{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3SNIQZNCKVX37HXUP2NFNNTESV","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":"b62d3b547d01b64f0705ff1322e65d214d0d42c571d3043a0e5d96f35939774e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-24T08:20:32Z","title_canon_sha256":"1c9ea8625ad2e2af165e044bc28bbfc8612ea019015ce406f118736ed34cbd37"},"schema_version":"1.0","source":{"id":"1408.5578","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5578","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5578v3","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5578","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"3SNIQZNCKVX3","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3SNIQZNCKVX37HXU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3SNIQZNC","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:36dc9b594264e199b7e8c8f9a861583fc2e8979e3f23963de991273a546135ba","target":"graph","created_at":"2026-05-18T00:21:00Z","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 prove a chord arc bound for disks embedded in $\\mathbb{R}^3$ with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal disks. Like in the minimal case, this chord arc bound is a fundamental tool for studying complete constant mean curvature surfaces embedded in $\\mathbb{R}^3$ with finite topology or with positive injectivity radius.","authors_text":"Giuseppe Tinaglia, William H. Meeks III","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-24T08:20:32Z","title":"Chord arc properties for constant mean curvature disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5578","kind":"arxiv","version":3},"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":"sha256:52cdcbbdf86c06c42a69a798e0833cd93980531907898c9d3c3d9f97a5d309fb","target":"record","created_at":"2026-05-18T00:21:00Z","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":"b62d3b547d01b64f0705ff1322e65d214d0d42c571d3043a0e5d96f35939774e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-24T08:20:32Z","title_canon_sha256":"1c9ea8625ad2e2af165e044bc28bbfc8612ea019015ce406f118736ed34cbd37"},"schema_version":"1.0","source":{"id":"1408.5578","kind":"arxiv","version":3}},"canonical_sha256":"dc9a8865a2556fbf9ef47e9a56b664954de60c9150c1512d03c5af4b6e66fc02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc9a8865a2556fbf9ef47e9a56b664954de60c9150c1512d03c5af4b6e66fc02","first_computed_at":"2026-05-18T00:21:00.834338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.834338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aag/ek6DMabrAm95qOB2lkArH6ljR5IaOAM32TeG9Iay92wuDiy2bkWiEcqbqc0p1OjvoqPLWK+FZK2OuLTDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.834907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5578","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52cdcbbdf86c06c42a69a798e0833cd93980531907898c9d3c3d9f97a5d309fb","sha256:36dc9b594264e199b7e8c8f9a861583fc2e8979e3f23963de991273a546135ba"],"state_sha256":"4433f3ac4cac2aac9beddb31e9ac2365e2422a87c81a2a34dfed35c4205f43c3"}