Paper Citation Record · LEDGER

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns

As of 3 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2607.28606.

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

pith.paper-citation-record.v1
2607.28606 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-31T02:23:27.698353Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+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

21 of 21 outbound references displayed

verified exact0
verified fuzzy0
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 517ef4aa-ec06-434a-8538-d0b7f4a8d985 · outbound

This paper cites Hasse principles for quadratic forms over function fields.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Hasse principles for quadratic forms over function fields

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.640282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e22d6494-9f97-4499-ba7a-f71c6c8c5554 · outbound

This paper cites Daans,Universally defining finitely generated subrings of global fields, Documenta Math.26(2021), 1851–1869.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Daans,Universally defining finitely generated subrings of global fields, Documenta Math.26(2021), 1851–1869

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.644380Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ced781c-483b-4f8d-852b-b01fd7a08335 · outbound

This paper cites Daans,Universally definingZinQwith10quantifiers, J.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Daans,Universally definingZinQwith10quantifiers, J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.647425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e19c057-e9d1-4315-a1e3-d4f60749ad27 · outbound

This paper cites Daans, P.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Daans, P

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.650525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00a673a3-ef69-46bd-bb00-f1bd3b4bc69f · outbound

This paper cites Gille and T.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Gille and T

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.653607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a41ae10b-a561-4974-a8ca-c74cb0c7d8fe · outbound

This paper cites Koenigsmann,DefiningZinQ, Annals of Math.183(2016), 73–93.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Koenigsmann,DefiningZinQ, Annals of Math.183(2016), 73–93

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.656589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0337d9de-ecfc-40e1-a72d-8cdfa7518d77 · outbound

This paper cites Matiyasevich,Enumerable sets are diophantine, Dokl.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Matiyasevich,Enumerable sets are diophantine, Dokl

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.659391Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 559c2f26-2406-42f3-a20f-044a524bddaa · outbound

This paper cites Lidl and H.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Lidl and H

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.662358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b91b23be-c121-409b-b851-834a74147ceb · outbound

This paper cites an unresolved cited work.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.665099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae2fea0a-0e33-460e-a80b-4eb52689970e · outbound

This paper cites an unresolved cited work.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.667885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59d634ed-1d28-45c9-a18c-948618a8edd5 · outbound

This paper cites Pollak,Orthogonal groups over global fields of characteristic2, J.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Pollak,Orthogonal groups over global fields of characteristic2, J

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.670700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b14a4345-f486-4f54-943c-c3c42e7e716d · outbound

This paper cites Poonen,Characterizing integers among rational numbers with a universal- existential formula, Amer.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Poonen,Characterizing integers among rational numbers with a universal- existential formula, Amer

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.673492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fd59cc8-1dbd-45bb-a19c-70059cf9cb1f · outbound

This paper cites Reiner,Maximal Orders, London Mathematical Society Monographs, New Series 28, Oxford University Press, 2003 reprint of the 1975 edition.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Reiner,Maximal Orders, London Mathematical Society Monographs, New Series 28, Oxford University Press, 2003 reprint of the 1975 edition

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.676362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78c85075-9e57-43bb-95f5-40fc4e1b876d · outbound

This paper cites Robinson,Definability and decision problems in arithmetic, J.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Robinson,Definability and decision problems in arithmetic, J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.679198Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2dd59e13-a06d-499a-8360-79e1c830a52f · outbound

This paper cites Scharlau,Quadratic and Hermitian Forms, Grundlehren der mathematischen Wis- senschaften 270, Springer, Berlin, 1985.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Scharlau,Quadratic and Hermitian Forms, Grundlehren der mathematischen Wis- senschaften 270, Springer, Berlin, 1985

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.681821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b68e090b-c002-499c-8e70-e7d4deed7699 · outbound

This paper cites Serre,Local Fields, Graduate Texts in Mathematics 67, Springer, New York, 1979.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Serre,Local Fields, Graduate Texts in Mathematics 67, Springer, New York, 1979

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.684413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 749ceaca-578b-4961-a8d5-0ccef829b0d1 · outbound

This paper cites Stichtenoth,Algebraic Function Fields and Codes, second ed., Graduate Texts in Mathematics 254, Springer, Berlin, 2009.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Stichtenoth,Algebraic Function Fields and Codes, second ed., Graduate Texts in Mathematics 254, Springer, Berlin, 2009

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.687401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42bc3d92-fcec-49af-b319-851a40fcf07c · outbound

This paper cites Sun,Further results on Hilbert’s Tenth Problem, Sci.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Sun,Further results on Hilbert’s Tenth Problem, Sci

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.689997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation febf805a-bf05-4cd9-8ee0-c1aaa4ffeb36 · outbound

This paper cites Mixed quantifier prefixes over Diophantine equations with integer variables.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Mixed quantifier prefixes over Diophantine equations with integer variables

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.692658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0214190-e58a-45e5-9497-a18416472951 · outbound

This paper cites Wu,Similarity of quadratic forms over global fields in characteristic2, Adv.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Wu,Similarity of quadratic forms over global fields in characteristic2, Adv

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.695500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21488b60-8784-4eac-9d0b-c8021d3cd6f5 · outbound

This paper cites Zhang and Z.-W.

$\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns Zhang and Z.-W

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T02:23:27.698353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.