{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6LBN22ZJB7GA4R25YYA5WAL5L4","short_pith_number":"pith:6LBN22ZJ","canonical_record":{"source":{"id":"1809.08873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-24T12:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"5aaf3a48080d52fc2fb809f59b1585d269ef0e9aeec4e4a70c944a2273d4b0f4","abstract_canon_sha256":"68d1d3115cff025a6c82dd091f87d91e0f0da0c92e7d4f67ced03ae8be9559af"},"schema_version":"1.0"},"canonical_sha256":"f2c2dd6b290fcc0e475dc601db017d5f2f7a7414f3bd7bb62f19371ae05045c3","source":{"kind":"arxiv","id":"1809.08873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08873","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08873v1","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08873","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"6LBN22ZJB7GA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6LBN22ZJB7GA4R25","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6LBN22ZJ","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6LBN22ZJB7GA4R25YYA5WAL5L4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-24T12:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"5aaf3a48080d52fc2fb809f59b1585d269ef0e9aeec4e4a70c944a2273d4b0f4","abstract_canon_sha256":"68d1d3115cff025a6c82dd091f87d91e0f0da0c92e7d4f67ced03ae8be9559af"},"schema_version":"1.0"},"canonical_sha256":"f2c2dd6b290fcc0e475dc601db017d5f2f7a7414f3bd7bb62f19371ae05045c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:39.013005Z","signature_b64":"UCJCY0iNBeSFIT+qe22dutpKUhfyc3ryqPZ/9zAJLFA+/+h6NiWF/waSdLdPQlOskRnvcwU4qwi7Z95Qbq3VDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2c2dd6b290fcc0e475dc601db017d5f2f7a7414f3bd7bb62f19371ae05045c3","last_reissued_at":"2026-05-18T00:04:39.012612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:39.012612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08873","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJxOpatyqDxQF405SJZCy+GWOy6p4KvdrR1OchItACiosK40D6JNgz0KU9qslDMwanzDTUOYHKNidms9xLuVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:17:29.274130Z"},"content_sha256":"f9238aa16b08309c195b41c5f47fe3d636cd1a770ca5a3352bb45bb066ae7865","schema_version":"1.0","event_id":"sha256:f9238aa16b08309c195b41c5f47fe3d636cd1a770ca5a3352bb45bb066ae7865"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6LBN22ZJB7GA4R25YYA5WAL5L4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hochschild homology of smash biproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Atabey Kaygun, Serkan S\\\"utl\\\"u","submitted_at":"2018-09-24T12:32:45Z","abstract_excerpt":"We develop a new spectral sequence in order to calculate Hochschild homology of smash biproducts (also called twisted tensor products) of unital associative algebras $A\\# B$ provided one of $A$ or $B$ has Hochschild dimension less than 2. We use this spectral sequence to calculate Hochschild homology of quantum tori, multiparametric quantum affine spaces, quantum complete intersections, quantum Weyl algebras, deformed completed Weyl algebras, and finally the algebra $M_q(2)$ of quantum $2\\times 2$-matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08873","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zp+2inv9YPdKoXNXLb/VT6JrJSNhheodkbgwof2ac3/dpZrsxu1eQot48Sb0X4d1Nx/KO8pTfGAz/5gCyvQICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:17:29.274511Z"},"content_sha256":"7e10a0dae41fe4ce828d522aafbe7ddc2e4d0aa661fe5ea9a26545ab18c8bc84","schema_version":"1.0","event_id":"sha256:7e10a0dae41fe4ce828d522aafbe7ddc2e4d0aa661fe5ea9a26545ab18c8bc84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/bundle.json","state_url":"https://pith.science/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/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":"2026-05-28T02:17:29Z","links":{"resolver":"https://pith.science/pith/6LBN22ZJB7GA4R25YYA5WAL5L4","bundle":"https://pith.science/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/bundle.json","state":"https://pith.science/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LBN22ZJB7GA4R25YYA5WAL5L4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6LBN22ZJB7GA4R25YYA5WAL5L4","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":"68d1d3115cff025a6c82dd091f87d91e0f0da0c92e7d4f67ced03ae8be9559af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-24T12:32:45Z","title_canon_sha256":"5aaf3a48080d52fc2fb809f59b1585d269ef0e9aeec4e4a70c944a2273d4b0f4"},"schema_version":"1.0","source":{"id":"1809.08873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08873","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08873v1","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08873","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"6LBN22ZJB7GA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6LBN22ZJB7GA4R25","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6LBN22ZJ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:7e10a0dae41fe4ce828d522aafbe7ddc2e4d0aa661fe5ea9a26545ab18c8bc84","target":"graph","created_at":"2026-05-18T00:04:39Z","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 develop a new spectral sequence in order to calculate Hochschild homology of smash biproducts (also called twisted tensor products) of unital associative algebras $A\\# B$ provided one of $A$ or $B$ has Hochschild dimension less than 2. We use this spectral sequence to calculate Hochschild homology of quantum tori, multiparametric quantum affine spaces, quantum complete intersections, quantum Weyl algebras, deformed completed Weyl algebras, and finally the algebra $M_q(2)$ of quantum $2\\times 2$-matrices.","authors_text":"Atabey Kaygun, Serkan S\\\"utl\\\"u","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-24T12:32:45Z","title":"On the Hochschild homology of smash biproducts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08873","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:f9238aa16b08309c195b41c5f47fe3d636cd1a770ca5a3352bb45bb066ae7865","target":"record","created_at":"2026-05-18T00:04:39Z","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":"68d1d3115cff025a6c82dd091f87d91e0f0da0c92e7d4f67ced03ae8be9559af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-24T12:32:45Z","title_canon_sha256":"5aaf3a48080d52fc2fb809f59b1585d269ef0e9aeec4e4a70c944a2273d4b0f4"},"schema_version":"1.0","source":{"id":"1809.08873","kind":"arxiv","version":1}},"canonical_sha256":"f2c2dd6b290fcc0e475dc601db017d5f2f7a7414f3bd7bb62f19371ae05045c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2c2dd6b290fcc0e475dc601db017d5f2f7a7414f3bd7bb62f19371ae05045c3","first_computed_at":"2026-05-18T00:04:39.012612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:39.012612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UCJCY0iNBeSFIT+qe22dutpKUhfyc3ryqPZ/9zAJLFA+/+h6NiWF/waSdLdPQlOskRnvcwU4qwi7Z95Qbq3VDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:39.013005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9238aa16b08309c195b41c5f47fe3d636cd1a770ca5a3352bb45bb066ae7865","sha256:7e10a0dae41fe4ce828d522aafbe7ddc2e4d0aa661fe5ea9a26545ab18c8bc84"],"state_sha256":"f3c608b9f57f46abd8cf1ff619cfd28134c4bdf4001628f2ada71239c3579e09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nInIxBd4b8QeYIsdlS9RMDpryNfG84IOM2SedWFd4xzV+6l9wLH5itc6fY2fT5pye3ajUA0/W1K/1YvKIGEnDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:17:29.276472Z","bundle_sha256":"fbc9b4041cd3f5146d611f605e4130215391042fd3e5494e429da8068880f500"}}