{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MHOBR46CWJ7EXCWVRLQCS6A4Q2","short_pith_number":"pith:MHOBR46C","canonical_record":{"source":{"id":"1303.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-17T23:49:34Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"575ee6a61f2fe469ea55433390bab50fc0624a469c34c9b2cf6cd760b75fc10c","abstract_canon_sha256":"e9b284c31a0e67c2bf382a692c7a2c44fa44b981f55b26275fd5dd8101e44630"},"schema_version":"1.0"},"canonical_sha256":"61dc18f3c2b27e4b8ad58ae029781c86b30d4b8b3e770697e83cb7e950d8ac5a","source":{"kind":"arxiv","id":"1303.4122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4122","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4122v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4122","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"MHOBR46CWJ7E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MHOBR46CWJ7EXCWV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MHOBR46C","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MHOBR46CWJ7EXCWVRLQCS6A4Q2","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-17T23:49:34Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"575ee6a61f2fe469ea55433390bab50fc0624a469c34c9b2cf6cd760b75fc10c","abstract_canon_sha256":"e9b284c31a0e67c2bf382a692c7a2c44fa44b981f55b26275fd5dd8101e44630"},"schema_version":"1.0"},"canonical_sha256":"61dc18f3c2b27e4b8ad58ae029781c86b30d4b8b3e770697e83cb7e950d8ac5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:39.710172Z","signature_b64":"J/dsrbpG5Cm3/ErbvJ+Kl1QzHv9oABcG81bzmDvI2bs6AS5hVyqjJbpjuVX3jlvMxI2wQU0Y3hSNC2JDp57WDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61dc18f3c2b27e4b8ad58ae029781c86b30d4b8b3e770697e83cb7e950d8ac5a","last_reissued_at":"2026-05-18T03:30:39.709234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:39.709234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4122","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/pIWoCK1sWviC7fSyL7Xb+vvfHQACb9FSkq/mdDZ15XOuMeC6+wytktZKaUTYNJuXnr1eJyaHBDBVTKMEZuuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:07:07.939992Z"},"content_sha256":"c73a85c1b5211f403e5b3fe1cfba144342e2681a5afab28e3104a6df858036df","schema_version":"1.0","event_id":"sha256:c73a85c1b5211f403e5b3fe1cfba144342e2681a5afab28e3104a6df858036df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MHOBR46CWJ7EXCWVRLQCS6A4Q2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the p-adic Second Main Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CV","authors_text":"Aaron Levin","submitted_at":"2013-03-17T23:49:34Z","abstract_excerpt":"We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. In particular, under a transversality assumption, if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are hypersurfaces of degree d, we prove the defect relation \\sum_{i=1}^q\\delta_f(D_i)\\leq n-1+1/d, which is sharp for all positive integers n and d."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4122","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/JRMbN7S3HnOvviL/isaB0TRwICOD3ru6L/9x8YYa1DsycmsM7L8A3aqHeE7pw3BxhfZjaQKS4D5aQ3IOfMMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:07:07.940352Z"},"content_sha256":"1790d871862e47d190b1a58d307fd267d829d4ae35b949c77bd2c3ad063e9cf0","schema_version":"1.0","event_id":"sha256:1790d871862e47d190b1a58d307fd267d829d4ae35b949c77bd2c3ad063e9cf0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/bundle.json","state_url":"https://pith.science/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/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":"2026-06-20T06:07:07Z","links":{"resolver":"https://pith.science/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2","bundle":"https://pith.science/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/bundle.json","state":"https://pith.science/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHOBR46CWJ7EXCWVRLQCS6A4Q2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MHOBR46CWJ7EXCWVRLQCS6A4Q2","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":"e9b284c31a0e67c2bf382a692c7a2c44fa44b981f55b26275fd5dd8101e44630","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-17T23:49:34Z","title_canon_sha256":"575ee6a61f2fe469ea55433390bab50fc0624a469c34c9b2cf6cd760b75fc10c"},"schema_version":"1.0","source":{"id":"1303.4122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4122","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4122v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4122","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"MHOBR46CWJ7E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MHOBR46CWJ7EXCWV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MHOBR46C","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:1790d871862e47d190b1a58d307fd267d829d4ae35b949c77bd2c3ad063e9cf0","target":"graph","created_at":"2026-05-18T03:30:39Z","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 study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. In particular, under a transversality assumption, if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are hypersurfaces of degree d, we prove the defect relation \\sum_{i=1}^q\\delta_f(D_i)\\leq n-1+1/d, which is sharp for all positive integers n and d.","authors_text":"Aaron Levin","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-17T23:49:34Z","title":"On the p-adic Second Main Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4122","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:c73a85c1b5211f403e5b3fe1cfba144342e2681a5afab28e3104a6df858036df","target":"record","created_at":"2026-05-18T03:30:39Z","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":"e9b284c31a0e67c2bf382a692c7a2c44fa44b981f55b26275fd5dd8101e44630","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-17T23:49:34Z","title_canon_sha256":"575ee6a61f2fe469ea55433390bab50fc0624a469c34c9b2cf6cd760b75fc10c"},"schema_version":"1.0","source":{"id":"1303.4122","kind":"arxiv","version":1}},"canonical_sha256":"61dc18f3c2b27e4b8ad58ae029781c86b30d4b8b3e770697e83cb7e950d8ac5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61dc18f3c2b27e4b8ad58ae029781c86b30d4b8b3e770697e83cb7e950d8ac5a","first_computed_at":"2026-05-18T03:30:39.709234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:39.709234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/dsrbpG5Cm3/ErbvJ+Kl1QzHv9oABcG81bzmDvI2bs6AS5hVyqjJbpjuVX3jlvMxI2wQU0Y3hSNC2JDp57WDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:39.710172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c73a85c1b5211f403e5b3fe1cfba144342e2681a5afab28e3104a6df858036df","sha256:1790d871862e47d190b1a58d307fd267d829d4ae35b949c77bd2c3ad063e9cf0"],"state_sha256":"97858f636942e7d618a94bc3d0a30872f02bc8221bd67bf351a9fe313327b9f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oraRZoJO+b4Y5Qh03JnmkWGkOZZrr5RIXXEPVHRfd6MASWBSsDFsW+RVDQgNheNnUjV6Bb2jjX+yiO/ml9msCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:07:07.942244Z","bundle_sha256":"4d10edfb56874d856cc39a875a2d050ec418fecb2bd3f7f40ac5aa6968df4ea0"}}