{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MBTUE2QGRC5I2U2X6QMMWOAEOJ","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":"39d620c43a0612b55886b2d84e7d2ef7f14f957046b08574443a8a6516c9cf8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-05T09:04:04Z","title_canon_sha256":"bbc9c530e503bd68ff1c24d7c8fc2c9fad789731dda67bf8c4333005848896fd"},"schema_version":"1.0","source":{"id":"1505.00926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00926","created_at":"2026-05-18T02:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00926v1","created_at":"2026-05-18T02:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00926","created_at":"2026-05-18T02:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"MBTUE2QGRC5I","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MBTUE2QGRC5I2U2X","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MBTUE2QG","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:19a8205004b99ef3cc6bda0d5129475f07b8072dfa884260ab480159f83ae319","target":"graph","created_at":"2026-05-18T02:16:59Z","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":"We provide a necessary and sufficient condition for the solvability of a rank one differential (resp. $q$-difference) equation over the Amice's ring. We also extend to that ring a Birkoff decomposition result, originally due to Motzkin.","authors_text":"Andrea Pulita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-05T09:04:04Z","title":"Solvability of rank one $p$-adic differential and $q$-difference equations over the Amice ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00926","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:a22f45e2442548b4c55a388b810939fe3f7fefab73dbd4d9f6b072deada693de","target":"record","created_at":"2026-05-18T02:16:59Z","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":"39d620c43a0612b55886b2d84e7d2ef7f14f957046b08574443a8a6516c9cf8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-05T09:04:04Z","title_canon_sha256":"bbc9c530e503bd68ff1c24d7c8fc2c9fad789731dda67bf8c4333005848896fd"},"schema_version":"1.0","source":{"id":"1505.00926","kind":"arxiv","version":1}},"canonical_sha256":"6067426a0688ba8d5357f418cb380472763a911b2f5f8306bcce857b00fc158d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6067426a0688ba8d5357f418cb380472763a911b2f5f8306bcce857b00fc158d","first_computed_at":"2026-05-18T02:16:59.562759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:59.562759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/nhtcEOHEQPSAgjUsKtwc3rsp9tGZ2xklcGcru3g/89BP+TwkRm5d36UJRr5Gvq/0b8vqFKmilEzfmHwjMaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:59.563476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a22f45e2442548b4c55a388b810939fe3f7fefab73dbd4d9f6b072deada693de","sha256:19a8205004b99ef3cc6bda0d5129475f07b8072dfa884260ab480159f83ae319"],"state_sha256":"11fb3c17ebbde2983adff7f036c3e230167e0fc42ced647eb03b276dff83a192"}