Paper Citation Record · LEDGER

Geometric Solution of Turbulence as Diffusion in Loop Space

As of 9 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 2 inbound Pith citation observations for arXiv:2511.02165.

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

pith.paper-citation-record.v1
2511.02165 v4

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T00:20:35.907881Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T05:53:49.146142Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

47 of 47 outbound references displayed

verified exact11
verified fuzzy0
unresolved36
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 4c2f3164-d3ec-430a-9061-382e1d914687 · outbound

This paper cites Connections between number theory and the theory of turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space Connections between number theory and the theory of turbulence

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:30.317392Z

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Observation 9f6057bc-58c2-41d7-850e-7319701dfbf8 · outbound

This paper cites On heisenberg's elementary theory of turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space On heisenberg's elementary theory of turbulence

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:30.426468Z

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Observation dee6b3a1-def8-4286-8382-f88eecf715d2 · outbound

This paper cites The use of a contraction to improve the isotropy of grid-generated turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space The use of a contraction to improve the isotropy of grid-generated turbulence

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:30.529873Z

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Observation e077de46-8dff-4578-a9bb-a7ebaf52957d · outbound

This paper cites Some rigorous remarks on Migdal's momentum loop equation.

Geometric Solution of Turbulence as Diffusion in Loop Space Some rigorous remarks on Migdal's momentum loop equation

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:30.661034Z

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Observation ef311cf8-1b73-4013-9529-8bb2d0ee6ce4 · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 5

Resolution: verified exact; doi, observed 2026-08-04T00:24:16.382441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 280e61dc-dd0f-4ed2-963a-6256f7b5e09c · outbound

This paper cites 3-7 how did it get that way? In Michael A.

Geometric Solution of Turbulence as Diffusion in Loop Space 3-7 how did it get that way? In Michael A

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:30.959081Z

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Observation b317b4e0-686f-4ba9-8644-3fe28d654547 · outbound

This paper cites o ckeler and Thomas Sch \.

Geometric Solution of Turbulence as Diffusion in Loop Space o ckeler and Thomas Sch \

Reference 7

Resolution: verified exact; doi, observed 2026-08-04T00:24:16.232364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 55cac2f8-bc6b-46a6-bdd0-8dbe7b3db69d · outbound

This paper cites On the theory of statistical and isotropic turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space On the theory of statistical and isotropic turbulence

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:31.272401Z

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Observation 9afde674-9daa-494f-b51b-e5429f6432a3 · outbound

This paper cites Ishihara, T.

Geometric Solution of Turbulence as Diffusion in Loop Space Ishihara, T

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:31.487091Z

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Observation 275ac268-0bc0-4123-a343-3d4cbfa4b30d · outbound

This paper cites The area rule for circulation in three-dimensional turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space The area rule for circulation in three-dimensional turbulence

Reference 10

Resolution: verified exact; doi, observed 2026-08-04T00:24:16.066935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 92e37fd6-9197-4d09-bd20-750b459c58ce · outbound

This paper cites Bewley, and Eberhard Bodenschatz.

Geometric Solution of Turbulence as Diffusion in Loop Space Bewley, and Eberhard Bodenschatz

Reference 11

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.901021Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b6ff8b3b-f9f7-4a8b-9fd4-51b8be9eed1d · outbound

This paper cites On the exponential solution of differential equations for a linear operator.

Geometric Solution of Turbulence as Diffusion in Loop Space On the exponential solution of differential equations for a linear operator

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:31.968724Z

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Observation dd5ce2b1-592c-4e5b-bbc2-b22b7a6c0c8b · outbound

This paper cites Makeenko and A.A.

Geometric Solution of Turbulence as Diffusion in Loop Space Makeenko and A.A

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.169814Z

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Observation e57c8a75-09e3-48ab-b170-a07da8380937 · outbound

This paper cites Makeenko and Alexander A.

