{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WWCIDNG6PJWLW3MB6TOMHNXB7Z","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":"40fc30f725d1fc988711c51ab8e52b2228366fb3c034ebb6bfcfc7819843077d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-09T20:28:27Z","title_canon_sha256":"ab077f0f82f631f8cd17af41a1b2ef4db31101ea1b4a80604397c089fa49e7de"},"schema_version":"1.0","source":{"id":"1510.02814","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02814","created_at":"2026-05-18T00:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02814v2","created_at":"2026-05-18T00:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02814","created_at":"2026-05-18T00:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"WWCIDNG6PJWL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WWCIDNG6PJWLW3MB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WWCIDNG6","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:5d419b499f08cd198073f58232d953743fca6914aa66957bd6c00535b3d04e69","target":"graph","created_at":"2026-05-18T00:42:51Z","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 introduce the notion of primitive elements in arbitrary truncated $p$-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the \"points of exact order $N$,\" developed by Drinfeld and Katz-Mazur for elliptic curves.","authors_text":"Preston Wake, Robert Kottwitz","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-09T20:28:27Z","title":"Primitive elements in $p$-divisible groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02814","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:a80aa3d2947d952f9312cff572f94e39572d4a83a74395795e10f3ea53f5f182","target":"record","created_at":"2026-05-18T00:42:51Z","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":"40fc30f725d1fc988711c51ab8e52b2228366fb3c034ebb6bfcfc7819843077d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-09T20:28:27Z","title_canon_sha256":"ab077f0f82f631f8cd17af41a1b2ef4db31101ea1b4a80604397c089fa49e7de"},"schema_version":"1.0","source":{"id":"1510.02814","kind":"arxiv","version":2}},"canonical_sha256":"b58481b4de7a6cbb6d81f4dcc3b6e1fe51abd772d4db36cf575fc1af759d65ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b58481b4de7a6cbb6d81f4dcc3b6e1fe51abd772d4db36cf575fc1af759d65ca","first_computed_at":"2026-05-18T00:42:51.927412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:51.927412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00cA7cn7ysvP85aTU2/xfhHf+fkO47k338z5Cr8o1XO76JEPOXKFjzVNTzk4iysx3c91s9iVglP4E8Gdj4SxCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:51.928097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02814","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a80aa3d2947d952f9312cff572f94e39572d4a83a74395795e10f3ea53f5f182","sha256:5d419b499f08cd198073f58232d953743fca6914aa66957bd6c00535b3d04e69"],"state_sha256":"9bd8c74775322fb35bcb0ec886156221c5de76e2c3b952d831528ffb11d09988"}