{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZP2PI7KTXNYLZJX7THUAZF6GEE","short_pith_number":"pith:ZP2PI7KT","canonical_record":{"source":{"id":"1809.05227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-14T02:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"20ea0fab81c9ab5255f4910f917696d3aa0210c238140c444948d4213987b12a","abstract_canon_sha256":"b080b826fe953697a83dccc1fb6ec7688d673521204c185048d63dcf41755acb"},"schema_version":"1.0"},"canonical_sha256":"cbf4f47d53bb70bca6ff99e80c97c6211ca9ba8a978779aa96c77484bfd9878a","source":{"kind":"arxiv","id":"1809.05227","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05227","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05227v2","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05227","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZP2PI7KTXNYL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZP2PI7KTXNYLZJX7","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZP2PI7KT","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZP2PI7KTXNYLZJX7THUAZF6GEE","target":"record","payload":{"canonical_record":{"source":{"id":"1809.05227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-14T02:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"20ea0fab81c9ab5255f4910f917696d3aa0210c238140c444948d4213987b12a","abstract_canon_sha256":"b080b826fe953697a83dccc1fb6ec7688d673521204c185048d63dcf41755acb"},"schema_version":"1.0"},"canonical_sha256":"cbf4f47d53bb70bca6ff99e80c97c6211ca9ba8a978779aa96c77484bfd9878a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:39.262859Z","signature_b64":"L1sMOEGWQ9ZsJ/c4Z1IL6c6umQj8GsQqwAIQsWLlchKiwKa+NydK6FDjQMRQi8/rsTXXvQi7IWvcbXDZRBvtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbf4f47d53bb70bca6ff99e80c97c6211ca9ba8a978779aa96c77484bfd9878a","last_reissued_at":"2026-05-17T23:54:39.262043Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:39.262043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.05227","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4E1/Kfp7Mj99eJ0Qg7AwhafbJm925RRsxEB/X1vxcQp9qMdt1GPyc5uqbSuco2FJ4Oyb0ZWwGaTPeyTNxJwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:56:42.959713Z"},"content_sha256":"91a3c70d5673de2f558ceb2429d017370fced332ffe9969bf80b195006c717b7","schema_version":"1.0","event_id":"sha256:91a3c70d5673de2f558ceb2429d017370fced332ffe9969bf80b195006c717b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZP2PI7KTXNYLZJX7THUAZF6GEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Branched covering surface-knots with degree three have the simplifying numbers less than three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Inasa Nakamura","submitted_at":"2018-09-14T02:33:57Z","abstract_excerpt":"A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05227","kind":"arxiv","version":2},"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":"2026-05-17T23:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zo8/24xcBxnTRvZPQ0S0iZvhJQXZUSvTV5UhtEntFP1tOKIo8im/QHto5dvPnSb9KZCh2w3X+7Lk/41RIiwWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:56:42.960395Z"},"content_sha256":"03bd3564cf2db6431896002e0e28e408f3753e6af719656c217ab8fea9ad0af0","schema_version":"1.0","event_id":"sha256:03bd3564cf2db6431896002e0e28e408f3753e6af719656c217ab8fea9ad0af0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/bundle.json","state_url":"https://pith.science/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/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":"2026-06-10T22:56:42Z","links":{"resolver":"https://pith.science/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE","bundle":"https://pith.science/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/bundle.json","state":"https://pith.science/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZP2PI7KTXNYLZJX7THUAZF6GEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZP2PI7KTXNYLZJX7THUAZF6GEE","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":"b080b826fe953697a83dccc1fb6ec7688d673521204c185048d63dcf41755acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-14T02:33:57Z","title_canon_sha256":"20ea0fab81c9ab5255f4910f917696d3aa0210c238140c444948d4213987b12a"},"schema_version":"1.0","source":{"id":"1809.05227","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05227","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05227v2","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05227","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZP2PI7KTXNYL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZP2PI7KTXNYLZJX7","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZP2PI7KT","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:03bd3564cf2db6431896002e0e28e408f3753e6af719656c217ab8fea9ad0af0","target":"graph","created_at":"2026-05-17T23:54:39Z","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":"A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.","authors_text":"Inasa Nakamura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-14T02:33:57Z","title":"Branched covering surface-knots with degree three have the simplifying numbers less than three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05227","kind":"arxiv","version":2},"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":"sha256:91a3c70d5673de2f558ceb2429d017370fced332ffe9969bf80b195006c717b7","target":"record","created_at":"2026-05-17T23:54:39Z","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":"b080b826fe953697a83dccc1fb6ec7688d673521204c185048d63dcf41755acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-14T02:33:57Z","title_canon_sha256":"20ea0fab81c9ab5255f4910f917696d3aa0210c238140c444948d4213987b12a"},"schema_version":"1.0","source":{"id":"1809.05227","kind":"arxiv","version":2}},"canonical_sha256":"cbf4f47d53bb70bca6ff99e80c97c6211ca9ba8a978779aa96c77484bfd9878a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbf4f47d53bb70bca6ff99e80c97c6211ca9ba8a978779aa96c77484bfd9878a","first_computed_at":"2026-05-17T23:54:39.262043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:39.262043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L1sMOEGWQ9ZsJ/c4Z1IL6c6umQj8GsQqwAIQsWLlchKiwKa+NydK6FDjQMRQi8/rsTXXvQi7IWvcbXDZRBvtAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:39.262859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05227","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91a3c70d5673de2f558ceb2429d017370fced332ffe9969bf80b195006c717b7","sha256:03bd3564cf2db6431896002e0e28e408f3753e6af719656c217ab8fea9ad0af0"],"state_sha256":"aac5bc13684f32242e0d4ac995ccca592d6fb804037e5f481471ccaed4a93b62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uS09DNC4zr++0wrVt0dONdKMggY69R4WxI3C8MKLu91i+BHtFS6FTvf0d46uoJ+Wi3eA2HfmjxvcBnW2XzMNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:56:42.964517Z","bundle_sha256":"710f2af4a20e45b57e70832635e8af2a904424a52bf68f96097686c545b6edf4"}}