{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4UI75YCNOY3HEXRHGNOLP5CSSI","short_pith_number":"pith:4UI75YCN","canonical_record":{"source":{"id":"1507.06142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-22T12:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"5d5130bda73082ded9dec82bd616f6c86396d2013f23374f000d414b0d4f5a79","abstract_canon_sha256":"7e583c1ad8d460fef7b3c97520c9cbb1295264717a6d689d5efcd3afed43ff24"},"schema_version":"1.0"},"canonical_sha256":"e511fee04d7636725e27335cb7f452921e8be9459d0fc028fb9e34515122c895","source":{"kind":"arxiv","id":"1507.06142","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06142","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06142v2","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06142","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"4UI75YCNOY3H","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UI75YCNOY3HEXRH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UI75YCN","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4UI75YCNOY3HEXRHGNOLP5CSSI","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-22T12:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"5d5130bda73082ded9dec82bd616f6c86396d2013f23374f000d414b0d4f5a79","abstract_canon_sha256":"7e583c1ad8d460fef7b3c97520c9cbb1295264717a6d689d5efcd3afed43ff24"},"schema_version":"1.0"},"canonical_sha256":"e511fee04d7636725e27335cb7f452921e8be9459d0fc028fb9e34515122c895","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:31.828812Z","signature_b64":"a782DPNpVXp8bOUsC6e3FXrB26fAyT89Bu5J5CvfjB6uhI3ZH+AslYMfEv1jGSa5jf1J6P9GLeX8MfSQopXcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e511fee04d7636725e27335cb7f452921e8be9459d0fc028fb9e34515122c895","last_reissued_at":"2026-05-18T01:21:31.828210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:31.828210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06142","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":"2026-05-18T01:21:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/a8HIzcQ0VOJB/pM8RJW43SAASW0lw2iJ8pRgflsO6J+P/IV3FIGyXo4briFWWX7+MFPa2TjYQKY4LYYbq/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:14:45.885097Z"},"content_sha256":"7d5eb6421034ba5a618bb9c771a126c8b46659dd52dbd587b2d02fc823fcefb5","schema_version":"1.0","event_id":"sha256:7d5eb6421034ba5a618bb9c771a126c8b46659dd52dbd587b2d02fc823fcefb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4UI75YCNOY3HEXRHGNOLP5CSSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hochschild cohomology of relation extension algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, M. Andrea Gatica, Rachel Taillefer (LMBP), Ralf Schiffler","submitted_at":"2015-07-22T12:03:53Z","abstract_excerpt":"Let  $B$ be the split extension of a finite dimensional algebra $C$ by a $C$-$C$-bimodule $E$.  We define a morphism of associative graded algebras $\\varphi^*:\\HH^*(B)\\rightarrow \\HH^*(C)$ from the Hochschild cohomology of $B$ to that of $C$, extending similar constructions for the first cohomology groups made and studied by Assem, Bustamante, Igusa, Redondo and Schiffler. In the case of a trivial extension $B=C\\ltimes E$, we give necessary and sufficient conditions for each $\\varphi^n$ to be surjective.  We prove the surjectivity of $\\varphi^1$ for a class of trivial extensions that includes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06142","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":"2026-05-18T01:21:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ih+qXwxIxd6NfxzW1Pamb4f2PazYSQzZKSlK1vjlD0UkJeGas+l8EqOP1ON3ZjbST3PHR9q3Z6S+KWqLe3e+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:14:45.885472Z"},"content_sha256":"e7d0c1dda3445b053b4c26d773648dcee9b05f0181b58b95f52c5189cc498579","schema_version":"1.0","event_id":"sha256:e7d0c1dda3445b053b4c26d773648dcee9b05f0181b58b95f52c5189cc498579"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/bundle.json","state_url":"https://pith.science/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/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":"2026-06-11T06:14:45Z","links":{"resolver":"https://pith.science/pith/4UI75YCNOY3HEXRHGNOLP5CSSI","bundle":"https://pith.science/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/bundle.json","state":"https://pith.science/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4UI75YCNOY3HEXRHGNOLP5CSSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4UI75YCNOY3HEXRHGNOLP5CSSI","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":"7e583c1ad8d460fef7b3c97520c9cbb1295264717a6d689d5efcd3afed43ff24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-22T12:03:53Z","title_canon_sha256":"5d5130bda73082ded9dec82bd616f6c86396d2013f23374f000d414b0d4f5a79"},"schema_version":"1.0","source":{"id":"1507.06142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06142","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06142v2","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06142","created_at":"2026-05-18T01:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"4UI75YCNOY3H","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UI75YCNOY3HEXRH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UI75YCN","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:e7d0c1dda3445b053b4c26d773648dcee9b05f0181b58b95f52c5189cc498579","target":"graph","created_at":"2026-05-18T01:21:31Z","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":"Let  $B$ be the split extension of a finite dimensional algebra $C$ by a $C$-$C$-bimodule $E$.  We define a morphism of associative graded algebras $\\varphi^*:\\HH^*(B)\\rightarrow \\HH^*(C)$ from the Hochschild cohomology of $B$ to that of $C$, extending similar constructions for the first cohomology groups made and studied by Assem, Bustamante, Igusa, Redondo and Schiffler. In the case of a trivial extension $B=C\\ltimes E$, we give necessary and sufficient conditions for each $\\varphi^n$ to be surjective.  We prove the surjectivity of $\\varphi^1$ for a class of trivial extensions that includes ","authors_text":"Ibrahim Assem, M. Andrea Gatica, Rachel Taillefer (LMBP), Ralf Schiffler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-22T12:03:53Z","title":"Hochschild cohomology of relation extension algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06142","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":"sha256:7d5eb6421034ba5a618bb9c771a126c8b46659dd52dbd587b2d02fc823fcefb5","target":"record","created_at":"2026-05-18T01:21:31Z","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":"7e583c1ad8d460fef7b3c97520c9cbb1295264717a6d689d5efcd3afed43ff24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-22T12:03:53Z","title_canon_sha256":"5d5130bda73082ded9dec82bd616f6c86396d2013f23374f000d414b0d4f5a79"},"schema_version":"1.0","source":{"id":"1507.06142","kind":"arxiv","version":2}},"canonical_sha256":"e511fee04d7636725e27335cb7f452921e8be9459d0fc028fb9e34515122c895","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e511fee04d7636725e27335cb7f452921e8be9459d0fc028fb9e34515122c895","first_computed_at":"2026-05-18T01:21:31.828210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:31.828210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a782DPNpVXp8bOUsC6e3FXrB26fAyT89Bu5J5CvfjB6uhI3ZH+AslYMfEv1jGSa5jf1J6P9GLeX8MfSQopXcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:31.828812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d5eb6421034ba5a618bb9c771a126c8b46659dd52dbd587b2d02fc823fcefb5","sha256:e7d0c1dda3445b053b4c26d773648dcee9b05f0181b58b95f52c5189cc498579"],"state_sha256":"7297d44108514f24d49fa0566ab144e8a4703203e48d97d171326fb78727d93e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xjMJEriSo9YbceDyNGxXcYp3PXwuZG9hFwT3/u/D+VtGy5gwlK/V3mESjBuKd/Sc0yf/HrLkp5jSTjuXE/8HDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:14:45.888145Z","bundle_sha256":"ce6d9f2800fd33a6540ce9c432fcb94c8a166b8a1a95cf91ef0638249adc9a39"}}