Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-04T19:19:15.603067Z
Paper Citation Record · LEDGER
Minimality of Tree Tensor Network Ranks
As of 12 August 2026, this Paper Citation Record lists 6 of 6 outbound references and 1 inbound Pith citation observation for arXiv:2509.09463.
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 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T18:06:24.322685Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
6 of 6 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 26e5758a-8488-45c6-a284-0d8f8b7a02b1 · outbound
This paper cites Tensor Decomposition for Signal Processing and Machine Learning.
Minimality of Tree Tensor Network Ranks Tensor Decomposition for Signal Processing and Machine Learning
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:15.371026Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 748b21c9-2e36-49a8-9494-0c8755db6d29 · outbound
This paper cites On the geometry of tensor net- work states.
Minimality of Tree Tensor Network Ranks On the geometry of tensor net- work states
Reference 128
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:15.098411Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 895e7cd0-5312-4b9a-8c98-cc3e16ea4f42 · outbound
This paper cites Origi- nally published as Band 136 of Grundlehren der mathematischen Wis- senschaften.
Minimality of Tree Tensor Network Ranks Origi- nally published as Band 136 of Grundlehren der mathematischen Wis- senschaften
Reference 136
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:12.939943Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1dcffaf7-7252-49d2-9016-72352ca98676 · outbound
This paper cites A Multilinear Sin- gular Value Decomposition.
Minimality of Tree Tensor Network Ranks A Multilinear Sin- gular Value Decomposition
Reference 296
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:14.313458Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 91ec1394-5741-4de5-84e3-099e31186e16 · outbound
This paper cites Supervised Learning with Tensor Networks.
Minimality of Tree Tensor Network Ranks Supervised Learning with Tensor Networks
Reference 2016
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:15.221952Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1c1a385b-2193-44f2-861b-db8da6958027 · outbound
This paper cites Tensor network ranks.
Minimality of Tree Tensor Network Ranks Tensor network ranks
Reference 2019
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T19:19:15.603067Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 828099f5-9896-474d-9139-04d6c0085aee · inbound
Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties cites this paper.
Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties Minimality of Tree Tensor Network Ranks
Reference 41
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T18:06:24.322685Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.