{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:VYEA5LCPJT6QXLX73BFCF25UI6","short_pith_number":"pith:VYEA5LCP","schema_version":"1.0","canonical_sha256":"ae080eac4f4cfd0baeffd84a22ebb44783ee3f270c177002452eebf3ae4324ad","source":{"kind":"arxiv","id":"math/0202229","version":1},"attestation_state":"computed","paper":{"title":"On the existence of F-crystals","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"M. Rapoport, R. Kottwitz","submitted_at":"2002-02-22T13:56:00Z","abstract_excerpt":"Let (N,F) be an F-isocrystal, with associated Newton vector \\nu in (Q^n)_+. To any lattice M in N (an F-crystal) is associated its Hodge vector \\mu(M) in (Z^n)_+. By Mazur's inequality we have \\mu(M)>= \\nu. We show that, conversely, for any \\mu in (Z^n)_+ with \\mu >= \\nu, there exists a lattice M in N such that \\mu=\\mu(M). We also give variants of this existence theorem for symplectic\n F-isocrystals, and for periodic lattice chains."},"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":"math/0202229","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2002-02-22T13:56:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4393a3684a6796403014424bd74cd122894acdc8b69260bd8c257bb6e344753a","abstract_canon_sha256":"9dcf1ca048b9a0588d903a0b76fd9a3d5997f28ef2b72a1b759daa2ec169c88f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.755617Z","signature_b64":"7rXnBcdH+/dzwXdj2XQV1KUy3d3Edq6gmGE7kv4q6C29mig6M/Sb8ztjT0ApOTKj1R55Vr+nKvA2Dz8v4l9vBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae080eac4f4cfd0baeffd84a22ebb44783ee3f270c177002452eebf3ae4324ad","last_reissued_at":"2026-05-18T01:05:29.755131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.755131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of F-crystals","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"M. Rapoport, R. Kottwitz","submitted_at":"2002-02-22T13:56:00Z","abstract_excerpt":"Let (N,F) be an F-isocrystal, with associated Newton vector \\nu in (Q^n)_+. To any lattice M in N (an F-crystal) is associated its Hodge vector \\mu(M) in (Z^n)_+. By Mazur's inequality we have \\mu(M)>= \\nu. We show that, conversely, for any \\mu in (Z^n)_+ with \\mu >= \\nu, there exists a lattice M in N such that \\mu=\\mu(M). We also give variants of this existence theorem for symplectic\n F-isocrystals, and for periodic lattice chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202229","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":""},"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":"math/0202229","created_at":"2026-05-18T01:05:29.755213+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0202229v1","created_at":"2026-05-18T01:05:29.755213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202229","created_at":"2026-05-18T01:05:29.755213+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYEA5LCPJT6Q","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYEA5LCPJT6QXLX7","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYEA5LCP","created_at":"2026-05-18T12:25:51.375804+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/VYEA5LCPJT6QXLX73BFCF25UI6","json":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6.json","graph_json":"https://pith.science/api/pith-number/VYEA5LCPJT6QXLX73BFCF25UI6/graph.json","events_json":"https://pith.science/api/pith-number/VYEA5LCPJT6QXLX73BFCF25UI6/events.json","paper":"https://pith.science/paper/VYEA5LCP"},"agent_actions":{"view_html":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6","download_json":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6.json","view_paper":"https://pith.science/paper/VYEA5LCP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0202229&json=true","fetch_graph":"https://pith.science/api/pith-number/VYEA5LCPJT6QXLX73BFCF25UI6/graph.json","fetch_events":"https://pith.science/api/pith-number/VYEA5LCPJT6QXLX73BFCF25UI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6/action/storage_attestation","attest_author":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6/action/author_attestation","sign_citation":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6/action/citation_signature","submit_replication":"https://pith.science/pith/VYEA5LCPJT6QXLX73BFCF25UI6/action/replication_record"}},"created_at":"2026-05-18T01:05:29.755213+00:00","updated_at":"2026-05-18T01:05:29.755213+00:00"}