Paper Citation Record · LEDGER

PhasorFlow: A Python Library for Unit Circle Based Computing

As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2603.15886.

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

pith.paper-citation-record.v1
2603.15886 v4

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T18:10:24.765335Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T23:10:44.751091Z

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 fuzzy0
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1f43eed2-03f8-4b74-a7d8-600076fd7b0d · outbound

This paper cites Cambridge University Press, 2010.

PhasorFlow: A Python Library for Unit Circle Based Computing Cambridge University Press, 2010

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:22.596715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11460da9-ff94-4b7c-b931-04d49fb5f507 · outbound

This paper cites Springer, 2012.

PhasorFlow: A Python Library for Unit Circle Based Computing Springer, 2012

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:22.725028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d87c9bb3-7c6b-416e-a46d-29f2802ef825 · outbound

This paper cites On the importance of phase in neural representations.Proceedings of the National Academy of Sciences, 113(42):11808–11813, 2016.

PhasorFlow: A Python Library for Unit Circle Based Computing On the importance of phase in neural representations.Proceedings of the National Academy of Sciences, 113(42):11808–11813, 2016

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:22.843727Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b5b950e-cfab-4535-ac52-005c9de37706 · outbound

This paper cites Qiskit: An open-source framework for quantum computing.

PhasorFlow: A Python Library for Unit Circle Based Computing Qiskit: An open-source framework for quantum computing

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.028735Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d9e540b-c764-4249-af9d-5a0adcaf6bdf · outbound

This paper cites Oxford University Press, 2006.

PhasorFlow: A Python Library for Unit Circle Based Computing Oxford University Press, 2006

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.194569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e05a6bd-b6cf-4e95-97a9-739884abd2fe · outbound

This paper cites Cambridge university press, 1996.

PhasorFlow: A Python Library for Unit Circle Based Computing Cambridge university press, 1996

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.283760Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbaf3ffc-e869-40e4-889e-097825e87620 · outbound

This paper cites Oxidative stress and cellular resonances.MDPI Molecular Sciences, 2023.

PhasorFlow: A Python Library for Unit Circle Based Computing Oxidative stress and cellular resonances.MDPI Molecular Sciences, 2023

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.343187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fad1d1c9-fb58-4748-b20f-efd9ec724512 · outbound

This paper cites Market agentome: Multi-agent phase dynamics in trading.

PhasorFlow: A Python Library for Unit Circle Based Computing Market agentome: Multi-agent phase dynamics in trading

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.424611Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 115a64a2-039e-4bd5-8fa7-d00e3781580f · outbound

This paper cites Parameterized quan- tum circuits as machine learning models.Quantum Science and Technology, 4(4):043001, 2019.

PhasorFlow: A Python Library for Unit Circle Based Computing Parameterized quan- tum circuits as machine learning models.Quantum Science and Technology, 4(4):043001, 2019

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.511092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e219f5a-495c-4853-9979-0776b3d6a3eb · outbound

This paper cites Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021.

PhasorFlow: A Python Library for Unit Circle Based Computing Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.576547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc20216b-93eb-4c80-a9aa-6233a5ec4f08 · outbound

This paper cites an unresolved cited work.

PhasorFlow: A Python Library for Unit Circle Based Computing Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.623651Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e105bf1a-4787-4aa5-8599-d53b38784db0 · outbound

This paper cites Circuit-centric quantum classifiers.Physical Review A, 101(3):032308, 2020.

PhasorFlow: A Python Library for Unit Circle Based Computing Circuit-centric quantum classifiers.Physical Review A, 101(3):032308, 2020

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.692893Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99c4c9cd-df37-4e5f-a003-acdb05a16fa1 · outbound

This paper cites An algorithm for the machine calculation of complex Fourier series.Mathematics of Computation, 19(90):297–301, 1965.

PhasorFlow: A Python Library for Unit Circle Based Computing An algorithm for the machine calculation of complex Fourier series.Mathematics of Computation, 19(90):297–301, 1965

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.757993Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e28094ab-8a85-4de3-b3d1-db3760b2925d · outbound

This paper cites Neural networks and physical systems with emergent collective computa- tional abilities.Proceedings of the National Academy of Sciences, 79(8):2554–2558, 1982.

PhasorFlow: A Python Library for Unit Circle Based Computing Neural networks and physical systems with emergent collective computa- tional abilities.Proceedings of the National Academy of Sciences, 79(8):2554–2558, 1982

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.820436Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddd5f084-9da3-4106-8b80-b898897ae86f · outbound

This paper cites Associative memory in a network of tunable oscillators.Biological Cybernetics, 81(4):319–321, 1999.

