{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7TQ5S3243ROYDU2C55VFU7RAUA","short_pith_number":"pith:7TQ5S324","canonical_record":{"source":{"id":"1605.08731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-27T18:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"263ffa96451f07c1fdaa0eeabb9bac6a5a947ad72a00b7d26b0316062a8fde2a","abstract_canon_sha256":"737244b953981c90fe35d77aca7f6ef17bec3acf0315f8e8969cee0f94a48ef2"},"schema_version":"1.0"},"canonical_sha256":"fce1d96f5cdc5d81d342ef6a5a7e20a016172eb0790160c551c45e309a5fa178","source":{"kind":"arxiv","id":"1605.08731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08731","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08731v1","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08731","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"7TQ5S3243ROY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7TQ5S3243ROYDU2C","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7TQ5S324","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7TQ5S3243ROYDU2C55VFU7RAUA","target":"record","payload":{"canonical_record":{"source":{"id":"1605.08731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-27T18:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"263ffa96451f07c1fdaa0eeabb9bac6a5a947ad72a00b7d26b0316062a8fde2a","abstract_canon_sha256":"737244b953981c90fe35d77aca7f6ef17bec3acf0315f8e8969cee0f94a48ef2"},"schema_version":"1.0"},"canonical_sha256":"fce1d96f5cdc5d81d342ef6a5a7e20a016172eb0790160c551c45e309a5fa178","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:29.209671Z","signature_b64":"xq18dvfQ3CfShf+P0uCOHZloiuptrjCE3KUlnL/5/WZ+z5cTdWZGxhAwoth1VUvCoJyg5gtwa2fhM56DXxwYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fce1d96f5cdc5d81d342ef6a5a7e20a016172eb0790160c551c45e309a5fa178","last_reissued_at":"2026-05-18T01:13:29.209136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:29.209136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.08731","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6U3l6th6xucyBCS+GTtAxhM7SdlVnpSOxo2i+CyqbLnrYKlAM1tk4eLaw5uepsQLOPR1PnXhlnK/jzDsnFIDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:16:46.022034Z"},"content_sha256":"aa967386c144a7cf765632cd8b230e1e5ec0a4ed0befe64821d66b9d7e766fa7","schema_version":"1.0","event_id":"sha256:aa967386c144a7cf765632cd8b230e1e5ec0a4ed0befe64821d66b9d7e766fa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7TQ5S3243ROYDU2C55VFU7RAUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An elementary proof of a Theorem by Matsumoto","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luis Hernandez-Corbato","submitted_at":"2016-05-27T18:06:34Z","abstract_excerpt":"Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this fact using only simple planar topology is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08731","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJmg8MZ//ZZBqSoJBkASEy1XODFqQCwHhi3bRexcZ4bwpbyENvQ3S9yQNvyOe6iwKusWQhfSaEvou+rv6NLzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:16:46.022597Z"},"content_sha256":"b2210b26fc90d7e8013aa1f6017ab275e22fa7f92b0319b011fb7cb1a03596d0","schema_version":"1.0","event_id":"sha256:b2210b26fc90d7e8013aa1f6017ab275e22fa7f92b0319b011fb7cb1a03596d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TQ5S3243ROYDU2C55VFU7RAUA/bundle.json","state_url":"https://pith.science/pith/7TQ5S3243ROYDU2C55VFU7RAUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TQ5S3243ROYDU2C55VFU7RAUA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T11:16:46Z","links":{"resolver":"https://pith.science/pith/7TQ5S3243ROYDU2C55VFU7RAUA","bundle":"https://pith.science/pith/7TQ5S3243ROYDU2C55VFU7RAUA/bundle.json","state":"https://pith.science/pith/7TQ5S3243ROYDU2C55VFU7RAUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TQ5S3243ROYDU2C55VFU7RAUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7TQ5S3243ROYDU2C55VFU7RAUA","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":"737244b953981c90fe35d77aca7f6ef17bec3acf0315f8e8969cee0f94a48ef2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-27T18:06:34Z","title_canon_sha256":"263ffa96451f07c1fdaa0eeabb9bac6a5a947ad72a00b7d26b0316062a8fde2a"},"schema_version":"1.0","source":{"id":"1605.08731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08731","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08731v1","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08731","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"7TQ5S3243ROY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7TQ5S3243ROYDU2C","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7TQ5S324","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:b2210b26fc90d7e8013aa1f6017ab275e22fa7f92b0319b011fb7cb1a03596d0","target":"graph","created_at":"2026-05-18T01:13:29Z","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":"Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this fact using only simple planar topology is presented.","authors_text":"Luis Hernandez-Corbato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-27T18:06:34Z","title":"An elementary proof of a Theorem by Matsumoto"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08731","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:aa967386c144a7cf765632cd8b230e1e5ec0a4ed0befe64821d66b9d7e766fa7","target":"record","created_at":"2026-05-18T01:13:29Z","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":"737244b953981c90fe35d77aca7f6ef17bec3acf0315f8e8969cee0f94a48ef2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-27T18:06:34Z","title_canon_sha256":"263ffa96451f07c1fdaa0eeabb9bac6a5a947ad72a00b7d26b0316062a8fde2a"},"schema_version":"1.0","source":{"id":"1605.08731","kind":"arxiv","version":1}},"canonical_sha256":"fce1d96f5cdc5d81d342ef6a5a7e20a016172eb0790160c551c45e309a5fa178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fce1d96f5cdc5d81d342ef6a5a7e20a016172eb0790160c551c45e309a5fa178","first_computed_at":"2026-05-18T01:13:29.209136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:29.209136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xq18dvfQ3CfShf+P0uCOHZloiuptrjCE3KUlnL/5/WZ+z5cTdWZGxhAwoth1VUvCoJyg5gtwa2fhM56DXxwYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:29.209671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa967386c144a7cf765632cd8b230e1e5ec0a4ed0befe64821d66b9d7e766fa7","sha256:b2210b26fc90d7e8013aa1f6017ab275e22fa7f92b0319b011fb7cb1a03596d0"],"state_sha256":"f26741bad4d4535548ae5af214a3f975f9f44386f0d549b72083e8db04e56375"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqL1x3Q9SwF7KSO6gERtjmZamEwSW5RoCJJcOMoFM7SGYSZS9UNIBuOkXD9jg+E+XfF8Te653PMaOLeXiffqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T11:16:46.025336Z","bundle_sha256":"31c295b454eb3f03031380661ad1a031525e4471f57937d8570457dd8c77c86c"}}