{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5NBQRZZL3MNQQGQGZUT2FXCA3A","short_pith_number":"pith:5NBQRZZL","canonical_record":{"source":{"id":"1707.05053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-17T09:33:35Z","cross_cats_sorted":[],"title_canon_sha256":"71a2759a602ece834bb4561fa897fd25410956372ca9e78e22e6a8ed39b28afa","abstract_canon_sha256":"21a4c883e276022a903310c0f2872a30f775ee26ea94615e653808e01a66b8ec"},"schema_version":"1.0"},"canonical_sha256":"eb4308e72bdb1b081a06cd27a2dc40d8147b4d52c6f4a5b08110b46bcbb97df5","source":{"kind":"arxiv","id":"1707.05053","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05053","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05053v1","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05053","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"5NBQRZZL3MNQ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5NBQRZZL3MNQQGQG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5NBQRZZL","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5NBQRZZL3MNQQGQGZUT2FXCA3A","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-17T09:33:35Z","cross_cats_sorted":[],"title_canon_sha256":"71a2759a602ece834bb4561fa897fd25410956372ca9e78e22e6a8ed39b28afa","abstract_canon_sha256":"21a4c883e276022a903310c0f2872a30f775ee26ea94615e653808e01a66b8ec"},"schema_version":"1.0"},"canonical_sha256":"eb4308e72bdb1b081a06cd27a2dc40d8147b4d52c6f4a5b08110b46bcbb97df5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.487417Z","signature_b64":"zOew2TbAjpiiNkB5BWkptgs5x+B3XLbt0mWOT1XwF/E2l/iTufLVs8g+n9Yi+QOqHf9r/qPDVGXoupGzszrHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb4308e72bdb1b081a06cd27a2dc40d8147b4d52c6f4a5b08110b46bcbb97df5","last_reissued_at":"2026-05-18T00:40:11.486945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.486945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05053","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":"2026-05-18T00:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jw9kDwXt0Kp7/eN4ASG0pSiR7zupJ7+1nwOt74TKxquBKcKggSI+CogMnisb8Gn+IxUaXhA+darIx3iC/lKOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:42:50.077582Z"},"content_sha256":"eff799dd7ba63375949c0e2ec21e35400fc7d0df3cbd26d3b642d9c351b2fbb9","schema_version":"1.0","event_id":"sha256:eff799dd7ba63375949c0e2ec21e35400fc7d0df3cbd26d3b642d9c351b2fbb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5NBQRZZL3MNQQGQGZUT2FXCA3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An upper bound on distance degenerate handle additions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Yanqing Zou","submitted_at":"2017-07-17T09:33:35Z","abstract_excerpt":"We prove that for any distance at least 3 Heegaard splitting and a boundary component $F$, there is a diameter finite ball in the curve complex $\\mathcal {C}(F)$ so that it contains all distance degenerate curves or slopes in $F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05053","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":"2026-05-18T00:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MngEI6w7EIPy62e00nBsAXuho+3rLnjPoMDbid7AAtlq6mtAkCEWMsejdFrIDxt6jCCzZZ/jmQQXjgJOhZ/pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:42:50.077916Z"},"content_sha256":"14465e307d232228d67b53f468c7aa803c2bce0b8121cf92309b1ee474f12cfc","schema_version":"1.0","event_id":"sha256:14465e307d232228d67b53f468c7aa803c2bce0b8121cf92309b1ee474f12cfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/bundle.json","state_url":"https://pith.science/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/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":"2026-06-28T09:42:50Z","links":{"resolver":"https://pith.science/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A","bundle":"https://pith.science/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/bundle.json","state":"https://pith.science/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NBQRZZL3MNQQGQGZUT2FXCA3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5NBQRZZL3MNQQGQGZUT2FXCA3A","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":"21a4c883e276022a903310c0f2872a30f775ee26ea94615e653808e01a66b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-17T09:33:35Z","title_canon_sha256":"71a2759a602ece834bb4561fa897fd25410956372ca9e78e22e6a8ed39b28afa"},"schema_version":"1.0","source":{"id":"1707.05053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05053","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05053v1","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05053","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"5NBQRZZL3MNQ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5NBQRZZL3MNQQGQG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5NBQRZZL","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:14465e307d232228d67b53f468c7aa803c2bce0b8121cf92309b1ee474f12cfc","target":"graph","created_at":"2026-05-18T00:40:11Z","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 prove that for any distance at least 3 Heegaard splitting and a boundary component $F$, there is a diameter finite ball in the curve complex $\\mathcal {C}(F)$ so that it contains all distance degenerate curves or slopes in $F$.","authors_text":"Yanqing Zou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-17T09:33:35Z","title":"An upper bound on distance degenerate handle additions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05053","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:eff799dd7ba63375949c0e2ec21e35400fc7d0df3cbd26d3b642d9c351b2fbb9","target":"record","created_at":"2026-05-18T00:40:11Z","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":"21a4c883e276022a903310c0f2872a30f775ee26ea94615e653808e01a66b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-07-17T09:33:35Z","title_canon_sha256":"71a2759a602ece834bb4561fa897fd25410956372ca9e78e22e6a8ed39b28afa"},"schema_version":"1.0","source":{"id":"1707.05053","kind":"arxiv","version":1}},"canonical_sha256":"eb4308e72bdb1b081a06cd27a2dc40d8147b4d52c6f4a5b08110b46bcbb97df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb4308e72bdb1b081a06cd27a2dc40d8147b4d52c6f4a5b08110b46bcbb97df5","first_computed_at":"2026-05-18T00:40:11.486945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:11.486945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zOew2TbAjpiiNkB5BWkptgs5x+B3XLbt0mWOT1XwF/E2l/iTufLVs8g+n9Yi+QOqHf9r/qPDVGXoupGzszrHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:11.487417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eff799dd7ba63375949c0e2ec21e35400fc7d0df3cbd26d3b642d9c351b2fbb9","sha256:14465e307d232228d67b53f468c7aa803c2bce0b8121cf92309b1ee474f12cfc"],"state_sha256":"ba16a73bbb8e8ece0aaedf5fabd326911da621c360bff49c0c1517e388552120"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKXmttAknNpxH/hRQ53sWfwkOLtXFYL3DoX3tNufI2rWjt0IDGdfL7sAfGa91oFLmcdhb02eNpsmriEjvbkjDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:42:50.079708Z","bundle_sha256":"9161966cc24642032f48c0195c0999239aa9832a08cc1eb8684ac362e372d81b"}}