{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HP3UWV5J4JU5HGW53VCJA656ST","short_pith_number":"pith:HP3UWV5J","canonical_record":{"source":{"id":"1503.04099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-13T15:21:06Z","cross_cats_sorted":["cs.CC","cs.DS","cs.MS"],"title_canon_sha256":"7b13f0278d0f806f74d0700d19bf417d7290805f33891d9c400c2a58b8410bbc","abstract_canon_sha256":"4c7d57380e1feb240f15b61d68af2f83f01f92cb4d0e46bda400feb4ebf402bc"},"schema_version":"1.0"},"canonical_sha256":"3bf74b57a9e269d39adddd44907bbe94fe263bd5230c99caeb2f3115a6bcb7dd","source":{"kind":"arxiv","id":"1503.04099","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04099","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04099v1","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04099","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"HP3UWV5J4JU5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HP3UWV5J4JU5HGW5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HP3UWV5J","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HP3UWV5J4JU5HGW53VCJA656ST","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-13T15:21:06Z","cross_cats_sorted":["cs.CC","cs.DS","cs.MS"],"title_canon_sha256":"7b13f0278d0f806f74d0700d19bf417d7290805f33891d9c400c2a58b8410bbc","abstract_canon_sha256":"4c7d57380e1feb240f15b61d68af2f83f01f92cb4d0e46bda400feb4ebf402bc"},"schema_version":"1.0"},"canonical_sha256":"3bf74b57a9e269d39adddd44907bbe94fe263bd5230c99caeb2f3115a6bcb7dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:36.883764Z","signature_b64":"yl2aPiMnhB7MoJt8equ/XhjVbpu3sRWCyYhvbfHq9024Np4Acb0nI3dyN/rb78Y8tgH7zvhxy7aem6ssRCtMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf74b57a9e269d39adddd44907bbe94fe263bd5230c99caeb2f3115a6bcb7dd","last_reissued_at":"2026-05-18T00:02:36.883123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:36.883123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04099","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":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09XLe14GIVZ+GQleqxrakfkd4MT6T1aH1JfuM3MN7sYfOddgp1zCnFoObHeqR8CbWsfcYM4fdBSr/v7QSRFoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:25:47.552090Z"},"content_sha256":"88954f91784642cf9004c6e12c4aa4e812aa33943a05acb3bc33b7dc12a7ae5b","schema_version":"1.0","event_id":"sha256:88954f91784642cf9004c6e12c4aa4e812aa33943a05acb3bc33b7dc12a7ae5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HP3UWV5J4JU5HGW53VCJA656ST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms and complexity for Turaev-Viro invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","cs.MS"],"primary_cat":"math.GT","authors_text":"Benjamin A. Burton, Cl\\'ement Maria, Jonathan Spreer","submitted_at":"2015-03-13T15:21:06Z","abstract_excerpt":"The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time.\n  The invariants are parameterised by an integer $r \\geq 3$. We resolve the question of complexity for $r=3$ and $r=4$, giving simple proofs that computing Turaev-Viro invariants for $r=3$ is polynomial time, but for $r=4$ is \\#P-hard. Moreover, we give an explicit fixed-parameter tractable algorithm for arbitrary $r$, and show through concrete implementation a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04099","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":"2026-05-18T00:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"myIHyZVsl34xYV4pXYzE22xrSL20+fIukDt3er0TpJthOw+mLhxUIclwJON3sKwxNSmqgomX3v1w83xUcdRIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:25:47.552479Z"},"content_sha256":"1ee09c5a79550e1afa1c10c727e4af0544af165863b877313655c03eb8372995","schema_version":"1.0","event_id":"sha256:1ee09c5a79550e1afa1c10c727e4af0544af165863b877313655c03eb8372995"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HP3UWV5J4JU5HGW53VCJA656ST/bundle.json","state_url":"https://pith.science/pith/HP3UWV5J4JU5HGW53VCJA656ST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HP3UWV5J4JU5HGW53VCJA656ST/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":"2026-06-01T11:25:47Z","links":{"resolver":"https://pith.science/pith/HP3UWV5J4JU5HGW53VCJA656ST","bundle":"https://pith.science/pith/HP3UWV5J4JU5HGW53VCJA656ST/bundle.json","state":"https://pith.science/pith/HP3UWV5J4JU5HGW53VCJA656ST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HP3UWV5J4JU5HGW53VCJA656ST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HP3UWV5J4JU5HGW53VCJA656ST","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":"4c7d57380e1feb240f15b61d68af2f83f01f92cb4d0e46bda400feb4ebf402bc","cross_cats_sorted":["cs.CC","cs.DS","cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-13T15:21:06Z","title_canon_sha256":"7b13f0278d0f806f74d0700d19bf417d7290805f33891d9c400c2a58b8410bbc"},"schema_version":"1.0","source":{"id":"1503.04099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04099","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04099v1","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04099","created_at":"2026-05-18T00:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"HP3UWV5J4JU5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HP3UWV5J4JU5HGW5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HP3UWV5J","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:1ee09c5a79550e1afa1c10c727e4af0544af165863b877313655c03eb8372995","target":"graph","created_at":"2026-05-18T00:02:36Z","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":"The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time.\n  The invariants are parameterised by an integer $r \\geq 3$. We resolve the question of complexity for $r=3$ and $r=4$, giving simple proofs that computing Turaev-Viro invariants for $r=3$ is polynomial time, but for $r=4$ is \\#P-hard. Moreover, we give an explicit fixed-parameter tractable algorithm for arbitrary $r$, and show through concrete implementation a","authors_text":"Benjamin A. Burton, Cl\\'ement Maria, Jonathan Spreer","cross_cats":["cs.CC","cs.DS","cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-13T15:21:06Z","title":"Algorithms and complexity for Turaev-Viro invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04099","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":"sha256:88954f91784642cf9004c6e12c4aa4e812aa33943a05acb3bc33b7dc12a7ae5b","target":"record","created_at":"2026-05-18T00:02:36Z","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":"4c7d57380e1feb240f15b61d68af2f83f01f92cb4d0e46bda400feb4ebf402bc","cross_cats_sorted":["cs.CC","cs.DS","cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-13T15:21:06Z","title_canon_sha256":"7b13f0278d0f806f74d0700d19bf417d7290805f33891d9c400c2a58b8410bbc"},"schema_version":"1.0","source":{"id":"1503.04099","kind":"arxiv","version":1}},"canonical_sha256":"3bf74b57a9e269d39adddd44907bbe94fe263bd5230c99caeb2f3115a6bcb7dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf74b57a9e269d39adddd44907bbe94fe263bd5230c99caeb2f3115a6bcb7dd","first_computed_at":"2026-05-18T00:02:36.883123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:36.883123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yl2aPiMnhB7MoJt8equ/XhjVbpu3sRWCyYhvbfHq9024Np4Acb0nI3dyN/rb78Y8tgH7zvhxy7aem6ssRCtMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:36.883764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88954f91784642cf9004c6e12c4aa4e812aa33943a05acb3bc33b7dc12a7ae5b","sha256:1ee09c5a79550e1afa1c10c727e4af0544af165863b877313655c03eb8372995"],"state_sha256":"d6d77fa5e226d3b664dc005c47fe082cb85268e6d5de99bd56a8a95eee151cac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTH8hPbtvTY0Wx0AgpoAJhy1sM/aGzVaDg1PcvGeORnwJmu8stXHoxE2fHtvmhvwfnAJymksI8MlzJ/PP7VhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:25:47.554891Z","bundle_sha256":"5875ab966ab2323fe0e2b7758cbd7ea32d296e72f7475d47da62b59f596e6cca"}}