{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EXMVNBLG6YVE7HOKM65GXPJBLK","short_pith_number":"pith:EXMVNBLG","canonical_record":{"source":{"id":"1611.00066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T22:29:56Z","cross_cats_sorted":[],"title_canon_sha256":"f8a421b96c8156aba321c12d8c0147b3225391a270f41024b08abfc15e1c720b","abstract_canon_sha256":"19f205911151046f15cbb7811b2cde5e88668617f63f7a381771a3dd863f406d"},"schema_version":"1.0"},"canonical_sha256":"25d9568566f62a4f9dca67ba6bbd215aa20aa199123abede07917ac400584216","source":{"kind":"arxiv","id":"1611.00066","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00066","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00066v2","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00066","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"EXMVNBLG6YVE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXMVNBLG6YVE7HOK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXMVNBLG","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EXMVNBLG6YVE7HOKM65GXPJBLK","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T22:29:56Z","cross_cats_sorted":[],"title_canon_sha256":"f8a421b96c8156aba321c12d8c0147b3225391a270f41024b08abfc15e1c720b","abstract_canon_sha256":"19f205911151046f15cbb7811b2cde5e88668617f63f7a381771a3dd863f406d"},"schema_version":"1.0"},"canonical_sha256":"25d9568566f62a4f9dca67ba6bbd215aa20aa199123abede07917ac400584216","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:57.769967Z","signature_b64":"cHEz0Dij8+AgQz9QOknhsgzVDHa3vb71UwaHPxEtGxpJ3Pqbd2rx2D2hrFHXUaDxsE+SftzaKUxRzlJC4LA4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25d9568566f62a4f9dca67ba6bbd215aa20aa199123abede07917ac400584216","last_reissued_at":"2026-05-18T00:08:57.769239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:57.769239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00066","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":"2026-05-18T00:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjjxLt/YUbZ5fb3Ql4TA99qRnwFUb96yoM9PhII7j90RMN0rjZZp+ctGWGm+jRd5YnxKaILBzMynWGBqScykBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:27:44.100266Z"},"content_sha256":"461903f5f1e03ee902593bae36570bce5e01329f49a61b05d2e1e9b189bbaf3d","schema_version":"1.0","event_id":"sha256:461903f5f1e03ee902593bae36570bce5e01329f49a61b05d2e1e9b189bbaf3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EXMVNBLG6YVE7HOKM65GXPJBLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Many Haken Heegaard splittings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessandro Sisto","submitted_at":"2016-10-31T22:29:56Z","abstract_excerpt":"We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant.\n  Along the way we give simpler and shorter proofs of the existence of splittings with specified Heegaard distance, originally proven by Ido-Jang-Kobayashi, of the existence of hyperbolic manifolds with prescribed Casson invariant, originally due to Lubotzky-Maher-Wu, and of a result about subsurface projections of disc sets (for which we even"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00066","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":"2026-05-18T00:08:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWNXOI06YHpwrPC/a+80ddao4cvluQmjW1qIg6pyNA+1Sr3Xk1VPqYmVyCD1dQ+zkNzPtiZy2MR49jXd283ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:27:44.100640Z"},"content_sha256":"353cb45d848c230b106dd8cecbba623e43f487e24ebb2a66ea4e79b2a03dc4ea","schema_version":"1.0","event_id":"sha256:353cb45d848c230b106dd8cecbba623e43f487e24ebb2a66ea4e79b2a03dc4ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/bundle.json","state_url":"https://pith.science/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/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":"2026-05-28T06:27:44Z","links":{"resolver":"https://pith.science/pith/EXMVNBLG6YVE7HOKM65GXPJBLK","bundle":"https://pith.science/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/bundle.json","state":"https://pith.science/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXMVNBLG6YVE7HOKM65GXPJBLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EXMVNBLG6YVE7HOKM65GXPJBLK","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":"19f205911151046f15cbb7811b2cde5e88668617f63f7a381771a3dd863f406d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T22:29:56Z","title_canon_sha256":"f8a421b96c8156aba321c12d8c0147b3225391a270f41024b08abfc15e1c720b"},"schema_version":"1.0","source":{"id":"1611.00066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00066","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00066v2","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00066","created_at":"2026-05-18T00:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"EXMVNBLG6YVE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXMVNBLG6YVE7HOK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXMVNBLG","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:353cb45d848c230b106dd8cecbba623e43f487e24ebb2a66ea4e79b2a03dc4ea","target":"graph","created_at":"2026-05-18T00:08:57Z","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 give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant.\n  Along the way we give simpler and shorter proofs of the existence of splittings with specified Heegaard distance, originally proven by Ido-Jang-Kobayashi, of the existence of hyperbolic manifolds with prescribed Casson invariant, originally due to Lubotzky-Maher-Wu, and of a result about subsurface projections of disc sets (for which we even","authors_text":"Alessandro Sisto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T22:29:56Z","title":"Many Haken Heegaard splittings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00066","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":"sha256:461903f5f1e03ee902593bae36570bce5e01329f49a61b05d2e1e9b189bbaf3d","target":"record","created_at":"2026-05-18T00:08:57Z","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":"19f205911151046f15cbb7811b2cde5e88668617f63f7a381771a3dd863f406d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T22:29:56Z","title_canon_sha256":"f8a421b96c8156aba321c12d8c0147b3225391a270f41024b08abfc15e1c720b"},"schema_version":"1.0","source":{"id":"1611.00066","kind":"arxiv","version":2}},"canonical_sha256":"25d9568566f62a4f9dca67ba6bbd215aa20aa199123abede07917ac400584216","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25d9568566f62a4f9dca67ba6bbd215aa20aa199123abede07917ac400584216","first_computed_at":"2026-05-18T00:08:57.769239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:57.769239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHEz0Dij8+AgQz9QOknhsgzVDHa3vb71UwaHPxEtGxpJ3Pqbd2rx2D2hrFHXUaDxsE+SftzaKUxRzlJC4LA4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:57.769967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:461903f5f1e03ee902593bae36570bce5e01329f49a61b05d2e1e9b189bbaf3d","sha256:353cb45d848c230b106dd8cecbba623e43f487e24ebb2a66ea4e79b2a03dc4ea"],"state_sha256":"23f9c9840a49ae320e716e3b44ca01f4d86f2104eb36b5af39c814099b51c976"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hM2sUZvSpWq6GtfAipA9A0C9Xz0A67rINzxf6vPIN6zeR/AazrHRu0ef+n/XiBHpvXvn1Ze1+5djzcDSQBEEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:27:44.102718Z","bundle_sha256":"b41b14866094190846e9e5c6c56566c120cfd04d8ea58178eaf8fb9300ae1a1f"}}