{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VH5JL7Y5TBCT7EANJHZLJ7N5B4","short_pith_number":"pith:VH5JL7Y5","canonical_record":{"source":{"id":"math/0703376","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.KT","submitted_at":"2007-03-13T14:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"6245616e48ca1913e54f7062eaa52f2a8600a42e65f6c72d5db398357d07f2f8","abstract_canon_sha256":"e369ac7d9ae2f017b0d7fcfe1fbd7257f5aa189c091ea38658ac52fe163a277d"},"schema_version":"1.0"},"canonical_sha256":"a9fa95ff1d98453f900d49f2b4fdbd0f12607bace419b2a734b62997f1ff66f2","source":{"kind":"arxiv","id":"math/0703376","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703376","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703376v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703376","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"VH5JL7Y5TBCT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VH5JL7Y5TBCT7EAN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VH5JL7Y5","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VH5JL7Y5TBCT7EANJHZLJ7N5B4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0703376","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.KT","submitted_at":"2007-03-13T14:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"6245616e48ca1913e54f7062eaa52f2a8600a42e65f6c72d5db398357d07f2f8","abstract_canon_sha256":"e369ac7d9ae2f017b0d7fcfe1fbd7257f5aa189c091ea38658ac52fe163a277d"},"schema_version":"1.0"},"canonical_sha256":"a9fa95ff1d98453f900d49f2b4fdbd0f12607bace419b2a734b62997f1ff66f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.534434Z","signature_b64":"q2fnKqCBXUnixrJlS6gmHjUXfWLXo6Xv/eyvqi3iBDvlceo2msURYHgY9jw3OCbph3SQ/VnHBhQCRcQke4+QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9fa95ff1d98453f900d49f2b4fdbd0f12607bace419b2a734b62997f1ff66f2","last_reissued_at":"2026-05-18T02:41:26.533993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.533993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0703376","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qV75V7+OD5hwVBkcXp8rAFxEkgfqyQXTwX9JfWdgOdzGp5KWrg68/SBxxNKdAXzcOiUu62ovY0En411KI1hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T06:55:16.134001Z"},"content_sha256":"e92f7985a367f8e3446fc2170d948ebc2b87649c83edc52e06dacb2dfb0a3846","schema_version":"1.0","event_id":"sha256:e92f7985a367f8e3446fc2170d948ebc2b87649c83edc52e06dacb2dfb0a3846"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VH5JL7Y5TBCT7EANJHZLJ7N5B4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Hochschild homology and MacLane homology","license":"","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Teimuraz Pirashvili","submitted_at":"2007-03-13T14:52:01Z","abstract_excerpt":"We prove vanishing results for Hochschild and MacLane homologies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703376","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CA+uK2z6TOXJCZGAZeAvaRp/kGNX8EU4Y9wYjWRMzk3/ZfTCevoC2IqdQBBL/R7irfi2B/IzftNHG0EHrukdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T06:55:16.134354Z"},"content_sha256":"752d9c40b6707a5009f0b3663479e2e0e5ad923ccedd7ecb3867d70316efbf69","schema_version":"1.0","event_id":"sha256:752d9c40b6707a5009f0b3663479e2e0e5ad923ccedd7ecb3867d70316efbf69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/bundle.json","state_url":"https://pith.science/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/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":"2026-06-22T06:55:16Z","links":{"resolver":"https://pith.science/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4","bundle":"https://pith.science/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/bundle.json","state":"https://pith.science/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VH5JL7Y5TBCT7EANJHZLJ7N5B4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VH5JL7Y5TBCT7EANJHZLJ7N5B4","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":"e369ac7d9ae2f017b0d7fcfe1fbd7257f5aa189c091ea38658ac52fe163a277d","cross_cats_sorted":[],"license":"","primary_cat":"math.KT","submitted_at":"2007-03-13T14:52:01Z","title_canon_sha256":"6245616e48ca1913e54f7062eaa52f2a8600a42e65f6c72d5db398357d07f2f8"},"schema_version":"1.0","source":{"id":"math/0703376","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703376","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703376v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703376","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"VH5JL7Y5TBCT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VH5JL7Y5TBCT7EAN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VH5JL7Y5","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:752d9c40b6707a5009f0b3663479e2e0e5ad923ccedd7ecb3867d70316efbf69","target":"graph","created_at":"2026-05-18T02:41:26Z","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 prove vanishing results for Hochschild and MacLane homologies.","authors_text":"Teimuraz Pirashvili","cross_cats":[],"headline":"","license":"","primary_cat":"math.KT","submitted_at":"2007-03-13T14:52:01Z","title":"Twisted Hochschild homology and MacLane homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703376","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:e92f7985a367f8e3446fc2170d948ebc2b87649c83edc52e06dacb2dfb0a3846","target":"record","created_at":"2026-05-18T02:41:26Z","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":"e369ac7d9ae2f017b0d7fcfe1fbd7257f5aa189c091ea38658ac52fe163a277d","cross_cats_sorted":[],"license":"","primary_cat":"math.KT","submitted_at":"2007-03-13T14:52:01Z","title_canon_sha256":"6245616e48ca1913e54f7062eaa52f2a8600a42e65f6c72d5db398357d07f2f8"},"schema_version":"1.0","source":{"id":"math/0703376","kind":"arxiv","version":2}},"canonical_sha256":"a9fa95ff1d98453f900d49f2b4fdbd0f12607bace419b2a734b62997f1ff66f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9fa95ff1d98453f900d49f2b4fdbd0f12607bace419b2a734b62997f1ff66f2","first_computed_at":"2026-05-18T02:41:26.533993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.533993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q2fnKqCBXUnixrJlS6gmHjUXfWLXo6Xv/eyvqi3iBDvlceo2msURYHgY9jw3OCbph3SQ/VnHBhQCRcQke4+QCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.534434Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703376","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e92f7985a367f8e3446fc2170d948ebc2b87649c83edc52e06dacb2dfb0a3846","sha256:752d9c40b6707a5009f0b3663479e2e0e5ad923ccedd7ecb3867d70316efbf69"],"state_sha256":"33d111b90a2c6a919a1bff1a728c21899639ca50aa86d16a0316a6bb7fbfd610"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zgLU4egDWUPmzmfi8eJz9kwg/Fi+vMYCVpwN0vfI691pD+j6rcTVMXBymO/RIWlTAR+ZGhwUFuUTn7iIpC9oCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T06:55:16.136462Z","bundle_sha256":"7f11c9a67971a0052853a0a914091f87acd572c32c481978ee2e6a09da5f6b3f"}}