{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:356Y7EY336PLK2BT7TRRTH7XQG","short_pith_number":"pith:356Y7EY3","canonical_record":{"source":{"id":"1309.4637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-18T13:14:06Z","cross_cats_sorted":[],"title_canon_sha256":"89a96ed91847f31dfe6b4937ed0824e39907bf70a3aeb65eeff0bb9c827331ff","abstract_canon_sha256":"f9039f96d7c5d6479af4d979f7d61da5aada541f4de47dcdffeebc6c5435d6d1"},"schema_version":"1.0"},"canonical_sha256":"df7d8f931bdf9eb56833fce3199ff781b0226d25728052432b6c70fe0820f87d","source":{"kind":"arxiv","id":"1309.4637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4637","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4637v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4637","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"356Y7EY336PL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"356Y7EY336PLK2BT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"356Y7EY3","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:356Y7EY336PLK2BT7TRRTH7XQG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-18T13:14:06Z","cross_cats_sorted":[],"title_canon_sha256":"89a96ed91847f31dfe6b4937ed0824e39907bf70a3aeb65eeff0bb9c827331ff","abstract_canon_sha256":"f9039f96d7c5d6479af4d979f7d61da5aada541f4de47dcdffeebc6c5435d6d1"},"schema_version":"1.0"},"canonical_sha256":"df7d8f931bdf9eb56833fce3199ff781b0226d25728052432b6c70fe0820f87d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.760400Z","signature_b64":"yn3Ba+PN+nYmJseVa3DWpRVCvOrbtXnRcAo9HM4DPVa0vx0hRiTv3HBm3U9lK7EOW0EH2akmi3/jXz51mTGyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df7d8f931bdf9eb56833fce3199ff781b0226d25728052432b6c70fe0820f87d","last_reissued_at":"2026-05-18T03:12:58.759661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.759661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4637","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyHHJB/S1YfCRzQR7VxyW0eYe80ROVSRxmR1lIrU/swVfk2FLEw4LqQVye7hYwbabH/RY4UrS/dwbcmfFOfRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:36:24.243538Z"},"content_sha256":"e9083da1c76e66bc9fa7e4c4c1c079ccd3eeb3eb1c20857a3bd62af38c4bf947","schema_version":"1.0","event_id":"sha256:e9083da1c76e66bc9fa7e4c4c1c079ccd3eeb3eb1c20857a3bd62af38c4bf947"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:356Y7EY336PLK2BT7TRRTH7XQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When is a fourfold Massey product defined?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daniel C. Isaksen","submitted_at":"2013-09-18T13:14:06Z","abstract_excerpt":"We define a new invariant in the homology of a differential graded algebra. This invariant is the obstruction to defining a fourfold Massey product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4637","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4TqnqVS5eg3ORTm0AK9asoXsgFYmtBzR+eYA5bxTTbip0hbwFHOcEdYaHU4yqHK+oKUdtq6itvPGFmbqsjhCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:36:24.244183Z"},"content_sha256":"53ed7920635a8a683a3b2159d610939c9852291fb1ff707f180f7e66a581df5d","schema_version":"1.0","event_id":"sha256:53ed7920635a8a683a3b2159d610939c9852291fb1ff707f180f7e66a581df5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/356Y7EY336PLK2BT7TRRTH7XQG/bundle.json","state_url":"https://pith.science/pith/356Y7EY336PLK2BT7TRRTH7XQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/356Y7EY336PLK2BT7TRRTH7XQG/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":"2026-06-07T04:36:24Z","links":{"resolver":"https://pith.science/pith/356Y7EY336PLK2BT7TRRTH7XQG","bundle":"https://pith.science/pith/356Y7EY336PLK2BT7TRRTH7XQG/bundle.json","state":"https://pith.science/pith/356Y7EY336PLK2BT7TRRTH7XQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/356Y7EY336PLK2BT7TRRTH7XQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:356Y7EY336PLK2BT7TRRTH7XQG","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":"f9039f96d7c5d6479af4d979f7d61da5aada541f4de47dcdffeebc6c5435d6d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-18T13:14:06Z","title_canon_sha256":"89a96ed91847f31dfe6b4937ed0824e39907bf70a3aeb65eeff0bb9c827331ff"},"schema_version":"1.0","source":{"id":"1309.4637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4637","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4637v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4637","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"356Y7EY336PL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"356Y7EY336PLK2BT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"356Y7EY3","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:53ed7920635a8a683a3b2159d610939c9852291fb1ff707f180f7e66a581df5d","target":"graph","created_at":"2026-05-18T03:12:58Z","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 define a new invariant in the homology of a differential graded algebra. This invariant is the obstruction to defining a fourfold Massey product.","authors_text":"Daniel C. Isaksen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-18T13:14:06Z","title":"When is a fourfold Massey product defined?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4637","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:e9083da1c76e66bc9fa7e4c4c1c079ccd3eeb3eb1c20857a3bd62af38c4bf947","target":"record","created_at":"2026-05-18T03:12:58Z","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":"f9039f96d7c5d6479af4d979f7d61da5aada541f4de47dcdffeebc6c5435d6d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-18T13:14:06Z","title_canon_sha256":"89a96ed91847f31dfe6b4937ed0824e39907bf70a3aeb65eeff0bb9c827331ff"},"schema_version":"1.0","source":{"id":"1309.4637","kind":"arxiv","version":1}},"canonical_sha256":"df7d8f931bdf9eb56833fce3199ff781b0226d25728052432b6c70fe0820f87d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df7d8f931bdf9eb56833fce3199ff781b0226d25728052432b6c70fe0820f87d","first_computed_at":"2026-05-18T03:12:58.759661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.759661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yn3Ba+PN+nYmJseVa3DWpRVCvOrbtXnRcAo9HM4DPVa0vx0hRiTv3HBm3U9lK7EOW0EH2akmi3/jXz51mTGyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.760400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9083da1c76e66bc9fa7e4c4c1c079ccd3eeb3eb1c20857a3bd62af38c4bf947","sha256:53ed7920635a8a683a3b2159d610939c9852291fb1ff707f180f7e66a581df5d"],"state_sha256":"a1e52b39c0f960aaaa3b75e032ae20407b1b24bda94270c5b66f0e31c4457570"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUP1DYJORgciSqv8BIHmDqUl2ThLkft3Yx8L/U2Zs8bJ7JEfu9E6Vzv72SeDP3uo4a9q+E77eHc/+IFIk883BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:36:24.247401Z","bundle_sha256":"b5b250c1052ba8e83a6c2ae37ad5154b6e8ae7bb2ff0581536bc5a2ddb0d738c"}}