Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T12:24:27.643404Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:1908.06964.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T12:24:27.643404Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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
60 of 60 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 4cf26c10-4fab-426a-95ba-9498a24747dd · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Mathematics research page,
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f66d48c7-a872-4ee5-a049-322a60888208 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Prime and prejudice: Primality testing under adversarial conditions,
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation af9aafe6-424f-485f-baad-3e037741bcd4 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Euler’s criterion,
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 834103c8-2cd2-4759-bd1b-f75ca701c145 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation eec6f494-97a0-40e6-beae-10d4af2fd496 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Shoup,A computational introduction to number theory and algebra
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 81886281-6ccc-4540-9d39-01a3339492ba · outbound
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 31b4a70e-654e-4e69-859a-c0ce1e89d2ef · outbound
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ca789260-ba75-4f98-9407-fcf4ad76a50f · outbound
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b1acdbea-c6cd-4d68-be09-8217abd5331d · outbound
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 848d6f47-f026-42c3-9cbf-39fdafec45aa · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts PRIMES is in P,
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4a08103d-1355-43d5-96f3-716c49f3adcc · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation afb0ea61-378f-4779-9f09-78e7cb0bfb6a · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The distribution of quadratic and higher residues,
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 980b3a6c-3f0a-4b87-aecf-c1b4a98a0a7d · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The least quadratic non residue,
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f545b8e4-4535-44a0-b99a-3d44ba678425 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The distribution of quadratic residues and non-residues,
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e2d7b16a-1b68-4391-aaa4-5a46aa967917 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Lower bounds for least quadratic non-residues,
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b7ac022a-ff90-426b-a167-93a6d03d9551 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Constructing nonresidues in finite fields and the Extended Riemann Hypothesis,
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c193fe4a-bff4-4a37-ac61-d6ccd680aaf1 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On the distribution of quadratic residues and nonresidues modulo a prime number,
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e7c72aea-e80a-4966-af97-c7b356cc0251 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Quadratic nonresidues and applications,
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a0ae319e-7524-4b69-833f-762dfca10df4 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Complexity of Computing Quadratic Nonresidues
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bdea8dd6-ea53-46b4-863a-f61d9c822888 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On taking square roots and constructing quadratic nonresidues over finite fields,
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 56dbab5d-3824-4551-b3bd-f80b9deb51cd · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The least quadratic nonresidue, and the square root barrier,
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d37623a2-f276-4afe-9bb4-751085e3fe47 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On taking square roots without quadratic nonresidues over finite fields,
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 26843eca-152c-4caf-bdaf-5943fa5a44ef · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Conditional bounds for the least quadratic non- residue and related problems,
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 604f9364-9385-4d8f-be50-804c48074b15 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The elliott–halberstam conjecture implies the vinogradov least quadratic nonresidue conjecture,
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c39d9251-f33e-44df-88e6-49a2356a4c38 · outbound
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation abfea5bf-f2e6-4c96-a79c-3aa1c42a4878 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Primality testing with gaussian periods,
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d90cf7dc-700d-4315-a10d-f71468003d41 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Primality testing with gaussian periods,
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 551c3434-ae76-45fd-ad72-670286ea1ef6 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Proving primality in essentially quartic random time,
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 32f114a2-4834-42c9-bcd8-2ca08ec1e4a3 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On the complexity of multiplication in finite fields,
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ec38d332-e870-4ba6-9f19-299a2c4b2e33 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Hensel lifting and polynomial division,
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 90a205b9-38f2-4c84-8479-dbdca198a901 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Sparse polynomial multiplication and division in maple 14,
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5c88916b-b890-4b99-926b-6a4ebdfaa6f7 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts On newton–raphson iteration for multiplicative inverses modulo prime powers,
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8f37a351-3e1d-430f-997f-6e524f92d909 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Faster polynomial multiplication over finite fields using cyclotomic coefficient rings,
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 795e2cdd-71dd-45eb-be9a-d6932339b0e2 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Carmichael numbers,
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 22bfd9d0-80ed-4e66-8691-d77ed234f32f · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Strong pseudoprime,
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 290dd393-832a-4699-93e5-bfddc3ebb664 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Miller–Rabin primality test,
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b3490ed3-1949-4ec9-bbeb-42cd0f2561ee · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 69af1a07-bcb5-4213-931e-4d55b265a9f9 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Cyclotomic polynomial,
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 384ad439-a7b0-4435-879d-f9e0dede56bb · outbound
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6285a33a-a92a-4192-a1e7-7ca400bc64cc · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Parhami, Computer Arithmetic Algorithms and Hardware Designs
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 922e8011-0007-4659-9d18-6142d1f12473 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts New distributed algorithms for fast sign detection in residue number systems (rns),
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 078db4a6-bcf3-49f4-8a36-07867e5217c8 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Bertrand’s postulate,
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 12d5ec5d-e83f-4c19-8fdf-3b551cb9388b · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Prime–counting function,
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 52a0117b-5041-431d-82bd-0288c6063686 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Baillie–PSW primality test,
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2e77c9df-1819-4170-961b-aade6b0049cc · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Quadratic residue,
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 71842e25-8e26-44c2-9c08-d1a1cf1bfb56 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Carmichael numbers in number rings,
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fb68eaf1-1c9b-48d1-bdbf-8d6a3d234f13 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Constructing carmichael numbers which are strong pseudoprimes to several bases,
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 31df7f33-a9d5-4a0e-a940-96a00b1561b9 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts The carmichael numbers up to 1021,
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation afd3e5a0-e9c4-4f45-953f-77a3d7b7191e · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts PRP Records, Probable Primes Top 10000 ,
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a667b6bf-b1ce-4e39-b960-2738060aa37e · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts A014233 : Smallest odd number for which Miller-Rabin primality test on bases≤n-th prime does not reveal compositeness
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f99c5b10-bb50-4290-8948-217ab5f794e0 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts A001262 : Strong pseudoprimes to base 2,
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation eea7f230-e2dd-4f73-bb90-28bd8176dfd2 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Higher-order Carmichael numbers,
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 73789536-1f43-4995-a25e-c96181a73cab · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Higher-order carmichael numbers,
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6b55cf2a-c6ef-42c6-ab6d-c8be1cba331b · outbound
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b72f67b5-c881-437f-a718-52ae800ddd6d · outbound
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation df189629-dd93-4830-b7be-97e84c6bece2 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Mersenne prime,
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a1d86ce6-315c-49a4-83ce-83f7236cd096 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Lucas–Lehmer primality test,
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8b7ac6e2-053b-4562-bfba-eaf8b88d1534 · outbound
PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts Unresolved cited work
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fbba230a-d446-4f6f-90a7-34bdee89472f · outbound
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 33321de1-54ea-4f23-8207-82a4ba37dbc1 · outbound
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
No inbound Pith citation observations are available.