{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:3QPUUGAYID3DN4NTZ72X4HPI4C","short_pith_number":"pith:3QPUUGAY","schema_version":"1.0","canonical_sha256":"dc1f4a181840f636f1b3cff57e1de8e091d1b1ec3c1d132ded448f2bf89a897d","source":{"kind":"arxiv","id":"1012.0856","version":3},"attestation_state":"computed","paper":{"title":"A note on the Petri loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Bruno, Edoardo Sernesi","submitted_at":"2010-12-03T21:28:15Z","abstract_excerpt":"Let $\\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\\rho(g,r,n)$ is non-negative every component of the Petri locus $P^r_{g,n}\\subset \\M_g$ whose general member is a curve $C$ such that $W^{r+1}_n(C) = \\emptyset$, has codimension one in $\\M_g$."},"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":"1012.0856","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-03T21:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"62b9735b09b5ab2e714f2731820bc1f4c9a467c1459d544586343f7e1b7374a9","abstract_canon_sha256":"e56bfea9a5474a9869ba3e7f3adedd6307ce5f300273dcb860b412af40e34c62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:12.990072Z","signature_b64":"uTwQw8+vojngFZPJbtO58kI8QRmIfI0qYCjxrxGWOxwB5Cu1qqPeByfJfNrlUnRAGeV0zlbi/Mu8exU/cUBKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc1f4a181840f636f1b3cff57e1de8e091d1b1ec3c1d132ded448f2bf89a897d","last_reissued_at":"2026-05-18T04:23:12.989570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:12.989570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the Petri loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Bruno, Edoardo Sernesi","submitted_at":"2010-12-03T21:28:15Z","abstract_excerpt":"Let $\\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\\rho(g,r,n)$ is non-negative every component of the Petri locus $P^r_{g,n}\\subset \\M_g$ whose general member is a curve $C$ such that $W^{r+1}_n(C) = \\emptyset$, has codimension one in $\\M_g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0856","kind":"arxiv","version":3},"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":"1012.0856","created_at":"2026-05-18T04:23:12.989638+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.0856v3","created_at":"2026-05-18T04:23:12.989638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0856","created_at":"2026-05-18T04:23:12.989638+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QPUUGAYID3D","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QPUUGAYID3DN4NT","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QPUUGAY","created_at":"2026-05-18T12:26:03.138858+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/3QPUUGAYID3DN4NTZ72X4HPI4C","json":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C.json","graph_json":"https://pith.science/api/pith-number/3QPUUGAYID3DN4NTZ72X4HPI4C/graph.json","events_json":"https://pith.science/api/pith-number/3QPUUGAYID3DN4NTZ72X4HPI4C/events.json","paper":"https://pith.science/paper/3QPUUGAY"},"agent_actions":{"view_html":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C","download_json":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C.json","view_paper":"https://pith.science/paper/3QPUUGAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.0856&json=true","fetch_graph":"https://pith.science/api/pith-number/3QPUUGAYID3DN4NTZ72X4HPI4C/graph.json","fetch_events":"https://pith.science/api/pith-number/3QPUUGAYID3DN4NTZ72X4HPI4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C/action/storage_attestation","attest_author":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C/action/author_attestation","sign_citation":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C/action/citation_signature","submit_replication":"https://pith.science/pith/3QPUUGAYID3DN4NTZ72X4HPI4C/action/replication_record"}},"created_at":"2026-05-18T04:23:12.989638+00:00","updated_at":"2026-05-18T04:23:12.989638+00:00"}