{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NA77KAEADPISDMIJKUFGVBW2EV","short_pith_number":"pith:NA77KAEA","canonical_record":{"source":{"id":"1610.05832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T00:26:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ae3a4fc4daedb7309fcf1e2d62716bc91ad440eec8e0c8435c38dd2b3b4be8fc","abstract_canon_sha256":"572d266e64132628fbcd6a98ccb107adba1ecca602d66dd18a7b6b32ded204db"},"schema_version":"1.0"},"canonical_sha256":"683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7","source":{"kind":"arxiv","id":"1610.05832","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05832","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05832v3","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05832","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"NA77KAEADPIS","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NA77KAEADPISDMIJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NA77KAEA","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NA77KAEADPISDMIJKUFGVBW2EV","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T00:26:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ae3a4fc4daedb7309fcf1e2d62716bc91ad440eec8e0c8435c38dd2b3b4be8fc","abstract_canon_sha256":"572d266e64132628fbcd6a98ccb107adba1ecca602d66dd18a7b6b32ded204db"},"schema_version":"1.0"},"canonical_sha256":"683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.098951Z","signature_b64":"jv3rGDoRq/ojS4L/C8zOWucZ6URSt2pmqnlTRH0/nLiXUoZib9fAMRbT+h83JjnyLNWSHMYRgP55eX5Cys+eDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7","last_reissued_at":"2026-05-18T00:20:57.098414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.098414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05832","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeQAteC7lvkZkL+tqAJVqsatGRLJj19PoGPjd5dwT9+cB751LyHUb3/+TchQ2/x8GmRhZK1thH3GYIAGRCMWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:01:30.042207Z"},"content_sha256":"714be690980372a644bdebc4927af54299366752dd1c4d7874c73bbcd4006a2d","schema_version":"1.0","event_id":"sha256:714be690980372a644bdebc4927af54299366752dd1c4d7874c73bbcd4006a2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NA77KAEADPISDMIJKUFGVBW2EV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform fellow traveling between surgery paths in the sphere graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Kasra Rafi, Matt Clay, Yulan Qing","submitted_at":"2016-10-19T00:26:03Z","abstract_excerpt":"We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how surgeries affect the Guirardel core associated to sphere systems. We show that applying a surgery is equivalent to performing a Rips move on the Guirardel core."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05832","kind":"arxiv","version":3},"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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yPVkaeL2OC1HctgiDvOQMgr+CYAsbRSZa0YrZZnf0QtlbmfHYZMqibrDl80cV3c5v01peMqW9m2YGS95F6QDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:01:30.042954Z"},"content_sha256":"ae0aab12725b1881f3b027456734942bbc4246325dc370c3f920c716b3d77e87","schema_version":"1.0","event_id":"sha256:ae0aab12725b1881f3b027456734942bbc4246325dc370c3f920c716b3d77e87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NA77KAEADPISDMIJKUFGVBW2EV/bundle.json","state_url":"https://pith.science/pith/NA77KAEADPISDMIJKUFGVBW2EV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NA77KAEADPISDMIJKUFGVBW2EV/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":"2026-06-08T21:01:30Z","links":{"resolver":"https://pith.science/pith/NA77KAEADPISDMIJKUFGVBW2EV","bundle":"https://pith.science/pith/NA77KAEADPISDMIJKUFGVBW2EV/bundle.json","state":"https://pith.science/pith/NA77KAEADPISDMIJKUFGVBW2EV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NA77KAEADPISDMIJKUFGVBW2EV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NA77KAEADPISDMIJKUFGVBW2EV","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":"572d266e64132628fbcd6a98ccb107adba1ecca602d66dd18a7b6b32ded204db","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T00:26:03Z","title_canon_sha256":"ae3a4fc4daedb7309fcf1e2d62716bc91ad440eec8e0c8435c38dd2b3b4be8fc"},"schema_version":"1.0","source":{"id":"1610.05832","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05832","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05832v3","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05832","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"NA77KAEADPIS","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NA77KAEADPISDMIJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NA77KAEA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:ae0aab12725b1881f3b027456734942bbc4246325dc370c3f920c716b3d77e87","target":"graph","created_at":"2026-05-18T00:20:57Z","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 show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how surgeries affect the Guirardel core associated to sphere systems. We show that applying a surgery is equivalent to performing a Rips move on the Guirardel core.","authors_text":"Kasra Rafi, Matt Clay, Yulan Qing","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T00:26:03Z","title":"Uniform fellow traveling between surgery paths in the sphere graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05832","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":"sha256:714be690980372a644bdebc4927af54299366752dd1c4d7874c73bbcd4006a2d","target":"record","created_at":"2026-05-18T00:20:57Z","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":"572d266e64132628fbcd6a98ccb107adba1ecca602d66dd18a7b6b32ded204db","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T00:26:03Z","title_canon_sha256":"ae3a4fc4daedb7309fcf1e2d62716bc91ad440eec8e0c8435c38dd2b3b4be8fc"},"schema_version":"1.0","source":{"id":"1610.05832","kind":"arxiv","version":3}},"canonical_sha256":"683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7","first_computed_at":"2026-05-18T00:20:57.098414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.098414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jv3rGDoRq/ojS4L/C8zOWucZ6URSt2pmqnlTRH0/nLiXUoZib9fAMRbT+h83JjnyLNWSHMYRgP55eX5Cys+eDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.098951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05832","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:714be690980372a644bdebc4927af54299366752dd1c4d7874c73bbcd4006a2d","sha256:ae0aab12725b1881f3b027456734942bbc4246325dc370c3f920c716b3d77e87"],"state_sha256":"3f219e9a760148a4f2f10df25a73e33e0d21c581168c5eb5f5aba3cb962c058b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfuV/vOOvozY0cs2bf8qYJCHl9Hf1PYyN2oCeMVaayry5wi/Pxr7mNO/2qfZZFaAgm+hs1nYo2mmmAXjLIo/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:01:30.047257Z","bundle_sha256":"d26d9bd7e6fd684368a1dc28b1ed925614bf569ea6bf696c380f95b0b8ccc321"}}