Paper Citation Record · LEDGER

Neural networks leverage nominally quantum and post-quantum representations

As of 7 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 3 inbound Pith citation observations for arXiv:2507.07432.

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

pith.paper-citation-record.v1
2507.07432 v2

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:48:04.776385Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:22:26.038430Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-01T21:16:14.970265Z

Reference resolution

45 of 45 outbound references displayed

verified exact1
verified fuzzy27
unresolved17
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External citation measurements

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Outbound references

Observation ba6730c2-6eda-415d-a1fe-52642b9640e1 · outbound

This paper cites In this case, our GHMM is constructed from the initial vector⟨⟨η(∅)| = ℧(ρ0) and from the transition operatorsT (x) =∑ yK⊤ x,y⊗K† x,y.

Neural networks leverage nominally quantum and post-quantum representations In this case, our GHMM is constructed from the initial vector⟨⟨η(∅)| = ℧(ρ0) and from the transition operatorsT (x) =∑ yK⊤ x,y⊗K† x,y

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.235399Z

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Observation ef474547-4272-4ce8-a845-cc95d35eed63 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:11.214820Z

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Observation f0ba499a-eedd-42e9-8695-e5a5a158b1be · outbound

This paper cites However, because of the measurement, the CPTP map has|X| subchannels, each a trace-non-preserving superoperator Ax on the density matrix.

Neural networks leverage nominally quantum and post-quantum representations However, because of the measurement, the CPTP map has|X| subchannels, each a trace-non-preserving superoperator Ax on the density matrix

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.195561Z

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Observation b34524aa-962a-4471-8998-97ca53f01d4b · outbound

This paper cites The process is defined by two parameters,α and x, with dependent quantitiesβ = (1−α)/2 and y = 1− 2x.

Neural networks leverage nominally quantum and post-quantum representations The process is defined by two parameters,α and x, with dependent quantitiesβ = (1−α)/2 and y = 1− 2x

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.178407Z

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Observation 5fce4327-930e-4d22-bccd-ef06c5e69519 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:11.161150Z

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Observation 8ec6a268-7af3-4d44-a19e-df5fbc6d8868 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 6

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Observation e55bb717-06ff-4f11-85eb-8d0191099655 · outbound

This paper cites Following Ref.

Neural networks leverage nominally quantum and post-quantum representations Following Ref

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.128672Z

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Observation 76a925e5-5642-4d29-8dc9-7e7708e07bdf · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:11.112664Z

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Observation b3568f49-01af-44d4-bac9-8b254e05df27 · outbound

This paper cites The model uses multi-head attention with 4 heads (dimension 16 per head), 64-dimensional embeddings, and a 256-dimensional feed-forward network with ReLU activation.

Neural networks leverage nominally quantum and post-quantum representations The model uses multi-head attention with 4 heads (dimension 16 per head), 64-dimensional embeddings, and a 256-dimensional feed-forward network with ReLU activation

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.095814Z

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Observation 041af852-3867-4a67-8821-d7e37f3f4eed · outbound

This paper cites All experiments use consistent random seeding (seed=42) for reproducibility.

Neural networks leverage nominally quantum and post-quantum representations All experiments use consistent random seeding (seed=42) for reproducibility

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:11.078946Z

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Observation a551aafe-3823-4516-b53b-4a53f8b72582 · outbound

This paper cites Training is distributed across multiple GPUs, with specific GPU assignments managed through a parallel execution framework.

Neural networks leverage nominally quantum and post-quantum representations Training is distributed across multiple GPUs, with specific GPU assignments managed through a parallel execution framework

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:10.795564Z

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Observation 8503cedf-1fce-424b-9f82-183ee2b32457 · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:10.520042Z

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Observation d1fbc222-33db-4918-a522-acba86c45289 · outbound

This paper cites Deduplication Before regression, we identify and aggregate duplicate token prefixes.

Neural networks leverage nominally quantum and post-quantum representations Deduplication Before regression, we identify and aggregate duplicate token prefixes

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:10.304181Z

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Observation 9053055d-10bc-470e-9861-5d972cf55e3e · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:10.106047Z

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Observation 84c1a825-d345-4523-9277-610c90bcb562 · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:09.962774Z

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Observation 64c9f300-d474-4597-b9a1-2cbae6e694ab · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 16

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Observation 67278913-6842-4044-8c53-786f2221ccdd · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:09.680315Z

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Observation ba191711-813e-4c1f-b5c9-bad1eaea6345 · outbound

This paper cites This provides a complementary view to the distance-based metrics, focusing on angular rather than Euclidean-distance relationships.

