{"as_of":"2026-08-18T03:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d7ad0fd69770e411b055cd2b121ecd10cc898207c6210006f3eb0040627080fe","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:30:13.591573Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.02574/citation-record","integrity":"/paper/2507.02574/integrity","json":"/paper/2507.02574/citation-record.json","paper":"/paper/2507.02574"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.752999Z","title":null,"venue":null,"work_id":"b31a3346-0655-4160-803a-2550ecb72665","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:11.835748Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:10529a25bceacc6242f552315ca024c24db8f088895502bad03e403f694483ed","observation_id":"b9fca49c-47c0-486e-a35a-e3cc8dfee06d","resolution":{"observed_at":"2026-08-06T20:30:16.756150Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.763887Z","title":"Here we have explicitly written the likelihood in terms of the Boltzmann-Gibbs distribution Eq","venue":null,"work_id":"5cca59ef-e9a9-44dc-b0c7-0099bcbc7b85","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:11.783443Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:386ad6f6986723fa97289f51d41673a5f81af7e445b242c04ce69cecc68c2fc8","observation_id":"758cb512-3d16-4519-95ff-df33b76c4fd1","resolution":{"observed_at":"2026-08-06T20:30:16.767522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.741940Z","title":"(13), and the theoretical average magnetization and correlation, Eqs","venue":null,"work_id":"6bdf4769-0151-4051-a1ef-7bdc08bd8097","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:11.921579Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:93107419d442544714dffedbc032bb9efe4bc651db8191612fa77b6b4b4bf9af","observation_id":"590a2f16-13a0-42c4-8eac-3fa3e10d76a9","resolution":{"observed_at":"2026-08-06T20:30:16.745128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.730631Z","title":"Eventually, {J, h} will converge to the parameter values maximizing the log-Likelihood","venue":null,"work_id":"c7bec7d9-71ca-4478-ac90-dc60eef5112e","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.052727Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:09611bf06fa59862cfd19d311046112ea224579a1e18de64dab894ffbc40272b","observation_id":"dcc5f84a-1f47-42a2-860d-2feedd461780","resolution":{"observed_at":"2026-08-06T20:30:16.734738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.718931Z","title":"(38), because all sites can be addressed in parallel","venue":null,"work_id":"f2e6927f-8173-4bd0-ad22-099d3ecf239d","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.127843Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:b59148c38f94a124ece19187b12a8c21788ac796cba788d48f9498477374db08","observation_id":"20e700d2-267d-4926-b970-1a75e304235f","resolution":{"observed_at":"2026-08-06T20:30:16.722102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.706488Z","title":null,"venue":null,"work_id":"89b98f04-5907-4e4d-9abf-79c45b7fe0b0","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.211303Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:210e0d68cd72fce78b5c1de4e5f47a818f4cf36644f10ecdd5e68cd4b76122f9","observation_id":"fd00c194-e7ff-4b8f-b3d0-7e9682aa8694","resolution":{"observed_at":"2026-08-06T20:30:16.711907Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.695548Z","title":null,"venue":null,"work_id":"c438d1b3-497a-4c58-a969-a46c5991f96e","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.297301Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:e748c9356bbcbd9230c8b75f6a86840f5878608254294f4a121b20446498d8ec","observation_id":"10e161aa-e6be-4af3-b8b1-a88732e25246","resolution":{"observed_at":"2026-08-06T20:30:16.699103Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.679409Z","title":"Li({Ji∂i, hi}) + λJ X j̸=i |Jij| + λhhi # , {J inf ij , hinf i }ℓ2 j∈∂i = argmax {Ji∂i ,hi}","venue":null,"work_id":"4e9c9e05-066f-478a-a3ec-ce6a68616b66","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.400580Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:933930585d4c9a5b57d3ac7364a64b1a54ef4579ae9ade253da7e660270bbc8e","observation_id":"574587bd-3fa3-4020-9a19-52fef67a83ec","resolution":{"observed_at":"2026-08-06T20:30:16.687743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.506074Z","title":"(35), as a logistic regression