Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:30:13.591573Z
Paper Citation Record · LEDGER
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition
As of 16 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.02574.
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 2026-08-16T06:30:59.297886+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
25 of 25 outbound references displayed
- verified exact0
- verified fuzzy17
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b9fca49c-47c0-486e-a35a-e3cc8dfee06d · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:16.756150Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 758cb512-3d16-4519-95ff-df33b76c4fd1 · outbound
This paper cites Here we have explicitly written the likelihood in terms of the Boltzmann-Gibbs distribution Eq.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Here we have explicitly written the likelihood in terms of the Boltzmann-Gibbs distribution Eq
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.767522Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 590a2f16-13a0-42c4-8eac-3fa3e10d76a9 · outbound
This paper cites (13), and the theoretical average magnetization and correlation, Eqs.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (13), and the theoretical average magnetization and correlation, Eqs
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.745128Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dcc5f84a-1f47-42a2-860d-2feedd461780 · outbound
This paper cites Eventually, {J, h} will converge to the parameter values maximizing the log-Likelihood.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Eventually, {J, h} will converge to the parameter values maximizing the log-Likelihood
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.734738Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 20e700d2-267d-4926-b970-1a75e304235f · outbound
This paper cites (38), because all sites can be addressed in parallel.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (38), because all sites can be addressed in parallel
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.722102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fd00c194-e7ff-4b8f-b3d0-7e9682aa8694 · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:16.711907Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 10e161aa-e6be-4af3-b8b1-a88732e25246 · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:16.699103Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 574587bd-3fa3-4020-9a19-52fef67a83ec · outbound
This paper cites Li({Ji∂i, hi}) + λJ X j̸=i |Jij| + λhhi # , {J inf ij , hinf i }ℓ2 j∈∂i = argmax {Ji∂i ,hi}.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Li({Ji∂i, hi}) + λJ X j̸=i |Jij| + λhhi # , {J inf ij , hinf i }ℓ2 j∈∂i = argmax {Ji∂i ,hi}
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.687743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bfc66d4b-07b3-4db6-9223-d98a9dbf47d5 · outbound
This paper cites (35), as a logistic regression function.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (35), as a logistic regression function
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.608810Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08fd26b0-cbce-4dd0-9c2f-c5dc0a312602 · outbound
This paper cites low dimension.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition low dimension
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.382507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 187fc663-96a8-4d7c-8920-30773ba59104 · outbound
This paper cites In formulas, this amount to have vanishing connected correlation functions, Eq.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition In formulas, this amount to have vanishing connected correlation functions, Eq
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:16.115204Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5959145f-aa85-4d75-920d-b42b945cbe72 · outbound
This paper cites Let us start from the Helmholtz free energy, whose equilibrium definition is F ({J, h}) = − 1 β ln Z({J, h}).
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Let us start from the Helmholtz free energy, whose equilibrium definition is F ({J, h}) = − 1 β ln Z({J, h})
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:15.646041Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0c3c931f-54f6-4c19-9f07-7c84892063a5 · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:15.456803Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5539a7fd-7fa0-4007-95c1-cd184868b9c9 · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:15.203177Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation da9aa683-3911-4187-89c5-ecd86dd74fc4 · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:14.918739Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 42235508-7e24-4ac5-9c93-705233a88be6 · outbound
This paper cites 5 in the case of N = 64 spins.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition 5 in the case of N = 64 spins
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:14.738241Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 885789f0-118d-437d-9dc2-12edd40ba042 · outbound
This paper cites 6 in the case of N = 64 spins for the vectorial Potts model with q = 4.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition 6 in the case of N = 64 spins for the vectorial Potts model with q = 4
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:14.595369Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c428918b-b691-41ce-bd25-e6ebb62bf5c4 · outbound
This paper cites Finding Patient Zero: Learning Contagion Source with Graph Neural Networks.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Finding Patient Zero: Learning Contagion Source with Graph Neural Networks
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T20:30:13.248473Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6c9739a6-40f8-40d2-a90f-fbe4f0a84b5f · outbound
This paper cites (A2) The only difference between the two models is that Ising variables can have value si = ±1, while Blume-Capel spins can also have value zero.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (A2) The only difference between the two models is that Ising variables can have value si = ±1, while Blume-Capel spins can also have value zero
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:14.309605Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d3ee74eb-a5b4-4734-9a0c-ca73456de95c · outbound
This paper cites Indeed, for each color c, we define a magnetization mc as89: mc = fc − Pq r̸=c fr q − 1 = fcq − 1 q − 1 , (A3) where fc is the fraction of spins of color c.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Indeed, for each color c, we define a magnetization mc as89: mc = fc − Pq r̸=c fr q − 1 = fcq − 1 q − 1 , (A3) where fc is the fraction of spins of color c
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:14.200539Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c569551b-31f7-4e4f-bb93-b27e22b3f85a · outbound
This paper cites For the Ising model with zero-mean Gaussian couplings on an Erd˝ os–R´ enyi random graph—the Viana–Bray model45—geometric frustration forbids any ferromagnetic order- ing.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition For the Ising model with zero-mean Gaussian couplings on an Erd˝ os–R´ enyi random graph—the Viana–Bray model45—geometric frustration forbids any ferromagnetic order- ing
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:14.074905Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 446fc02b-c16e-4d1a-a4a5-15471de0ab9e · outbound
This paper cites an unresolved cited work.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:30:13.956333Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6eaf64f9-e56a-4e6a-8318-900612b7baf5 · outbound
This paper cites In this way the s = 0 is suppressed.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition In this way the s = 0 is suppressed
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:13.846366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 43fadcf1-5318-4c01-b510-41647a03e8bf · outbound
This paper cites (C15) where Z is a normalization required to ensure ν(1) + ν(2) + ν(3) + ν(4) = 1.
Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (C15) where Z is a normalization required to ensure ν(1) + ν(2) + ν(3) + ν(4) = 1
Reference 25
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- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:13.723561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b863fc1-3072-4107-9df5-9749febb7c1d · outbound
This paper cites 60 and 61.
Reference 77
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- verified fuzzy
- raw_fallback, observed 2026-08-06T20:30:15.860912Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
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