Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-10T05:04:10.503198Z
Paper Citation Record · LEDGER
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric
As of 5 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2607.08631.
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 2026-08-05T06:32:48.257954+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
44 of 44 outbound references displayed
- verified exact7
- verified fuzzy20
- unresolved14
- parse uncertain0
- malformed identifier0
- metadata mismatch3
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1284c2b0-06c6-40f8-b485-354a6ff7a4d8 · outbound
This paper cites MR0146835.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric MR0146835
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.233917Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a95d5eaf-932c-4822-99d4-c070f596ef50 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.235503Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation de098165-721f-44d8-84be-77aa0cbda11e · outbound
This paper cites Rigidity theorems for the area widths of Riemannian manifolds.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Rigidity theorems for the area widths of Riemannian manifolds
Reference 3
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-07-10T05:06:47.876440Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation eb44491e-c2da-45cf-b9a6-f13468934ee9 · outbound
This paper cites Ricci flow and contractibility of spaces of metrics.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Ricci flow and contractibility of spaces of metrics
Reference 4
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-07-10T05:06:47.891571Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 160a46bd-b73e-4de6-9219-b5edea1594f2 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.265917Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation f50ab3f0-5397-4f48-a553-8853c1f311d3 · outbound
This paper cites Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature
Reference 6
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T05:06:47.884131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 76a7faa9-fbd1-46a1-82fc-837f034f838b · outbound
This paper cites Existence of 5 minimal tori in 3-spheres of positive Ricci curvature.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Existence of 5 minimal tori in 3-spheres of positive Ricci curvature
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T05:06:47.873919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c53e556a-d394-4266-9c6a-41f84c6f58f3 · outbound
This paper cites Chun-Pong Chu, Y.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Chun-Pong Chu, Y
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-07-10T05:06:47.879075Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e9ac5da8-bef3-4e9c-a519-37183d4a7b7b · outbound
This paper cites Min-max theory and minimal surfaces with prescribed genus.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Min-max theory and minimal surfaces with prescribed genus
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T05:06:47.886729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e1ff35f6-aa0f-4cb4-b2cf-103ebc1f5b1a · outbound
This paper cites Colding and Camillo De Lellis, The min-max construction of minimal surfaces , Surveys in differ- ential geometry, Vol.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Colding and Camillo De Lellis, The min-max construction of minimal surfaces , Surveys in differ- ential geometry, Vol
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.276003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 5f85ef91-4534-4c52-8af2-487923d48ab6 · outbound
This paper cites Colding and William P.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Colding and William P
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.281139Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1f4210c2-c625-4501-b960-557a15aadf7a · outbound
This paper cites Minimal $2$-Spheres and Optimal Foliations in $3$-Spheres with Arbitrary Metric.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Minimal $2$-Spheres and Optimal Foliations in $3$-Spheres with Arbitrary Metric
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T05:06:47.881661Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a027095c-142a-40c9-88a7-7b0e4ce607ab · outbound
This paper cites MR02573 25.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric MR02573 25
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.267617Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 65d6f7ee-2885-4f64-85ad-605899d842b7 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.272450Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e376c55c-4e24-413a-bd3f-6a33a896a64e · outbound
This paper cites 80, Birkh¨ auser Verlag, Basel, 1984.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric 80, Birkh¨ auser Verlag, Basel, 1984
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.237159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation d3cb4a60-f99d-4e88-a241-9fe813ecce13 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.244010Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a4afc493-3ead-4d83-b38b-dab8f65845fa · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.270821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 265cf6f8-474f-4ee1-8745-5864cbeccb7e · outbound
This paper cites Hatcher, A proof of the Smale conjecture, Diff( S3) ≃ O(4), Ann.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Hatcher, A proof of the Smale conjecture, Diff( S3) ≃ O(4), Ann
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.279522Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation f2c79de5-50e7-4e0a-9d6d-a305f7cb4910 · outbound
This paper cites MR1867354.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric MR1867354
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.282726Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b641c4f6-b425-4708-a24f-9ae26a53fc48 · outbound
This paper cites Marques, and Andr´ e Neves, Density of minimal hypersurfaces for generic metrics , Ann.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Marques, and Andr´ e Neves, Density of minimal hypersurfaces for generic metrics , Ann
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.284561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1ed8dc96-05f2-45a6-a657-a8fdabf41112 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.252243Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a9c82a25-e980-4ba2-b663-f1bcc9b99d31 · outbound
