Paper Citation Record · LEDGER

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds

As of 12 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 3 inbound Pith citation observations for arXiv:2506.06259.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.06259 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T06:11:01.555058Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:24:24.671125Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-06-30T23:35:08.060820Z

Reference resolution

41 of 41 outbound references displayed

verified exact1
verified fuzzy35
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ca85f659-83e6-405a-b64e-a4326fb31b9a · outbound

This paper cites Group testing: an information theory perspective.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Group testing: an information theory perspective

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:08.813618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cc06e787-a192-4ec8-93ad-a9cda58489e0 · outbound

This paper cites High-dimensional analysis of semidefinite relaxations for sparse principal com- ponents.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds High-dimensional analysis of semidefinite relaxations for sparse principal com- ponents

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:08.580073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a493923e-3c2c-4335-9873-488f679fd558 · outbound

This paper cites Algorithmic thresholds for tensor pca.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Algorithmic thresholds for tensor pca

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:08.360596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation beda2de9-affe-4c8d-9a6e-6c99b0f1a462 · outbound

This paper cites Free energy wells and overlap gap property in sparse pca.Communi- cations on Pure and Applied Mathematics , 76(10):2410–2473, 2023.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Free energy wells and overlap gap property in sparse pca.Communi- cations on Pure and Applied Mathematics , 76(10):2410–2473, 2023

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:08.171266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a2ff4c46-b285-441f-b21c-ba8afb863869 · outbound

This paper cites Statistical-computational tradeoffs in mixed sparse linear regression.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical-computational tradeoffs in mixed sparse linear regression

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:07.971137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c06b818d-e5f5-4f3b-a88d-874d29c50ba5 · outbound

This paper cites The franz-parisi criterion and computational trade-offs in high dimensional statistics.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds The franz-parisi criterion and computational trade-offs in high dimensional statistics

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:07.772992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8805d37b-1ac7-47c3-95ab-803e39677df8 · outbound

This paper cites Universality of computational lower bounds for submatrix detection.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Universality of computational lower bounds for submatrix detection

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:07.566014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c3c61fee-9df3-4de8-9510-1969f36c897d · outbound

This paper cites Statistical query algorithms and low degree tests are almost equivalent.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical query algorithms and low degree tests are almost equivalent

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:07.316035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2a1e9bb6-2ca1-47aa-9dc9-d04dd937840f · outbound

This paper cites Can neural networks achieve optimal computational- statistical tradeoff? an analysis on single-index model.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Can neural networks achieve optimal computational- statistical tradeoff? an analysis on single-index model

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:07.084717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8e7441da-027c-487b-b9f6-e5f6a43a724d · outbound

This paper cites On the Low-Temperature MCMC threshold: the cases of sparse tensor PCA, sparse regression, and a geometric rule.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds On the Low-Temperature MCMC threshold: the cases of sparse tensor PCA, sparse regression, and a geometric rule

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T06:10:58.418408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1cd42cc6-ec96-4bd6-8c81-e63404a209ad · outbound

This paper cites Statistical and computational phase transitions in group testing.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical and computational phase transitions in group testing

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:06.918419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5d191fc4-d161-4879-b776-b65b39cdaa4e · outbound

This paper cites Computational-statistical gaps in gaussian single-index models.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Computational-statistical gaps in gaussian single-index models

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:06.701791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f5ca800e-99a4-4cb4-99c1-9a44c718e92f · outbound

This paper cites Efficient statistics, in high dimen- sions, from truncated samples.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Efficient statistics, in high dimen- sions, from truncated samples

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:06.501908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 726dd982-4db8-41c3-834a-17b180422be3 · outbound

This paper cites Computationally and statistically efficient truncated regression.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Computationally and statistically efficient truncated regression

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:06.330199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 84b0b7d5-7baf-4f67-ae20-86801832a6bf · outbound

This paper cites Testing convex truncation.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Testing convex truncation

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:06.174288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5f432d70-2e34-4f3f-88c5-02674352d819 · outbound

This paper cites Statistical query lower bounds for robust estimation of high- dimensional gaussians and gaussian mixtures.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical query lower bounds for robust estimation of high- dimensional gaussians and gaussian mixtures

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.986414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 27d47d12-8eac-4f63-8713-41952b850d4c · outbound

This paper cites Efficient algorithms and lower bounds for robust linear regression.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Efficient algorithms and lower bounds for robust linear regression

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.798388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 17a72045-0f4e-437b-a46a-3629b3344b58 · outbound

This paper cites Subexponential-time algorithms for sparse pca.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Subexponential-time algorithms for sparse pca

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.619854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 06128d4a-521a-4e95-925b-734d354546b2 · outbound

This paper cites Curse of Heterogeneity: Computational Barriers in Sparse Mixture Models and Phase Retrieval.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Curse of Heterogeneity: Computational Barriers in Sparse Mixture Models and Phase Retrieval

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:11:01.756934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 31ec4b73-3dea-4dd9-af7e-7c36f3733c5d · outbound

This paper cites Statistical algorithms and a lower bound for detecting planted cliques.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical algorithms and a lower bound for detecting planted cliques

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.426388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7c7010f9-859d-4403-b1ce-cc4cadfbcb1c · outbound

This paper cites Recipes for metastable states in spin glasses.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Recipes for metastable states in spin glasses

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.262466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fa3439a0-ac8a-4a99-900b-c38721162f09 · outbound