Neural networks leverage nominally quantum and post-quantum representations This provides a complementary view to the distance-based metrics, focusing on angular rather than Euclidean-distance relationships

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:09.491984Z

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Observation ef9046b6-d068-49db-a483-0cd0b2117611 · outbound

This paper cites This control undergoes the same regression analysis, allowing us to quantify how much structure arises from training versus architecture.

Neural networks leverage nominally quantum and post-quantum representations This control undergoes the same regression analysis, allowing us to quantify how much structure arises from training versus architecture

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:09.374680Z

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Observation 603dc11c-578b-4074-9a05-e0407d53f676 · outbound

This paper cites Please see the README.md for instructions on how to recreate all training and figure generation in this manuscript.

Neural networks leverage nominally quantum and post-quantum representations Please see the README.md for instructions on how to recreate all training and figure generation in this manuscript

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:09.239926Z

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Observation 7889d57e-3a0a-4185-8131-295e3ff54179 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:09.055893Z

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Observation e6a156e8-7ca8-4aa3-a32b-568f9f5118a7 · outbound

This paper cites Note that losses in these files/links are reported normalized to the minimal possible loss given the process the network is trained on.

Neural networks leverage nominally quantum and post-quantum representations Note that losses in these files/links are reported normalized to the minimal possible loss given the process the network is trained on

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:08.913292Z

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Observation a42862c8-10fd-4384-9c28-85ff3e3d5a7e · outbound

This paper cites Transformers represent belief state geometry in their residual stream.

Neural networks leverage nominally quantum and post-quantum representations Transformers represent belief state geometry in their residual stream

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T18:48:02.447587Z

Source-reported events for the cited work

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Observation 1b975aaf-a343-44d8-9eaf-a03469f5c939 · outbound

This paper cites Riechers, Daniel Filan, and Adam S.

Neural networks leverage nominally quantum and post-quantum representations Riechers, Daniel Filan, and Adam S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:08.766593Z

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Observation fe6b3d70-1c17-4ac8-aff7-ce3926c87a4a · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:08.622538Z

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Observation dbb1d4c3-3d15-488f-9a93-27e0e21bf37f · outbound

This paper cites Cambridge university press, 2010.

Neural networks leverage nominally quantum and post-quantum representations Cambridge university press, 2010

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:08.461361Z

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Observation 3fdaf1c0-7d96-4e13-a4ea-4f7d0b884826 · outbound

This paper cites General probabilistic theories: An introduction.Physics Reports, 1033:1–64, 2023.

Neural networks leverage nominally quantum and post-quantum representations General probabilistic theories: An introduction.Physics Reports, 1033:1–64, 2023

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:08.286436Z

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Observation d53cef0f-db75-40fe-92d9-beece3d4beed · outbound

This paper cites Quantum theory in finite dimension cannot explain every general process with finite memory.Communications in Mathematical Physics, 405(2):50, 2024.

Neural networks leverage nominally quantum and post-quantum representations Quantum theory in finite dimension cannot explain every general process with finite memory.Communications in Mathematical Physics, 405(2):50, 2024

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:08.127708Z

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Observation a655eebc-f62f-412d-a4d7-c689a09a1b27 · outbound

This paper cites Quantum learning of classical stochastic processes: The completely positive realization problem.

Neural networks leverage nominally quantum and post-quantum representations Quantum learning of classical stochastic processes: The completely positive realization problem

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:07.993835Z

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Observation 8a1ac30e-9a07-407b-93d1-9c1d2815d957 · outbound

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Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:07.740164Z

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Observation 1f677b8d-1708-4f85-bdd8-c283150f1395 · outbound

This paper cites A canonical form for weighted automata and applications to approximate minimization.

Neural networks leverage nominally quantum and post-quantum representations A canonical form for weighted automata and applications to approximate minimization

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:07.445136Z

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Observation 62da2aaa-aaeb-4471-9f2f-b3c8ebaf7a73 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:07.293132Z

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Observation 26cc1fac-27bd-435b-b5d8-a6ebe3b80f93 · outbound

This paper cites Quantum adaptive agents with efficient long-term memories.