PhasorFlow: A Python Library for Unit Circle Based Computing Associative memory in a network of tunable oscillators.Biological Cybernetics, 81(4):319–321, 1999

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.861490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26c46f78-e67a-4a9a-be2c-41869adbb5e0 · outbound

This paper cites High-capacity memory via phase-coded synapses.Neuron, 66(2):250–264, 2010.

PhasorFlow: A Python Library for Unit Circle Based Computing High-capacity memory via phase-coded synapses.Neuron, 66(2):250–264, 2010

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.922515Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e1b0ec3-b96e-452c-a45b-9ce768b80154 · outbound

This paper cites Hopfield networks is all you need.International Conference on Learning Representa- tions, 2021.

PhasorFlow: A Python Library for Unit Circle Based Computing Hopfield networks is all you need.International Conference on Learning Representa- tions, 2021

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:23.975642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70676d7a-acdd-407a-89d0-c3015930b982 · outbound

This paper cites Self-entrainment of a population of coupled non-linear oscillators.In- ternational Symposium on Mathematical Problems in Theoretical Physics, pages 420–422, 1975.

PhasorFlow: A Python Library for Unit Circle Based Computing Self-entrainment of a population of coupled non-linear oscillators.In- ternational Symposium on Mathematical Problems in Theoretical Physics, pages 420–422, 1975

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.046827Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45ac27cc-386c-4c16-b83d-f5315ffd1cb3 · outbound

This paper cites Springer Science & Business Media, 2001.

PhasorFlow: A Python Library for Unit Circle Based Computing Springer Science & Business Media, 2001

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.109596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 238672e9-ce95-4d9b-82ac-4005149c572e · outbound

This paper cites Holographic reduced representations.IEEE Transactions on Neural Net- works, 6(3):623–641, 1995.

PhasorFlow: A Python Library for Unit Circle Based Computing Holographic reduced representations.IEEE Transactions on Neural Net- works, 6(3):623–641, 1995

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.175134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b8e1761-dc64-42e0-9066-6b262ba73335 · outbound

This paper cites Attention is all you need.Advances in Neural Information Processing Systems, 30, 2017.

PhasorFlow: A Python Library for Unit Circle Based Computing Attention is all you need.Advances in Neural Information Processing Systems, 30, 2017

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.244347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa911a24-b68b-4267-8b30-12a0cdbe59a4 · outbound

This paper cites Algorithms for quantum computation: discrete logarithms and factoring.

PhasorFlow: A Python Library for Unit Circle Based Computing Algorithms for quantum computation: discrete logarithms and factoring

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.344066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f85215ef-d1a9-49e2-8822-f3831d3333a5 · outbound

This paper cites Deep complex networks.International Conference on Learning Representations, 2018.

PhasorFlow: A Python Library for Unit Circle Based Computing Deep complex networks.International Conference on Learning Representations, 2018

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.404132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c3396a4-43f1-4b16-a5d9-0b2fd402d339 · outbound

This paper cites Unitary evolution recurrent neural networks.Proceedings of the 33rd International Conference on Machine Learning, pages 1120–1128, 2016.

PhasorFlow: A Python Library for Unit Circle Based Computing Unitary evolution recurrent neural networks.Proceedings of the 33rd International Conference on Machine Learning, pages 1120–1128, 2016

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.488649Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44f7de8a-0ad5-4cab-acff-1768b767b154 · outbound

This paper cites Full- capacity unitary recurrent neural networks.Advances in Neural Information Processing Systems, 29, 2016.

PhasorFlow: A Python Library for Unit Circle Based Computing Full- capacity unitary recurrent neural networks.Advances in Neural Information Processing Systems, 29, 2016

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.557444Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 624471cc-781d-4e5a-b410-612186830d4e · outbound

This paper cites Computing on Functions Using Randomized Vector Representations.

PhasorFlow: A Python Library for Unit Circle Based Computing Computing on Functions Using Randomized Vector Representations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.622527Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e677d182-28b8-4ee6-83d6-c1d3e25c5a79 · outbound

This paper cites Quaternionic neural networks and rotation invariance.IEEE Transactions on Neural Networks, 14(3):687–693, 2003.

PhasorFlow: A Python Library for Unit Circle Based Computing Quaternionic neural networks and rotation invariance.IEEE Transactions on Neural Networks, 14(3):687–693, 2003

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.686618Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c277ed2d-9bde-4cfc-ab1c-2fc712cc15c6 · outbound

This paper cites MIT press, 2007.

PhasorFlow: A Python Library for Unit Circle Based Computing MIT press, 2007

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T18:10:24.765335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 3541a558-cbc2-4209-acec-2cf8e798a679 · inbound

The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle cites this paper.

The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle PhasorFlow: A Python Library for Unit Circle Based Computing

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-13T23:10:44.751091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.