{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DZNDCVQRKQYKTX6GFMFEHLJBTD","short_pith_number":"pith:DZNDCVQR","canonical_record":{"source":{"id":"1804.05096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-04-13T19:45:23Z","cross_cats_sorted":[],"title_canon_sha256":"c70c45e7a1e314763ffe46528821c0ab3e13cbdb3fc9cfd403ecc18699da24ab","abstract_canon_sha256":"99a53ca4dca8c6dd763f176dfdee4b5a847a6b3c69ce0e9addbf198e9b63f67c"},"schema_version":"1.0"},"canonical_sha256":"1e5a3156115430a9dfc62b0a43ad2198ec98f56bfb2c36bfc84e75ca8756182a","source":{"kind":"arxiv","id":"1804.05096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05096","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05096v1","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05096","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"DZNDCVQRKQYK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DZNDCVQRKQYKTX6G","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DZNDCVQR","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DZNDCVQRKQYKTX6GFMFEHLJBTD","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-04-13T19:45:23Z","cross_cats_sorted":[],"title_canon_sha256":"c70c45e7a1e314763ffe46528821c0ab3e13cbdb3fc9cfd403ecc18699da24ab","abstract_canon_sha256":"99a53ca4dca8c6dd763f176dfdee4b5a847a6b3c69ce0e9addbf198e9b63f67c"},"schema_version":"1.0"},"canonical_sha256":"1e5a3156115430a9dfc62b0a43ad2198ec98f56bfb2c36bfc84e75ca8756182a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:30.561588Z","signature_b64":"ZooRDgPyFleEGuP7kgCWb5t/s38gVNsSF4c0JV7kuFMckbn1FfGdIf/bs9WjSAo28et/ivo7f/eSHbwrYxFRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e5a3156115430a9dfc62b0a43ad2198ec98f56bfb2c36bfc84e75ca8756182a","last_reissued_at":"2026-05-18T00:18:30.561187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:30.561187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05096","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":"2026-05-18T00:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oscIpj4p55Al8gQ/BXz5Yl6DTOnMPMmdJU6JEMDnpxZCRpx4RSz/I91Fm0Fp/vk2/aOYTOXDYFP2+JBr6ZsIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:36:42.495036Z"},"content_sha256":"5f6f95ba858af33f1e04af0903ce4f6a12564cea8c53b04ffda48d3e10a9583e","schema_version":"1.0","event_id":"sha256:5f6f95ba858af33f1e04af0903ce4f6a12564cea8c53b04ffda48d3e10a9583e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DZNDCVQRKQYKTX6GFMFEHLJBTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$G$-Algebra Structure on the Higher Order Hochschild Cohomology $H^*_{S^2}(A,A)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mihai D. Staic, Samuel Carolus","submitted_at":"2018-04-13T19:45:23Z","abstract_excerpt":"We present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05096","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":"2026-05-18T00:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMqT8bCnmDfDlcN6Dxl9STEN2e28Te4FWVl4NhkWm971S85eFPrzxIZofW/uCqXNY7dNGUh6E6dFGTqmzXOiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:36:42.495381Z"},"content_sha256":"a158bd29be3acb5435e85928028ce0ca94bdf30bfe8fbe67c7ae3a97ea50f593","schema_version":"1.0","event_id":"sha256:a158bd29be3acb5435e85928028ce0ca94bdf30bfe8fbe67c7ae3a97ea50f593"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/bundle.json","state_url":"https://pith.science/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/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":"2026-06-20T10:36:42Z","links":{"resolver":"https://pith.science/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD","bundle":"https://pith.science/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/bundle.json","state":"https://pith.science/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DZNDCVQRKQYKTX6GFMFEHLJBTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DZNDCVQRKQYKTX6GFMFEHLJBTD","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":"99a53ca4dca8c6dd763f176dfdee4b5a847a6b3c69ce0e9addbf198e9b63f67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-04-13T19:45:23Z","title_canon_sha256":"c70c45e7a1e314763ffe46528821c0ab3e13cbdb3fc9cfd403ecc18699da24ab"},"schema_version":"1.0","source":{"id":"1804.05096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05096","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05096v1","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05096","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"DZNDCVQRKQYK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DZNDCVQRKQYKTX6G","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DZNDCVQR","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:a158bd29be3acb5435e85928028ce0ca94bdf30bfe8fbe67c7ae3a97ea50f593","target":"graph","created_at":"2026-05-18T00:18:30Z","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 present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory.","authors_text":"Mihai D. Staic, Samuel Carolus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-04-13T19:45:23Z","title":"$G$-Algebra Structure on the Higher Order Hochschild Cohomology $H^*_{S^2}(A,A)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05096","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":"sha256:5f6f95ba858af33f1e04af0903ce4f6a12564cea8c53b04ffda48d3e10a9583e","target":"record","created_at":"2026-05-18T00:18:30Z","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":"99a53ca4dca8c6dd763f176dfdee4b5a847a6b3c69ce0e9addbf198e9b63f67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-04-13T19:45:23Z","title_canon_sha256":"c70c45e7a1e314763ffe46528821c0ab3e13cbdb3fc9cfd403ecc18699da24ab"},"schema_version":"1.0","source":{"id":"1804.05096","kind":"arxiv","version":1}},"canonical_sha256":"1e5a3156115430a9dfc62b0a43ad2198ec98f56bfb2c36bfc84e75ca8756182a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e5a3156115430a9dfc62b0a43ad2198ec98f56bfb2c36bfc84e75ca8756182a","first_computed_at":"2026-05-18T00:18:30.561187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:30.561187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZooRDgPyFleEGuP7kgCWb5t/s38gVNsSF4c0JV7kuFMckbn1FfGdIf/bs9WjSAo28et/ivo7f/eSHbwrYxFRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:30.561588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6f95ba858af33f1e04af0903ce4f6a12564cea8c53b04ffda48d3e10a9583e","sha256:a158bd29be3acb5435e85928028ce0ca94bdf30bfe8fbe67c7ae3a97ea50f593"],"state_sha256":"2ffb3fcd58ba81518951ac50d0706643676bf18f722731a10990ba21b7b498e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQjNAYWFJj+VrAtucNXSy5oRAvQ8ritqk7TNXbJmPbviD1Sm6fLcFbNPMcZVfObJmV+HhIpop34LSLokJi7MCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:36:42.497267Z","bundle_sha256":"5182197f1f1572d8658cba791f154847df3714569318aac7c9856353437e37f9"}}