{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KBOJQNIEVEGV5ZEPI2GRIMUFV4","short_pith_number":"pith:KBOJQNIE","canonical_record":{"source":{"id":"1310.2555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T17:41:46Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"77896dc3c16272831f871eb1a546a64544760598bfd2aff38c4126bba5c6eeb1","abstract_canon_sha256":"b7600832ec07a7598d91c07a91eb0752bf61f1c22e80944e850697eac9dfab1f"},"schema_version":"1.0"},"canonical_sha256":"505c983504a90d5ee48f468d143285af0efd8c93d22d566bdd68fd16351645b8","source":{"kind":"arxiv","id":"1310.2555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2555","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2555v1","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2555","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"KBOJQNIEVEGV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KBOJQNIEVEGV5ZEP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KBOJQNIE","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KBOJQNIEVEGV5ZEPI2GRIMUFV4","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T17:41:46Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"77896dc3c16272831f871eb1a546a64544760598bfd2aff38c4126bba5c6eeb1","abstract_canon_sha256":"b7600832ec07a7598d91c07a91eb0752bf61f1c22e80944e850697eac9dfab1f"},"schema_version":"1.0"},"canonical_sha256":"505c983504a90d5ee48f468d143285af0efd8c93d22d566bdd68fd16351645b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:42.674974Z","signature_b64":"N9p+T7xGpkyQsfKorCe1zSEndumhd1oac5aFTEyGsGPlTrQeIHWMkon4wFGyw97TYlZxXRZOi/eKxzPJ2P24Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"505c983504a90d5ee48f468d143285af0efd8c93d22d566bdd68fd16351645b8","last_reissued_at":"2026-05-18T01:19:42.674399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:42.674399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2555","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":"2026-05-18T01:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+wKju6h+fLzyZvzOSl+BXkymvF71qKzt/i3AsTPUNYQC6ltJt4C8kM2YXrY/BCz38UxzK/y6yLEdZ6A3lvZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:06:29.679050Z"},"content_sha256":"88f06c314e4754b011a893e85cf27fa6b74664ec2e25a337594ac74bb36b8818","schema_version":"1.0","event_id":"sha256:88f06c314e4754b011a893e85cf27fa6b74664ec2e25a337594ac74bb36b8818"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KBOJQNIEVEGV5ZEPI2GRIMUFV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separated Belyi Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Michael E. Zieve, Zachary Scherr","submitted_at":"2013-10-09T17:41:46Z","abstract_excerpt":"We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q-bar, and any disjoint finite subsets S, T in C(Q-bar), we construct a finite morphism f: C -> P^1 such that f ramifies at each point in S, the branch locus of f is {0,1, infty}, and f(T) is disjoint from {0,1, infty}. This refines a result of Mochizuki's. We also prove an analogous result over fields of positive characteristic, and in addition we analyze how many different Belyi maps f are required to imply the above conclusion for a single C and S and all sets T in C(Q-bar) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2555","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":"2026-05-18T01:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+0RqlkrJxLhlpgyWAubimUXnYF+y9YOm6IDOjAZkRCpe/2mnumEhJsFH1vvfh5OxyBykTL4eyZR44MJ9vq6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:06:29.679641Z"},"content_sha256":"26d911c456bfdda9d5eeb8e549866bc3597a07c79ee17b0da10d78001f817904","schema_version":"1.0","event_id":"sha256:26d911c456bfdda9d5eeb8e549866bc3597a07c79ee17b0da10d78001f817904"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/bundle.json","state_url":"https://pith.science/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/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":"2026-06-04T23:06:29Z","links":{"resolver":"https://pith.science/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4","bundle":"https://pith.science/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/bundle.json","state":"https://pith.science/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBOJQNIEVEGV5ZEPI2GRIMUFV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KBOJQNIEVEGV5ZEPI2GRIMUFV4","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":"b7600832ec07a7598d91c07a91eb0752bf61f1c22e80944e850697eac9dfab1f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T17:41:46Z","title_canon_sha256":"77896dc3c16272831f871eb1a546a64544760598bfd2aff38c4126bba5c6eeb1"},"schema_version":"1.0","source":{"id":"1310.2555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2555","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2555v1","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2555","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"KBOJQNIEVEGV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KBOJQNIEVEGV5ZEP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KBOJQNIE","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:26d911c456bfdda9d5eeb8e549866bc3597a07c79ee17b0da10d78001f817904","target":"graph","created_at":"2026-05-18T01:19:42Z","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 construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q-bar, and any disjoint finite subsets S, T in C(Q-bar), we construct a finite morphism f: C -> P^1 such that f ramifies at each point in S, the branch locus of f is {0,1, infty}, and f(T) is disjoint from {0,1, infty}. This refines a result of Mochizuki's. We also prove an analogous result over fields of positive characteristic, and in addition we analyze how many different Belyi maps f are required to imply the above conclusion for a single C and S and all sets T in C(Q-bar) ","authors_text":"Michael E. Zieve, Zachary Scherr","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T17:41:46Z","title":"Separated Belyi Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2555","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":"sha256:88f06c314e4754b011a893e85cf27fa6b74664ec2e25a337594ac74bb36b8818","target":"record","created_at":"2026-05-18T01:19:42Z","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":"b7600832ec07a7598d91c07a91eb0752bf61f1c22e80944e850697eac9dfab1f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T17:41:46Z","title_canon_sha256":"77896dc3c16272831f871eb1a546a64544760598bfd2aff38c4126bba5c6eeb1"},"schema_version":"1.0","source":{"id":"1310.2555","kind":"arxiv","version":1}},"canonical_sha256":"505c983504a90d5ee48f468d143285af0efd8c93d22d566bdd68fd16351645b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"505c983504a90d5ee48f468d143285af0efd8c93d22d566bdd68fd16351645b8","first_computed_at":"2026-05-18T01:19:42.674399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:42.674399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N9p+T7xGpkyQsfKorCe1zSEndumhd1oac5aFTEyGsGPlTrQeIHWMkon4wFGyw97TYlZxXRZOi/eKxzPJ2P24Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:42.674974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88f06c314e4754b011a893e85cf27fa6b74664ec2e25a337594ac74bb36b8818","sha256:26d911c456bfdda9d5eeb8e549866bc3597a07c79ee17b0da10d78001f817904"],"state_sha256":"2a91e4462ad1c4cb254e384ebf45e5d0fd48be1e17ad8cca09144897c06b6e2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xi2tH1iKZXZdoc9+AuD+p4tCPgZ3BYPfTUrk67otxPhPw0lGX7+oWkiVW8EgArcfcyI/VJb4Rmt3KD/Cxbw7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:06:29.682748Z","bundle_sha256":"559b3245bc41b14323a7957a12b47bf1f59f1054f9e363592956ddf7d20c74ef"}}