Paper Citation Record · LEDGER

Bounds for Geometric rank in Terms of Subrank

As of 18 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2506.16132.

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

pith.paper-citation-record.v1
2506.16132 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:41:50.577187Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

55 of 55 outbound references displayed

verified exact0
verified fuzzy35
unresolved20
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 491cc02f-63a7-4d3a-b639-58c676de44d4 · outbound

This paper cites On the Schmidt and analytic ranks for trilinear forms.

Bounds for Geometric rank in Terms of Subrank On the Schmidt and analytic ranks for trilinear forms

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.343442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e98cdd87-fddd-43df-b2bd-aee76cf2d921 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.349127Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cf4c3f0-47bc-4ddb-b4e4-5b7fb9b56d8c · outbound

This paper cites Ambainis, Y.

Bounds for Geometric rank in Terms of Subrank Ambainis, Y

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.389607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4f3fc641-c3f3-471d-b0d0-34a71a391858 · outbound

This paper cites Ananyan and M.

Bounds for Geometric rank in Terms of Subrank Ananyan and M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.375668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation facf145a-e08c-4cf9-925f-d5b43d70fb47 · outbound

This paper cites Baily and A.

Bounds for Geometric rank in Terms of Subrank Baily and A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.361879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5ce228ef-1bce-47e0-881f-218c1c2867c7 · outbound

This paper cites Biaggi, C.-Y.

Bounds for Geometric rank in Terms of Subrank Biaggi, C.-Y

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.348848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4c0de92b-d08a-4bfe-8be3-8ade071670c5 · outbound

This paper cites Real subrank of order-three tensors.

Bounds for Geometric rank in Terms of Subrank Real subrank of order-three tensors

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.371927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1efbee8-b789-476a-b600-32de44160f81 · outbound

This paper cites Uniformity for limits of tensors.

Bounds for Geometric rank in Terms of Subrank Uniformity for limits of tensors

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.376396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6c2f183-b69f-431c-ba66-1b43e2e8da20 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:51.334604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e9710ba4-fe34-4c03-a94b-433e4ad88b2a · outbound

This paper cites Strength and partition rank under limits and field extensions.

Bounds for Geometric rank in Terms of Subrank Strength and partition rank under limits and field extensions

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.385524Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d7fce98-0af1-4b59-b942-1b58719ac7d2 · outbound

This paper cites Bl¨ aser, J.

Bounds for Geometric rank in Terms of Subrank Bl¨ aser, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.320514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4866f103-4fee-4718-932b-8c36f79e335b · outbound

This paper cites Bri¨ et, M.

Bounds for Geometric rank in Terms of Subrank Bri¨ et, M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.306559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 99a05d48-0219-42bf-b3c1-8d45561c362d · outbound

This paper cites Bruns and J.

Bounds for Geometric rank in Terms of Subrank Bruns and J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.292924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c6286243-e223-4539-8454-3db4f4e0ac8b · outbound

This paper cites Chen and K.

Bounds for Geometric rank in Terms of Subrank Chen and K

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.403803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6023114-9ea9-4acf-8daa-54a3beabf814 · outbound

This paper cites Christandl, F.

Bounds for Geometric rank in Terms of Subrank Christandl, F

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.279404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5967fed6-de11-43ba-b494-6bbb4ca92b1e · outbound

This paper cites Christandl, P.

Bounds for Geometric rank in Terms of Subrank Christandl, P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.266474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c3dfcc9d-74e7-4d2f-a29f-4ccee38d7c52 · outbound

This paper cites Cohen and G.

Bounds for Geometric rank in Terms of Subrank Cohen and G

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.253355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4b88abdf-eff1-4167-8e88-cd5a4597265a · outbound

This paper cites Cohen and G.

Bounds for Geometric rank in Terms of Subrank Cohen and G

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.239807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 84cb8f80-0393-4119-bd00-7f44c645fc12 · outbound

This paper cites Costa and M.

Bounds for Geometric rank in Terms of Subrank Costa and M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.225403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 423e3e6b-0b2e-4c8b-91f6-eaa55002bf27 · outbound

This paper cites Croot, V.

Bounds for Geometric rank in Terms of Subrank Croot, V

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.210817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 134f56de-7b56-4aba-9744-afd9bd75a594 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:51.196365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 030117d0-1202-4f04-aa72-4cab0f26d3fe · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:51.182414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5eecadee-1741-470b-9b4e-8456d53a2486 · outbound

This paper cites Derksen, V.

Bounds for Geometric rank in Terms of Subrank Derksen, V

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.168592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 081f96ef-d6ba-4b17-9b61-d6e9878e54fc · outbound

This paper cites Dutta, F.

Bounds for Geometric rank in Terms of Subrank Dutta, F

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.152555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 95d0f133-d5ca-40b6-8282-cb3f236c257b · outbound

This paper cites Dutta, F.

Bounds for Geometric rank in Terms of Subrank Dutta, F

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.137855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d4cd59fd-0372-415f-a361-515d85d0e0d1 · outbound

This paper cites Filmus, K.

Bounds for Geometric rank in Terms of Subrank Filmus, K

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.124002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 35ecac4c-fa07-4bdd-9313-1e9aab72bb63 · outbound

This paper cites Fulton.Intersection theory, volume 2 ofErgebnisse der Mathematik und ihrer Grenzgebiete.

