Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:36:41.305932Z
Paper Citation Record · LEDGER
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses
As of 8 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2506.02238.
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 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-30T20:32:01.738964Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-06-30T20:35:02.531947Z
Reference resolution
25 of 25 outbound references displayed
- verified exact0
- verified fuzzy19
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 7680c155-5508-4a57-9cab-f3f3b3b59131 · outbound
This paper cites The Parisi formula has a unique minimizer.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses The Parisi formula has a unique minimizer
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.803723Z
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 b4d46ff1-0641-4c1d-bd05-89965a3ded94 · outbound
This paper cites Near-optimal shattering in the Ising pure p-spin and rarity of solutions returned by stable algorithms.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Near-optimal shattering in the Ising pure p-spin and rarity of solutions returned by stable algorithms
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.207748Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b17a56e9-0101-466d-8811-c7b3a1bcde25 · outbound
This paper cites Sampling from mean-field gibbs measures via diffusion processes.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Sampling from mean-field gibbs measures via diffusion processes
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.789353Z
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 3661e185-095b-4c5d-b95c-ec6d4c61f2a4 · outbound
This paper cites Shattering in pure spherical spin glasses.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Shattering in pure spherical spin glasses
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.216734Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation db1f9005-0e72-49a2-bdbc-884d6e743eea · outbound
This paper cites Concentration inequalities: A nonasymptotic theory of independence.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Concentration inequalities: A nonasymptotic theory of independence
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.765442Z
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 b98fa560-a675-43e8-bd78-29f8ca20f8d2 · outbound
This paper cites The Aizenman-Sims-Starr scheme and Parisi Formula for Mixed p -spin Spherical Models.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses The Aizenman-Sims-Starr scheme and Parisi Formula for Mixed p -spin Spherical Models
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.752293Z
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 b5cca77c-0735-4f99-b1cc-ecd482b61706 · outbound
This paper cites Variational representations for the Parisi functional and the two-dimensional Guerra--Talagrand bound.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Variational representations for the Parisi functional and the two-dimensional Guerra--Talagrand bound
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.738588Z
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 0e6f1466-dc58-4001-ba44-6e5d397661b5 · outbound
This paper cites The spherical p-spin interaction spin-glass model: the dynamics.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses The spherical p-spin interaction spin-glass model: the dynamics
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.724032Z
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 7d27e27b-096c-4d0a-9643-b5751f6732df · outbound
This paper cites Disordered Gibbs measures and Gaussian conditioning.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Disordered Gibbs measures and Gaussian conditioning
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.238107Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 624ee6dd-315a-4b40-83b9-23a0a3c656f5 · outbound
This paper cites Dynamics for spherical spin glasses: Gibbs distributed initial conditions.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Dynamics for spherical spin glasses: Gibbs distributed initial conditions
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.242254Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6699741c-6379-4412-828d-10689515001e · outbound
This paper cites A spectral condition for spectral gap: fast mixing in high-temperature Ising models.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses A spectral condition for spectral gap: fast mixing in high-temperature Ising models
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.710800Z
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 d9d96793-0285-48ef-a6ef-685a83addec1 · outbound
This paper cites A note on weakly discontinuous dynamical transitions.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses A note on weakly discontinuous dynamical transitions
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.697129Z
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 d079b84d-d56c-41b7-84f6-3aaa6d45a544 · outbound
This paper cites On the spectral gap of spherical spin glass dynamics.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses On the spectral gap of spherical spin glass dynamics
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.683378Z
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 4f17452b-0867-45fc-9e10-11252a5f409e · outbound
This paper cites Universal aspects of the structural glass transition from density functional theory.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Universal aspects of the structural glass transition from density functional theory
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.669961Z
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 1847fa3d-85f5-4e5b-b633-601dc6657607 · outbound
This paper cites Fundamental limits of symmetric low-rank matrix estimation.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Fundamental limits of symmetric low-rank matrix estimation
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.264879Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 48532ec2-a2fa-4f94-bf2f-1f5224cbe974 · outbound
This paper cites Statistical and computational phase transitions in spiked tensor estimation.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Statistical and computational phase transitions in spiked tensor estimation
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.646075Z
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 865e0690-1cd3-4119-b50d-01e282621bdd · outbound
This paper cites A tentative replica study of the glass transition.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses A tentative replica study of the glass transition
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.632743Z
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 fa6297b3-3ac6-4ce8-870b-c9c65ec945e8 · outbound
This paper cites Envelope theorems for arbitrary choice sets.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Envelope theorems for arbitrary choice sets
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.618752Z
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 b2cf36bc-9eaf-497c-97a8-1db059c8177e · outbound
This paper cites On differentiability of the Parisi formula.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses On differentiability of the Parisi formula
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.604326Z
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 646bc6c1-13db-493c-8d89-d9734125f622 · outbound
This paper cites The Parisi ultrametricity conjecture.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses The Parisi ultrametricity conjecture
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.572866Z
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 de5c31d9-e138-4eec-b8f6-64b8ab0021de · outbound
This paper cites Infinite number of order parameters for spin-glasses.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Infinite number of order parameters for spin-glasses
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:36:41.290290Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b98201cd-e106-4bd2-a876-4238326e86b6 · outbound
This paper cites Free energy subadditivity for symmetric random Hamiltonians.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Free energy subadditivity for symmetric random Hamiltonians
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.518841Z
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 bd3008bd-8c9b-4423-8f49-0bfc3f9c96d1 · outbound
This paper cites Free energy of the spherical mean field model.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Free energy of the spherical mean field model
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.487259Z
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 18cf4445-4b94-4d1d-9ab6-fe360c8ede67 · outbound
This paper cites Parisi measures.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Parisi measures
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.440140Z
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 954f1c35-db08-4d79-a685-b4e874d98786 · outbound
This paper cites The Parisi formula.
On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses The Parisi formula
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:36:41.393244Z
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
Observation 8575bb3b-9983-46e8-81a1-38c9955e2132 · inbound
Lower bound on the mixing time of $p$-spin glasses cites this paper.
Lower bound on the mixing time of $p$-spin glasses On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T20:35:02.533700Z
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.