Paper Citation Record · LEDGER

Algorithms for the Multiplication Table Problem

As of 23 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:1908.04251.

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

pith.paper-citation-record.v1
1908.04251 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:55:49.745702Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

28 of 28 outbound references displayed

verified exact0
verified fuzzy16
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 88795ae8-2742-4b75-845b-ccb1beeef11b · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:50.129002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b1b6233b-b809-43e9-aae9-94bc105411e0 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:50.117652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 607072d8-ef02-46e6-b344-107a17964e92 · outbound

This paper cites Balazard, J.

Algorithms for the Multiplication Table Problem Balazard, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.106416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dd4052c1-206a-4120-a43d-04c90f5a44a3 · outbound

This paper cites Bernstein, Detecting perfect powers in essentially linear time , Math.

Algorithms for the Multiplication Table Problem Bernstein, Detecting perfect powers in essentially linear time , Math

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.094687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b31d24bb-b9b8-45c3-a656-ee5183a25fa3 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:50.082458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d0e43549-d6af-4178-9d21-2c5c93a5db5b · outbound

This paper cites Brent, The multiplication table, and random factored integers , slides from a semi- nar given at Hong Kong Baptist University, Hong Kong, Feb.

Algorithms for the Multiplication Table Problem Brent, The multiplication table, and random factored integers , slides from a semi- nar given at Hong Kong Baptist University, Hong Kong, Feb

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.070104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a9873df9-4a01-4e52-9491-66ca8615db0d · outbound

This paper cites Brent, Algorithms for the multiplication table , slides from a seminar given at CARMA, Newcastle, NSW, May 29, 2018.

Algorithms for the Multiplication Table Problem Brent, Algorithms for the multiplication table , slides from a seminar given at CARMA, Newcastle, NSW, May 29, 2018

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.056594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 78602a25-15cf-48e4-909e-5c9e4d39201b · outbound

This paper cites Brent and H.

Algorithms for the Multiplication Table Problem Brent and H

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.043896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8ba64c94-f08f-4667-8a2f-4aed300644d3 · outbound

This paper cites Burthe, Jr., Further investigations with the strong probable prime test , Math.

Algorithms for the Multiplication Table Problem Burthe, Jr., Further investigations with the strong probable prime test , Math

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:50.030698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bb3f0efb-4160-4ac5-a1ae-63cfe917651f · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:50.018382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1d1c0d35-28a8-4b42-a896-00399c6bac5a · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:50.005951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 71bbe7dc-2ada-4464-9962-1ddc7f77108c · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.991367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c760aec2-c1f0-47e1-a810-f52db644f327 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.978741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f60ccc8e-69fa-4405-89b8-64f1e8cb07b3 · outbound

This paper cites Tenenbaum, Sur la structure de la suite des diviseurs d’un entier , Ann.

Algorithms for the Multiplication Table Problem Tenenbaum, Sur la structure de la suite des diviseurs d’un entier , Ann

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.964947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7e82640b-5c18-444c-9f7c-061a34126a97 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.950926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aefbabcb-0c7e-4178-81bc-7ac39a9694ad · outbound

This paper cites Lecture Notes, vol.

Algorithms for the Multiplication Table Problem Lecture Notes, vol

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.938763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 31c88153-6b48-4adb-a581-1fb215f5a22e · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.925615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7ce6d2a3-15d4-4be3-a9b3-2d00e65c5ae2 · outbound

This paper cites Helfgott, An improved sieve of Eratosthenes , Math.

Algorithms for the Multiplication Table Problem Helfgott, An improved sieve of Eratosthenes , Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.910966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0f224f63-ae00-48d7-b069-960922e53457 · outbound

This paper cites Hennessy and David A.

Algorithms for the Multiplication Table Problem Hennessy and David A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.899050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d24212ef-28f4-42cd-8ddf-0c87ff8c8503 · outbound

This paper cites Cryptology 16 (2003), 287–289.

Algorithms for the Multiplication Table Problem Cryptology 16 (2003), 287–289

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.887143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 78b49dcb-c166-4756-ac86-06be0a107996 · outbound

This paper cites Khinchin, ¨Uber einen Satz der Wahrscheinlichkeitsrechnung , Fundamenta Mathematicae 6 (1924), 9–20 (in German).

Algorithms for the Multiplication Table Problem Khinchin, ¨Uber einen Satz der Wahrscheinlichkeitsrechnung , Fundamenta Mathematicae 6 (1924), 9–20 (in German)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.875800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fe3fc0b0-69ae-4292-8193-b773d7de3c83 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.863963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aee8ce9c-6403-4f41-abff-cbca25163947 · outbound

This paper cites Lichtman and Carl Pomerance, Improved error bounds for the Fermat primality test on random inputs , Math.

Algorithms for the Multiplication Table Problem Lichtman and Carl Pomerance, Improved error bounds for the Fermat primality test on random inputs , Math

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.850129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dbf041db-7372-4d2d-a43f-ee49b336284a · outbound

This paper cites Miller, Riemann ’s hypothesis and tests for primality, J.

Algorithms for the Multiplication Table Problem Miller, Riemann ’s hypothesis and tests for primality, J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.836410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aa319a8d-309f-4ca1-8c25-2ea36db55816 · outbound

This paper cites Norton On the number of restricted prime factors of an integer, I , Illinois J.

Algorithms for the Multiplication Table Problem Norton On the number of restricted prime factors of an integer, I , Illinois J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.822096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 00fc04f6-6991-4fb8-9627-d0ddb9117260 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.807594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 272766f0-8c50-43df-b562-2c9fe1388568 · outbound

This paper cites an unresolved cited work.

Algorithms for the Multiplication Table Problem Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:55:49.794111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d4c4fd54-939c-4b9a-a15a-db9a853af72e · outbound

This paper cites Rabin, Probabilistic algorithm for testing primality , J.

Algorithms for the Multiplication Table Problem Rabin, Probabilistic algorithm for testing primality , J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:55:49.780496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.