Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T00:42:52.421809Z
Paper Citation Record · LEDGER
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
As of 14 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 6 inbound Pith citation observations for arXiv:2506.13242.
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 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T22:23:31.332270Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T16:38:39.962227Z
Reference resolution
15 of 15 outbound references displayed
- verified exact1
- verified fuzzy6
- unresolved7
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 95b12c03-a137-4507-adc2-ce00d353fc2b · outbound
This paper cites PLinOpt, a collection of C++ routines handling linear & bilinear programs, January 2024.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications PLinOpt, a collection of C++ routines handling linear & bilinear programs, January 2024
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.854821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f5e9928d-ee5a-4bcc-8f02-3847717e3940 · outbound
This paper cites Strassen’s algorithm is not op- timally accurate.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Strassen’s algorithm is not op- timally accurate
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.836808Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9cbeac1b-3fb5-4964-a7ca-472a5205647d · outbound
This paper cites A non-commutative algorithm for multiplying a 3 × 4 matrix by a 4 × 7 matrix using 63 non-complex multiplications.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications A non-commutative algorithm for multiplying a 3 × 4 matrix by a 4 × 7 matrix using 63 non-complex multiplications
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.820694Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b1f19e76-2c44-41b4-ac6f-45e25fe8de0f · outbound
This paper cites Towards automated generation of fast and accurate algorithms for recursive matrix multiplication.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.804433Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ea8c4a05-3d82-441c-846d-ab0afebbae67 · outbound
This paper cites an unresolved cited work.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Unresolved cited work
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.377566Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 81d63498-295f-4460-95dd-b327bfa82a82 · outbound
This paper cites On varieties of optimal algorithms for the computation of bilinear mappings I.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications On varieties of optimal algorithms for the computation of bilinear mappings I
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.788403Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3d022f82-07c8-45b3-8bbd-3c4080361caf · outbound
This paper cites On varieties of optimal algorithms for the computation of bilinear mappings II.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications On varieties of optimal algorithms for the computation of bilinear mappings II
Reference 7
- Resolution
- verified exact
- doi, observed 2026-08-07T00:42:52.496245Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 83f9d5f1-4ff7-4d09-8053-fe15b611072d · outbound
This paper cites Finding complex-valued solutions of Brent equations using nonlinear least squares.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Finding complex-valued solutions of Brent equations using nonlinear least squares
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.397587Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cb511e1e-05a4-4a5a-a407-d868656ee7f2 · outbound
This paper cites Matrix multiplication, a little faster.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Matrix multiplication, a little faster
Reference 9
- Resolution
- metadata mismatch
- raw_fallback, observed 2026-08-07T00:42:52.679006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fce3b96f-d7c8-4d60-8691-ed0ba08c0d12 · outbound
This paper cites Landsberg.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Landsberg
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.407062Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 53ac997a-3a7d-4293-94e0-57cf49bcb070 · outbound
This paper cites AlphaEvolve: A coding agent for scientific and algorithmic discovery.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications AlphaEvolve: A coding agent for scientific and algorithmic discovery
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.411937Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59993721-9b44-401a-838f-8338eb7f8084 · outbound
This paper cites Fast matrix multiplication database [online].
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Fast matrix multiplication database [online]
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T00:42:52.771617Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9a10d3f6-f113-4126-90bf-19585442cf16 · outbound
This paper cites Gaussian elimination is not optimal.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications Gaussian elimination is not optimal
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.421809Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5ea34c45-96fa-44ed-bec8-60d8c8718a54 · outbound
This paper cites (cited in sec.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications (cited in sec
Reference 1978
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.387234Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5ef9ad16-c1d0-41c6-8edc-2204ab2344f1 · outbound
This paper cites URL: https://hal.science/hal-04441653, doi:10.1145/3666000.3669697.
A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications URL: https://hal.science/hal-04441653, doi:10.1145/3666000.3669697
Reference 2024
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T00:42:52.362973Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation a51cb1e6-4996-4494-af38-1de95f14b08c · inbound
Exploring Commutative Matrix Multiplication Schemes via Flip Graphs cites this paper.
Exploring Commutative Matrix Multiplication Schemes via Flip Graphs A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T22:23:31.332270Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e84a04ef-0eb1-41b0-a75d-1f4a1c2cd0f2 · inbound
Towards Faster Feasible Matrix Multiplication by Trilinear Aggregation cites this paper.
Towards Faster Feasible Matrix Multiplication by Trilinear Aggregation A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T05:41:53.889326Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16ec32be-fc9c-4098-acaa-38dff32598c8 · inbound
Exploiting the Structure in Tensor Decompositions for Matrix Multiplication cites this paper.
Exploiting the Structure in Tensor Decompositions for Matrix Multiplication A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 10
- Resolution
- verified exact
- arxiv_id, observed 2026-07-28T03:23:17.841006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 455063b8-b725-44e4-b286-15cebf86f8fd · inbound
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications cites this paper.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.483002Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4c89084-13f7-4361-be47-16d0c2bd88b0 · inbound
A catalog of fast matrix multiplication algorithms with frontier-closure search cites this paper.
A catalog of fast matrix multiplication algorithms with frontier-closure search A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-07-28T03:23:17.841006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a469b146-4cfb-44d9-be71-f7cffd686ffe · inbound
Substitution and quotient of the isotropy group action cites this paper.
Substitution and quotient of the isotropy group action A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T00:18:33.365532Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.