{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PCFR7ZNJMDSPXIX2ASSGPU4QCO","short_pith_number":"pith:PCFR7ZNJ","canonical_record":{"source":{"id":"1309.6186","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T14:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"7f75dea4a3aa09be4ea5541a5a7a2b48e419cb09678520f28d6f6daa22afba95","abstract_canon_sha256":"1ccb844b3cde2308e097ad9e8ec05f574881274533d1f30e4dd229205c6b25a5"},"schema_version":"1.0"},"canonical_sha256":"788b1fe5a960e4fba2fa04a467d390139642f2020e8a2f8bb9367e901dbf080c","source":{"kind":"arxiv","id":"1309.6186","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6186","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6186v2","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6186","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"PCFR7ZNJMDSP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PCFR7ZNJMDSPXIX2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PCFR7ZNJ","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PCFR7ZNJMDSPXIX2ASSGPU4QCO","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6186","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T14:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"7f75dea4a3aa09be4ea5541a5a7a2b48e419cb09678520f28d6f6daa22afba95","abstract_canon_sha256":"1ccb844b3cde2308e097ad9e8ec05f574881274533d1f30e4dd229205c6b25a5"},"schema_version":"1.0"},"canonical_sha256":"788b1fe5a960e4fba2fa04a467d390139642f2020e8a2f8bb9367e901dbf080c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.515166Z","signature_b64":"/Qv90rajegBV0exUOOO5fGEHNI7Dh2xJQiJO7cjUS3idZ/la8ns7Ac9N+V5ueRY/rHf6BY5WpxhEr4VTVyvzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"788b1fe5a960e4fba2fa04a467d390139642f2020e8a2f8bb9367e901dbf080c","last_reissued_at":"2026-05-18T00:52:04.514493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.514493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6186","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":"2026-05-18T00:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zX7vhi+Ww0WUfTbjRxQLbfTY+xQsn7TQ9gOh93RVZEmExHml9YvU1vHgiohgCPTjuMxd81oRsvEE9laOk8eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:38:48.263209Z"},"content_sha256":"347e4cc678ce28505be45ad007209fc4f9570e8d16822414067e93619bebea0f","schema_version":"1.0","event_id":"sha256:347e4cc678ce28505be45ad007209fc4f9570e8d16822414067e93619bebea0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PCFR7ZNJMDSPXIX2ASSGPU4QCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on a p-adic exponential map for the Picard group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wataru Kai","submitted_at":"2013-09-24T14:43:39Z","abstract_excerpt":"Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first cohomology group of the structure sheaf. When the Picard scheme is available and smooth, it recovers the isomorphism coming from its formal completion. A reinterpretation of an old theorem of Mattuck is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6186","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":"2026-05-18T00:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZ/chkGcv8N5Rhd2QyEqHIBpJF7pQu9dfspj151UfDIVpsrPw7stex23RnYbWvdwSWtol3oLZFJUUQDd4s2BDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:38:48.263878Z"},"content_sha256":"2a43d32b19691ad6b97b6b651d4dacda9ac9250970c51d57a19b9c32fbf1c27b","schema_version":"1.0","event_id":"sha256:2a43d32b19691ad6b97b6b651d4dacda9ac9250970c51d57a19b9c32fbf1c27b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/bundle.json","state_url":"https://pith.science/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/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":"2026-06-06T19:38:48Z","links":{"resolver":"https://pith.science/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO","bundle":"https://pith.science/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/bundle.json","state":"https://pith.science/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCFR7ZNJMDSPXIX2ASSGPU4QCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PCFR7ZNJMDSPXIX2ASSGPU4QCO","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":"1ccb844b3cde2308e097ad9e8ec05f574881274533d1f30e4dd229205c6b25a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T14:43:39Z","title_canon_sha256":"7f75dea4a3aa09be4ea5541a5a7a2b48e419cb09678520f28d6f6daa22afba95"},"schema_version":"1.0","source":{"id":"1309.6186","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6186","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6186v2","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6186","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"PCFR7ZNJMDSP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PCFR7ZNJMDSPXIX2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PCFR7ZNJ","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:2a43d32b19691ad6b97b6b651d4dacda9ac9250970c51d57a19b9c32fbf1c27b","target":"graph","created_at":"2026-05-18T00:52:04Z","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":"Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first cohomology group of the structure sheaf. When the Picard scheme is available and smooth, it recovers the isomorphism coming from its formal completion. A reinterpretation of an old theorem of Mattuck is given.","authors_text":"Wataru Kai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T14:43:39Z","title":"Notes on a p-adic exponential map for the Picard group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6186","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":"sha256:347e4cc678ce28505be45ad007209fc4f9570e8d16822414067e93619bebea0f","target":"record","created_at":"2026-05-18T00:52:04Z","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":"1ccb844b3cde2308e097ad9e8ec05f574881274533d1f30e4dd229205c6b25a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T14:43:39Z","title_canon_sha256":"7f75dea4a3aa09be4ea5541a5a7a2b48e419cb09678520f28d6f6daa22afba95"},"schema_version":"1.0","source":{"id":"1309.6186","kind":"arxiv","version":2}},"canonical_sha256":"788b1fe5a960e4fba2fa04a467d390139642f2020e8a2f8bb9367e901dbf080c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"788b1fe5a960e4fba2fa04a467d390139642f2020e8a2f8bb9367e901dbf080c","first_computed_at":"2026-05-18T00:52:04.514493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:04.514493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Qv90rajegBV0exUOOO5fGEHNI7Dh2xJQiJO7cjUS3idZ/la8ns7Ac9N+V5ueRY/rHf6BY5WpxhEr4VTVyvzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:04.515166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6186","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:347e4cc678ce28505be45ad007209fc4f9570e8d16822414067e93619bebea0f","sha256:2a43d32b19691ad6b97b6b651d4dacda9ac9250970c51d57a19b9c32fbf1c27b"],"state_sha256":"615335781458df96e7e387dda50a3ba69c516e22a2888d6247049cd5a3b6851c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wN4fMtRTpijaUE4eNxyaLv7br0GLtZgQiuevYLn5rc6pimyxap02SWZ41qZgcKeLwTpd5M+yNWwHiA5wZKG7Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:38:48.266947Z","bundle_sha256":"e9715632df12936759bd3e17ab4bd797b28c40f9cb105ea60b26dce28d898645"}}