{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UOYPQ2UAB4D3GC5HP3QKDQS7YO","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":"ce12342b73cd636ad53b3c7e3341f89ec26f0e478bd8f0cf9963d30795752758","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.DG","submitted_at":"2007-02-19T19:47:01Z","title_canon_sha256":"1c330a65f9c7ae195f3304439727a5f0eb526d189d9b694a58c36df4fd408c53"},"schema_version":"1.0","source":{"id":"math/0702561","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702561","created_at":"2026-05-18T04:08:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702561v3","created_at":"2026-05-18T04:08:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702561","created_at":"2026-05-18T04:08:52Z"},{"alias_kind":"pith_short_12","alias_value":"UOYPQ2UAB4D3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UOYPQ2UAB4D3GC5H","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UOYPQ2UA","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d8261e53ceff6950f4f34bcc4311a5525d427140045e632fdf7d584527ecf28b","target":"graph","created_at":"2026-05-18T04:08:52Z","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":"The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.","authors_text":"Aleks Kleyn","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-02-19T19:47:01Z","title":"Fibered F-Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702561","kind":"arxiv","version":3},"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:e4a17f37f4d7878920195d5160fa8435d09ab67af05354366af8e1da5a8bb332","target":"record","created_at":"2026-05-18T04:08:52Z","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":"ce12342b73cd636ad53b3c7e3341f89ec26f0e478bd8f0cf9963d30795752758","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.DG","submitted_at":"2007-02-19T19:47:01Z","title_canon_sha256":"1c330a65f9c7ae195f3304439727a5f0eb526d189d9b694a58c36df4fd408c53"},"schema_version":"1.0","source":{"id":"math/0702561","kind":"arxiv","version":3}},"canonical_sha256":"a3b0f86a800f07b30ba77ee0a1c25fc39eacba727790cbdd5b9e23e1724c092a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3b0f86a800f07b30ba77ee0a1c25fc39eacba727790cbdd5b9e23e1724c092a","first_computed_at":"2026-05-18T04:08:52.879401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:52.879401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3HRQf4vWuQczpW7tMgDxsNyUCv8f0E9N1oJFr1YmZ4+rG4MF9PV0xiZv4e5GnFXtGjmxdv2CMpvC+LBowT2sBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:52.879840Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702561","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a17f37f4d7878920195d5160fa8435d09ab67af05354366af8e1da5a8bb332","sha256:d8261e53ceff6950f4f34bcc4311a5525d427140045e632fdf7d584527ecf28b"],"state_sha256":"b6e6ec255c23623c08ee39874eca7f4f8212b81e4b7c6b26a298306d28ca9ed8"}