Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:36:10.612696Z
Paper Citation Record · LEDGER
Approximation theorems for classifying stacks over number fields
As of 12 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2507.13900.
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 2026-05-17T02:54:47.873081Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-17T02:58:55.195850Z
Reference resolution
28 of 28 outbound references displayed
- verified exact2
- verified fuzzy18
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b1b4321b-c5a1-4268-9797-ff0e5464f231 · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:36:08.979235Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 10df7993-5d1a-44ba-853e-b0e604b6f656 · outbound
This paper cites On the motivic class of the stack of bundles.
Approximation theorems for classifying stacks over number fields On the motivic class of the stack of bundles
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:15.180108Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 98a6405f-c11c-4b98-883f-0b47584aa4fd · outbound
This paper cites Derivedl-adic categories for algebraic stacks.
Approximation theorems for classifying stacks over number fields Derivedl-adic categories for algebraic stacks
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.987106Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9dc392a2-2cc3-4fa8-9766-f40a6a015903 · outbound
This paper cites The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.
Approximation theorems for classifying stacks over number fields The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.794270Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f1e69ea9-ad94-4829-95be-23806c6204ef · outbound
This paper cites Manin obstruction to strong approximation for homo- geneous spaces.
Approximation theorems for classifying stacks over number fields Manin obstruction to strong approximation for homo- geneous spaces
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.630983Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 95137ce8-c65d-4709-90e3-5fe247ae041d · outbound
This paper cites Strong approximation with Brauer-Manin obstruction for groupic varieties.
Approximation theorems for classifying stacks over number fields Strong approximation with Brauer-Manin obstruction for groupic varieties
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.411259Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e6b3ddd5-1def-438a-8fcb-cd11e30038e6 · outbound
This paper cites A Topology on Points on Stacks.
Approximation theorems for classifying stacks over number fields A Topology on Points on Stacks
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:10.741430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 082498e9-c60a-44db-b7d1-73f1dbcb78c7 · outbound
This paper cites Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms.
Approximation theorems for classifying stacks over number fields Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.217743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1d746a9d-0cad-47cf-be7c-600ecf060ec5 · outbound
This paper cites Weil and Grothendieck approaches to adelic points.
Approximation theorems for classifying stacks over number fields Weil and Grothendieck approaches to adelic points
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:36:09.517429Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c3b8fc4b-be9f-409e-9bcd-10f461b89f9f · outbound
This paper cites Le d´ efaut d’approximation forte dans les groupes lin´ eaires con- nexes.
Approximation theorems for classifying stacks over number fields Le d´ efaut d’approximation forte dans les groupes lin´ eaires con- nexes
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:14.035453Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6e5ad2df-2af1-43ec-a67f-f25cf95ee781 · outbound
This paper cites On the Motivic Homotopy Type of Algebraic Stacks.
Approximation theorems for classifying stacks over number fields On the Motivic Homotopy Type of Algebraic Stacks
Reference 11
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:10.882454Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 80999504-f955-4e10-8f20-e410d5715516 · outbound
This paper cites Brauer groups and quotient stacks.
Approximation theorems for classifying stacks over number fields Brauer groups and quotient stacks
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:13.899750Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ff879cf1-1773-4008-9634-3c60dcdaadcc · outbound
This paper cites Coherent Tannaka duality and algebraicity of Hom- stacks.
Approximation theorems for classifying stacks over number fields Coherent Tannaka duality and algebraicity of Hom- stacks
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:13.752346Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c1d0a36f-f22d-41d7-9488-838ef2df952f · outbound
This paper cites Le d´ efaut d’approximation forte pour les groupes alg´ ebriques commu- tatifs.
Approximation theorems for classifying stacks over number fields Le d´ efaut d’approximation forte pour les groupes alg´ ebriques commu- tatifs
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:13.617589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 725f0f2f-a133-4c02-b97a-8d9d146e33e0 · outbound
This paper cites The bigger Brauer group and twisted sheaves.
Approximation theorems for classifying stacks over number fields The bigger Brauer group and twisted sheaves
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:13.468767Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2a640322-423e-43df-b075-1c84764e2b03 · outbound
This paper cites Starke Approximation in algebraischen Gruppen. I.
Approximation theorems for classifying stacks over number fields Starke Approximation in algebraischen Gruppen. I
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:13.391957Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2a5c64e7-9d9c-4e8e-a73e-f6c880375f05 · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:13.263723Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c6a96563-adaf-4aab-9fed-8d640136cd2d · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:13.130201Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 30716c49-c81c-4fe8-9856-6c29edf3d157 · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:12.984754Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 973394ab-2346-46bc-8126-719bf16329e2 · outbound
This paper cites Hasse principle and approximation theorems for homogeneous spaces.
Approximation theorems for classifying stacks over number fields Hasse principle and approximation theorems for homogeneous spaces
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:12.819359Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8f988763-b6b4-49f9-8d5f-09b4e85b88ef · outbound
This paper cites Mumford, J.
Approximation theorems for classifying stacks over number fields Mumford, J
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:12.668271Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8b9bb13a-b0b3-41ac-8fa2-65cdd0666e69 · outbound
This paper cites Sheaves on Artin stacks.
Approximation theorems for classifying stacks over number fields Sheaves on Artin stacks
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:12.506630Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 72ded02f-483c-4b17-a7e0-baa4cc148c51 · outbound
This paper cites The problem of strong approximation and the Kneser-Tits hypothesis for algebraic groups.
Approximation theorems for classifying stacks over number fields The problem of strong approximation and the Kneser-Tits hypothesis for algebraic groups
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:12.252835Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation bd09e980-377e-4212-8a4b-9ef0b1ee4fee · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:12.037388Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9912c2d2-b2a6-41bb-8cfd-3601d16a0413 · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:11.779199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e1480b43-b0d1-4761-838b-5498f0a40892 · outbound
This paper cites Toroidal algebraic groups.
Approximation theorems for classifying stacks over number fields Toroidal algebraic groups
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:11.542440Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 30dc3366-b22c-417f-b4d9-046271282437 · outbound
This paper cites Groupe de Brauer et arithm´ etique des groupes alg´ ebriques lin´ eaires sur un corps de nombres.
Approximation theorems for classifying stacks over number fields Groupe de Brauer et arithm´ etique des groupes alg´ ebriques lin´ eaires sur un corps de nombres
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:11.300654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 16a4b14f-2722-45ba-9488-5ea70daef9b5 · outbound
This paper cites an unresolved cited work.
Approximation theorems for classifying stacks over number fields Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:11.071735Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
Observation 7c2c4ae4-991d-451c-9816-e58fe04ccda9 · inbound
The \'{e}tale Brauer-Manin obstruction for classifying stacks cites this paper.
The \'{e}tale Brauer-Manin obstruction for classifying stacks Approximation theorems for classifying stacks over number fields
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T01:16:49.063682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.