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Paper Citation Record · LEDGER

Complexity rank one implies real rank zero

As of 17 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2608.12089.

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

pith.paper-citation-record.v1
2608.12089 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:24:02.921188Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

14 of 14 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved4
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5aac5440-5c34-4a89-8257-8873f9384a19 · outbound

This paper cites an unresolved cited work.

Complexity rank one implies real rank zero Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:24:03.088670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.873574Z digest=sha256:3c85d8b46417feeb01273e7137015aae47b9f19b4e40f5ff60f2bd2ef0cc73c6

Observation 9b235267-956b-4ce6-8036-1a681f6665d3 · outbound

This paper cites Diestel and J.

Complexity rank one implies real rank zero Diestel and J

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.078247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.878421Z digest=sha256:a8cbf1e6673a8505d624a1e9a8080d08660162ba58cf85359894f932d02318be

Observation 7e05430a-4483-42e8-8a20-c8d47dc9c55e · outbound

This paper cites Friis and M.

Complexity rank one implies real rank zero Friis and M

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.066813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.882139Z digest=sha256:c0dfa9835e23d870dd3a5ed24ce99970d8e07cba6d75d09bf8042d6d769a7d42

Observation 500efb16-a32a-4520-b413-41f590b970f6 · outbound

This paper cites Guentner, R.

Complexity rank one implies real rank zero Guentner, R

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.055114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.885848Z digest=sha256:778b5eb842f78049d8cbd90cce2861052f916db3cffabd4c13346a9e2f70056d

Observation e323f76c-c2a4-4cd8-bbe8-d8a8d553402a · outbound

This paper cites Guentner, R.

Complexity rank one implies real rank zero Guentner, R

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.044787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.889403Z digest=sha256:13c1d4a8a461c268ca53afe776e48f83a1c874f6aa41edfd95a2d9466a4ba0ea

Observation c35c486b-4681-4bea-a62b-3eab1a81aef0 · outbound

This paper cites Dynamical complexity and controlled operator K-theory.

Complexity rank one implies real rank zero Dynamical complexity and controlled operator K-theory

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-16T00:24:02.893138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:24:02.893138Z digest=sha256:3fe5e92125a62f8a799507755a53d61e97e1811d9c2b7d90f6359ae1d0446c69

Observation 883a5aa8-ecc4-4b18-8da5-39ca95377bfa · outbound

This paper cites Hyt¨ onen, J.

Complexity rank one implies real rank zero Hyt¨ onen, J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.033659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.897022Z digest=sha256:fb18692cf9aff63f51b90c1e7e97c4f3814ad1e358282f13cc1811b5d32876bf

Observation 20e61a25-a87e-4733-9a0f-0520a2d3f8bc · outbound

This paper cites Jaime and R.

Complexity rank one implies real rank zero Jaime and R

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.022357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.900746Z digest=sha256:682bdc9b2b1b17dc16f8e8bfb85a745448767b21a7f9c404b64601e48c6f7bcd

Observation 814f4a9b-2cc0-4b47-917f-70d80b34f361 · outbound

This paper cites Li and R.

Complexity rank one implies real rank zero Li and R

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:03.010588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.904053Z digest=sha256:0963723c8577e1c41aa7199c74492e92224ecfb1729d66144d22597a4c8fe843

Observation 887adff8-99e5-4506-a1c7-81108c40f316 · outbound

This paper cites Lin,Almost commuting selfadjoint matrices and applications, in P.

Complexity rank one implies real rank zero Lin,Almost commuting selfadjoint matrices and applications, in P

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:02.998759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.907706Z digest=sha256:6fd54a186fec2a1aac37d88cee11b44ab8d66b2c44b55c974f01abf72f13e6b4

Observation d677ee24-cccd-4a74-bcbe-b11b412e67f3 · outbound

This paper cites Rosenblum,On the operator equation BX−XA = Q, Duke Math.

Complexity rank one implies real rank zero Rosenblum,On the operator equation BX−XA = Q, Duke Math

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-16T00:24:02.911122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:24:02.911122Z digest=sha256:21e8794e10c8dac69f3b876c3a4048d0d1e4402a66f8fad23c3f7c6dedf14dc6

Observation 53a6af09-d0c1-4d9b-9861-d1d913379703 · outbound

This paper cites ˇSpakula and R.

Complexity rank one implies real rank zero ˇSpakula and R

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:02.987899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.914463Z digest=sha256:83cba788b808842fc6e346cce4e2975b05a73d9de37be1c46a5e895dc3bd1aea

Observation 1eb14354-6bd7-427d-a5dc-97cbe70be959 · outbound

This paper cites an unresolved cited work.

Complexity rank one implies real rank zero Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-16T00:24:02.976954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.917787Z digest=sha256:c2467398c4a5dca68bc4dc18ea416d1797bc29eabd20b302789269ade04e0db8

Observation fb715c46-9d3b-45f1-b8c2-f7f546429691 · outbound

This paper cites Willett and G.

Complexity rank one implies real rank zero Willett and G

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T00:24:02.966602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-16T00:24:02.921188Z digest=sha256:a12f3ebd16047b2c16aa1d6f2ac8576a24492a6db6207c11e840e4d38d24d539

Pith citing papers

No inbound Pith citation observations are available.