{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FMADW6GGYDA5MWSJIAZDHXSUIO","short_pith_number":"pith:FMADW6GG","canonical_record":{"source":{"id":"1505.00563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T09:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"4ede5242796d79403aaf84070f6f166691e0f20f0131cf60809a599396894c00","abstract_canon_sha256":"210d9349e23f66656e650100dde8e65430b508472c98e255c8ffafd75e122ad1"},"schema_version":"1.0"},"canonical_sha256":"2b003b78c6c0c1d65a49403233de54438be627962a8e5fa6cd4d522e2e90bb2d","source":{"kind":"arxiv","id":"1505.00563","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00563","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00563v2","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00563","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"FMADW6GGYDA5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FMADW6GGYDA5MWSJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FMADW6GG","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FMADW6GGYDA5MWSJIAZDHXSUIO","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T09:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"4ede5242796d79403aaf84070f6f166691e0f20f0131cf60809a599396894c00","abstract_canon_sha256":"210d9349e23f66656e650100dde8e65430b508472c98e255c8ffafd75e122ad1"},"schema_version":"1.0"},"canonical_sha256":"2b003b78c6c0c1d65a49403233de54438be627962a8e5fa6cd4d522e2e90bb2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:23.297481Z","signature_b64":"Tnm/39q4nGSxpW90yJtKBHlom+tRzss6GNzy/G7g1GGmguSsvtYqIxFLNaLSLL33BBMWEQ++Z9NCTaWxigQEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b003b78c6c0c1d65a49403233de54438be627962a8e5fa6cd4d522e2e90bb2d","last_reissued_at":"2026-05-17T23:44:23.296931Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:23.296931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00563","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":"2026-05-17T23:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfviMyxmAvBNQ4hx7cd5V6EtfymALS/qz8j00b/CQrwjqL7K02gHq4sW+SFVZ5z1HGE6tj3X1xb2OOecz0qQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:11.959810Z"},"content_sha256":"b27e7239d6620c1ad0f456d52fefef5f524bfbed92410d68f644c52204378e19","schema_version":"1.0","event_id":"sha256:b27e7239d6620c1ad0f456d52fefef5f524bfbed92410d68f644c52204378e19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FMADW6GGYDA5MWSJIAZDHXSUIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The action of the Cremona group on rational curves of $ \\mathbb{P}^{3} $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini, Massimiliano Mella","submitted_at":"2015-05-04T09:11:11Z","abstract_excerpt":"A Cremona transformation is a birational self-map of the projective space $ \\mathbb{P}^{n} $. Cremona transformations of $ \\mathbb{P}^{n} $ form a group and this group has a rational action on subvarieties of $ \\mathbb{P}^{n} $ and hence on its Hilbert scheme. We study this action on the family of rational curves of $ \\mathbb{P}^{3} $ and we prove the rectifiability of any one dimensional family. This shows that any uniruled surface is Cremona equivalent to a scroll and it answers a question of Bogomolov-B\\\"ohning related to the study of uniformly rational varieties. We provide examples of inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00563","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":"2026-05-17T23:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSDLpw3thlRfwLNw3/PSivFVMmYgPHgtFuh8LtwxmuEtBoIpBLIAqDI5yKNKHDG7/94UqvFIc5StFlgaLBObDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:11.960442Z"},"content_sha256":"ab8687ea652dce515011442efe37f0da34605536807c6321d483a2f732b8b897","schema_version":"1.0","event_id":"sha256:ab8687ea652dce515011442efe37f0da34605536807c6321d483a2f732b8b897"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/bundle.json","state_url":"https://pith.science/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/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":"2026-05-30T06:54:11Z","links":{"resolver":"https://pith.science/pith/FMADW6GGYDA5MWSJIAZDHXSUIO","bundle":"https://pith.science/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/bundle.json","state":"https://pith.science/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMADW6GGYDA5MWSJIAZDHXSUIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FMADW6GGYDA5MWSJIAZDHXSUIO","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":"210d9349e23f66656e650100dde8e65430b508472c98e255c8ffafd75e122ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T09:11:11Z","title_canon_sha256":"4ede5242796d79403aaf84070f6f166691e0f20f0131cf60809a599396894c00"},"schema_version":"1.0","source":{"id":"1505.00563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00563","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00563v2","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00563","created_at":"2026-05-17T23:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"FMADW6GGYDA5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FMADW6GGYDA5MWSJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FMADW6GG","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:ab8687ea652dce515011442efe37f0da34605536807c6321d483a2f732b8b897","target":"graph","created_at":"2026-05-17T23:44:23Z","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":"A Cremona transformation is a birational self-map of the projective space $ \\mathbb{P}^{n} $. Cremona transformations of $ \\mathbb{P}^{n} $ form a group and this group has a rational action on subvarieties of $ \\mathbb{P}^{n} $ and hence on its Hilbert scheme. We study this action on the family of rational curves of $ \\mathbb{P}^{3} $ and we prove the rectifiability of any one dimensional family. This shows that any uniruled surface is Cremona equivalent to a scroll and it answers a question of Bogomolov-B\\\"ohning related to the study of uniformly rational varieties. We provide examples of inf","authors_text":"Elena Angelini, Massimiliano Mella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T09:11:11Z","title":"The action of the Cremona group on rational curves of $ \\mathbb{P}^{3} $"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00563","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:b27e7239d6620c1ad0f456d52fefef5f524bfbed92410d68f644c52204378e19","target":"record","created_at":"2026-05-17T23:44:23Z","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":"210d9349e23f66656e650100dde8e65430b508472c98e255c8ffafd75e122ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T09:11:11Z","title_canon_sha256":"4ede5242796d79403aaf84070f6f166691e0f20f0131cf60809a599396894c00"},"schema_version":"1.0","source":{"id":"1505.00563","kind":"arxiv","version":2}},"canonical_sha256":"2b003b78c6c0c1d65a49403233de54438be627962a8e5fa6cd4d522e2e90bb2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b003b78c6c0c1d65a49403233de54438be627962a8e5fa6cd4d522e2e90bb2d","first_computed_at":"2026-05-17T23:44:23.296931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:23.296931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tnm/39q4nGSxpW90yJtKBHlom+tRzss6GNzy/G7g1GGmguSsvtYqIxFLNaLSLL33BBMWEQ++Z9NCTaWxigQEDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:23.297481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b27e7239d6620c1ad0f456d52fefef5f524bfbed92410d68f644c52204378e19","sha256:ab8687ea652dce515011442efe37f0da34605536807c6321d483a2f732b8b897"],"state_sha256":"0f580ee1efa9ad1b4fa772df332bf1eb392609619b9e974c25f4c98d102dee88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTE/qoG3yxFPZNro3s2bE8ygEKY+qfs0OC5bFlR9nW8NKWcI4LSOmMh5S0VlM4XJwVMZYLxDLCFAiv0f0mRADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:54:11.963632Z","bundle_sha256":"e3e5c7c189138e87115991ecf3755ea731c3f3b4524da94e1a3e5f4677642631"}}