{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B5MNPRBOI66SWOOJWFFT45VG2N","short_pith_number":"pith:B5MNPRBO","schema_version":"1.0","canonical_sha256":"0f58d7c42e47bd2b39c9b14b3e76a6d351046bb0e6943f9bb0f7212ba19cd5d9","source":{"kind":"arxiv","id":"1403.7818","version":2},"attestation_state":"computed","paper":{"title":"Piecewise Principal Coactions of Co-Commutative Hopf Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bartosz Zieli\\'nski","submitted_at":"2014-03-30T21:36:10Z","abstract_excerpt":"Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern-Galois characters, an explicit formula for a strong connection is necessary. It has been known for some time how to construct a strong connection map on a multi-pullback comodule algebra from strong connections on multi-pullback components, but the known expli"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.7818","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2014-03-30T21:36:10Z","cross_cats_sorted":[],"title_canon_sha256":"d50fdfee52d6e2fd520e909667ef05b499cc0c3aea601258395a85c009eb177b","abstract_canon_sha256":"f88481a0a88704012e536880c8e66c4013deaf8c0d9171dbb592c62ddbf370e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:56.477890Z","signature_b64":"Ww4Jqs75RVV9UdzEa5CLY6BMJyNnEIbSsWSXuTHy9UGuc26BPzdCwcN7NWLLxkVD3Yi04BrRLsBt6LIf5eEtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f58d7c42e47bd2b39c9b14b3e76a6d351046bb0e6943f9bb0f7212ba19cd5d9","last_reissued_at":"2026-05-18T02:44:56.477436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:56.477436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise Principal Coactions of Co-Commutative Hopf Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bartosz Zieli\\'nski","submitted_at":"2014-03-30T21:36:10Z","abstract_excerpt":"Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern-Galois characters, an explicit formula for a strong connection is necessary. It has been known for some time how to construct a strong connection map on a multi-pullback comodule algebra from strong connections on multi-pullback components, but the known expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7818","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.7818","created_at":"2026-05-18T02:44:56.477501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7818v2","created_at":"2026-05-18T02:44:56.477501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7818","created_at":"2026-05-18T02:44:56.477501+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5MNPRBOI66S","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5MNPRBOI66SWOOJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5MNPRBO","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N","json":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N.json","graph_json":"https://pith.science/api/pith-number/B5MNPRBOI66SWOOJWFFT45VG2N/graph.json","events_json":"https://pith.science/api/pith-number/B5MNPRBOI66SWOOJWFFT45VG2N/events.json","paper":"https://pith.science/paper/B5MNPRBO"},"agent_actions":{"view_html":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N","download_json":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N.json","view_paper":"https://pith.science/paper/B5MNPRBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7818&json=true","fetch_graph":"https://pith.science/api/pith-number/B5MNPRBOI66SWOOJWFFT45VG2N/graph.json","fetch_events":"https://pith.science/api/pith-number/B5MNPRBOI66SWOOJWFFT45VG2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N/action/storage_attestation","attest_author":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N/action/author_attestation","sign_citation":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N/action/citation_signature","submit_replication":"https://pith.science/pith/B5MNPRBOI66SWOOJWFFT45VG2N/action/replication_record"}},"created_at":"2026-05-18T02:44:56.477501+00:00","updated_at":"2026-05-18T02:44:56.477501+00:00"}