Paper Citation Record · LEDGER

Optimal Online Bookmaking for Any Number of Outcomes

As of 21 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2506.16253.

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

pith.paper-citation-record.v1
2506.16253 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T23:57:11.237451Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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

15 of 15 outbound references displayed

verified exact1
verified fuzzy8
unresolved5
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9e851aa5-69b5-4f83-ac4b-15a64c0d48c2 · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 1

Resolution: parse uncertain; raw_fallback, observed 2026-08-06T23:57:11.581742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b63bc5b4-2ebc-4e65-8517-ba3c7090ea90 · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:57:11.562396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b6edbd1e-1e49-4cb2-aaaa-290ba32b8d87 · outbound

This paper cites They satisfy the recurrence relation: n + 1 k = n n k + n k − 1 , for n ≥ 1, k≥ 1, with base cases: 0 0 = 1, n 0 = 0 for n >0, 0 k = 0 for k >0.

Optimal Online Bookmaking for Any Number of Outcomes They satisfy the recurrence relation: n + 1 k = n n k + n k − 1 , for n ≥ 1, k≥ 1, with base cases: 0 0 = 1, n 0 = 0 for n >0, 0 k = 0 for k >0

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.543150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6292bd1c-3151-4d03-aec3-68faac09e2d3 · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:57:11.522482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a5b71adc-2f5e-4663-a177-d96638fd69d6 · outbound

This paper cites The proof of Lemma 29 is presented in Appendix B.2.

Optimal Online Bookmaking for Any Number of Outcomes The proof of Lemma 29 is presented in Appendix B.2

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.503276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2c29ee71-bfab-4f08-bdf5-90e04f633a86 · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:57:11.484310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 350a9554-d5a9-455f-ae66-4cde2dca6041 · outbound

This paper cites , im} the expression ∂mvI stands for ∂v(i1).

Optimal Online Bookmaking for Any Number of Outcomes , im} the expression ∂mvI stands for ∂v(i1)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.466095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6e3265b7-4a81-4ffc-a284-f58a398f5790 · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:57:11.444982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e78c7d59-53b6-4f95-b5ff-a3e940cf2d5e · outbound

This paper cites an unresolved cited work.

Optimal Online Bookmaking for Any Number of Outcomes Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T23:57:11.424393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6e639152-29d9-49af-a619-2cc1f88672b6 · outbound

This paper cites These coefficients can be precomputed before the algorithm begins.

Optimal Online Bookmaking for Any Number of Outcomes These coefficients can be precomputed before the algorithm begins

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.401306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 05ff32cd-8581-4a78-ad74-747dd85ac4d6 · outbound

This paper cites ,DH−1,K−1(v\K) in O(K2).

Optimal Online Bookmaking for Any Number of Outcomes ,DH−1,K−1(v\K) in O(K2)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.380438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c1c845e1-8dfa-4beb-8bea-9b43c6838fca · outbound

This paper cites Hence DH,K is itself a multivariate polynomial, and therefore C∞ on RK.

Optimal Online Bookmaking for Any Number of Outcomes Hence DH,K is itself a multivariate polynomial, and therefore C∞ on RK

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.357851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7098e8ad-042f-48b1-a83f-ef1adebbc180 · outbound

This paper cites • Base case (m = 1): Let k ∈ [K] be some index.

Optimal Online Bookmaking for Any Number of Outcomes • Base case (m = 1): Let k ∈ [K] be some index

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.337233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 771b590f-3c9d-4585-b91d-2767645287cc · outbound

This paper cites By Lemma 36.2 it holds that ∂m ∂v(k)m DH,K (v) = ∂m−1 ∂v(k)m−1 DH,K−1 v\k = 0.

Optimal Online Bookmaking for Any Number of Outcomes By Lemma 36.2 it holds that ∂m ∂v(k)m DH,K (v) = ∂m−1 ∂v(k)m−1 DH,K−1 v\k = 0

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:57:11.318165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f753cb4c-7334-45b4-b3c3-4b6aa9314950 · outbound

This paper cites Optimal Online Bookmaking for Binary Games.

Optimal Online Bookmaking for Any Number of Outcomes Optimal Online Bookmaking for Binary Games

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-06T23:57:11.296432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

No inbound Pith citation observations are available.