{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5C5IEV45FLLEG5K2SWQLWPGJSN","short_pith_number":"pith:5C5IEV45","canonical_record":{"source":{"id":"2406.09629","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-13T23:36:51Z","cross_cats_sorted":[],"title_canon_sha256":"db15c125d89592c2fc56e31454695e63109f3d6bb1c4ae876320a894f4954bfb","abstract_canon_sha256":"0377e2df2488bac3b299f38666d32df00074596bf33fbc7d7c0547158d1e6eae"},"schema_version":"1.0"},"canonical_sha256":"e8ba82579d2ad643755a95a0bb3cc993423223dd93c7653bd703a69cde5770ec","source":{"kind":"arxiv","id":"2406.09629","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09629","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09629v2","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09629","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_12","alias_value":"5C5IEV45FLLE","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_16","alias_value":"5C5IEV45FLLEG5K2","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_8","alias_value":"5C5IEV45","created_at":"2026-07-01T14:23:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5C5IEV45FLLEG5K2SWQLWPGJSN","target":"record","payload":{"canonical_record":{"source":{"id":"2406.09629","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-13T23:36:51Z","cross_cats_sorted":[],"title_canon_sha256":"db15c125d89592c2fc56e31454695e63109f3d6bb1c4ae876320a894f4954bfb","abstract_canon_sha256":"0377e2df2488bac3b299f38666d32df00074596bf33fbc7d7c0547158d1e6eae"},"schema_version":"1.0"},"canonical_sha256":"e8ba82579d2ad643755a95a0bb3cc993423223dd93c7653bd703a69cde5770ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T14:23:05.495355Z","signature_b64":"fWg31hma9r6zM4XhP45cepdtf2AGjE1Uzde5DNAVdqaFcLVDrgFnqbrMAx/SEgwx3kwxBPlUld6olEyikrpsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ba82579d2ad643755a95a0bb3cc993423223dd93c7653bd703a69cde5770ec","last_reissued_at":"2026-07-01T14:23:05.494860Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T14:23:05.494860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.09629","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":"2026-07-01T14:23:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYtT+SqFmM8eWXfisjbqR0ltttVAeEEg684PQL0RpVNbOA2JuqHGV/uX9W9dR03yDsvXiWurdEz/WWCIcsbeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:57:34.712138Z"},"content_sha256":"dbd64674c778bb8d3f5d80fb62b036bbf59a77655050516ae3ae07e68c97661e","schema_version":"1.0","event_id":"sha256:dbd64674c778bb8d3f5d80fb62b036bbf59a77655050516ae3ae07e68c97661e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5C5IEV45FLLEG5K2SWQLWPGJSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of 2-bridge link complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"James Morgan, Jonathan Spreer","submitted_at":"2024-06-13T23:36:51Z","abstract_excerpt":"We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09629","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.09629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-01T14:23:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGUSy+YgDR6XR22vwZ2h4pSUzLIrO3HnciJxyvs7KmYhEv6ln5DPujPdQAeaEPF8xNRXJA8iqsyIy/tPnBwQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:57:34.712526Z"},"content_sha256":"55bdcddc5ec9f4dc16de1be2945ed371d44fb890b04b45ddba1cd9d3c76c7502","schema_version":"1.0","event_id":"sha256:55bdcddc5ec9f4dc16de1be2945ed371d44fb890b04b45ddba1cd9d3c76c7502"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/bundle.json","state_url":"https://pith.science/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/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":"2026-07-03T08:57:34Z","links":{"resolver":"https://pith.science/pith/5C5IEV45FLLEG5K2SWQLWPGJSN","bundle":"https://pith.science/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/bundle.json","state":"https://pith.science/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C5IEV45FLLEG5K2SWQLWPGJSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5C5IEV45FLLEG5K2SWQLWPGJSN","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":"0377e2df2488bac3b299f38666d32df00074596bf33fbc7d7c0547158d1e6eae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-13T23:36:51Z","title_canon_sha256":"db15c125d89592c2fc56e31454695e63109f3d6bb1c4ae876320a894f4954bfb"},"schema_version":"1.0","source":{"id":"2406.09629","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09629","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09629v2","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09629","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_12","alias_value":"5C5IEV45FLLE","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_16","alias_value":"5C5IEV45FLLEG5K2","created_at":"2026-07-01T14:23:05Z"},{"alias_kind":"pith_short_8","alias_value":"5C5IEV45","created_at":"2026-07-01T14:23:05Z"}],"graph_snapshots":[{"event_id":"sha256:55bdcddc5ec9f4dc16de1be2945ed371d44fb890b04b45ddba1cd9d3c76c7502","target":"graph","created_at":"2026-07-01T14:23:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.09629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined.","authors_text":"James Morgan, Jonathan Spreer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-13T23:36:51Z","title":"On the complexity of 2-bridge link complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09629","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:dbd64674c778bb8d3f5d80fb62b036bbf59a77655050516ae3ae07e68c97661e","target":"record","created_at":"2026-07-01T14:23:05Z","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":"0377e2df2488bac3b299f38666d32df00074596bf33fbc7d7c0547158d1e6eae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-06-13T23:36:51Z","title_canon_sha256":"db15c125d89592c2fc56e31454695e63109f3d6bb1c4ae876320a894f4954bfb"},"schema_version":"1.0","source":{"id":"2406.09629","kind":"arxiv","version":2}},"canonical_sha256":"e8ba82579d2ad643755a95a0bb3cc993423223dd93c7653bd703a69cde5770ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ba82579d2ad643755a95a0bb3cc993423223dd93c7653bd703a69cde5770ec","first_computed_at":"2026-07-01T14:23:05.494860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T14:23:05.494860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fWg31hma9r6zM4XhP45cepdtf2AGjE1Uzde5DNAVdqaFcLVDrgFnqbrMAx/SEgwx3kwxBPlUld6olEyikrpsDg==","signature_status":"signed_v1","signed_at":"2026-07-01T14:23:05.495355Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.09629","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbd64674c778bb8d3f5d80fb62b036bbf59a77655050516ae3ae07e68c97661e","sha256:55bdcddc5ec9f4dc16de1be2945ed371d44fb890b04b45ddba1cd9d3c76c7502"],"state_sha256":"0240e58e0733045dc0032133948997889240671c808c09c77f9689e9ebd11b8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q54L3UmBd6bipO8awAm/6bB/jYDFnach5M0ZZo7p6bRPSPvXPJdqvGXnpaxYA7kDdX9PSPHsC1ac3GVEUXPKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T08:57:34.715263Z","bundle_sha256":"977fb2d4777fd3837088ae5de2f41a99240ea40f8c1aea6a1ea398eb58198983"}}