{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JHKFCQIYBDJZJHJW4HRTZAVYA5","short_pith_number":"pith:JHKFCQIY","schema_version":"1.0","canonical_sha256":"49d451411808d3949d36e1e33c82b8075eb2145b008bc639c0e7cda01c9ed87d","source":{"kind":"arxiv","id":"1208.3317","version":2},"attestation_state":"computed","paper":{"title":"Rational curves on \\bar{M}_g and K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Benzo","submitted_at":"2012-08-16T08:59:01Z","abstract_excerpt":"Let $(S,L)$ be a smooth primitively polarized K3 surface of genus $g$ and $f:X \\rightarrow \\mathbb{P}^1$ the fibration defined by a linear pencil in $|L|$. For $f$ general and $g \\geq 7$, we work out the splitting type of the locally free sheaf $\\Psi^{*}_f T_{{\\overline{M}}_g}$, where $\\Psi_f$ is the modular morphism associated to $f$. We show that this splitting type encodes the fundamental geometrical information attached to Mukai's projection map $\\mathcal{P}_g \\rightarrow \\overline{\\mathcal{M}}_g$, where $\\mathcal{P}_g$ is the stack parameterizing pairs $(S,C)$ with $(S,L)$ as above and $C"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.3317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-16T08:59:01Z","cross_cats_sorted":[],"title_canon_sha256":"ed28b3b4b67eca8c875036f1fa5b042c7e2f016ebb454fed9134e65d226613aa","abstract_canon_sha256":"98cb1ab9a4416654fd0a1fd0fc923a2b8be88468732b8f66772116cc68d500ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:11.031179Z","signature_b64":"8oeKzboM60aXkYkeVMD2O9o6EuY6oPSnxm0obWsi1/JsNklWxUqMdaExJVpx4KksiB9sjdUehADOYm0jQE1GCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49d451411808d3949d36e1e33c82b8075eb2145b008bc639c0e7cda01c9ed87d","last_reissued_at":"2026-05-18T02:20:11.030654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:11.030654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational curves on \\bar{M}_g and K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Benzo","submitted_at":"2012-08-16T08:59:01Z","abstract_excerpt":"Let $(S,L)$ be a smooth primitively polarized K3 surface of genus $g$ and $f:X \\rightarrow \\mathbb{P}^1$ the fibration defined by a linear pencil in $|L|$. For $f$ general and $g \\geq 7$, we work out the splitting type of the locally free sheaf $\\Psi^{*}_f T_{{\\overline{M}}_g}$, where $\\Psi_f$ is the modular morphism associated to $f$. We show that this splitting type encodes the fundamental geometrical information attached to Mukai's projection map $\\mathcal{P}_g \\rightarrow \\overline{\\mathcal{M}}_g$, where $\\mathcal{P}_g$ is the stack parameterizing pairs $(S,C)$ with $(S,L)$ as above and $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3317","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.3317","created_at":"2026-05-18T02:20:11.030741+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3317v2","created_at":"2026-05-18T02:20:11.030741+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3317","created_at":"2026-05-18T02:20:11.030741+00:00"},{"alias_kind":"pith_short_12","alias_value":"JHKFCQIYBDJZ","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JHKFCQIYBDJZJHJW","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JHKFCQIY","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5","json":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5.json","graph_json":"https://pith.science/api/pith-number/JHKFCQIYBDJZJHJW4HRTZAVYA5/graph.json","events_json":"https://pith.science/api/pith-number/JHKFCQIYBDJZJHJW4HRTZAVYA5/events.json","paper":"https://pith.science/paper/JHKFCQIY"},"agent_actions":{"view_html":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5","download_json":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5.json","view_paper":"https://pith.science/paper/JHKFCQIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3317&json=true","fetch_graph":"https://pith.science/api/pith-number/JHKFCQIYBDJZJHJW4HRTZAVYA5/graph.json","fetch_events":"https://pith.science/api/pith-number/JHKFCQIYBDJZJHJW4HRTZAVYA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5/action/storage_attestation","attest_author":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5/action/author_attestation","sign_citation":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5/action/citation_signature","submit_replication":"https://pith.science/pith/JHKFCQIYBDJZJHJW4HRTZAVYA5/action/replication_record"}},"created_at":"2026-05-18T02:20:11.030741+00:00","updated_at":"2026-05-18T02:20:11.030741+00:00"}