{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:I4GLAVI6WSSBKRVI4EFIT54OWQ","short_pith_number":"pith:I4GLAVI6","canonical_record":{"source":{"id":"1203.2246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-10T10:27:06Z","cross_cats_sorted":[],"title_canon_sha256":"e189ff5de150992e1b048f9a20ee84a2e4b2a1880bb743444cec952b6886cc19","abstract_canon_sha256":"6db6a7268bc8f7de319507d08f57dfbb827596c59b73d6d17d2820b673c17c20"},"schema_version":"1.0"},"canonical_sha256":"470cb0551eb4a41546a8e10a89f78eb408178f023659f16493219cc82f325900","source":{"kind":"arxiv","id":"1203.2246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2246","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2246v1","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2246","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"I4GLAVI6WSSB","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I4GLAVI6WSSBKRVI","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I4GLAVI6","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:I4GLAVI6WSSBKRVI4EFIT54OWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-10T10:27:06Z","cross_cats_sorted":[],"title_canon_sha256":"e189ff5de150992e1b048f9a20ee84a2e4b2a1880bb743444cec952b6886cc19","abstract_canon_sha256":"6db6a7268bc8f7de319507d08f57dfbb827596c59b73d6d17d2820b673c17c20"},"schema_version":"1.0"},"canonical_sha256":"470cb0551eb4a41546a8e10a89f78eb408178f023659f16493219cc82f325900","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:26.017428Z","signature_b64":"vbrGpzA89+K6o+OD7w1I4cKpCsxTFFrnM+NltCOjdhgbIoi0PPy8JpHdvMLuxaIMTF0buEcVJaUmrb1C+TDMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"470cb0551eb4a41546a8e10a89f78eb408178f023659f16493219cc82f325900","last_reissued_at":"2026-05-18T04:00:26.016662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:26.016662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2246","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":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkJDoAX9KJRz/UwOPML6Hs3MRhZvx4xy+/eMhFLA3bQjQF+/j/NUVq+yovGnj3wUAOEX5Q3Ch5ThbY4c99kEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:23:48.846253Z"},"content_sha256":"a15766ff6ce520db8d484ccd3cb8b26dd55ecc684569a1402861063206a660ce","schema_version":"1.0","event_id":"sha256:a15766ff6ce520db8d484ccd3cb8b26dd55ecc684569a1402861063206a660ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:I4GLAVI6WSSBKRVI4EFIT54OWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametrization of rational maps on a variety of general type, and the finiteness theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gian Pietro Pirola, Lucio Guerra","submitted_at":"2012-03-10T10:27:06Z","abstract_excerpt":"In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing the natural parametrization of maps by means of the space of linear projections in a suitable projective space, and this leads to some new insight in the geometry of the finiteness theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2246","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":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"njrP7xxIguyRsnyeGUcBoZwwWLkJO4kuuzFeX/CRbRlfJGAH/44CZMPy0byQOE+3xgu+rmQjxwcKm/2nc0HRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:23:48.846622Z"},"content_sha256":"e664e88fac037a05f670d58ca394b44e150847e0de520ff668bbf196b0c992f1","schema_version":"1.0","event_id":"sha256:e664e88fac037a05f670d58ca394b44e150847e0de520ff668bbf196b0c992f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/bundle.json","state_url":"https://pith.science/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/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":"2026-05-28T09:23:48Z","links":{"resolver":"https://pith.science/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ","bundle":"https://pith.science/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/bundle.json","state":"https://pith.science/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4GLAVI6WSSBKRVI4EFIT54OWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I4GLAVI6WSSBKRVI4EFIT54OWQ","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":"6db6a7268bc8f7de319507d08f57dfbb827596c59b73d6d17d2820b673c17c20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-10T10:27:06Z","title_canon_sha256":"e189ff5de150992e1b048f9a20ee84a2e4b2a1880bb743444cec952b6886cc19"},"schema_version":"1.0","source":{"id":"1203.2246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2246","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2246v1","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2246","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"I4GLAVI6WSSB","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I4GLAVI6WSSBKRVI","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I4GLAVI6","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:e664e88fac037a05f670d58ca394b44e150847e0de520ff668bbf196b0c992f1","target":"graph","created_at":"2026-05-18T04:00:26Z","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":"In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing the natural parametrization of maps by means of the space of linear projections in a suitable projective space, and this leads to some new insight in the geometry of the finiteness theorem.","authors_text":"Gian Pietro Pirola, Lucio Guerra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-10T10:27:06Z","title":"Parametrization of rational maps on a variety of general type, and the finiteness theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2246","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:a15766ff6ce520db8d484ccd3cb8b26dd55ecc684569a1402861063206a660ce","target":"record","created_at":"2026-05-18T04:00:26Z","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":"6db6a7268bc8f7de319507d08f57dfbb827596c59b73d6d17d2820b673c17c20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-10T10:27:06Z","title_canon_sha256":"e189ff5de150992e1b048f9a20ee84a2e4b2a1880bb743444cec952b6886cc19"},"schema_version":"1.0","source":{"id":"1203.2246","kind":"arxiv","version":1}},"canonical_sha256":"470cb0551eb4a41546a8e10a89f78eb408178f023659f16493219cc82f325900","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"470cb0551eb4a41546a8e10a89f78eb408178f023659f16493219cc82f325900","first_computed_at":"2026-05-18T04:00:26.016662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:26.016662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbrGpzA89+K6o+OD7w1I4cKpCsxTFFrnM+NltCOjdhgbIoi0PPy8JpHdvMLuxaIMTF0buEcVJaUmrb1C+TDMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:26.017428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15766ff6ce520db8d484ccd3cb8b26dd55ecc684569a1402861063206a660ce","sha256:e664e88fac037a05f670d58ca394b44e150847e0de520ff668bbf196b0c992f1"],"state_sha256":"6f5a639e0b44ef30850c58bc5045367557600d05c91cfae24751e08673881ddc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xz70kTDgg4o8SvmdTSK5SgAm9t3qWK1GmR7KKTqj+MNy+hlk4hHf8rF4EMAiA+BQqTC+AuhaFRZl+cet0m2DAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:23:48.848748Z","bundle_sha256":"8a28be6aba0ebaed66891577f168724d4073db5c886bfe9e088ec01d2bcbf32a"}}