afc-365b6222709f · outbound

This paper cites Cook and P.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Cook and P

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:04.300484Z

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 015b014e-6d63-4835-960f-2ab3bfa7b88d · outbound

This paper cites Durand, A.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Durand, A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:04.123233Z

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 74a9bb47-7440-4ca7-a9c9-4a571d23aa37 · outbound

This paper cites Furst, J.B.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Furst, J.B

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:04.003351Z

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 f472f125-49c7-412a-bf4f-eec58dec7a75 · outbound

This paper cites Gurevich and H.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Gurevich and H

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.860765Z

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 d22c0d88-85c7-43f3-a094-af66832156db · outbound

This paper cites Hesse, E.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Hesse, E

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.760058Z

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 ab6c2ae2-a155-431b-9df1-8703e4f75553 · outbound

This paper cites Immerman.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Immerman

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.649896Z

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 be244de9-35c3-454e-ae0f-0384d20fc469 · outbound

This paper cites Johannsen.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Johannsen

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.544124Z

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 f437cce3-6ac9-4f39-be58-240c7c246dfc · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:03.440285Z

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 55853f33-782b-452b-9ae6-6f7eff19f251 · outbound

This paper cites Leivant and J.-Y.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Leivant and J.-Y

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.324099Z

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 421fc301-d191-4ca5-a723-5970f7241ac6 · outbound

This paper cites Leivant and Y.-Y.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Leivant and Y.-Y

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:03.203065Z

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 4020939f-fed5-4a7f-b4d1-15bd14051b52 · outbound

This paper cites an unresolved cited work.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:53:03.061221Z

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 eae26a63-9d67-49b8-b06a-b1b7429b04b5 · outbound

This paper cites Lower bounds on the size of bounded depth circuits over a complete basis with logical addition.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Lower bounds on the size of bounded depth circuits over a complete basis with logical addition

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:02.945476Z

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 59bb1b55-234e-446b-b980-0c6a3d4de81e · outbound

This paper cites Algebraic methods in the theory of lower bounds for boolean circuit complexity.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations Algebraic methods in the theory of lower bounds for boolean circuit complexity

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T21:53:02.436668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a63caad8-1725-40ae-9c72-3cf04a3c0a05 · outbound

This paper cites iterated multiplication.

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations iterated multiplication

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:53:02.815578Z

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.

Pith citing papers

No inbound Pith citation observations are available.