{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KNQHLEC7NB45OURYADDQKFI22J","short_pith_number":"pith:KNQHLEC7","schema_version":"1.0","canonical_sha256":"536075905f6879d7523800c705151ad264e0127d26599d3bfc42f65521de067f","source":{"kind":"arxiv","id":"1504.04778","version":5},"attestation_state":"computed","paper":{"title":"Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"David Simmons, Lior Fishman, Mariusz Urba\\'nski, Tushar Das","submitted_at":"2015-04-19T01:01:03Z","abstract_excerpt":"We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis ('98) resolving Sprind\\v{z}uk's conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss ('04), hereafter abbreviated KLW. As applications we prove the extremality of all hyperbolic measures of smooth dynamical systems with sufficiently large Hausdorff dimension, and of the Patterson--Sullivan measures of all nonplanar geometrically fi"},"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":"1504.04778","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-19T01:01:03Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"460da130ecf6d9ca15d631760de0f7b040b7a3f427d270d001ff189ff14d35a0","abstract_canon_sha256":"a3824cf3145eb11c800dec03eaa4f79a004324a7412507405cfb67986fcbf5b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.902286Z","signature_b64":"ANYS8MtXWzRhAt3d4lL7uYg696HMBzrC8+HpFthwwQEQao1OP4uRYvVgum1y2Mfm1LvL1bee+GX3IRCLphBcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"536075905f6879d7523800c705151ad264e0127d26599d3bfc42f65521de067f","last_reissued_at":"2026-05-17T23:43:18.901595Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.901595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"David Simmons, Lior Fishman, Mariusz Urba\\'nski, Tushar Das","submitted_at":"2015-04-19T01:01:03Z","abstract_excerpt":"We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis ('98) resolving Sprind\\v{z}uk's conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss ('04), hereafter abbreviated KLW. As applications we prove the extremality of all hyperbolic measures of smooth dynamical systems with sufficiently large Hausdorff dimension, and of the Patterson--Sullivan measures of all nonplanar geometrically fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04778","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1504.04778","created_at":"2026-05-17T23:43:18.901702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04778v5","created_at":"2026-05-17T23:43:18.901702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04778","created_at":"2026-05-17T23:43:18.901702+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNQHLEC7NB45","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNQHLEC7NB45OURY","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNQHLEC7","created_at":"2026-05-18T12:29:29.992203+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/KNQHLEC7NB45OURYADDQKFI22J","json":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J.json","graph_json":"https://pith.science/api/pith-number/KNQHLEC7NB45OURYADDQKFI22J/graph.json","events_json":"https://pith.science/api/pith-number/KNQHLEC7NB45OURYADDQKFI22J/events.json","paper":"https://pith.science/paper/KNQHLEC7"},"agent_actions":{"view_html":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J","download_json":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J.json","view_paper":"https://pith.science/paper/KNQHLEC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04778&json=true","fetch_graph":"https://pith.science/api/pith-number/KNQHLEC7NB45OURYADDQKFI22J/graph.json","fetch_events":"https://pith.science/api/pith-number/KNQHLEC7NB45OURYADDQKFI22J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J/action/storage_attestation","attest_author":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J/action/author_attestation","sign_citation":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J/action/citation_signature","submit_replication":"https://pith.science/pith/KNQHLEC7NB45OURYADDQKFI22J/action/replication_record"}},"created_at":"2026-05-17T23:43:18.901702+00:00","updated_at":"2026-05-17T23:43:18.901702+00:00"}