{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ID3FM7X4A5A5JJHRC4RU4C23I6","short_pith_number":"pith:ID3FM7X4","canonical_record":{"source":{"id":"1412.7875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T01:16:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cde2938d9878976a036bec67d73213ecc992bb199f781f8cf8d7aefc86695288","abstract_canon_sha256":"a5cba2aa842ff5c773af4c370800301ebcecb657784b086017bedd19f4fc9787"},"schema_version":"1.0"},"canonical_sha256":"40f6567efc0741d4a4f117234e0b5b47ba212d762aed9f6c7cba70fa789bac60","source":{"kind":"arxiv","id":"1412.7875","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7875","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7875v2","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7875","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"ID3FM7X4A5A5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ID3FM7X4A5A5JJHR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ID3FM7X4","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ID3FM7X4A5A5JJHRC4RU4C23I6","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T01:16:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cde2938d9878976a036bec67d73213ecc992bb199f781f8cf8d7aefc86695288","abstract_canon_sha256":"a5cba2aa842ff5c773af4c370800301ebcecb657784b086017bedd19f4fc9787"},"schema_version":"1.0"},"canonical_sha256":"40f6567efc0741d4a4f117234e0b5b47ba212d762aed9f6c7cba70fa789bac60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.371740Z","signature_b64":"UmeCuMWEXVME1wQFyLOntpDZ6YXEsRVXMhBwsFvKfZFE0+1m9splgq/CpaDN3I2xy8+w1Jux74KkmOkeoLsmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f6567efc0741d4a4f117234e0b5b47ba212d762aed9f6c7cba70fa789bac60","last_reissued_at":"2026-05-18T00:14:29.370877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.370877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7875","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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJO3bK8X8mkaoUwIT0idZey1PfK5Vzh/mbiqr8xSbIaahTc9JSM5v8VsZmgCLWVwaqApmjtPKnc2A8qY+ChJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:49:56.612464Z"},"content_sha256":"754e1a6effb7509ecdd17d85fa7f1de3833d3486dbbbc5902b0d9212f3a3bf81","schema_version":"1.0","event_id":"sha256:754e1a6effb7509ecdd17d85fa7f1de3833d3486dbbbc5902b0d9212f3a3bf81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ID3FM7X4A5A5JJHRC4RU4C23I6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic solutions of differential equations over the projective line minus three points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yunqing Tang","submitted_at":"2014-12-26T01:16:48Z","abstract_excerpt":"The Grothendieck--Katz $p$-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo $p$ has vanishing $p$-curvatures for {\\em almost all} $p,$ has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on $\\mathbb{P}^{1}-\\{0,1,\\infty\\}.$ We prove a variant of this conjecture for $\\mathbb{P}^{1}-\\{0,1,\\infty\\},$ which asserts that if the equation satisfies a certain convergence condition for {\\em all} $p,$ then its monodromy is trivial. For those $p$ for which the $p$-curvature makes sense, its vanishing implies our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7875","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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrxiC3Aldi0/owqdkGviLUObbxjm01fJEBxljG1aFLWc6UyadNQuc7Igxlt8+5HQnI432Y5+grDujTqnD3OkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:49:56.612853Z"},"content_sha256":"185ed293430a663ec1a826aef8a9ace8a9488a0398f95d77cfc8c3ee67bc1d9a","schema_version":"1.0","event_id":"sha256:185ed293430a663ec1a826aef8a9ace8a9488a0398f95d77cfc8c3ee67bc1d9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/bundle.json","state_url":"https://pith.science/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/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":"2026-06-12T04:49:56Z","links":{"resolver":"https://pith.science/pith/ID3FM7X4A5A5JJHRC4RU4C23I6","bundle":"https://pith.science/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/bundle.json","state":"https://pith.science/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ID3FM7X4A5A5JJHRC4RU4C23I6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ID3FM7X4A5A5JJHRC4RU4C23I6","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":"a5cba2aa842ff5c773af4c370800301ebcecb657784b086017bedd19f4fc9787","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T01:16:48Z","title_canon_sha256":"cde2938d9878976a036bec67d73213ecc992bb199f781f8cf8d7aefc86695288"},"schema_version":"1.0","source":{"id":"1412.7875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7875","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7875v2","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7875","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"ID3FM7X4A5A5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ID3FM7X4A5A5JJHR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ID3FM7X4","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:185ed293430a663ec1a826aef8a9ace8a9488a0398f95d77cfc8c3ee67bc1d9a","target":"graph","created_at":"2026-05-18T00:14:29Z","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 predicts that an arithmetic differential equation whose reduction modulo $p$ has vanishing $p$-curvatures for {\\em almost all} $p,$ has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on $\\mathbb{P}^{1}-\\{0,1,\\infty\\}.$ We prove a variant of this conjecture for $\\mathbb{P}^{1}-\\{0,1,\\infty\\},$ which asserts that if the equation satisfies a certain convergence condition for {\\em all} $p,$ then its monodromy is trivial. For those $p$ for which the $p$-curvature makes sense, its vanishing implies our","authors_text":"Yunqing Tang","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T01:16:48Z","title":"Algebraic solutions of differential equations over the projective line minus three points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7875","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":"sha256:754e1a6effb7509ecdd17d85fa7f1de3833d3486dbbbc5902b0d9212f3a3bf81","target":"record","created_at":"2026-05-18T00:14:29Z","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":"a5cba2aa842ff5c773af4c370800301ebcecb657784b086017bedd19f4fc9787","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T01:16:48Z","title_canon_sha256":"cde2938d9878976a036bec67d73213ecc992bb199f781f8cf8d7aefc86695288"},"schema_version":"1.0","source":{"id":"1412.7875","kind":"arxiv","version":2}},"canonical_sha256":"40f6567efc0741d4a4f117234e0b5b47ba212d762aed9f6c7cba70fa789bac60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40f6567efc0741d4a4f117234e0b5b47ba212d762aed9f6c7cba70fa789bac60","first_computed_at":"2026-05-18T00:14:29.370877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.370877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UmeCuMWEXVME1wQFyLOntpDZ6YXEsRVXMhBwsFvKfZFE0+1m9splgq/CpaDN3I2xy8+w1Jux74KkmOkeoLsmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.371740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:754e1a6effb7509ecdd17d85fa7f1de3833d3486dbbbc5902b0d9212f3a3bf81","sha256:185ed293430a663ec1a826aef8a9ace8a9488a0398f95d77cfc8c3ee67bc1d9a"],"state_sha256":"6d9463d32e2a44af9ab27b61b23f3690a91d6e5ff8961af05f210a21c281f053"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zqizZk0Ol275XkQS1lshw97kcml8kXDjLGlqZ0yGiQE/s7mVmaR8HgkN9O97LR0gWUBgM4PD3oD+yQ7tmO2TDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:49:56.614873Z","bundle_sha256":"ae96553852dc9b369852e8c90fd6095d7ab1c076d58523492f134376ebda2de4"}}