{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:MHVFWRMU4HKMNSYF2GHMX7W2EC","short_pith_number":"pith:MHVFWRMU","canonical_record":{"source":{"id":"0802.3652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-25T17:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"744f6cf2f3ab1abb116c219bd6a3ba1e8f3b86a6fce1b41675d1795134225773","abstract_canon_sha256":"89c91f2286e10216f2accdc23f0ddc95dd0374bb0229a1d00071ddeb2e1319c3"},"schema_version":"1.0"},"canonical_sha256":"61ea5b4594e1d4c6cb05d18ecbfeda208179913044ce916c05de21cfb1143ef3","source":{"kind":"arxiv","id":"0802.3652","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3652","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3652v2","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3652","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"MHVFWRMU4HKM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"MHVFWRMU4HKMNSYF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"MHVFWRMU","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:MHVFWRMU4HKMNSYF2GHMX7W2EC","target":"record","payload":{"canonical_record":{"source":{"id":"0802.3652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-25T17:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"744f6cf2f3ab1abb116c219bd6a3ba1e8f3b86a6fce1b41675d1795134225773","abstract_canon_sha256":"89c91f2286e10216f2accdc23f0ddc95dd0374bb0229a1d00071ddeb2e1319c3"},"schema_version":"1.0"},"canonical_sha256":"61ea5b4594e1d4c6cb05d18ecbfeda208179913044ce916c05de21cfb1143ef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.751267Z","signature_b64":"FMFm2RyQspkaKQYp+fJOY6Snd9AJ2QOnLmq/jov/j2X2MVvkrYRMx5IgNvtzRoUPpxjY1hQmOheg/q4XaX+oBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61ea5b4594e1d4c6cb05d18ecbfeda208179913044ce916c05de21cfb1143ef3","last_reissued_at":"2026-05-18T02:41:51.750754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.750754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.3652","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+0CQnSP5n9DjkosAW7AvCkeqzFaIf41rMc+Z/pvCztBvbJRU9n5HcXiiTUaRq3ok0wN6aMDdZxcCP+IddUUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:41:44.261103Z"},"content_sha256":"83b944e7baf5a3e97e4a972dae5491db6cbe64390503f2dcc32be6c0626851b5","schema_version":"1.0","event_id":"sha256:83b944e7baf5a3e97e4a972dae5491db6cbe64390503f2dcc32be6c0626851b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:MHVFWRMU4HKMNSYF2GHMX7W2EC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincare duality complexes in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Beatrice Bleile, Hans Joachim Baues","submitted_at":"2008-02-25T17:05:53Z","abstract_excerpt":"We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of Poincare duality complexes of dimension 4. Generalizing Turaev's fundamental triples of Poincare duality complexes of dimension 3, we introduce fundamental triples for Poincare duality complexes of dimension n > 2 and show that two Poincare duality complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional mani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3652","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0M3Ok6EuZlezVxXlWzhgAXsegG/jnbXCMvdbXu1SGkfpc3FdFytQ3fRFm/BbiJ/sB7zowsoi5bEkkpkaJjxdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:41:44.261790Z"},"content_sha256":"63e125679bc15ca7844cdbb21abc7ef3a05581e4ba6ba1d967a3f2f4db5d3a2b","schema_version":"1.0","event_id":"sha256:63e125679bc15ca7844cdbb21abc7ef3a05581e4ba6ba1d967a3f2f4db5d3a2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/bundle.json","state_url":"https://pith.science/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/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":"2026-06-04T20:41:44Z","links":{"resolver":"https://pith.science/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC","bundle":"https://pith.science/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/bundle.json","state":"https://pith.science/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHVFWRMU4HKMNSYF2GHMX7W2EC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:MHVFWRMU4HKMNSYF2GHMX7W2EC","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":"89c91f2286e10216f2accdc23f0ddc95dd0374bb0229a1d00071ddeb2e1319c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-25T17:05:53Z","title_canon_sha256":"744f6cf2f3ab1abb116c219bd6a3ba1e8f3b86a6fce1b41675d1795134225773"},"schema_version":"1.0","source":{"id":"0802.3652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3652","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3652v2","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3652","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"MHVFWRMU4HKM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"MHVFWRMU4HKMNSYF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"MHVFWRMU","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:63e125679bc15ca7844cdbb21abc7ef3a05581e4ba6ba1d967a3f2f4db5d3a2b","target":"graph","created_at":"2026-05-18T02:41:51Z","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 describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of Poincare duality complexes of dimension 4. Generalizing Turaev's fundamental triples of Poincare duality complexes of dimension 3, we introduce fundamental triples for Poincare duality complexes of dimension n > 2 and show that two Poincare duality complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional mani","authors_text":"Beatrice Bleile, Hans Joachim Baues","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-25T17:05:53Z","title":"Poincare duality complexes in dimension four"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3652","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":"sha256:83b944e7baf5a3e97e4a972dae5491db6cbe64390503f2dcc32be6c0626851b5","target":"record","created_at":"2026-05-18T02:41:51Z","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":"89c91f2286e10216f2accdc23f0ddc95dd0374bb0229a1d00071ddeb2e1319c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-25T17:05:53Z","title_canon_sha256":"744f6cf2f3ab1abb116c219bd6a3ba1e8f3b86a6fce1b41675d1795134225773"},"schema_version":"1.0","source":{"id":"0802.3652","kind":"arxiv","version":2}},"canonical_sha256":"61ea5b4594e1d4c6cb05d18ecbfeda208179913044ce916c05de21cfb1143ef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ea5b4594e1d4c6cb05d18ecbfeda208179913044ce916c05de21cfb1143ef3","first_computed_at":"2026-05-18T02:41:51.750754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.750754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FMFm2RyQspkaKQYp+fJOY6Snd9AJ2QOnLmq/jov/j2X2MVvkrYRMx5IgNvtzRoUPpxjY1hQmOheg/q4XaX+oBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.751267Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.3652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83b944e7baf5a3e97e4a972dae5491db6cbe64390503f2dcc32be6c0626851b5","sha256:63e125679bc15ca7844cdbb21abc7ef3a05581e4ba6ba1d967a3f2f4db5d3a2b"],"state_sha256":"976d7740697cae1844ee1644f15280b8e315a090b88f0c56ed869c898e743173"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzCwKroLH7wunp6wu2S+udfdtvfSRZViP/JAYELqu4jaBq8ntgaY1bHWkfvwZeI8JfsfgjA1SeUX+d6RxArLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:41:44.265616Z","bundle_sha256":"ce277dd6a231460aef6cee1794101b48a26f56fd0a58038fe01e80620afba232"}}