This paper cites Effective potential in glassy systems: theory and simulations.Physica A: Statistical Mechanics and its Applications, 261(3-4):317–339, 1998.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Effective potential in glassy systems: theory and simulations.Physica A: Statistical Mechanics and its Applications, 261(3-4):317–339, 1998

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:05.084301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation da88aff0-b6ac-4b44-bdf5-2f2d873c7f8a · outbound

This paper cites An examination into the registered speeds of american trotting horses, with remarks on their value as hereditary data.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds An examination into the registered speeds of american trotting horses, with remarks on their value as hereditary data

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.966343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2f7ee15c-f406-477b-af67-79ac55f015d9 · outbound

This paper cites Sharp Thresholds Imply Circuit Lower Bounds: from random 2-SAT to Planted Clique.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Sharp Thresholds Imply Circuit Lower Bounds: from random 2-SAT to Planted Clique

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T06:10:59.887144Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c56e8c9-efcd-4922-a464-4e976ae2ada8 · outbound

This paper cites Sparse high-dimensional linear regression.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Sparse high-dimensional linear regression

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.760802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a8515308-d264-4497-a770-76f09610b259 · outbound

This paper cites Inequalities on the probability content of convex regions for elliptically contoured distributions.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Inequalities on the probability content of convex regions for elliptically contoured distributions

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.577675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e2bc758f-b37c-449a-9e07-7b169646bc56 · outbound

This paper cites Statistical Inference and the Sum of Squares Method.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Statistical Inference and the Sum of Squares Method

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.397365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8c6f5083-6a87-4bd0-876a-df50b6288f18 · outbound

This paper cites Near-optimal statistical query lower bounds for agnostically learning intersections of halfspaces with gaussian marginals.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Near-optimal statistical query lower bounds for agnostically learning intersections of halfspaces with gaussian marginals

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.236025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 908b2a9b-ab45-4864-b8cf-6c1664be0613 · outbound

This paper cites Semiparametric least squares (sls) and weighted sls estimation of single-index models.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Semiparametric least squares (sls) and weighted sls estimation of single-index models

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:04.094954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8a08c4c6-c53a-4490-9313-1e5d982e73c4 · outbound

This paper cites Large cliques elude the metropolis process.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Large cliques elude the metropolis process

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:03.946345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2c83bae3-9bee-44d0-be93-7f16611153a3 · outbound

This paper cites Efficient noise-tolerant learning from statistical queries.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Efficient noise-tolerant learning from statistical queries

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T06:11:00.595020Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1c2c520-c98c-4493-86db-03148b49f894 · outbound

This paper cites Notes on computational hardness of hypothesis testing: Pre- dictions using the low-degree likelihood ratio.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Notes on computational hardness of hypothesis testing: Pre- dictions using the low-degree likelihood ratio

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:03.570559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 779093c9-8f7c-4626-89c9-37ab8f8f30f6 · outbound

This paper cites Royen’s proof of the gaussian correlation inequality.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Royen’s proof of the gaussian correlation inequality

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:03.229405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7eb5c93d-b91f-49cf-9d0e-9fefa0d410a1 · outbound

This paper cites Generalized linear models.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Generalized linear models

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T06:11:00.880662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 023d57d1-f4d2-48a1-ba0c-c6dded8343c5 · outbound

This paper cites On the limitation of spectral methods: From the gaussian hidden clique problem to rank-one perturbations of gaussian tensors.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds On the limitation of spectral methods: From the gaussian hidden clique problem to rank-one perturbations of gaussian tensors

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:03.013689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation da129ca5-900f-4b35-a9b1-0accfc6dba80 · outbound

This paper cites On the systematic fitting of curves to observations and measurements.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds On the systematic fitting of curves to observations and measurements

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:02.720424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 664b6853-b8db-4790-a219-03c7af6be8cf · outbound

This paper cites A statistical model for tensor pca.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds A statistical model for tensor pca

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:02.480548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6ca2241c-f615-4804-ae1c-b82b9cc2a39d · outbound

This paper cites A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T06:11:01.238292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 966954e4-ff0a-48f1-a52d-6db827ec95a0 · outbound

This paper cites Computational barriers to estimation from low-degree polynomials.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Computational barriers to estimation from low-degree polynomials

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:02.330466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4a4f7662-cc8d-414c-b476-51cc8cee9069 · outbound

This paper cites Lattice-based methods surpass sum-of-squares in clustering.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds Lattice-based methods surpass sum-of-squares in clustering

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:02.139396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 27a63020-5789-4976-b44f-3245b7695322 · outbound

This paper cites low-degree likelihood ratio.

An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds low-degree likelihood ratio

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:11:01.938527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 975c7fce-92aa-4c05-bc50-3e84d9ffd1b9 · inbound

Computational Complexity of Statistics: New Insights from Low-Degree Polynomials cites this paper.

Computational Complexity of Statistics: New Insights from Low-Degree Polynomials An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T04:24:24.671125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 677be1bb-4177-4328-8ede-619f3f9da0fb · inbound

High-Dimensional Statistics: Reflections on Progress and Open Problems cites this paper.

High-Dimensional Statistics: Reflections on Progress and Open Problems An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-11T18:36:06.454209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 256d2856-2324-4fcb-ae3d-2e79e53f81a7 · inbound

High-Dimensional Statistics: Reflections on Progress and Open Problems cites this paper.

High-Dimensional Statistics: Reflections on Progress and Open Problems An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-06-30T23:35:08.062616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.