{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:36OLFN7H7SKLIQ7CVYRRJWBB27","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fb1f448b6b7a029c0cc935a00f8b005c7ca419246ed56de725e1a0e3c9488eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:19:04Z","title_canon_sha256":"aa641d0cc7bc4fd9de3e61eaa5ff59e57da40fdc46fa587e9db7295f74bd73de"},"schema_version":"1.0","source":{"id":"1307.5453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5453","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5453v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5453","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"36OLFN7H7SKL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"36OLFN7H7SKLIQ7C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"36OLFN7H","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:415abe5f163533fb10c38d874e1b464f30a3d9996c0fc8ec313f7885d3395788","target":"graph","created_at":"2026-05-18T03:17:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider a version of height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog of Mahler's measure arises in connection with extremal problems for Bergman spaces. It inherits many nice properties such as the multiplicative one. However, this height is a lower bound for Mahler's measure, and it can be substantially lower. We discuss some similarities and differences between the two.","authors_text":"Igor E. Pritsker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:19:04Z","title":"An areal analog of Mahler's measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5453","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c14c98258151360cdadbc2dfda810c206941f60bd067145324bef90d2751e234","target":"record","created_at":"2026-05-18T03:17:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fb1f448b6b7a029c0cc935a00f8b005c7ca419246ed56de725e1a0e3c9488eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-20T19:19:04Z","title_canon_sha256":"aa641d0cc7bc4fd9de3e61eaa5ff59e57da40fdc46fa587e9db7295f74bd73de"},"schema_version":"1.0","source":{"id":"1307.5453","kind":"arxiv","version":1}},"canonical_sha256":"df9cb2b7e7fc94b443e2ae2314d821d7f47e9bb08289bd32ba1cf35a1b44b123","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df9cb2b7e7fc94b443e2ae2314d821d7f47e9bb08289bd32ba1cf35a1b44b123","first_computed_at":"2026-05-18T03:17:55.677052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:55.677052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AUgaHNPyNTGap44apjf1t6cKfDDw/whn/U7Wc3MskPME1rmNxYnAWScCwxYY8vliqojNv9/3QEiGuuK0Jb7gDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:55.677977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c14c98258151360cdadbc2dfda810c206941f60bd067145324bef90d2751e234","sha256:415abe5f163533fb10c38d874e1b464f30a3d9996c0fc8ec313f7885d3395788"],"state_sha256":"f36fa0a83d82bf925e80fc78ffe7587da820764022870e427476029130a986a8"}