This paper cites Marques, and Andr´ e Neves, The catenoid estimate and its geometric applica- tions, J.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Marques, and Andr´ e Neves, The catenoid estimate and its geometric applica- tions, J
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.254063Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation d7f89671-447d-4ddf-817d-eeda367ae0f6 · outbound
This paper cites Reine Angew.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Reine Angew
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.257528Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 42da4969-125e-4ce2-9586-cb233d103c6c · outbound
This paper cites Existence of embedded minimal tori in three-spheres with positive Ricci curvature.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Existence of embedded minimal tori in three-spheres with positive Ricci curvature
Reference 24
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T05:06:47.896925Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 02a11243-7576-43ca-83c4-b8085f846dd9 · outbound
This paper cites Marques, and Andr´ e N eves, Weyl law for the volume spectrum , Ann.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Marques, and Andr´ e N eves, Weyl law for the volume spectrum , Ann
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.274133Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8cc4c972-5c0c-4045-ab80-87493084900b · outbound
This paper cites Marques and Andr´ e Neves, Min-max theory and the Willmore conjecture , Ann.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Marques and Andr´ e Neves, Min-max theory and the Willmore conjecture , Ann
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.277809Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 41e6e907-6e97-42ee-bb76-003c3b2cad50 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.260920Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8a738708-44e7-44f5-aae2-350fe5a159c8 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.247213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 7d36b345-35e2-43ea-b291-8534b5f6b43b · outbound
This paper cites Marques, Andr´ e Neves, and Antoine Song, Equidistribution of minimal hypersurfaces for generic metrics, Invent.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Marques, Andr´ e Neves, and Antoine Song, Equidistribution of minimal hypersurfaces for generic metrics, Invent
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.238914Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 828c39a7-b254-4d99-8e18-327c94a3ce1f · outbound
This paper cites Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Mathematical Notes, vol.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Mathematical Notes, vol
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.240730Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation f19b8b2c-882f-4207-b5dd-9b6671a8507a · outbound
This paper cites 348, Birkh¨ auser/Springer, Cham, 2023.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric 348, Birkh¨ auser/Springer, Cham, 2023
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.242405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 72237ad3-16d9-4b8b-b323-835a8543058e · outbound
This paper cites Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.250608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 7917794a-3106-481f-9c22-4db5637da7f0 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.232393Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e23275fa-f298-4046-b34c-7ea38b886174 · outbound
This paper cites Pure Appl.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Pure Appl
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.269207Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 6e4d7776-9970-496e-a24c-baffe420d62a · outbound
This paper cites 3, Australian Nation al University, Centre for Mathematical Analysis, Canberra, 1983.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric 3, Australian Nation al University, Centre for Mathematical Analysis, Canberra, 1983
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.228927Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1486d32a-826d-4f20-9597-db64f57d81f7 · outbound
This paper cites Smith, On the existence of embedded minimal 2-spheres in the 3-sphe re, endowed with an arbitrary Riemannian metric , Ph.D.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Smith, On the existence of embedded minimal 2-spheres in the 3-sphe re, endowed with an arbitrary Riemannian metric , Ph.D
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.230733Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 3d6cfb55-f236-4497-9255-d3f8975a7a8e · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.264252Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 4c6e685a-0aa4-406a-9b07-137c00da2a76 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 38
- Resolution
- verified exact
- arxiv_id, observed 2026-07-10T05:06:47.889181Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c3dbe3d9-2a37-4fec-a5f1-cf5ce386e099 · outbound
This paper cites Improved $C^{1,1}$ regularity for multiple membranes problem.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Improved $C^{1,1}$ regularity for multiple membranes problem
Reference 39
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-07-10T05:06:47.894385Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c587bfb8-af2a-45cc-a8c8-ebb9b24db14e · outbound
This paper cites Differential Geom.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Differential Geom
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-10T05:06:48.245596Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 0cad47d5-6ae7-4235-8500-f0f1af7dbf86 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.259238Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 5e6c48c8-ba2e-40c8-bdba-f5a7394fb253 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.248884Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a78cbafc-f130-49e0-be85-0b83142dd015 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.262597Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 02811478-8376-4961-b8e7-b8b309d5adf2 · outbound
This paper cites an unresolved cited work.
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-07-10T05:06:48.255828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Pith citing papers
No inbound Pith citation observations are available.