Paper Citation Record · LEDGER

Low Sets and Closure Properties of Counting Function Classes

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2507.04110.

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

pith.paper-citation-record.v1
2507.04110 v5

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:17:28.057284Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

34 of 34 outbound references displayed

verified exact0
verified fuzzy28
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1010954f-ddee-41fe-861a-75e30b309ee2 · outbound

This paper cites an unresolved cited work.

Low Sets and Closure Properties of Counting Function Classes Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:33.750127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e98064e0-14d8-4139-96db-d98f12445a0c · outbound

This paper cites In: Annual Confer- ence on Theory and Applications of Models of Computation.

Low Sets and Closure Properties of Counting Function Classes In: Annual Confer- ence on Theory and Applications of Models of Computation

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.735848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cb09ead7-daac-4c1e-86bb-8887959f741f · outbound

This paper cites SIAM Journal on Computing13(3), 461–487 (1984).

Low Sets and Closure Properties of Counting Function Classes SIAM Journal on Computing13(3), 461–487 (1984)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.720891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 05ff38fd-f7eb-49ac-ac87-88429473c4e4 · outbound

This paper cites Journal of Computer and System Sciences30(3), 395–413 (1985).

Low Sets and Closure Properties of Counting Function Classes Journal of Computer and System Sciences30(3), 395–413 (1985)

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.707195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1a902816-e6de-4183-b6c4-97973e491452 · outbound

This paper cites In: Logic, automata, and computational complexity: The works of Stephen A.

Low Sets and Closure Properties of Counting Function Classes In: Logic, automata, and computational complexity: The works of Stephen A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.693135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 94a6a0a1-5ef8-4a18-8013-f2b8b15154de · outbound

This paper cites Journal of Computer and System Sciences48(1), 116–148 (1994).

Low Sets and Closure Properties of Counting Function Classes Journal of Computer and System Sciences48(1), 116–148 (1994)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.678909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a306b3b4-1223-4316-a0d5-e12b617b58e7 · outbound

This paper cites In: Hemaspaandra, L., Selman, A.

Low Sets and Closure Properties of Counting Function Classes In: Hemaspaandra, L., Selman, A

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.663605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 255b468c-5da7-47d3-83a0-e7222cba3701 · outbound

This paper cites SIAM Journal on Computing6(4), 675–695 (1977).

Low Sets and Closure Properties of Counting Function Classes SIAM Journal on Computing6(4), 675–695 (1977)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.464792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 422f4327-918a-4811-952e-0d7213c2b946 · outbound

This paper cites In: 1991 Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

Low Sets and Closure Properties of Counting Function Classes In: 1991 Proceedings of the Sixth Annual Structure in Complexity Theory Conference

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:33.207986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dc2b3bd7-bb80-43ae-9e88-a007cad0cb46 · outbound

This paper cites SIAM Journal on Computing36(5), 1264–1300 (2006).

Low Sets and Closure Properties of Counting Function Classes SIAM Journal on Computing36(5), 1264–1300 (2006)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:32.928721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5f45dba3-f9b7-4da1-9f27-4fde7dd624cc · outbound

This paper cites ACM SIGACT News26(1), 2–13 (1995).

Low Sets and Closure Properties of Counting Function Classes ACM SIGACT News26(1), 2–13 (1995)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:32.681467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 13be5110-4e4d-40a2-8998-1beceba21ce8 · outbound

This paper cites International Journal of Foundations of Computer Science11(02), 315–342 (2000).

Low Sets and Closure Properties of Counting Function Classes International Journal of Foundations of Computer Science11(02), 315–342 (2000)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:32.408969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dfbda435-a1a1-4428-8731-e2c50db33d25 · outbound

This paper cites an unresolved cited work.

Low Sets and Closure Properties of Counting Function Classes Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:32.176067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ad7c5765-33b6-4e56-bfc7-44791a301e73 · outbound

This paper cites Closure Properties and Characterizations of TotP.

Low Sets and Closure Properties of Counting Function Classes Closure Properties and Characterizations of TotP

Reference 14

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T20:17:28.248809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 140e3d3a-973c-4243-835b-13862dda59fb · outbound

This paper cites In: Advances in Informatics: 8th Panhellenic Conference on Informatics, PCI 2001 Nicosia, Cyprus, November 8–10, 2001 Revised Selected Papers 8.

Low Sets and Closure Properties of Counting Function Classes In: Advances in Informatics: 8th Panhellenic Conference on Informatics, PCI 2001 Nicosia, Cyprus, November 8–10, 2001 Revised Selected Papers 8

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:31.924144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e5e75ba2-5a5d-4d0e-80b4-eb329c45533a · outbound

This paper cites Information Processing Letters14(1), 39–43 (1982).

