{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:43CODRU6D45NALM2ASOKVGRWVR","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":"f33270ed6073e6ca7c4678e4d63669682ede2a1ed50774e61d949818d333efab","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2004-06-01T16:10:48Z","title_canon_sha256":"1f228f600646013d1b6e871dbbc7a6cfc321fcff72222a820a3a239442579440"},"schema_version":"1.0","source":{"id":"math/0406017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406017","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406017v1","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406017","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"43CODRU6D45N","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_16","alias_value":"43CODRU6D45NALM2","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_8","alias_value":"43CODRU6","created_at":"2026-07-04T14:38:40Z"}],"graph_snapshots":[{"event_id":"sha256:7e6bfd853ad11b95cac8be2dfc87a188da19b22f93e0cfc42c8aeada2b53dccc","target":"graph","created_at":"2026-07-04T14:38:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0406017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in \\Bbb R^3.","authors_text":"Antonio Ros, Frank Morgan, Manuel Ritor\\'e, Michael Hutchings","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2004-06-01T16:10:48Z","title":"Proof of the Double Bubble Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406017","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":"sha256:9997609a25be396bc45fe8b489e4f877351b1069cd5797d30cdb09b78fe46afb","target":"record","created_at":"2026-07-04T14:38:40Z","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":"f33270ed6073e6ca7c4678e4d63669682ede2a1ed50774e61d949818d333efab","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2004-06-01T16:10:48Z","title_canon_sha256":"1f228f600646013d1b6e871dbbc7a6cfc321fcff72222a820a3a239442579440"},"schema_version":"1.0","source":{"id":"math/0406017","kind":"arxiv","version":1}},"canonical_sha256":"e6c4e1c69e1f3ad02d9a049caa9a36ac539240aa2b1e35e4a0b4f4986a7b9317","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6c4e1c69e1f3ad02d9a049caa9a36ac539240aa2b1e35e4a0b4f4986a7b9317","first_computed_at":"2026-07-04T14:38:40.472484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:40.472484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cjlVTe+tleeVEQUthXqChf8P0gBF7JRPguFfbUv3pPQsKP02vSMDITdEb7YFqBJTqRfwm+8ij/gzSXitDHleAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:40.472891Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9997609a25be396bc45fe8b489e4f877351b1069cd5797d30cdb09b78fe46afb","sha256:7e6bfd853ad11b95cac8be2dfc87a188da19b22f93e0cfc42c8aeada2b53dccc"],"state_sha256":"9530a3405dc3d50031fe6a465abec8b9bd662098fd1953b1d095578d351c30a5"}