{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EJUDVGDXTOUKVMLA3NASDKHQWG","short_pith_number":"pith:EJUDVGDX","canonical_record":{"source":{"id":"1904.10430","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-23T17:22:42Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"58b9de83e2c275d8d69112a30ac53a9ed789d7aec43db44bf6eae8a21017e3ae","abstract_canon_sha256":"0b3b8fce3742c69bfc50035c50c5eca0b10bc249db83908bd1bfb1096505b48e"},"schema_version":"1.0"},"canonical_sha256":"22683a98779ba8aab160db4121a8f0b19ff4c81cce51f7c35f3931c4f675351d","source":{"kind":"arxiv","id":"1904.10430","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10430","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10430v4","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10430","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"EJUDVGDXTOUK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EJUDVGDXTOUKVMLA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EJUDVGDX","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EJUDVGDXTOUKVMLA3NASDKHQWG","target":"record","payload":{"canonical_record":{"source":{"id":"1904.10430","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-23T17:22:42Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"58b9de83e2c275d8d69112a30ac53a9ed789d7aec43db44bf6eae8a21017e3ae","abstract_canon_sha256":"0b3b8fce3742c69bfc50035c50c5eca0b10bc249db83908bd1bfb1096505b48e"},"schema_version":"1.0"},"canonical_sha256":"22683a98779ba8aab160db4121a8f0b19ff4c81cce51f7c35f3931c4f675351d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:18.879098Z","signature_b64":"U/qXAeROS7662rmkPORr4pjYjCYbKFZOLeYRihkIE25hvm4v4JkIoW7PDfQQjzl0VxVtfnRQM7AR3Bs4JHYiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22683a98779ba8aab160db4121a8f0b19ff4c81cce51f7c35f3931c4f675351d","last_reissued_at":"2026-05-17T23:44:18.878529Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:18.878529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.10430","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Hewwx1PuYk4apK6xuyiBm4oORkfRePRcGx1dnQqJ9lMnMlwKOpogfwnsb90WhoZkycnvVHB72jffud+S6xfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:36:08.737633Z"},"content_sha256":"ea380dfd7a17757918043b916111ab2ae25d65fd4f82052882fee73e7826685d","schema_version":"1.0","event_id":"sha256:ea380dfd7a17757918043b916111ab2ae25d65fd4f82052882fee73e7826685d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EJUDVGDXTOUKVMLA3NASDKHQWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopfological algebra for infinite dimensional Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.KT","authors_text":"Marco A. Farinati","submitted_at":"2019-04-23T17:22:42Z","abstract_excerpt":"We consider \"Hopfological\" techniques as in \\cite{Ko} but for infinite dimensional Hopf algebras, under the assumption of being co-Frobenius. In particular, $H=k[{\\mathbb Z}]\\#k[x]/x^2$ is the first example, whose corepresentations category is d.g. vector spaces. Motivated by this example we define the \"Homology functor\" (we prove it is homological) for any co-Frobenius algebra, with coefficients in $H$-comodules, that recover usual homology of a complex when $H=k[{\\mathbb Z}]\\#k[x]/x^2$. Another easy example of co-Frobenius Hopf algebra gives the category of \"mixed complexes\" and we see (by c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10430","kind":"arxiv","version":4},"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":"2026-05-17T23:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnACSRsMDQ1zlMQblLpIoVvs3kQRGEBwOTRRnSoR5ZGlX/NYin+U7wl07E7HQlQZIk66YL1AAXlftffkNbyKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:36:08.737957Z"},"content_sha256":"53d163820b31b5683617574a57bde01718335ea9ef78fdfd7578acb886082011","schema_version":"1.0","event_id":"sha256:53d163820b31b5683617574a57bde01718335ea9ef78fdfd7578acb886082011"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/bundle.json","state_url":"https://pith.science/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/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":"2026-06-27T02:36:08Z","links":{"resolver":"https://pith.science/pith/EJUDVGDXTOUKVMLA3NASDKHQWG","bundle":"https://pith.science/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/bundle.json","state":"https://pith.science/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJUDVGDXTOUKVMLA3NASDKHQWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EJUDVGDXTOUKVMLA3NASDKHQWG","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":"0b3b8fce3742c69bfc50035c50c5eca0b10bc249db83908bd1bfb1096505b48e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-23T17:22:42Z","title_canon_sha256":"58b9de83e2c275d8d69112a30ac53a9ed789d7aec43db44bf6eae8a21017e3ae"},"schema_version":"1.0","source":{"id":"1904.10430","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10430","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10430v4","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10430","created_at":"2026-05-17T23:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"EJUDVGDXTOUK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EJUDVGDXTOUKVMLA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EJUDVGDX","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:53d163820b31b5683617574a57bde01718335ea9ef78fdfd7578acb886082011","target":"graph","created_at":"2026-05-17T23:44:18Z","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 consider \"Hopfological\" techniques as in \\cite{Ko} but for infinite dimensional Hopf algebras, under the assumption of being co-Frobenius. In particular, $H=k[{\\mathbb Z}]\\#k[x]/x^2$ is the first example, whose corepresentations category is d.g. vector spaces. Motivated by this example we define the \"Homology functor\" (we prove it is homological) for any co-Frobenius algebra, with coefficients in $H$-comodules, that recover usual homology of a complex when $H=k[{\\mathbb Z}]\\#k[x]/x^2$. Another easy example of co-Frobenius Hopf algebra gives the category of \"mixed complexes\" and we see (by c","authors_text":"Marco A. Farinati","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-23T17:22:42Z","title":"Hopfological algebra for infinite dimensional Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10430","kind":"arxiv","version":4},"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:ea380dfd7a17757918043b916111ab2ae25d65fd4f82052882fee73e7826685d","target":"record","created_at":"2026-05-17T23:44:18Z","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":"0b3b8fce3742c69bfc50035c50c5eca0b10bc249db83908bd1bfb1096505b48e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-04-23T17:22:42Z","title_canon_sha256":"58b9de83e2c275d8d69112a30ac53a9ed789d7aec43db44bf6eae8a21017e3ae"},"schema_version":"1.0","source":{"id":"1904.10430","kind":"arxiv","version":4}},"canonical_sha256":"22683a98779ba8aab160db4121a8f0b19ff4c81cce51f7c35f3931c4f675351d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22683a98779ba8aab160db4121a8f0b19ff4c81cce51f7c35f3931c4f675351d","first_computed_at":"2026-05-17T23:44:18.878529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:18.878529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/qXAeROS7662rmkPORr4pjYjCYbKFZOLeYRihkIE25hvm4v4JkIoW7PDfQQjzl0VxVtfnRQM7AR3Bs4JHYiBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:18.879098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10430","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea380dfd7a17757918043b916111ab2ae25d65fd4f82052882fee73e7826685d","sha256:53d163820b31b5683617574a57bde01718335ea9ef78fdfd7578acb886082011"],"state_sha256":"1874c5b3119f7225bcaef15ee9dec65ec5f113f1141b569ef6047bbc93e6489f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2DpH/Kgu5xweZtWel2R+QjAUwDLEQIurb1TntY20DLVAM5ctqqzcQmLbF1CxDRqQDe/3AXP/fW4J6zSzD1XBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:36:08.739663Z","bundle_sha256":"ced0e044cc57dd0d1316158474540d7990e7aa5ce829bcf30401138ccd04f831"}}