{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UHDLCUXEWTE2AJIIIBHZQFMWGE","short_pith_number":"pith:UHDLCUXE","canonical_record":{"source":{"id":"1507.02227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-08T17:16:40Z","cross_cats_sorted":[],"title_canon_sha256":"96814528a3f552a47aa2090978149245103946482710fa88a59ce9ecb007b990","abstract_canon_sha256":"3762da9c7b2152ba34d4118fb645c3fce35c15151c03d75bdc704926587f2cb7"},"schema_version":"1.0"},"canonical_sha256":"a1c6b152e4b4c9a02508404f9815963125a4c0e826f2a99eae45a121e795be76","source":{"kind":"arxiv","id":"1507.02227","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02227","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02227v1","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02227","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"UHDLCUXEWTE2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UHDLCUXEWTE2AJII","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UHDLCUXE","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UHDLCUXEWTE2AJIIIBHZQFMWGE","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-08T17:16:40Z","cross_cats_sorted":[],"title_canon_sha256":"96814528a3f552a47aa2090978149245103946482710fa88a59ce9ecb007b990","abstract_canon_sha256":"3762da9c7b2152ba34d4118fb645c3fce35c15151c03d75bdc704926587f2cb7"},"schema_version":"1.0"},"canonical_sha256":"a1c6b152e4b4c9a02508404f9815963125a4c0e826f2a99eae45a121e795be76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:08.340325Z","signature_b64":"IVV6bl+qOuCDPUtZE5OsnuguMFuCNOU5oTBRmwMXMyy2RtNjX11fstdTtxVznoL+PhcmuNUdhKAjXgGhbdSMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1c6b152e4b4c9a02508404f9815963125a4c0e826f2a99eae45a121e795be76","last_reissued_at":"2026-05-18T01:37:08.339658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:08.339658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02227","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":"2026-05-18T01:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLmz7/3qlRpIaA9AgXYdJ1VbRHSpSd6/lNDsz9pQuvhVtJvWw933Rw4dy8hYxMj/+BurgQBKBvDGWotCtYAFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:32.120026Z"},"content_sha256":"98e20cd76c47b0133a61ac7051df26211d39795c6c000da8541391ffce4d5465","schema_version":"1.0","event_id":"sha256:98e20cd76c47b0133a61ac7051df26211d39795c6c000da8541391ffce4d5465"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UHDLCUXEWTE2AJIIIBHZQFMWGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Parameterizations of plane rational curves and their syzygies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Alessandro Gimigliano, Monica Id\\`a","submitted_at":"2015-07-08T17:16:40Z","abstract_excerpt":"Let $C$ be a plane rational curve of degree $d$ and $p:\\tilde C \\rightarrow C$ its normalization. We are interested in the splitting type $(a,b)$ of $C$, where $\\mathcal{O}_{\\mathbb{P}^1}(-a-d)\\oplus \\mathcal{O}_{\\mathbb{P}^1}(-b-d)$ gives the syzigies of the ideal $(f_0,f_1,f_2)\\subset K[s,t]$, and $(f_0,f_1,f_2)$ is a parameterization of $C$. We want to describe in which cases $(a,b)=(k,d-k)$ ($2k\\leq d)$, via a geometric description; namely we show that $(a,b)=(k,d-k)$ if and only if $C$ is the projection of a rational curve on a rational normal surface in $\\mathbb{P}^{k+1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02227","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":"2026-05-18T01:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEfrfv/GWDxmpDpshJEVppceRi5rFgPK3dDxnN9JxZohBE0V2m+3uBGYm5x9dshnQZRduGPpTc16ndW3vKYCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:32.120418Z"},"content_sha256":"2e094a36ee3e5946efe301ba5051486421ef1870d6c58e7fb95ff68e8ada5d39","schema_version":"1.0","event_id":"sha256:2e094a36ee3e5946efe301ba5051486421ef1870d6c58e7fb95ff68e8ada5d39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/bundle.json","state_url":"https://pith.science/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/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":"2026-05-31T08:37:32Z","links":{"resolver":"https://pith.science/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE","bundle":"https://pith.science/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/bundle.json","state":"https://pith.science/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UHDLCUXEWTE2AJIIIBHZQFMWGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UHDLCUXEWTE2AJIIIBHZQFMWGE","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":"3762da9c7b2152ba34d4118fb645c3fce35c15151c03d75bdc704926587f2cb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-08T17:16:40Z","title_canon_sha256":"96814528a3f552a47aa2090978149245103946482710fa88a59ce9ecb007b990"},"schema_version":"1.0","source":{"id":"1507.02227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02227","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02227v1","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02227","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"UHDLCUXEWTE2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UHDLCUXEWTE2AJII","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UHDLCUXE","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:2e094a36ee3e5946efe301ba5051486421ef1870d6c58e7fb95ff68e8ada5d39","target":"graph","created_at":"2026-05-18T01:37:08Z","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":"Let $C$ be a plane rational curve of degree $d$ and $p:\\tilde C \\rightarrow C$ its normalization. We are interested in the splitting type $(a,b)$ of $C$, where $\\mathcal{O}_{\\mathbb{P}^1}(-a-d)\\oplus \\mathcal{O}_{\\mathbb{P}^1}(-b-d)$ gives the syzigies of the ideal $(f_0,f_1,f_2)\\subset K[s,t]$, and $(f_0,f_1,f_2)$ is a parameterization of $C$. We want to describe in which cases $(a,b)=(k,d-k)$ ($2k\\leq d)$, via a geometric description; namely we show that $(a,b)=(k,d-k)$ if and only if $C$ is the projection of a rational curve on a rational normal surface in $\\mathbb{P}^{k+1}$.","authors_text":"Alessandra Bernardi, Alessandro Gimigliano, Monica Id\\`a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-08T17:16:40Z","title":"On Parameterizations of plane rational curves and their syzygies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02227","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":"sha256:98e20cd76c47b0133a61ac7051df26211d39795c6c000da8541391ffce4d5465","target":"record","created_at":"2026-05-18T01:37:08Z","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":"3762da9c7b2152ba34d4118fb645c3fce35c15151c03d75bdc704926587f2cb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-08T17:16:40Z","title_canon_sha256":"96814528a3f552a47aa2090978149245103946482710fa88a59ce9ecb007b990"},"schema_version":"1.0","source":{"id":"1507.02227","kind":"arxiv","version":1}},"canonical_sha256":"a1c6b152e4b4c9a02508404f9815963125a4c0e826f2a99eae45a121e795be76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1c6b152e4b4c9a02508404f9815963125a4c0e826f2a99eae45a121e795be76","first_computed_at":"2026-05-18T01:37:08.339658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:08.339658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVV6bl+qOuCDPUtZE5OsnuguMFuCNOU5oTBRmwMXMyy2RtNjX11fstdTtxVznoL+PhcmuNUdhKAjXgGhbdSMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:08.340325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98e20cd76c47b0133a61ac7051df26211d39795c6c000da8541391ffce4d5465","sha256:2e094a36ee3e5946efe301ba5051486421ef1870d6c58e7fb95ff68e8ada5d39"],"state_sha256":"de576f2ab941eec87ab6699ec6219b5aac844901f05b5a960c42de02cd39494f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGOSPI5BWB5xxvjoctyQH3gK3FtsI5PHb542nDt84HPFBA7Rf7No4YOSSGft9sEgH+w/1C6SiCl8PADZobapBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:37:32.122968Z","bundle_sha256":"5b866342c90a8833aa3d76db0918eb29e6cb5b2977b7623b482a0152b3e964f3"}}