Neural networks leverage nominally quantum and post-quantum representations Quantum adaptive agents with efficient long-term memories

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:07.134025Z

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Observation e65a121f-b0bf-472b-bf96-c275a8032c70 · outbound

This paper cites Quantum generation of stochastic processes: spectral invariants and memory bounds.

Neural networks leverage nominally quantum and post-quantum representations Quantum generation of stochastic processes: spectral invariants and memory bounds

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:06.951639Z

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Observation 314a2eda-7921-4a52-bf46-f7d324d4fb86 · outbound

This paper cites Fundamentals of quantum mechanics in Liouville space.European Journal of Physics, 41(6):063002,.

Neural networks leverage nominally quantum and post-quantum representations Fundamentals of quantum mechanics in Liouville space.European Journal of Physics, 41(6):063002,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:06.669210Z

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Observation 93930815-6a0a-421f-a125-b9ddc1ad8f25 · outbound

This paper cites Riechers, Chaitanya Gupta, Artemy Kolchinsky, and Mile Gu.

Neural networks leverage nominally quantum and post-quantum representations Riechers, Chaitanya Gupta, Artemy Kolchinsky, and Mile Gu

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:06.466259Z

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Observation 620ff0fb-5e80-48b0-94af-bcacb72c3226 · outbound

This paper cites Riechers and Thomas J.

Neural networks leverage nominally quantum and post-quantum representations Riechers and Thomas J

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:06.204056Z

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Observation f67753ce-c384-4f34-b3c1-66bbb79291cf · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:06.022359Z

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Observation 2ff66226-394b-4bba-a1ea-dd798fcc82f5 · outbound

This paper cites Position: The platonic representation hypothesis.

Neural networks leverage nominally quantum and post-quantum representations Position: The platonic representation hypothesis

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:05.886848Z

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Observation 593e3cf8-0e90-4eea-ac71-e4f9b2a66443 · outbound

This paper cites an unresolved cited work.

Neural networks leverage nominally quantum and post-quantum representations Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:48:05.649254Z

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Observation 187d8f78-fb70-46c9-bf18-8099f0a84908 · outbound

This paper cites RNNs represent belief state geometry in their hidden states.

Neural networks leverage nominally quantum and post-quantum representations RNNs represent belief state geometry in their hidden states

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:05.477478Z

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Observation 0dd0ea06-82f7-4f61-83ad-f01dbb981ebb · outbound

This paper cites Next-token pretraining implies in-context learning.

Neural networks leverage nominally quantum and post-quantum representations Next-token pretraining implies in-context learning

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-06T18:48:04.570803Z

Source-reported events for the cited work

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Observation 0e7bfdc0-4d19-475d-8798-bb7742ab7eed · outbound

This paper cites Jakóbczyk and M.

Neural networks leverage nominally quantum and post-quantum representations Jakóbczyk and M

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:05.328431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b9c0c3ae-04a7-4cd7-b07a-678f80024921 · outbound

This paper cites Transformerlens.https://github.com/TransformerLensOrg/TransformerLens, 2022.

Neural networks leverage nominally quantum and post-quantum representations Transformerlens.https://github.com/TransformerLensOrg/TransformerLens, 2022

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:48:05.204101Z

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Observation 37398e48-6fe4-4f2f-9ab5-bffd9fe414b5 · outbound

This paper cites Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation.

Neural networks leverage nominally quantum and post-quantum representations Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation

Reference 2010

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:48:04.992939Z

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Pith citing papers

Observation 16042aea-f744-4c8d-814a-4f2fac008107 · inbound

Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes cites this paper.

Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes Neural networks leverage nominally quantum and post-quantum representations

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-05T11:22:26.038430Z

Source-reported events for the cited work

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Observation 0d295968-ee12-4f5e-a8e6-2b53b919aeaf · inbound

PreScience: A Dataset and Benchmark for Scientific Forecasting cites this paper.

PreScience: A Dataset and Benchmark for Scientific Forecasting Neural networks leverage nominally quantum and post-quantum representations

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T21:25:10.509998Z

Source-reported events for the cited work

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Observation dd03823b-243a-413b-a2b9-54b57584f6f0 · inbound

Structure and Scale in Simplicial Sequence Modelling cites this paper.

Structure and Scale in Simplicial Sequence Modelling Neural networks leverage nominally quantum and post-quantum representations

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-07-01T21:16:14.971896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.