Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T14:47:31.976401Z
Paper Citation Record · LEDGER
Propagation of smallness near codimension two for gradients of harmonic functions
As of 20 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2508.21214.
A citation records a reference. It does not transfer a finding from one paper to another.
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One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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
20 of 20 outbound references displayed
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- unresolved7
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- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1f551aa3-d180-4a03-b6a6-840e93169efc · outbound
This paper cites Apraiz, L.
Propagation of smallness near codimension two for gradients of harmonic functions Apraiz, L
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.422915Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bcc672db-a447-4fcc-a61d-ac36bca5f1a1 · outbound
This paper cites Almgren, Jr.
Propagation of smallness near codimension two for gradients of harmonic functions Almgren, Jr
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.400386Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1f9ca6c6-725e-424c-a3f3-9cbd69dd9547 · outbound
This paper cites Propagation of smallness and control for heat equations.
Propagation of smallness near codimension two for gradients of harmonic functions Propagation of smallness and control for heat equations
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.377821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a661d443-9f01-42bc-b776-b098be755f69 · outbound
This paper cites Results on gradients of harmonic functions on Lipschitz surfaces.
Propagation of smallness near codimension two for gradients of harmonic functions Results on gradients of harmonic functions on Lipschitz surfaces
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T14:47:32.059427Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d9cbf5fc-25ab-4e33-840c-0e1734713971 · outbound
This paper cites On the dimension of observable sets for the heat equation.
Propagation of smallness near codimension two for gradients of harmonic functions On the dimension of observable sets for the heat equation
Reference 5
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-05T14:47:32.031096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 71f23bd8-4543-456e-9ee9-afc8524f8bca · outbound
This paper cites Monotonicity properties of variational integrals, A_p weights and unique continuation.
Propagation of smallness near codimension two for gradients of harmonic functions Monotonicity properties of variational integrals, A_p weights and unique continuation
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:47:31.893306Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9bd1a3d0-f60a-4e92-a24d-72379c716268 · outbound
This paper cites Unique continuation for elliptic operators: a geometric-variational approach.
Propagation of smallness near codimension two for gradients of harmonic functions Unique continuation for elliptic operators: a geometric-variational approach
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.335729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7f655218-4f87-4b80-880e-7a11efe09c22 · outbound
This paper cites Nodal sets of L aplace eigenfunctions: estimates of the H ausdorff measure in dimensions two and three.
Propagation of smallness near codimension two for gradients of harmonic functions Nodal sets of L aplace eigenfunctions: estimates of the H ausdorff measure in dimensions two and three
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.313992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3be409e0-7225-4a15-bfef-e820dbfe5097 · outbound
This paper cites Quantitative propagation of smallness for solutions of elliptic equations.
Propagation of smallness near codimension two for gradients of harmonic functions Quantitative propagation of smallness for solutions of elliptic equations
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:47:31.912548Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 83f634bc-f266-4c0a-a06b-8e29d3a424e7 · outbound
This paper cites Lecture notes on quantitative unique continuation for solutions of second order elliptic equations.
Propagation of smallness near codimension two for gradients of harmonic functions Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.273313Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d0c2987d-198d-4d23-bd80-d6b0cfe237a2 · outbound
This paper cites Nodal sets of L aplace eigenfunctions: polynomial upper estimates of the H ausdorff measure.
Propagation of smallness near codimension two for gradients of harmonic functions Nodal sets of L aplace eigenfunctions: polynomial upper estimates of the H ausdorff measure
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:47:31.923905Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5f90e61-4ce9-4648-bfef-8cd4504641b1 · outbound
This paper cites Nodal sets of L aplace eigenfunctions: proof of N adirashvili's conjecture and of the lower bound in Y au's conjecture.
Propagation of smallness near codimension two for gradients of harmonic functions Nodal sets of L aplace eigenfunctions: proof of N adirashvili's conjecture and of the lower bound in Y au's conjecture
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:47:31.929690Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 54822017-5bc1-493d-b011-fa14246adb78 · outbound
This paper cites Malinnikova.
Propagation of smallness near codimension two for gradients of harmonic functions Malinnikova
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.224387Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c991059f-772f-4b33-bdc6-6beb216dbd9c · outbound
This paper cites Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability.
Propagation of smallness near codimension two for gradients of harmonic functions Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.201951Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c52ea238-74a0-4c7e-b1f7-3bd08043871a · outbound
This paper cites an unresolved cited work.
Propagation of smallness near codimension two for gradients of harmonic functions Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:47:32.176193Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a7fef1c3-69a0-4216-a8a6-f99fae3dd395 · outbound
This paper cites an unresolved cited work.
Propagation of smallness near codimension two for gradients of harmonic functions Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:47:32.153299Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 02aaf493-ec17-4e8d-af51-737df85bd91f · outbound
This paper cites Volume estimates on the critical sets of solutions to elliptic PDE s.
Propagation of smallness near codimension two for gradients of harmonic functions Volume estimates on the critical sets of solutions to elliptic PDE s
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:47:31.960740Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4e455f30-053f-4bdc-94dc-e4b447dd0cc1 · outbound
This paper cites A continuous dependence result in the analytic continuation problem.
Propagation of smallness near codimension two for gradients of harmonic functions A continuous dependence result in the analytic continuation problem
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.121421Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1ba65a7f-50b5-4a80-b745-d8b619e20acc · outbound
This paper cites Vessella.
Propagation of smallness near codimension two for gradients of harmonic functions Vessella
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.101802Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c6999405-e879-4aa1-a5dd-104ccf5db95d · outbound
This paper cites Propagation of smallness for solutions of elliptic equations in the plane.
Propagation of smallness near codimension two for gradients of harmonic functions Propagation of smallness for solutions of elliptic equations in the plane
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:47:32.079830Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
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