Geometric Solution of Turbulence as Diffusion in Loop Space Makeenko and Alexander A

Reference 14

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.762446Z

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Observation 25fc0e65-3d7e-4d3f-b945-feafe2d25d2c · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.476889Z

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Observation 49c90387-448e-4b98-9b99-690cc67b3a69 · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.596197Z

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Observation 4fa3d043-e06e-40b4-b9c6-950c30c67ab9 · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.686267Z

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Observation 1e05bac4-b162-462c-8de8-825beab955f1 · outbound

This paper cites Loop Equation and Area Law in Turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space Loop Equation and Area Law in Turbulence

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.836722Z

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Observation 1e555d1f-c210-41eb-a407-6c89bdd55aef · outbound

This paper cites To the theory of decaying turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space To the theory of decaying turbulence

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:32.958461Z

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Observation 79468150-2409-4f10-b21c-5d599d742a75 · outbound

This paper cites "bernsum".

Geometric Solution of Turbulence as Diffusion in Loop Space "bernsum"

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.079983Z

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Observation 6f87f2c9-13c3-42d2-a18b-e361733a78b2 · outbound

This paper cites instantoncomputations.

Geometric Solution of Turbulence as Diffusion in Loop Space instantoncomputations

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.147152Z

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Observation 0a4cda90-528d-48b4-b4aa-f2e0e6be9d43 · outbound

This paper cites instantoncomputations.

Geometric Solution of Turbulence as Diffusion in Loop Space instantoncomputations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.249609Z

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Observation 57b258fc-a411-4647-a508-7f88b0c11cb8 · outbound

This paper cites instantoncomputations.

Geometric Solution of Turbulence as Diffusion in Loop Space instantoncomputations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.306902Z

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Observation a393d300-9e4c-4f4f-a258-fda642c6bc9e · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.401968Z

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Observation 0df442c2-c11a-4d09-93f7-dc3454993599 · outbound

This paper cites "dnsfit".

Geometric Solution of Turbulence as Diffusion in Loop Space "dnsfit"

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.507882Z

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Observation 41d3851c-c5be-487b-96a4-a48c22f1ce8f · outbound

This paper cites corroscillations.

Geometric Solution of Turbulence as Diffusion in Loop Space corroscillations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.562981Z

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Observation 09fa8d60-0dfa-471c-b1ee-e06e2cdc7fc8 · outbound

This paper cites Quantum solution of classical turbulence: Decaying energy spectrum.

Geometric Solution of Turbulence as Diffusion in Loop Space Quantum solution of classical turbulence: Decaying energy spectrum

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.690777Z

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Observation 4cbe241e-1583-479f-bb71-4df824b5609d · outbound

This paper cites Exact holomorphic solution for the hodge-dual minimal surface as a geometric model of the qcd string.

Geometric Solution of Turbulence as Diffusion in Loop Space Exact holomorphic solution for the hodge-dual minimal surface as a geometric model of the qcd string

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.835322Z

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Observation aca15945-0dc3-42ef-b355-fea24c62ffc4 · outbound

This paper cites Spontaneous quantization of the yang–mills gradient flow.

Geometric Solution of Turbulence as Diffusion in Loop Space Spontaneous quantization of the yang–mills gradient flow

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:33.897827Z

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Observation 944231f0-0428-4f00-a919-980a377d0c43 · outbound

This paper cites Spontaneous quantization of the yang-mills gradient flow, 2025 c.

Geometric Solution of Turbulence as Diffusion in Loop Space Spontaneous quantization of the yang-mills gradient flow, 2025 c

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.074379Z

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Observation c880c6b0-9e94-43c3-8267-d0878d118e09 · outbound

This paper cites Dual Theory of MHD Turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space Dual Theory of MHD Turbulence

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.246596Z

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Observation 9550a444-0003-4345-b3d5-ea38d0fa3cae · outbound

This paper cites Dual theory of turbulent mixing.

Geometric Solution of Turbulence as Diffusion in Loop Space Dual theory of turbulent mixing

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.383793Z

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Observation 25081af8-0504-4ef4-80b0-c6f2ab36e1fe · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.611348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4cf088e4-25b5-49b1-859c-a87f6c9a0c4b · outbound

This paper cites Study of the hopf functional equation for turbulence: Duhamel principle and dynamical scaling.

Geometric Solution of Turbulence as Diffusion in Loop Space Study of the hopf functional equation for turbulence: Duhamel principle and dynamical scaling

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.584330Z

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Observation 39e2b082-37d1-4b93-b3ce-04e651e8e464 · outbound

This paper cites Laws of turbulence decay from direct numerical simulations.