Low Sets and Closure Properties of Counting Function Classes Information Processing Letters14(1), 39–43 (1982)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:31.693895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4fa62984-aa8a-4b98-9d89-7ba22e06fd65 · outbound

This paper cites Acta Infor- matica26(4), 363–379 (1989).

Low Sets and Closure Properties of Counting Function Classes Acta Infor- matica26(4), 363–379 (1989)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:31.566952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8be925b1-dbc5-40df-87f0-ed3af66f1e99 · outbound

This paper cites Birkhäuser Boston, MA (1993).

Low Sets and Closure Properties of Counting Function Classes Birkhäuser Boston, MA (1993)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:31.425297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0ddf6306-47b7-491e-b099-06b1ab161f1b · outbound

This paper cites Information Processing Letters 72(5-6), 197–203 (1999).

Low Sets and Closure Properties of Counting Function Classes Information Processing Letters 72(5-6), 197–203 (1999)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:31.283224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 971fac74-9321-4c5d-94be-53c8ed887b9c · outbound

This paper cites an unresolved cited work.

Low Sets and Closure Properties of Counting Function Classes Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:31.137693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 94c88a4a-f88c-4360-aef4-d408ed666963 · outbound

This paper cites an unresolved cited work.

Low Sets and Closure Properties of Counting Function Classes Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:30.981738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4b527d7c-3059-414f-9161-c4837fa9fd20 · outbound

This paper cites Infor- mation Processing Letters51(1), 7–10 (1994).

Low Sets and Closure Properties of Counting Function Classes Infor- mation Processing Letters51(1), 7–10 (1994)

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:30.756974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation da5e4cd2-beab-48d1-b8f5-1fdd3b1a1bfa · outbound

This paper cites Journal of Computer and System Sciences46(3), 295–325 (1993).

Low Sets and Closure Properties of Counting Function Classes Journal of Computer and System Sciences46(3), 295–325 (1993)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:30.563353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9d333024-2b47-4bf7-b55c-85b1cd1c3a60 · outbound

This paper cites Journal of Computer and System Sciences27(1), 14–28 (1983).

Low Sets and Closure Properties of Counting Function Classes Journal of Computer and System Sciences27(1), 14–28 (1983)

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:30.385879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 37034760-5b7f-475e-af5a-b328168f3517 · outbound

This paper cites Journal of Computer and System Sciences48(2), 357–381 (1994).

Low Sets and Closure Properties of Counting Function Classes Journal of Computer and System Sciences48(2), 357–381 (1994)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:30.204739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 41b7b505-d0ba-4bc2-9da6-197989cf8622 · outbound

This paper cites PhD thesis, Cornell University, Ithaca (1975).

Low Sets and Closure Properties of Counting Function Classes PhD thesis, Cornell University, Ithaca (1975)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:30.013446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7e40c797-9a40-4d81-89ed-cbd6d56ea5a1 · outbound

This paper cites computa- tional complexity4, 242–261 (1994).

Low Sets and Closure Properties of Counting Function Classes computa- tional complexity4, 242–261 (1994)

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:29.776606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fd8ddfa5-ee94-4dd8-a82e-114ec702cc45 · outbound

This paper cites SIAM Journal on Com- puting20(5), 865–877 (1991).

Low Sets and Closure Properties of Counting Function Classes SIAM Journal on Com- puting20(5), 865–877 (1991)

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:29.608407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b4afdb4c-523b-43be-9ad3-c74ddf09b0a3 · outbound

This paper cites Theoretical Computer Science100(1), 205–221 (1992).

Low Sets and Closure Properties of Counting Function Classes Theoretical Computer Science100(1), 205–221 (1992)

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:29.453647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8725669c-ad12-4e75-8fa9-dcaa9b7ef5e2 · outbound

This paper cites an unresolved cited work.

Low Sets and Closure Properties of Counting Function Classes Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:29.279296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ffcb7bd0-e820-49a2-a0a9-f3e4beaa1ff2 · outbound

This paper cites Information pro- cessing letters5(1), 20–23 (1976).

Low Sets and Closure Properties of Counting Function Classes Information pro- cessing letters5(1), 20–23 (1976)

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:29.085823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e9f3d3d3-9536-40de-ac3e-38d471de52fd · outbound

This paper cites Theoretical computer science8(2), 189–201 (1979).

Low Sets and Closure Properties of Counting Function Classes Theoretical computer science8(2), 189–201 (1979)

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:28.844672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8a504a79-b68a-499b-9fda-ecc7e8ea7ac2 · outbound

This paper cites Univ., Inst.

Low Sets and Closure Properties of Counting Function Classes Univ., Inst

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:28.657236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d04ef54e-7701-4d1d-b3b2-e23ec6201302 · outbound

This paper cites Acta informatica23, 325–356 (1986).

Low Sets and Closure Properties of Counting Function Classes Acta informatica23, 325–356 (1986)

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:28.458585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.