Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T19:37:56.635977Z
Paper Citation Record · LEDGER
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation
As of 18 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2508.12138.
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 2026-08-18T06:34:40.430872+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
30 of 30 outbound references displayed
- verified exact2
- verified fuzzy22
- unresolved3
- parse uncertain2
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 47ddb561-67d0-4554-a630-e43a5979f49d · outbound
This paper cites an unresolved cited work.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Unresolved cited work
Reference 1
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-05T19:37:57.989205Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e0f93251-e78c-4a06-8aae-e79e78fdfeac · outbound
This paper cites Weighted Sobolev spaces, Perron solutions, and harmonic measure 3 2.2.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Weighted Sobolev spaces, Perron solutions, and harmonic measure 3 2.2
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.936991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 710ab81e-9e2f-46e4-ad45-ccedcc41b515 · outbound
This paper cites an unresolved cited work.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T19:37:57.889866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 637a2d1e-f616-43cb-8d67-b6e00dca6db8 · outbound
This paper cites an unresolved cited work.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Unresolved cited work
Reference 4
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-05T19:37:57.826646Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9d4a8c9c-d8b0-4bbf-ae7b-81a9c6217254 · outbound
This paper cites GHMD s σ⇒ LHMDs σ 17.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation GHMD s σ⇒ LHMDs σ 17
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.770469Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 72e315d1-eafc-4b22-8e54-455af88b69d0 · outbound
This paper cites an unresolved cited work.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T19:37:57.720433Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c4afdb65-9fac-47c7-9c05-cd79d2280a87 · outbound
This paper cites H\"older extension for fractional Laplacian.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation H\"older extension for fractional Laplacian
Reference 7
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-05T19:37:56.771641Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 659d73cd-2215-4a2f-a2e6-2d13e39fc253 · outbound
This paper cites We mainly refer to the results in [15, 19, 2].
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation We mainly refer to the results in [15, 19, 2]
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.666432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5701343c-00c2-4468-b4cd-1a4738c6bb0c · outbound
This paper cites Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.612885Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ca6629f2-a70c-4374-88ce-8aba1a677606 · outbound
This paper cites Nonlinear potential theory on metric spaces.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Nonlinear potential theory on metric spaces
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.551555Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0b19c761-dc90-4c6e-813f-1599fa228f5d · outbound
This paper cites Boundary estimates and a Wiener criterion for the fractional Laplacian.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Boundary estimates and a Wiener criterion for the fractional Laplacian
Reference 11
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T19:37:56.738305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5188e6b8-3518-4f59-bc1a-be317d91edf3 · outbound
This paper cites Fat sets and pointwise boundary estimates for p- harmonic functions in metric spaces.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Fat sets and pointwise boundary estimates for p- harmonic functions in metric spaces
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.483911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a3fc9752-5a9d-4e0a-a287-478ebf945471 · outbound
This paper cites The boundary Harnack principle for the fractional Laplacian.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation The boundary Harnack principle for the fractional Laplacian
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.418603Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b1bb28ad-2664-4cac-9fb1-aa92c6b72b3c · outbound
This paper cites The fractional Cheeger problem.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation The fractional Cheeger problem
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.355066Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a1df4377-59f9-4679-9320-1904d5d2eb17 · outbound
This paper cites Higher H ¨older regularity for the fractional p-Laplacian in the superquadratic case.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Higher H ¨older regularity for the fractional p-Laplacian in the superquadratic case
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.296546Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 38854614-3948-4e06-a1e4-240eab7b8a6e · outbound
This paper cites Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian[J].
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian[J]
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.236647Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 79cb768d-1a92-4875-a761-3564b38a0216 · outbound
This paper cites An extension problem related to the fractional Laplacian.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation An extension problem related to the fractional Laplacian
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.174447Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a0ad0fa2-9e5f-487f-814a-00b995f21f4a · outbound
This paper cites an unresolved cited work.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T19:37:57.126183Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f57a67cd-223f-4036-b4d4-5b6285c2ec21 · outbound
This paper cites A regularity condition at the boundary for solutions of quasilinear elliptic equations.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation A regularity condition at the boundary for solutions of quasilinear elliptic equations
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.101415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 52325adf-ce42-466b-95f9-f56fbd6579df · outbound
This paper cites Nonlinear potential theory of degenerate elliptic equa- tions.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Nonlinear potential theory of degenerate elliptic equa- tions
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.074000Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b1aa10e5-2c14-49ff-8318-44b59127cba2 · outbound
This paper cites Existence results for fractional p-Laplacian problems via Morse theory.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Existence results for fractional p-Laplacian problems via Morse theory
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.050672Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f3878772-f9f8-4452-aa6f-b0170b460389 · outbound
This paper cites Global H ¨older regularity for the fractional p- Laplacian.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Global H ¨older regularity for the fractional p- Laplacian
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:57.023919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c8782b73-d5b1-4f05-af05-f641bbe9e6af · outbound
This paper cites The Wiener criterion for non-local Dirichlet problems.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation The Wiener criterion for non-local Dirichlet problems
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.990662Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c1f87e89-6704-4a3a-9651-0329d6b18f07 · outbound
This paper cites Regularity of quasi-minimizers on metric spaces.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Regularity of quasi-minimizers on metric spaces
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.952298Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 222ad5d9-43c0-4da8-9f5b-7db92c938d3e · outbound
This paper cites Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.922214Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 849111a7-af71-497e-9562-ddfe3f49292d · outbound
This paper cites Uniformly fat sets.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Uniformly fat sets
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.893727Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 59d39728-af74-4b58-971f-14be359cc2ea · outbound
This paper cites Asymptotic behavior of nonlocal $p$-Rayleigh quotients.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Asymptotic behavior of nonlocal $p$-Rayleigh quotients
Reference 27
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T19:37:56.699822Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 572efd10-3ebd-403c-a35a-4f9ec9b0611b · outbound
This paper cites Boundary H¨older regularity for elliptic equations.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Boundary H¨older regularity for elliptic equations
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.864088Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ef3f0aa3-b54f-4b99-b385-33b4e15c9b4b · outbound
This paper cites Perron’s Method and Wiener’s Theorem for a non-local Equation.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Perron’s Method and Wiener’s Theorem for a non-local Equation
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.837197Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a89e2fc3-cbec-48ee-9fbf-655edc801929 · outbound
This paper cites G., Regularity at the boundary of solutions of elliptic equations and conformal mapping, Dokl.
Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation G., Regularity at the boundary of solutions of elliptic equations and conformal mapping, Dokl
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T19:37:56.807993Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
No inbound Pith citation observations are available.