Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T10:33:48.398849Z
Paper Citation Record · LEDGER
On sums of $\mathscr{P}$-free forms under mis\`ere play
As of 7 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2506.05257.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
15 of 15 outbound references displayed
- verified exact2
- verified fuzzy9
- unresolved2
- parse uncertain0
- malformed identifier1
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 40fe61bb-14f7-46cc-af1c-431b1d1b0105 · outbound
This paper cites Taylor & Francis, London, England,2nd edition, January2023.
On sums of $\mathscr{P}$-free forms under mis\`ere play Taylor & Francis, London, England,2nd edition, January2023
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:52.736657Z
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 7d0bee02-4e89-434c-9b6b-bb30bf044f9e · outbound
This paper cites Invertibility in the misère multiverse,.
On sums of $\mathscr{P}$-free forms under mis\`ere play Invertibility in the misère multiverse,
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:52.445058Z
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 2642a1b5-2296-4a74-914a-fc612b010e14 · outbound
This paper cites Davies, Neil A.
On sums of $\mathscr{P}$-free forms under mis\`ere play Davies, Neil A
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:52.166777Z
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 ac530703-8f6f-46a6-aa0d-72a8cb8bc505 · outbound
This paper cites Davies and Rebecca Milley.
On sums of $\mathscr{P}$-free forms under mis\`ere play Davies and Rebecca Milley
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:51.885918Z
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 3ae2f87d-6dfd-44a8-b802-f7f9ecbdd777 · outbound
This paper cites Nowakowski, and Carlos Pereira dos Santos.
On sums of $\mathscr{P}$-free forms under mis\`ere play Nowakowski, and Carlos Pereira dos Santos
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:51.588997Z
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 0cfc88ed-f48e-4a97-985b-bbc17c492ccc · outbound
This paper cites Nowakowski, and Carlos P.
On sums of $\mathscr{P}$-free forms under mis\`ere play Nowakowski, and Carlos P
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:51.278247Z
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 5a407bb6-2f71-4dcc-8a31-59ab0c835b76 · outbound
This paper cites Nowakowski, and Carlos P.
On sums of $\mathscr{P}$-free forms under mis\`ere play Nowakowski, and Carlos P
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:50.976196Z
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 4d72608e-4bef-48f8-b8d7-8d2565b784e0 · outbound
This paper cites an unresolved cited work.
On sums of $\mathscr{P}$-free forms under mis\`ere play Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T10:33:50.719799Z
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 42383774-f4db-4a3d-99c9-b55262e43c78 · outbound
This paper cites Partizan Kayles and misère invertibility.Integers, 15:Paper No.
On sums of $\mathscr{P}$-free forms under mis\`ere play Partizan Kayles and misère invertibility.Integers, 15:Paper No
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:50.459501Z
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 de0b855d-f2a2-4aed-8862-f77781e1bcc1 · outbound
This paper cites The invertible elements of the monoid of dead-ending misère games.Discrete Math.,345(12):Paper No.113084,13,2022.doi:10.1016/j.disc.2022.113084.
On sums of $\mathscr{P}$-free forms under mis\`ere play The invertible elements of the monoid of dead-ending misère games.Discrete Math.,345(12):Paper No.113084,13,2022.doi:10.1016/j.disc.2022.113084
Reference 10
- Resolution
- metadata mismatch
- raw_fallback, observed 2026-08-07T10:33:49.054826Z
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 90f50219-7996-474e-b877-cda380b4f1cf · outbound
This paper cites Plambeck.
On sums of $\mathscr{P}$-free forms under mis\`ere play Plambeck
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T10:33:50.161861Z
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 abcf05e2-7394-4a95-b7b7-ea61319b1852 · outbound
This paper cites Plambeck and Aaron N.
On sums of $\mathscr{P}$-free forms under mis\`ere play Plambeck and Aaron N
Reference 12
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-07T10:33:49.872673Z
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 e95f6779-3165-4665-9459-26a22750d9a0 · outbound
This paper cites Siegel.Combinatorial game theory, volume146ofGraduate Studies in Mathematics.
On sums of $\mathscr{P}$-free forms under mis\`ere play Siegel.Combinatorial game theory, volume146ofGraduate Studies in Mathematics
Reference 13
- Resolution
- verified exact
- doi, observed 2026-08-07T10:33:48.639887Z
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 21ab3594-33a2-41c0-80db-b4276d16e84a · outbound
This paper cites an unresolved cited work.
On sums of $\mathscr{P}$-free forms under mis\`ere play Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T10:33:49.618834Z
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 2105d828-f080-4af1-96b5-8fe7b8fdd05e · outbound
This paper cites Invertibility in the mis\`ere multiverse.
On sums of $\mathscr{P}$-free forms under mis\`ere play Invertibility in the mis\`ere multiverse
Reference 2024
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T10:33:49.329367Z
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.