{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GO5N2R7C23UZBFMSZFUXF5N637","short_pith_number":"pith:GO5N2R7C","schema_version":"1.0","canonical_sha256":"33badd47e2d6e9909592c96972f5bedfda3cca71bc63fce756554dc76c9372d7","source":{"kind":"arxiv","id":"2505.21782","version":1},"attestation_state":"computed","paper":{"title":"Further remarks on fractional vs. expectation thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas Fischer, Yury Person","submitted_at":"2025-05-27T21:29:28Z","abstract_excerpt":"A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. In this note we generalize a method of DeMarco and Kahn and settle a few more special cases."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.21782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-27T21:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"1daeceb698685fdb2b8f763f3d6235c558b17048028963c194519dbfabb2615a","abstract_canon_sha256":"7707ec08abaa6e1b6c2966df0513c62c5a682b27f2c782682b6fde3224fa4728"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:03.452820Z","signature_b64":"1g2oX5KRMkupwNxJAZtr0kuJRXgyKcHxAEWOR8B/Hr/6bOgxRP73vxNLMR3nKcKMhA8WbE7+Fio1Q+J6hZF4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33badd47e2d6e9909592c96972f5bedfda3cca71bc63fce756554dc76c9372d7","last_reissued_at":"2026-07-05T11:11:03.452365Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:03.452365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Further remarks on fractional vs. expectation thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas Fischer, Yury Person","submitted_at":"2025-05-27T21:29:28Z","abstract_excerpt":"A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. In this note we generalize a method of DeMarco and Kahn and settle a few more special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21782","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21782/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.21782","created_at":"2026-07-05T11:11:03.452424+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.21782v1","created_at":"2026-07-05T11:11:03.452424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21782","created_at":"2026-07-05T11:11:03.452424+00:00"},{"alias_kind":"pith_short_12","alias_value":"GO5N2R7C23UZ","created_at":"2026-07-05T11:11:03.452424+00:00"},{"alias_kind":"pith_short_16","alias_value":"GO5N2R7C23UZBFMS","created_at":"2026-07-05T11:11:03.452424+00:00"},{"alias_kind":"pith_short_8","alias_value":"GO5N2R7C","created_at":"2026-07-05T11:11:03.452424+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637","json":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637.json","graph_json":"https://pith.science/api/pith-number/GO5N2R7C23UZBFMSZFUXF5N637/graph.json","events_json":"https://pith.science/api/pith-number/GO5N2R7C23UZBFMSZFUXF5N637/events.json","paper":"https://pith.science/paper/GO5N2R7C"},"agent_actions":{"view_html":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637","download_json":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637.json","view_paper":"https://pith.science/paper/GO5N2R7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.21782&json=true","fetch_graph":"https://pith.science/api/pith-number/GO5N2R7C23UZBFMSZFUXF5N637/graph.json","fetch_events":"https://pith.science/api/pith-number/GO5N2R7C23UZBFMSZFUXF5N637/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637/action/storage_attestation","attest_author":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637/action/author_attestation","sign_citation":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637/action/citation_signature","submit_replication":"https://pith.science/pith/GO5N2R7C23UZBFMSZFUXF5N637/action/replication_record"}},"created_at":"2026-07-05T11:11:03.452424+00:00","updated_at":"2026-07-05T11:11:03.452424+00:00"}