Paper Citation Record · LEDGER

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$

As of 11 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2506.21380.

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

pith.paper-citation-record.v1
2506.21380 v2

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:48:44.211829Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T09:42:09.105629Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T09:39:46.851885Z

Reference resolution

35 of 35 outbound references displayed

verified exact0
verified fuzzy25
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d8c1af01-08e4-4fc3-a7f7-3e9516812839 · outbound

This paper cites write newline.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:40.148840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a14bce7e-6522-4af9-82be-c8e35f0c4b2d · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:49.227667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dc5cdc1a-4177-44c7-83be-260b80a72929 · outbound

This paper cites Artin, \" U ber die Z erlegung definiter F unktionen in Q uadrate , Abh.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Artin, \" U ber die Z erlegung definiter F unktionen in Q uadrate , Abh

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:49.098536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c96240ad-7394-4a94-adb7-84499a469793 · outbound

This paper cites Artin, Algebraic approximation of structures over complete local rings, Publ.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Artin, Algebraic approximation of structures over complete local rings, Publ

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.937693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1e404508-1f67-4cc8-9253-72086b555c1a · outbound

This paper cites Artin and O.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Artin and O

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.806507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 24d136f4-4319-4fbe-8283-f771d3f6bd1d · outbound

This paper cites Artin and G.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Artin and G

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.640947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 41fbd731-2070-490b-9ebf-548f2f7ba4f7 · outbound

This paper cites Bochnak, M.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Bochnak, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.467843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fd860e30-f4f8-4d12-8072-b389b7d05eb7 · outbound

This paper cites Bosch, U.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Bosch, U

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.336521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8e2f69e3-d2aa-4fc3-b625-62ed9652d14a · outbound

This paper cites Binda, A.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Binda, A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:48.205062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f90309ad-faf0-45ed-baf6-3f740c9fbe1a · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:48.066925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 145b3076-0a9c-43d6-914d-f0e381f76b7b · outbound

This paper cites Borel, Linear algebraic groups, 2nd ed., Grad.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Borel, Linear algebraic groups, 2nd ed., Grad

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.893693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 25c36a4e-6b51-4a80-8136-cee485230ed1 · outbound

This paper cites Colliot-Th\'el\`ene, Appendix to a Hasse principle for two dimensional global fields by K.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Colliot-Th\'el\`ene, Appendix to a Hasse principle for two dimensional global fields by K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.750691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 49d25bff-1441-4083-8cab-1ac53057b422 · outbound

This paper cites Colliot-Th \'e l \`e ne and U.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Colliot-Th \'e l \`e ne and U

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.588920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f75e6d0e-a045-49a8-a91f-43464bf0c3e2 · outbound

This paper cites Elman, N.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Elman, N

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.461513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8780b340-3583-46f8-b46d-f178a7182542 · outbound

This paper cites Euler, Demonstratio theorematis F ermatiani omnem numerum sive integrum sive fractum esse summam quatuor pauciorumve quadratorum , Novi Comment.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Euler, Demonstratio theorematis F ermatiani omnem numerum sive integrum sive fractum esse summam quatuor pauciorumve quadratorum , Novi Comment

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.338884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48b9e7ea-3d3f-4720-ac61-46bec252a349 · outbound

This paper cites Jannsen, Hasse principles for higher-dimensional fields, Ann.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Jannsen, Hasse principles for higher-dimensional fields, Ann

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.212779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7573b1d3-9ddd-4d08-b45f-52fafcc53851 · outbound

This paper cites Jannsen and R.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Jannsen and R

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:47.094485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ca41f972-ea91-4d10-bf72-6fc30630a0b9 · outbound

This paper cites Kato, A Hasse principle for two dimensional global fields , J.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Kato, A Hasse principle for two dimensional global fields , J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.985937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e00726d0-2eb6-449d-86ff-cb85ce704105 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:46.839767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2397ffc5-d6d0-45e4-986b-5e2f162bf0a3 · outbound

This paper cites Landau, \"U ber die D arstellung definiter F unktionen durch Q uadrate , Math.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Landau, \"U ber die D arstellung definiter F unktionen durch Q uadrate , Math

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.720939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c61952b1-7a00-4711-8ec7-27a76f8b8126 · outbound

This paper cites Lang, The theory of real places, Ann.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Lang, The theory of real places, Ann

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.581634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 42ac4a95-5ba7-4893-9102-e6602af68a40 · outbound

This paper cites Lang and A.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Lang and A

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.477002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b66a9125-053e-4546-9427-8b5f32788266 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:46.334578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1d79460b-14f8-48d9-b5b0-30a0b5d26445 · outbound

This paper cites Pfister, Quadratic forms with applications to algebraic geometry and topology, LMS Lect.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Pfister, Quadratic forms with applications to algebraic geometry and topology, LMS Lect

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.153285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 573efa49-a366-4c7d-a5ba-cdc9392c6ca5 · outbound

This paper cites Pieper, On E uler's contributions to the four-squares theorem , Historia Math.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Pieper, On E uler's contributions to the four-squares theorem , Historia Math

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:46.014363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 252f3120-427f-423d-8123-301ca43af2dd · outbound

This paper cites Pollak, Orthogonal groups over global fields of characteristic 2, J.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Pollak, Orthogonal groups over global fields of characteristic 2, J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:45.844593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation df258fed-44b2-4fb6-9e48-c13f790eaa9e · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:45.671575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2262892a-f9c8-46f3-9e16-ac33d5039cf2 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:45.541471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e871f071-6781-4f87-ac54-267fc9a50f59 · outbound

This paper cites Pourchet, Sur la repr \'e sentation en somme de carr \'e s des polyn \^o mes \`a une ind \'e termin \'e e sur un corps de nombres alg \'e briques , Acta Arith.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Pourchet, Sur la repr \'e sentation en somme de carr \'e s des polyn \^o mes \`a une ind \'e termin \'e e sur un corps de nombres alg \'e briques , Acta Arith

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:45.341775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aab64e18-8164-45d0-8e0b-214f1bdcabb2 · outbound

This paper cites Serre, Corps locaux, Hermann, Paris, 1968.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Serre, Corps locaux, Hermann, Paris, 1968

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:45.175769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 88c60540-af11-46d4-bc57-ce93bad1ff44 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:44.962927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 54d4f196-2737-48eb-ba08-7f6900a84ac7 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:43.884736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd3ceeb8-ee38-4321-bd5f-06d2a8778997 · outbound

This paper cites an unresolved cited work.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:44.820401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aabc2ae8-b3c5-4718-8114-f8dbaa8da291 · outbound

This paper cites Voevodsky, Motivic cohomology with $ Z/2$ -coefficients , Publ.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ Voevodsky, Motivic cohomology with $ Z/2$ -coefficients , Publ

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:44.621584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2625c824-5300-4388-9765-be44cc7c074b · outbound

This paper cites o rper \.

The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$ o rper \

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:44.466117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 59e3a31e-6915-47fe-bae6-c4333c3e238d · inbound

Sums of squares on curves and surfaces cites this paper.

Sums of squares on curves and surfaces The Pythagoras number of fields of transcendence degree $1$ over $\mathbb{Q}$

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:39:46.853653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.