function","venue":null,"work_id":"b9bd27f1-8606-4a2e-85d7-74c486c924da","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.473641Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:57eefcd12731db1df6eaaf67595d5377ed7f27d0b7f3d2795e687267782bee7d","observation_id":"bfc66d4b-07b3-4db6-9223-d98a9dbf47d5","resolution":{"observed_at":"2026-08-06T20:30:16.608810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.258533Z","title":"low dimension","venue":null,"work_id":"55548c47-af00-4129-9afc-31371a169d37","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.544391Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:ba10116a8abac8fff0e79946852ba4b844010f078242980a6f52d9cd9a1a6023","observation_id":"08fd26b0-cbce-4dd0-9c2f-c5dc0a312602","resolution":{"observed_at":"2026-08-06T20:30:16.382507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:16.038249Z","title":"In formulas, this amount to have vanishing connected correlation functions, Eq","venue":null,"work_id":"1063a9d0-c269-49ea-8d01-f09ffc2c2def","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.668754Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:38f58e6e25004c5c677b6d5da73cc4ef2f1aeecf2e9b2d3d87a0c56b0a2bfc95","observation_id":"187fc663-96a8-4d7c-8920-30773ba59104","resolution":{"observed_at":"2026-08-06T20:30:16.115204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:15.549385Z","title":"Let us start from the Helmholtz free energy, whose equilibrium definition is F ({J, h}) = − 1 β ln Z({J, h})","venue":null,"work_id":"bec3dee7-d51b-4330-87b9-20dc431121f8","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.841022Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:6f45fa60ffa83505f873e1d15e6e1e6fb2db82251f5d4d908691775b941d345b","observation_id":"5959145f-aa85-4d75-920d-b42b945cbe72","resolution":{"observed_at":"2026-08-06T20:30:15.646041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:15.312759Z","title":null,"venue":null,"work_id":"078ff80e-1a70-41af-bcf5-41242bc28b9e","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.937973Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:bf77d9aa705df0314d9947485d7f61e964dc18dda72eeac1c79c0b509021f647","observation_id":"0c3c931f-54f6-4c19-9f07-7c84892063a5","resolution":{"observed_at":"2026-08-06T20:30:15.456803Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:15.082749Z","title":null,"venue":null,"work_id":"3b987ab8-74ae-4412-9893-e98231fba212","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.006737Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:fc63b1d5b085c4b7d453ac9c5f7d6267b35dd270862f4d5ecd934b641f0c523e","observation_id":"5539a7fd-7fa0-4007-95c1-cd184868b9c9","resolution":{"observed_at":"2026-08-06T20:30:15.203177Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.828516Z","title":null,"venue":null,"work_id":"82143e88-7e27-4cda-a318-9b07db643dd5","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.065439Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:a3627ab44c4514405d40df7def4625f8dcf55690123e2d3b128bf09639c98763","observation_id":"da9aa683-3911-4187-89c5-ecd86dd74fc4","resolution":{"observed_at":"2026-08-06T20:30:14.918739Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.645257Z","title":"5 in the case of N = 64 spins","venue":null,"work_id":"90dfca78-a80f-444f-bebb-34628acdbee1","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.125282Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:9d6fb25899f2d1af6a83b188642680d4c01b3cf75fd8d68b03f826799d0e905e","observation_id":"42235508-7e24-4ac5-9c93-705233a88be6","resolution":{"observed_at":"2026-08-06T20:30:14.738241Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.444660Z","title":"6 in the case of N = 64 spins for the vectorial Potts model with q = 4","venue":null,"work_id":"3954e1a3-6858-43e4-9da9-f9e9a9310697","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.190709Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:5f4b8e2df81a46d4c5265a8af7f73609fb5bd15d7271c6b54ebe62e3982c61f9","observation_id":"885789f0-118d-437d-9dc2-12edd40ba042","resolution":{"observed_at":"2026-08-06T20:30:14.595369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.11913","last_updated":"2020-06-27T04:38:54Z","snapshot_observed_at":"2026-08-16T04:21:05.831287Z","submitted_at":"2020-06-21T21:12:44Z","title":"Finding Patient Zero: Learning Contagion Source with