Paper Citation Record · LEDGER

Operator K-complexity in DSSYK: Krylov complexity equals bulk length

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 28 inbound Pith citation observations for arXiv:2412.15318.

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

pith.paper-citation-record.v1
2412.15318 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 28 of 28 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 28 of 28 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:29:27.082018Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T05:29:34.963549Z

Reference resolution

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verified exact0
verified fuzzy0
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External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 20204377-176e-4748-b141-e41412d001a6 · inbound

Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity cites this paper.

Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 101

Resolution: verified exact; arxiv_id, observed 2026-05-23T02:27:25.424188Z

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 5fac758a-ec08-4438-8da4-dbd21e9d243b · inbound

York time in JT gravity cites this paper.

York time in JT gravity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-07T14:29:27.082018Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 798de28e-f69b-4cbf-b24b-c8cea5dfb98b · inbound

Towards a microscopic description of de Sitter dynamics cites this paper.

Towards a microscopic description of de Sitter dynamics Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-19T11:07:15.504850Z

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 a463b9a3-ae1f-4aa5-b864-fda15dd2c83d · inbound

Krylov Complexity cites this paper.

Krylov Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-16T14:58:01.258581Z

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 eba6cca2-f7b9-4a0c-acef-a8b77ea471ff · inbound

Universal Time Evolution of Holographic and Quantum Complexity cites this paper.

Universal Time Evolution of Holographic and Quantum Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 62

Resolution: verified exact; arxiv_id, observed 2026-05-19T02:21:59.538599Z

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 3e495c40-287e-4cdc-9033-51e386b19d77 · inbound

A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification cites this paper.

A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 169

Resolution: unresolved; no resolver link, observed 2026-08-05T17:53:38.772461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6cb725e-3c95-45e7-9c2a-1860eb444b40 · inbound

Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons cites this paper.

Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 169

Resolution: unresolved; no resolver link, observed 2026-08-05T17:59:41.297201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9a0c25e-13aa-452b-be07-3a6412b87b63 · inbound

Holography of K-complexity: Switchbacks and Shockwaves cites this paper.

Holography of K-complexity: Switchbacks and Shockwaves Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T09:05:26.321003Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f2155c7-4cf9-45bf-b479-3c0253ba943a · inbound

Toward Krylov-based holography in double-scaled SYK cites this paper.

Toward Krylov-based holography in double-scaled SYK Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-18T04:20:52.577622Z

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 252d8ea8-ac73-431f-8a02-391447f3040c · inbound

Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity cites this paper.

Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 115

Resolution: verified exact; arxiv_id, observed 2026-05-18T00:55:34.952977Z

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 7d2a1919-bd84-4508-9e84-8fb822f0c9fe · inbound

Krylov Complexity of Supersymmetric SYK Models cites this paper.

Krylov Complexity of Supersymmetric SYK Models Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-03T20:15:04.207825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6521c9c-62e4-4cf2-ae74-3713c5c5ecbc · inbound

Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model cites this paper.

Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T17:58:40.492169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdf3e15e-4f2c-4d55-a678-4b536281ec04 · inbound

Probing the Chaos to Integrability Transition in Double-Scaled SYK cites this paper.

Probing the Chaos to Integrability Transition in Double-Scaled SYK Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 103

Resolution: verified exact; arxiv_id, observed 2026-05-16T14:17:59.378982Z

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 2e276c4b-047f-4e07-903a-79a3c18a6e1c · inbound

Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity cites this paper.

Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-03T04:36:21.868550Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b853a04-ab07-4642-9578-6ffe267f0f9f · inbound

Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography cites this paper.

Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 70

Resolution: verified exact; arxiv_id, observed 2026-05-16T06:37:28.421113Z

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 bb6609ca-538d-46d4-8d29-a25db574b423 · inbound

Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography cites this paper.

Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-16T06:07:25.627659Z

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 334b97e2-83ea-49c7-ac49-399611f2fd50 · inbound

Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons cites this paper.

Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 72

Resolution: verified exact; arxiv_id, observed 2026-05-14T00:08:29.068011Z

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 9ae32f43-dcaa-4ba2-8312-9b9ca738c644 · inbound

Emergent States and Algebras from the Double-Scaling limit of Pure States in SYK cites this paper.

Emergent States and Algebras from the Double-Scaling limit of Pure States in SYK Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 69

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:20:22.680906Z

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 63ec6e68-db4e-44f9-a860-aba25e532d8e · inbound

q-Askey Deformations of Double-Scaled SYK cites this paper.

q-Askey Deformations of Double-Scaled SYK Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 70

Resolution: verified exact; arxiv_id, observed 2026-05-15T02:43:33.087142Z

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 660cbeb5-c76c-4ea0-924e-94de1c774d59 · inbound

q-Askey Deformations of Double-Scaled SYK cites this paper.

q-Askey Deformations of Double-Scaled SYK Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 70

Resolution: verified exact; arxiv_id, observed 2026-06-30T21:25:04.799014Z

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 dc0b69bd-dda8-4776-986c-1b0d798aad7c · inbound

Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity cites this paper.

Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-25T05:50:24.462554Z

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 f2739739-79ce-45e2-91cd-0fe473a0cc7f · inbound

Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity cites this paper.

Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-06-30T19:15:00.546010Z

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 800a1caf-040b-4645-ade7-d3cfc794d541 · inbound

Krylov complexity has it all cites this paper.

Krylov complexity has it all Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T11:23:21.961108Z

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 384683cd-5821-436b-b899-ba529fbcec03 · inbound

Krylov complexity has it all cites this paper.

Krylov complexity has it all Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T13:01:52.049789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f647ed2-6f35-4ba3-ae7e-9c4d1e1ac642 · inbound

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity cites this paper.

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-04T05:29:34.964884Z

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 65f0fc23-e8b2-47fe-b6e3-7d9ccb2439fc · inbound

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity cites this paper.

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-06-30T10:44:36.636408Z

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 47d93659-4072-425d-8bbd-723d47659bc0 · inbound

Comments on holographic spread complexity cites this paper.

Comments on holographic spread complexity Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T16:31:56.991886Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8df70380-87d8-437d-a72c-511963cc1409 · inbound

Holographic timelike complexity for de Sitter cites this paper.

Holographic timelike complexity for de Sitter Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-03T02:25:54.276510Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.