{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VO3DRZEMAWKOH3BZHN7V5YZIOF","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":"109f9bd34a156185ca61151b89cea0a83289e2cf9b071ca5589bd814215035bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-18T15:39:47Z","title_canon_sha256":"1f39590d44af3d3fbee6b514096445fb9ba61ea3f776086bb5fe7ff90a61f85b"},"schema_version":"1.0","source":{"id":"1610.05674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05674","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05674v1","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05674","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"VO3DRZEMAWKO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VO3DRZEMAWKOH3BZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VO3DRZEM","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:4e08b8b2c43d3c1cd47a82742a68a60ca8cc9f25abfd2020a777ab813e8d4b13","target":"graph","created_at":"2026-05-18T00:10:32Z","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":"The Grothendieck-Katz $p$-curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its $p$-curvature vanishes modulo $p$, for almost all primes $p$. We prove that if the variety is a generic curve, then every simple closed loop on the curve has finite monodromy.","authors_text":"Ananth N. Shankar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-18T15:39:47Z","title":"The $p$-curvature conjecture and monodromy about simple closed loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05674","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":"sha256:2fca58ce601b2907e1a26415390c26a8767f471fb55b1187c88ff19c37caeb45","target":"record","created_at":"2026-05-18T00:10:32Z","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":"109f9bd34a156185ca61151b89cea0a83289e2cf9b071ca5589bd814215035bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-18T15:39:47Z","title_canon_sha256":"1f39590d44af3d3fbee6b514096445fb9ba61ea3f776086bb5fe7ff90a61f85b"},"schema_version":"1.0","source":{"id":"1610.05674","kind":"arxiv","version":1}},"canonical_sha256":"abb638e48c0594e3ec393b7f5ee328714d289ef07648648c1df34fea185ec058","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abb638e48c0594e3ec393b7f5ee328714d289ef07648648c1df34fea185ec058","first_computed_at":"2026-05-18T00:10:32.469584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:32.469584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0NVm0mJx0d2mgCjuGmIYHpFiQ+3iBKDqqbGh+AUYzgzBiahPg/bjBHePz3VW511DiUIzrKP1U2VoMAFG3D3FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:32.470206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fca58ce601b2907e1a26415390c26a8767f471fb55b1187c88ff19c37caeb45","sha256:4e08b8b2c43d3c1cd47a82742a68a60ca8cc9f25abfd2020a777ab813e8d4b13"],"state_sha256":"1e6987265d8996f8d6a774bc41dfe7ef5e790c192e177641f519058bf5e27917"}