Geometric Solution of Turbulence as Diffusion in Loop Space Laws of turbulence decay from direct numerical simulations

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.688664Z

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Observation 0f58c425-3c33-4a90-a741-390d32e6efcf · outbound

This paper cites Donzis, and Katepalli R.

Geometric Solution of Turbulence as Diffusion in Loop Space Donzis, and Katepalli R

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:34.832654Z

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Observation c1af44a8-1b44-4cad-8b9b-958d093b666f · outbound

This paper cites On the singularity structure of fully developed turbulence turbulence and predictability.

Geometric Solution of Turbulence as Diffusion in Loop Space On the singularity structure of fully developed turbulence turbulence and predictability

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:35.012243Z

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Observation c1a3a038-eaad-4f9f-aa12-2585729e7f47 · outbound

This paper cites Minimal surfaces unveiled from the statistics of turbulent circulation fluctuations.

Geometric Solution of Turbulence as Diffusion in Loop Space Minimal surfaces unveiled from the statistics of turbulent circulation fluctuations

Reference 38

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.479935Z

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Observation 72e759c2-1582-43db-9edc-417e7490a368 · outbound

This paper cites Frontiers of Turbulence and Statistical Physics Meet.

Geometric Solution of Turbulence as Diffusion in Loop Space Frontiers of Turbulence and Statistical Physics Meet

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:35.267623Z

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Observation ef455aa1-049a-4e40-8917-e5443db900fe · outbound

This paper cites Sreenivasan.

Geometric Solution of Turbulence as Diffusion in Loop Space Sreenivasan

Reference 40

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.309146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6be58363-17d5-4cb4-95d9-2673b7e168e1 · outbound

This paper cites Sreenivasan.

Geometric Solution of Turbulence as Diffusion in Loop Space Sreenivasan

Reference 41

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Observation f0f6e535-6e70-4e24-a577-5e9720e0a072 · outbound

This paper cites Sreenivasan and Victor Yakhot.

Geometric Solution of Turbulence as Diffusion in Loop Space Sreenivasan and Victor Yakhot

Reference 42

Resolution: verified exact; doi, observed 2026-08-04T00:24:15.171553Z

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Observation 22a0b03b-54cf-46cf-bc5f-35846cf1eb8d · outbound

This paper cites Sreenivasan.

Geometric Solution of Turbulence as Diffusion in Loop Space Sreenivasan

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:35.622127Z

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Observation 1c469b9f-e8ef-47c2-956b-024b17beaf02 · outbound

This paper cites an unresolved cited work.

Geometric Solution of Turbulence as Diffusion in Loop Space Unresolved cited work

Reference 44

Resolution: verified exact; doi, observed 2026-08-04T00:24:14.989770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c6d4eddc-6d81-44f3-ab95-5e9dc66cf425 · outbound

This paper cites Sreenivasan.

Geometric Solution of Turbulence as Diffusion in Loop Space Sreenivasan

Reference 45

Resolution: verified exact; doi, observed 2026-08-04T00:24:14.811969Z

Source-reported events for the cited work

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Observation 1e320d4c-1a0b-4177-bed1-b60e69b9348f · outbound

This paper cites Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence.

Geometric Solution of Turbulence as Diffusion in Loop Space Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:35.821390Z

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Observation f1dd339f-2721-4ded-8719-ba81819e1779 · outbound

This paper cites write newline.

Geometric Solution of Turbulence as Diffusion in Loop Space write newline

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-04T00:20:35.907881Z

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Pith citing papers

Observation ee30a1d5-8678-4cc6-afe7-bb34ce8940c2 · inbound

Geometric QCD II: The Confining Twistor String and Meson Spectrum cites this paper.

Geometric QCD II: The Confining Twistor String and Meson Spectrum Geometric Solution of Turbulence as Diffusion in Loop Space

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-06-02T03:04:01.989304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 82dd24c0-ffb6-4267-ae62-ff4978747ae2 · inbound

Numerical Validation of Lyapunov-Liouville Theory and Non-Diffusive Closures in Decaying Isotropic Fluid and Scalar Turbulence cites this paper.

Numerical Validation of Lyapunov-Liouville Theory and Non-Diffusive Closures in Decaying Isotropic Fluid and Scalar Turbulence Geometric Solution of Turbulence as Diffusion in Loop Space

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T05:53:49.146142Z

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Unavailable: canonical work link unavailable.