{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YW753ZXSPIZCNIXLUDIAZVNYKL","short_pith_number":"pith:YW753ZXS","canonical_record":{"source":{"id":"1203.2454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:45:35Z","cross_cats_sorted":[],"title_canon_sha256":"c9c716a6eafb49fb058c4668187694048f7e00f3c6deb72a8c21ac7da1f28dd4","abstract_canon_sha256":"16b6e5d054f8a68c3ed28baa200ecd31551b4b474c6fb167802ab2663dc04b31"},"schema_version":"1.0"},"canonical_sha256":"c5bfdde6f27a3226a2eba0d00cd5b852fbba9d7c3889acbef046e0e841d4b9ef","source":{"kind":"arxiv","id":"1203.2454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2454","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2454v2","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2454","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"YW753ZXSPIZC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YW753ZXSPIZCNIXL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YW753ZXS","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YW753ZXSPIZCNIXLUDIAZVNYKL","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:45:35Z","cross_cats_sorted":[],"title_canon_sha256":"c9c716a6eafb49fb058c4668187694048f7e00f3c6deb72a8c21ac7da1f28dd4","abstract_canon_sha256":"16b6e5d054f8a68c3ed28baa200ecd31551b4b474c6fb167802ab2663dc04b31"},"schema_version":"1.0"},"canonical_sha256":"c5bfdde6f27a3226a2eba0d00cd5b852fbba9d7c3889acbef046e0e841d4b9ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:23.735389Z","signature_b64":"iSDLrCIMD+kNqQRlYn5HhNkcWbaqEmC6ZStLMDx8urWDYFnWhTTAHdHkl6lisZEv6vEE5/BZjLjSI6ml/uqyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5bfdde6f27a3226a2eba0d00cd5b852fbba9d7c3889acbef046e0e841d4b9ef","last_reissued_at":"2026-05-18T02:58:23.734906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:23.734906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2454","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":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9UTMnHUyOddw7AY9aGhKzntYhI9Q/hSsxJRlvx/ZfT5LAeepNf3Q1/86xgqUwNouuvTG5DOcwR9mLtliYHvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:04:10.671535Z"},"content_sha256":"5c49d847abe5b1b56093203f4bcf3e1a63c7c70d70107c547d2ee58e26becb73","schema_version":"1.0","event_id":"sha256:5c49d847abe5b1b56093203f4bcf3e1a63c7c70d70107c547d2ee58e26becb73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YW753ZXSPIZCNIXLUDIAZVNYKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crossed product of Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A. L. Agore","submitted_at":"2012-03-12T10:45:35Z","abstract_excerpt":"The main properties of the crossed product in the category of Hopf algebras are investigated. Let $A$ and $H$ be two Hopf algebras connected by two morphism of coalgebras $\\triangleright : H\\ot A \\to A$, $f:H\\ot H\\to A$. The crossed product $A #_{f}^{\\triangleright} H$ is a new Hopf algebra containing $A$ as a normal Hopf subalgebra. Furthermore, a Hopf algebra $E$ is isomorphic as a Hopf algebra to a crossed product of Hopf algebras $A #_{f}^{\\triangleright} H$ if and only if $E$ factorizes through a normal Hopf subalgebra $A$ and a subcoalgebra $H$ such that $1_{E} \\in H$. The universality o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2454","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":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5Fil87NQONAWmY+umPsp35xR4vhZo8F1ujddNP8u0l3Kwd8nqtUjmFgzGrLx/q7sPDYhzy+wFUomQoLgXnHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:04:10.671867Z"},"content_sha256":"f3bb73e70c810db9118d29456701a93222d79552a7a39b7d3fec627bec59b36b","schema_version":"1.0","event_id":"sha256:f3bb73e70c810db9118d29456701a93222d79552a7a39b7d3fec627bec59b36b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/bundle.json","state_url":"https://pith.science/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/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":"2026-06-27T19:04:10Z","links":{"resolver":"https://pith.science/pith/YW753ZXSPIZCNIXLUDIAZVNYKL","bundle":"https://pith.science/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/bundle.json","state":"https://pith.science/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YW753ZXSPIZCNIXLUDIAZVNYKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YW753ZXSPIZCNIXLUDIAZVNYKL","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":"16b6e5d054f8a68c3ed28baa200ecd31551b4b474c6fb167802ab2663dc04b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:45:35Z","title_canon_sha256":"c9c716a6eafb49fb058c4668187694048f7e00f3c6deb72a8c21ac7da1f28dd4"},"schema_version":"1.0","source":{"id":"1203.2454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2454","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2454v2","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2454","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"YW753ZXSPIZC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YW753ZXSPIZCNIXL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YW753ZXS","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f3bb73e70c810db9118d29456701a93222d79552a7a39b7d3fec627bec59b36b","target":"graph","created_at":"2026-05-18T02:58:23Z","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 main properties of the crossed product in the category of Hopf algebras are investigated. Let $A$ and $H$ be two Hopf algebras connected by two morphism of coalgebras $\\triangleright : H\\ot A \\to A$, $f:H\\ot H\\to A$. The crossed product $A #_{f}^{\\triangleright} H$ is a new Hopf algebra containing $A$ as a normal Hopf subalgebra. Furthermore, a Hopf algebra $E$ is isomorphic as a Hopf algebra to a crossed product of Hopf algebras $A #_{f}^{\\triangleright} H$ if and only if $E$ factorizes through a normal Hopf subalgebra $A$ and a subcoalgebra $H$ such that $1_{E} \\in H$. The universality o","authors_text":"A. L. Agore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:45:35Z","title":"Crossed product of Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2454","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":"sha256:5c49d847abe5b1b56093203f4bcf3e1a63c7c70d70107c547d2ee58e26becb73","target":"record","created_at":"2026-05-18T02:58:23Z","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":"16b6e5d054f8a68c3ed28baa200ecd31551b4b474c6fb167802ab2663dc04b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-03-12T10:45:35Z","title_canon_sha256":"c9c716a6eafb49fb058c4668187694048f7e00f3c6deb72a8c21ac7da1f28dd4"},"schema_version":"1.0","source":{"id":"1203.2454","kind":"arxiv","version":2}},"canonical_sha256":"c5bfdde6f27a3226a2eba0d00cd5b852fbba9d7c3889acbef046e0e841d4b9ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5bfdde6f27a3226a2eba0d00cd5b852fbba9d7c3889acbef046e0e841d4b9ef","first_computed_at":"2026-05-18T02:58:23.734906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:23.734906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iSDLrCIMD+kNqQRlYn5HhNkcWbaqEmC6ZStLMDx8urWDYFnWhTTAHdHkl6lisZEv6vEE5/BZjLjSI6ml/uqyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:23.735389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c49d847abe5b1b56093203f4bcf3e1a63c7c70d70107c547d2ee58e26becb73","sha256:f3bb73e70c810db9118d29456701a93222d79552a7a39b7d3fec627bec59b36b"],"state_sha256":"d8340f98d4403f414c48254a9473ed160e22d03057a5b94a9dcd5b67ae91dedf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXdsW7URgDyzBzfO9pDGmoLlaUER3XBuYPqHZaQWDBfkhOEHS12lRL7Ii6Me74UOS6Umi5vWoaJ8xArwkScuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T19:04:10.673677Z","bundle_sha256":"0cfa2b12d69433191d3d87a96b0990328ba050ff1ae2c7945a653bb95ee0f6cc"}}