{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4AQLVAZUT47W6SQLKY4YEWZNY5","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":"532110482f845b77520f2b296619fe7590a8dbaad705dfa927c561386f4cc648","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-13T22:59:39Z","title_canon_sha256":"9807c71b5bfd6ea85610bbc80cf86b4dc62c98d574e54c415ab41c4166cf890c"},"schema_version":"1.0","source":{"id":"1311.3334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3334","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3334v1","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3334","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"4AQLVAZUT47W","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4AQLVAZUT47W6SQL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4AQLVAZU","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:6e31fe39f8fe6db8f8a564781c7bc7087410d220bcaee1effee5864033e5875b","target":"graph","created_at":"2026-05-18T03:07:11Z","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 minimal graphs u(x,y)>0 over unbounded domains D (with u vanishing on the boundary of D). Assuming D contains a sector properly containing a halfplane, we obtain estimates on growth and provide examples illustrating a range of growth.","authors_text":"Allen Weitsman, Erik Lundberg","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-13T22:59:39Z","title":"On the growth of solutions to the minimal surface equation over domains containing a halfplane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3334","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:dca6e5c8fc827665202468354bae9f908abb959eb53e660ef28fcf1d85cc7baf","target":"record","created_at":"2026-05-18T03:07:11Z","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":"532110482f845b77520f2b296619fe7590a8dbaad705dfa927c561386f4cc648","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-13T22:59:39Z","title_canon_sha256":"9807c71b5bfd6ea85610bbc80cf86b4dc62c98d574e54c415ab41c4166cf890c"},"schema_version":"1.0","source":{"id":"1311.3334","kind":"arxiv","version":1}},"canonical_sha256":"e020ba83349f3f6f4a0b5639825b2dc75203f9513f5e7bd28cf4af39efa26119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e020ba83349f3f6f4a0b5639825b2dc75203f9513f5e7bd28cf4af39efa26119","first_computed_at":"2026-05-18T03:07:11.764355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:11.764355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z0SGQMsoosD9XvDGTBv+j4rH6TzXj7VPU6l4e3PGmxRS8jzpYazVHgACBY1FrynzUN3NrvN10YRlWRVETMECAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:11.764885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dca6e5c8fc827665202468354bae9f908abb959eb53e660ef28fcf1d85cc7baf","sha256:6e31fe39f8fe6db8f8a564781c7bc7087410d220bcaee1effee5864033e5875b"],"state_sha256":"f11509cccaaa8527e3e1cf4f84e84785640cf2a4168bf88c4ded639660360603"}