Graph Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.11913","snapshot_observed_at":"2026-08-06T20:30:13.248473Z","title":"Complexity, disorder and fluctuations","venue":null,"work_id":null,"year":1924},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.248473Z"},"links":{"cited_paper":"/paper/2006.11913","citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:df90d09dd79d184459eee2f7b38aa8f67262203f41e7befcf904ef83cb35b727","observation_id":"c428918b-b691-41ce-bd25-e6ebb62bf5c4","resolution":{"observed_at":"2026-08-06T20:30:13.248473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.266990Z","title":"(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","venue":null,"work_id":"5f6aca18-9455-44a2-8b26-a4a845c9a570","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.307049Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:ea9a2d0dde45e19bc737f7511f3544f92088cdf3142a273075084b4071f252b5","observation_id":"6c9739a6-40f8-40d2-a90f-fbe4f0a84b5f","resolution":{"observed_at":"2026-08-06T20:30:14.309605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.137682Z","title":"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","venue":null,"work_id":"40afd8a4-062e-4836-83d6-30bfca5e5027","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.373476Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:9f0d5b6a60a9e1059f133e1bae0dc451f019be3f9247953697c0427e4a9fb206","observation_id":"d3ee74eb-a5b4-4734-9a0c-ca73456de95c","resolution":{"observed_at":"2026-08-06T20:30:14.200539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:14.016859Z","title":"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","venue":null,"work_id":"20c79317-568d-4e1c-8887-4a510d47ed34","year":1970},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.421832Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:3e9720b657eb23b6ffc4c1de996e34f9fb71ed8e696296b5b4fd28d8f0fd5fb1","observation_id":"c569551b-31f7-4e4f-bb93-b27e22b3f85a","resolution":{"observed_at":"2026-08-06T20:30:14.074905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:13.912649Z","title":null,"venue":null,"work_id":"c0d006eb-5e76-4cfe-9c90-e9fd5d1459db","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.495402Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:c8533d28446775dbe7f6ec013eaf66a9f9df317775c19921d648f43837f3ee6c","observation_id":"446fc02b-c16e-4d1a-a4a5-15471de0ab9e","resolution":{"observed_at":"2026-08-06T20:30:13.956333Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:13.786875Z","title":"In this way the s = 0 is suppressed","venue":null,"work_id":"c81eb70d-a460-4495-9a9f-13c38182cab1","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.537896Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:9acef1f3f2a422c0848186d3ae8a846c5865d8f012ee4fdfdee7a8efc17ecc21","observation_id":"6eaf64f9-e56a-4e6a-8318-900612b7baf5","resolution":{"observed_at":"2026-08-06T20:30:13.846366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:13.682826Z","title":"(C15) where Z is a normalization required to ensure ν(1) + ν(2) + ν(3) + ν(4) = 1","venue":null,"work_id":"18503721-1829-44a4-bf35-6c779cf4b20f","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:13.591573Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:ecc031de65cfcf8f34f3e927db70f243cca9961f57de1e603ee139def70f3581","observation_id":"43fadcf1-5318-4c01-b510-41647a03e8bf","resolution":{"observed_at":"2026-08-06T20:30:13.723561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:30:15.756407Z","title":"60 and 61","venue":null,"work_id":"03c78115-72c7-45cc-a0bc-8e62a77d6b29","year":null},"citing_paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition","version":2},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T20:30:12.764625Z"},"links":{"citing_paper":"/paper/2507.02574"},"observation_digest":"sha256:e59aa1b3cea8ff49751a80748b1d07660c453b46cbaeb646f03ce739b94582aa","observation_id":"4b863fc1-3072-4107-9df5-9749febb7c1d","resolution":{"observed_at":"2026-08-06T20:30:15.860912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.02574","last_updated":"2026-06-29T17:06:57Z","latest_version":2,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-08-16T18:58:23.108045Z","submitted_at":"2025-07-03T12:30:03Z","title":"Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":0,"verified_fuzzy":17},"total_outbound_references":25},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.02574."}