{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:XJAJJNILNAQ7SCGQVFY3QRAAK5","short_pith_number":"pith:XJAJJNIL","schema_version":"1.0","canonical_sha256":"ba4094b50b6821f908d0a971b84400576e3e14f85faa63f91e3d6c1db3c21d3f","source":{"kind":"arxiv","id":"math/0609629","version":1},"attestation_state":"computed","paper":{"title":"The Nash problem on arcs for surface singularities","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Marcel Morales","submitted_at":"2006-09-22T07:31:39Z","abstract_excerpt":"Let $(X,O)$ be a germ of a normal surface singularity, $\\pi : \\tilde X\\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\\times n$ symmetrical intersection matrix of the exceptional set of $\\tilde X$. In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme ${\\cal H}$, and defines a map ${\\cal N}$ from the set of irreducible components of ${\\cal H}$ to the set of exceptional components of the minimal resolution of singularities of $(X,O)$. He proved that this map is injective and ask if it is surjective. In this paper we"},"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":"math/0609629","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-09-22T07:31:39Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f68ce0118f3e6fa27ad433f7efe52a73af63f3af9e57db4766771e2571ee44b6","abstract_canon_sha256":"f9fab5291fdbfbfa9334d5fee7d26d3268b611003d41330092b0b82642e443ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.561668Z","signature_b64":"cF32COLxd/Z/OXDQDEHjStmfUh5ZW0AF14utwVjK5odUkONlJ9g693qXV87sVhW+b1818wSSsS+sP0UebGdXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4094b50b6821f908d0a971b84400576e3e14f85faa63f91e3d6c1db3c21d3f","last_reissued_at":"2026-05-18T01:05:22.561161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.561161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Nash problem on arcs for surface singularities","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Marcel Morales","submitted_at":"2006-09-22T07:31:39Z","abstract_excerpt":"Let $(X,O)$ be a germ of a normal surface singularity, $\\pi : \\tilde X\\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\\times n$ symmetrical intersection matrix of the exceptional set of $\\tilde X$. In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme ${\\cal H}$, and defines a map ${\\cal N}$ from the set of irreducible components of ${\\cal H}$ to the set of exceptional components of the minimal resolution of singularities of $(X,O)$. He proved that this map is injective and ask if it is surjective. In this paper we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609629","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0609629","created_at":"2026-05-18T01:05:22.561240+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0609629v1","created_at":"2026-05-18T01:05:22.561240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609629","created_at":"2026-05-18T01:05:22.561240+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJAJJNILNAQ7","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJAJJNILNAQ7SCGQ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJAJJNIL","created_at":"2026-05-18T12:25:54.717736+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/XJAJJNILNAQ7SCGQVFY3QRAAK5","json":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5.json","graph_json":"https://pith.science/api/pith-number/XJAJJNILNAQ7SCGQVFY3QRAAK5/graph.json","events_json":"https://pith.science/api/pith-number/XJAJJNILNAQ7SCGQVFY3QRAAK5/events.json","paper":"https://pith.science/paper/XJAJJNIL"},"agent_actions":{"view_html":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5","download_json":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5.json","view_paper":"https://pith.science/paper/XJAJJNIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0609629&json=true","fetch_graph":"https://pith.science/api/pith-number/XJAJJNILNAQ7SCGQVFY3QRAAK5/graph.json","fetch_events":"https://pith.science/api/pith-number/XJAJJNILNAQ7SCGQVFY3QRAAK5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5/action/storage_attestation","attest_author":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5/action/author_attestation","sign_citation":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5/action/citation_signature","submit_replication":"https://pith.science/pith/XJAJJNILNAQ7SCGQVFY3QRAAK5/action/replication_record"}},"created_at":"2026-05-18T01:05:22.561240+00:00","updated_at":"2026-05-18T01:05:22.561240+00:00"}