{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:ZGSJ63XMDQHSAVXBRGFQQ45MS4","short_pith_number":"pith:ZGSJ63XM","canonical_record":{"source":{"id":"math/0302325","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-02-26T11:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"6a0994761289407164f21a38e523b8eac9bac6004488ddbb25ce594a57fc3451","abstract_canon_sha256":"5d90f82b0f6114d5718e031bbbf02bb619ca46a19476cda83506a4387ffa4ae2"},"schema_version":"1.0"},"canonical_sha256":"c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719","source":{"kind":"arxiv","id":"math/0302325","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0302325","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/0302325v1","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302325","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZGSJ63XMDQHS","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_16","alias_value":"ZGSJ63XMDQHSAVXB","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_8","alias_value":"ZGSJ63XM","created_at":"2026-07-04T14:37:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:ZGSJ63XMDQHSAVXBRGFQQ45MS4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0302325","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-02-26T11:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"6a0994761289407164f21a38e523b8eac9bac6004488ddbb25ce594a57fc3451","abstract_canon_sha256":"5d90f82b0f6114d5718e031bbbf02bb619ca46a19476cda83506a4387ffa4ae2"},"schema_version":"1.0"},"canonical_sha256":"c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:06.482188Z","signature_b64":"mVUxwq1lVzqIUNYR91+U3gmzZgG3l7NcMiOuYcRk7pl5fE+lZNFA/gecOOTyOmuojVdtKLFEcvMoHJTVNWJhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719","last_reissued_at":"2026-07-04T14:37:06.481821Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:06.481821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0302325","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBLYJXxdvb/NexD8x1PtXgHrcfkFnG+5RN+iOC/c3a9ajVB3IwKXOQ2MnnbT0CFH7hY+XOYXRVyjrebAknojCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:24:12.371909Z"},"content_sha256":"9a09014bb30060c78e55b64bd53f7cb051ad486458f30b3d9d478a87a2272694","schema_version":"1.0","event_id":"sha256:9a09014bb30060c78e55b64bd53f7cb051ad486458f30b3d9d478a87a2272694"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:ZGSJ63XMDQHSAVXBRGFQQ45MS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf algebroids with bijective antipodes: axioms, integrals and duals","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Gabriella B\"ohm, Korn'el Szlach'anyi","submitted_at":"2003-02-26T11:49:00Z","abstract_excerpt":"Motivated by the study of depth 2 Frobenius extensions we introduce a new notion of Hopf algebroid. It is a 2-sided bialgebroid with a bijective antipode which connects the two, left and right handed, structures. While all the interesting examples of the Hopf algebroid of J.H. Lu turn out to be Hopf algebroids in the sense of this paper, there exist simple examples showing that our definition is not a special case of Lu's. Our Hopf algebroids, however, belong to the class of $\\times_L$-Hopf algebras proposed by P. Schauenburg. After discussing the axioms and some examples we study the theory o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302325","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0302325/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mv1x0FzalrbwJiCCMe+IRaivSXL5d+67AsYi0MBnWOil4SnK5J3DbprkvOSmFt+ypT++FOudFAjUGat5xOP0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:24:12.372459Z"},"content_sha256":"386b0a7428c981e5d5ec0e0e36a91ea7a0bec26d2f6b871b47d40d13b8e6b974","schema_version":"1.0","event_id":"sha256:386b0a7428c981e5d5ec0e0e36a91ea7a0bec26d2f6b871b47d40d13b8e6b974"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/bundle.json","state_url":"https://pith.science/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/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":"2026-08-08T17:24:12Z","links":{"resolver":"https://pith.science/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4","bundle":"https://pith.science/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/bundle.json","state":"https://pith.science/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGSJ63XMDQHSAVXBRGFQQ45MS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:ZGSJ63XMDQHSAVXBRGFQQ45MS4","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":"5d90f82b0f6114d5718e031bbbf02bb619ca46a19476cda83506a4387ffa4ae2","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2003-02-26T11:49:00Z","title_canon_sha256":"6a0994761289407164f21a38e523b8eac9bac6004488ddbb25ce594a57fc3451"},"schema_version":"1.0","source":{"id":"math/0302325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0302325","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/0302325v1","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302325","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZGSJ63XMDQHS","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_16","alias_value":"ZGSJ63XMDQHSAVXB","created_at":"2026-07-04T14:37:06Z"},{"alias_kind":"pith_short_8","alias_value":"ZGSJ63XM","created_at":"2026-07-04T14:37:06Z"}],"graph_snapshots":[{"event_id":"sha256:386b0a7428c981e5d5ec0e0e36a91ea7a0bec26d2f6b871b47d40d13b8e6b974","target":"graph","created_at":"2026-07-04T14:37:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0302325/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the study of depth 2 Frobenius extensions we introduce a new notion of Hopf algebroid. It is a 2-sided bialgebroid with a bijective antipode which connects the two, left and right handed, structures. While all the interesting examples of the Hopf algebroid of J.H. Lu turn out to be Hopf algebroids in the sense of this paper, there exist simple examples showing that our definition is not a special case of Lu's. Our Hopf algebroids, however, belong to the class of $\\times_L$-Hopf algebras proposed by P. Schauenburg. After discussing the axioms and some examples we study the theory o","authors_text":"Gabriella B\"ohm, Korn'el Szlach'anyi","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-02-26T11:49:00Z","title":"Hopf algebroids with bijective antipodes: axioms, integrals and duals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302325","kind":"arxiv","version":1},"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":"sha256:9a09014bb30060c78e55b64bd53f7cb051ad486458f30b3d9d478a87a2272694","target":"record","created_at":"2026-07-04T14:37:06Z","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":"5d90f82b0f6114d5718e031bbbf02bb619ca46a19476cda83506a4387ffa4ae2","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2003-02-26T11:49:00Z","title_canon_sha256":"6a0994761289407164f21a38e523b8eac9bac6004488ddbb25ce594a57fc3451"},"schema_version":"1.0","source":{"id":"math/0302325","kind":"arxiv","version":1}},"canonical_sha256":"c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719","first_computed_at":"2026-07-04T14:37:06.481821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:37:06.481821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mVUxwq1lVzqIUNYR91+U3gmzZgG3l7NcMiOuYcRk7pl5fE+lZNFA/gecOOTyOmuojVdtKLFEcvMoHJTVNWJhCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:37:06.482188Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0302325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a09014bb30060c78e55b64bd53f7cb051ad486458f30b3d9d478a87a2272694","sha256:386b0a7428c981e5d5ec0e0e36a91ea7a0bec26d2f6b871b47d40d13b8e6b974"],"state_sha256":"31989e557e93d7c08e02839cac7a718b479da1e5d275ec8a33955b8f02213bc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGxlCqKxz1WlHJWGLJOACESrVb3H3XUEN35rkFjYk21Gh3cuyDhQsrHAA5GTPc5crF1Iq6Gq9qmcuy0Hy3t/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:24:12.376506Z","bundle_sha256":"f51ac6bac6d74a811ed53504ae403e2dae0b4d09e4c066326dc833a185e9dca1"}}