Bounds for Geometric rank in Terms of Subrank Fulton.Intersection theory, volume 2 ofErgebnisse der Mathematik und ihrer Grenzgebiete

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.110580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 306dbae5-cf54-4e16-9887-68a5589c5582 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:51.096805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 820d4822-9325-4c7a-8f97-92b6b67eecbf · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.466578Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb732f85-c427-4c85-a1b0-9690c8c9c65a · outbound

This paper cites Green and T.

Bounds for Geometric rank in Terms of Subrank Green and T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.074786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e4612be5-8a83-4d8f-af83-bd3f646f9a6b · outbound

This paper cites Grothendieck.

Bounds for Geometric rank in Terms of Subrank Grothendieck

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.061418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fb8bc719-bfd1-4788-952c-f1508e150aee · outbound

This paper cites Hartshorne.Algebraic geometry, volume No.

Bounds for Geometric rank in Terms of Subrank Hartshorne.Algebraic geometry, volume No

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.478758Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2965422-2bab-4694-88b8-24cfb340f186 · outbound

This paper cites Hu and K.

Bounds for Geometric rank in Terms of Subrank Hu and K

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.039251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 73aa8512-591f-4cbc-9f7e-bcd6e47c36b5 · outbound

This paper cites Kemper.A course in commutative algebra, volume 1.

Bounds for Geometric rank in Terms of Subrank Kemper.A course in commutative algebra, volume 1

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.025814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f3aa3f95-a584-4c06-a70b-82eba4e80e4b · outbound

This paper cites Kopparty, G.

Bounds for Geometric rank in Terms of Subrank Kopparty, G

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:51.012813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c687e8c5-5d41-46d5-a37d-09635714cad9 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:50.998756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e81505bf-2da6-409f-9467-b06a87413f9b · outbound

This paper cites Lampert and T.

Bounds for Geometric rank in Terms of Subrank Lampert and T

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.984914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 52080fe3-4cde-417e-b8d6-68e8506dece5 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:50.971425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b1c3fb4b-5ca9-4bfa-9dbf-3577bf2e9618 · outbound

This paper cites Lehmkuhl and T.

Bounds for Geometric rank in Terms of Subrank Lehmkuhl and T

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.958003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c0228e00-c4df-4f4f-9157-61c47694945d · outbound

This paper cites Lim and P.

Bounds for Geometric rank in Terms of Subrank Lim and P

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.943874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8c483091-8232-4239-b3eb-6116282276aa · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:50.928476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9642028c-d454-4c9f-9a14-706e137e7eb3 · outbound

This paper cites Matsumura.Commutative algebra.

Bounds for Geometric rank in Terms of Subrank Matsumura.Commutative algebra

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.914870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 68de7a0c-db08-4e70-89e1-ff2a4af24df8 · outbound

This paper cites Matsumura.Commutative ring theory, volume 8 ofCambridge Studies in Advanced Mathematics.

Bounds for Geometric rank in Terms of Subrank Matsumura.Commutative ring theory, volume 8 ofCambridge Studies in Advanced Mathematics

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.901052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d83a84f8-ca4e-4115-a1b5-bb20dfaa1279 · outbound

This paper cites Mili´ cevi´ c.

Bounds for Geometric rank in Terms of Subrank Mili´ cevi´ c

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.885526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 42c099ac-c598-4274-aae4-143544ef6050 · outbound

This paper cites Moshkovitz and D.

Bounds for Geometric rank in Terms of Subrank Moshkovitz and D

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.872245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 431e2019-7a75-499f-b7e0-4821cae1ad8c · outbound

This paper cites Uniform stability of ranks.

Bounds for Geometric rank in Terms of Subrank Uniform stability of ranks

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.538539Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a79af5d-1e1a-40dd-850e-396d421ee7f8 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.542954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cdd3746-bd42-422d-9de9-52181d0988e9 · outbound

This paper cites Naslund and W.

Bounds for Geometric rank in Terms of Subrank Naslund and W

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.850331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ec45b8d6-efae-4775-9e96-68e8d528bd91 · outbound

This paper cites Pielasa, M.

Bounds for Geometric rank in Terms of Subrank Pielasa, M

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.836452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dc75b71d-3a24-4326-b1d0-a2b6c9587e71 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:50.822406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 56235043-145b-411d-95e5-ccca16b9b17d · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-15T19:41:50.560500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d387ca5b-1f8c-4903-8c5a-0cd4393813ac · outbound

This paper cites Strassen.

Bounds for Geometric rank in Terms of Subrank Strassen

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.799851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 353a8c95-aa7d-47a3-8f5c-42e2072ccd04 · outbound

This paper cites Strassen.

Bounds for Geometric rank in Terms of Subrank Strassen

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.784913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fd81e4c3-615b-471c-9454-f49c8ced3501 · outbound

This paper cites Strassen.

Bounds for Geometric rank in Terms of Subrank Strassen

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:41:50.770677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fbc42307-8b14-4fd2-ac3f-d95f487d9257 · outbound

This paper cites an unresolved cited work.

Bounds for Geometric rank in Terms of Subrank Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:41:50.755889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.