{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7BVFHI4CKTJNAQ63UM74SQFUBH","short_pith_number":"pith:7BVFHI4C","canonical_record":{"source":{"id":"1706.10044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T07:26:21Z","cross_cats_sorted":[],"title_canon_sha256":"88e5d438904535a990c020cb5a050dc62733737746c6d875b55de73a8835129a","abstract_canon_sha256":"c78a814f5391d5e783d619334461db37a68decbfe5603f225c59a873ec13042e"},"schema_version":"1.0"},"canonical_sha256":"f86a53a38254d2d043dba33fc940b409d3951e43ee118f87da9234033afeefd9","source":{"kind":"arxiv","id":"1706.10044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10044","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10044v2","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10044","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"7BVFHI4CKTJN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BVFHI4CKTJNAQ63","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BVFHI4C","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7BVFHI4CKTJNAQ63UM74SQFUBH","target":"record","payload":{"canonical_record":{"source":{"id":"1706.10044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T07:26:21Z","cross_cats_sorted":[],"title_canon_sha256":"88e5d438904535a990c020cb5a050dc62733737746c6d875b55de73a8835129a","abstract_canon_sha256":"c78a814f5391d5e783d619334461db37a68decbfe5603f225c59a873ec13042e"},"schema_version":"1.0"},"canonical_sha256":"f86a53a38254d2d043dba33fc940b409d3951e43ee118f87da9234033afeefd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:47.529030Z","signature_b64":"uSV8xnNVTCzo5ocnLTPnLyz2RL7dHvEKJg9nS/BiMhwMmbPH6N2yvBceEp6l5NvSCpNl8vL+fpJ/vOd0KrYhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f86a53a38254d2d043dba33fc940b409d3951e43ee118f87da9234033afeefd9","last_reissued_at":"2026-05-18T00:14:47.528460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:47.528460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.10044","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":"2026-05-18T00:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FN1D86S2VbgESfqzY2/EV4LFRS7TCxo3l9XNpKQLODM0U99lwtQ2R9RYdCb0Sw4zRApPJaQC5Rw+O5xej+JkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:51:35.370971Z"},"content_sha256":"7cce1592a64f3e41412c6ba7fad1e5e32b7fcd42d6a3f960e9139ba4c882ff93","schema_version":"1.0","event_id":"sha256:7cce1592a64f3e41412c6ba7fad1e5e32b7fcd42d6a3f960e9139ba4c882ff93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7BVFHI4CKTJNAQ63UM74SQFUBH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First Hochschild cohomology group and stable equivalence classification of Morita type of some tame symmetric algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rachel Taillefer (LMBP)","submitted_at":"2017-06-30T07:26:21Z","abstract_excerpt":"We use the dimension and the Lie algebra structure of the first Hochschild cohomology group to distinguish some algebras of dihedral, semi-dihedral and quaternion type up to stable equivalence of Morita type. In particular, we complete the classification of algebras of dihedral type that was mostly determined by Zhou and Zimmermann."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10044","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":"2026-05-18T00:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8iwEHC9Rrqz+9upEvpCbc/wZp+arJbqUWtOJ4n0p6o333cVvhW7xaEDNKhnUFPlrWZv6ER3BF5H9H+vIdhABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:51:35.371331Z"},"content_sha256":"7a7b875ef3a6268815bd9f070ba5f188210e97eb00f86b25773c014f94fc45e3","schema_version":"1.0","event_id":"sha256:7a7b875ef3a6268815bd9f070ba5f188210e97eb00f86b25773c014f94fc45e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/bundle.json","state_url":"https://pith.science/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/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":"2026-06-24T01:51:35Z","links":{"resolver":"https://pith.science/pith/7BVFHI4CKTJNAQ63UM74SQFUBH","bundle":"https://pith.science/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/bundle.json","state":"https://pith.science/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BVFHI4CKTJNAQ63UM74SQFUBH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7BVFHI4CKTJNAQ63UM74SQFUBH","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":"c78a814f5391d5e783d619334461db37a68decbfe5603f225c59a873ec13042e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T07:26:21Z","title_canon_sha256":"88e5d438904535a990c020cb5a050dc62733737746c6d875b55de73a8835129a"},"schema_version":"1.0","source":{"id":"1706.10044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10044","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10044v2","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10044","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"7BVFHI4CKTJN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BVFHI4CKTJNAQ63","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BVFHI4C","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:7a7b875ef3a6268815bd9f070ba5f188210e97eb00f86b25773c014f94fc45e3","target":"graph","created_at":"2026-05-18T00:14:47Z","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 use the dimension and the Lie algebra structure of the first Hochschild cohomology group to distinguish some algebras of dihedral, semi-dihedral and quaternion type up to stable equivalence of Morita type. In particular, we complete the classification of algebras of dihedral type that was mostly determined by Zhou and Zimmermann.","authors_text":"Rachel Taillefer (LMBP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T07:26:21Z","title":"First Hochschild cohomology group and stable equivalence classification of Morita type of some tame symmetric algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10044","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":"sha256:7cce1592a64f3e41412c6ba7fad1e5e32b7fcd42d6a3f960e9139ba4c882ff93","target":"record","created_at":"2026-05-18T00:14:47Z","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":"c78a814f5391d5e783d619334461db37a68decbfe5603f225c59a873ec13042e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T07:26:21Z","title_canon_sha256":"88e5d438904535a990c020cb5a050dc62733737746c6d875b55de73a8835129a"},"schema_version":"1.0","source":{"id":"1706.10044","kind":"arxiv","version":2}},"canonical_sha256":"f86a53a38254d2d043dba33fc940b409d3951e43ee118f87da9234033afeefd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f86a53a38254d2d043dba33fc940b409d3951e43ee118f87da9234033afeefd9","first_computed_at":"2026-05-18T00:14:47.528460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:47.528460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSV8xnNVTCzo5ocnLTPnLyz2RL7dHvEKJg9nS/BiMhwMmbPH6N2yvBceEp6l5NvSCpNl8vL+fpJ/vOd0KrYhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:47.529030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cce1592a64f3e41412c6ba7fad1e5e32b7fcd42d6a3f960e9139ba4c882ff93","sha256:7a7b875ef3a6268815bd9f070ba5f188210e97eb00f86b25773c014f94fc45e3"],"state_sha256":"37a38ac172a29c69d43fc501d1ca56fdd57f57b925f68acf2de68f6be515391d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiXwdBvH20UEOIQIDke3BrBOCl1seQquMT0Zqd2YAAVip5G+zUxx2CLAtCIQg10taEJa8wPmVYdJw30kZOwdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T01:51:35.373285Z","bundle_sha256":"508ed8895519598dc4abc3766769d048eb09b80ad70e772d1f7a8f6b1965ad92"}}