Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-02T17:55:40.395000Z
Paper Citation Record · LEDGER
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications
As of 14 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2603.18699.
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
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
22 of 22 outbound references displayed
- verified exact4
- verified fuzzy0
- unresolved16
- parse uncertain0
- malformed identifier2
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation af3bf1e9-f6bb-4e71-a7db-1c0fa0ba48fa · outbound
This paper cites Im- proving the numerical stability of fast matrix multiplication.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Im- proving the numerical stability of fast matrix multiplication
Reference 1
- Resolution
- verified exact
- doi, observed 2026-08-02T17:58:29.011596Z
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 30943d1b-559d-44c4-911c-61a6f382522e · outbound
This paper cites Stability of fast algorithms for matrix multiplication.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Stability of fast algorithms for matrix multiplication
Reference 2
- Resolution
- verified exact
- doi, observed 2026-08-02T17:58:28.785416Z
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 f1e4ec48-b05a-461c-be9f-5f907fc1ad31 · outbound
This paper cites Algorithms for matrix multiplication.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Algorithms for matrix multiplication
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:38.854595Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b51c524b-3220-4006-b9ed-4c03ebe9587c · outbound
This paper cites Fast matrix multipli- cation is stable.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Fast matrix multipli- cation is stable
Reference 4
- Resolution
- malformed identifier
- no resolver link, observed 2026-08-02T17:55:38.959539Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d68b0b6a-d66d-4799-a4d1-a89418b8b2fa · outbound
This paper cites PLinOpt, a collection of C++ routines handling linear & bilinear programs, January 2024.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications PLinOpt, a collection of C++ routines handling linear & bilinear programs, January 2024
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.066499Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 27cff689-4c03-4955-b689-352196cea09d · outbound
This paper cites Strassen’s algorithm is not opti- mally accurate.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Strassen’s algorithm is not opti- mally accurate
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.239520Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9629a21d-91c4-452a-bafa-f4a9fc45d242 · outbound
This paper cites FMM, accuracy of fast-matrix- multiplication algorithms, September 2025.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications FMM, accuracy of fast-matrix- multiplication algorithms, September 2025
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.407493Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 455063b8-b725-44e4-b286-15cebf86f8fd · outbound
This paper cites A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications.
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 d0db0d97-e810-4aab-996a-8589c8f5902d · outbound
This paper cites Towards automated generation of fast and accurate algorithms for recursive matrix multiplication.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.575435Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 63d0678b-7f71-4045-9b77-c772d3757522 · outbound
This paper cites On varieties of optimal algorithms for the computation of bilinear mappings I.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications On varieties of optimal algorithms for the computation of bilinear mappings I
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.641743Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cf5ab34f-6d59-40b5-a0b5-269bc35d0f03 · outbound
This paper cites Accuracy and Stability of Numerical Algorithms.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Accuracy and Stability of Numerical Algorithms
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.809160Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 63dbfbc8-e21e-4f37-a17c-19046ca07fb0 · outbound
This paper cites Finding complex-valued solutions of Brent equations using nonlinear least squares.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Finding complex-valued solutions of Brent equations using nonlinear least squares
Reference 12
- Resolution
- verified exact
- doi, observed 2026-08-02T17:58:28.011103Z
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 9a43a368-4ce3-4fed-92d3-543e7f4b66e1 · outbound
This paper cites Matrix multiplication, a little faster.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Matrix multiplication, a little faster
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.935096Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9060fcbc-a269-4aac-a1ca-7efa6d220a33 · outbound
This paper cites Geometry and complexity theory , volume 169 of Cambridge Stud- ies in Advanced Mathematics.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Geometry and complexity theory , volume 169 of Cambridge Stud- ies in Advanced Mathematics
Reference 14
- Resolution
- malformed identifier
- no resolver link, observed 2026-08-02T17:55:40.020274Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8f3feef6-736e-41fb-9a2f-50533be9ab7a · outbound
This paper cites Complex to rational fast matrix multiplication.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Complex to rational fast matrix multiplication
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:40.098159Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8725cc6e-d4a8-430b-b48a-7312dfbb4edd · outbound
This paper cites AlphaEvolve: A coding agent for scientific and algorithmic discovery.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications AlphaEvolve: A coding agent for scientific and algorithmic discovery
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:40.184295Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6ced2173-c277-41a1-848e-b59109a6cfe4 · outbound
This paper cites Alternative basis matrix multiplication is fast and stable.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Alternative basis matrix multiplication is fast and stable
Reference 17
- Resolution
- verified exact
- doi, observed 2026-08-02T17:58:27.520572Z
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 e00d7bac-7a46-4afd-8cce-4de86160e1cf · outbound
This paper cites Gaussian elimination is not optimal.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications Gaussian elimination is not optimal
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:40.294019Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8ccbf73e-b310-4527-b60e-b0de36fa9c32 · outbound
This paper cites La complexit´ e des calculs num´ eriques.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications La complexit´ e des calculs num´ eriques
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:40.349439Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7ab8217c-3a67-4862-9eb0-9f2b548cdd14 · outbound
This paper cites They satisfy that L = Lalt · Lcob, R= Ralt · Rcob and P = Pcob · Palt, with a common inner dimension of 47.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications They satisfy that L = Lalt · Lcob, R= Ralt · Rcob and P = Pcob · Palt, with a common inner dimension of 47
Reference 1977
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:40.395000Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation febda7a6-8910-42b6-adea-21585fc91dfc · outbound
This paper cites [Cited § 1.].
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications [Cited § 1.]
Reference 1978
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.723034Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 21e64b8e-7b54-47ad-9ca8-760a3d71f161 · outbound
This paper cites doi:10.1145/3666000.3669697.
A more accurate rational non-commutative algorithm for multiplying 4x4 matrices using 48 multiplications doi:10.1145/3666000.3669697
Reference 2024
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T17:55:39.336545Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.