Paper Citation Record · LEDGER

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation

As of 8 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.

pith.paper-citation-record.v1
2508.12138 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T19:37:56.635977Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.