{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:S56IAOYW2EDPW7BQ7UDQDM2GRW","short_pith_number":"pith:S56IAOYW","schema_version":"1.0","canonical_sha256":"977c803b16d106fb7c30fd0701b3468d8c4214a3d6e54a6d9a8550eef64e572a","source":{"kind":"arxiv","id":"1412.6174","version":4},"attestation_state":"computed","paper":{"title":"On the formal arc space of a reductive monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Alexis Bouthier, Ngo Bao Chau, Yiannis Sakellaridis","submitted_at":"2014-12-18T23:11:58Z","abstract_excerpt":"Let $X$ be a scheme of finite type over a finite field $k$, and let $\\mathcal L X$ denote its arc space; in particular, $\\mathcal L X(k) = X(k[[t]])$. Using the theory of Grinberg, Kazhdan, and Drinfeld on the finite-dimensionality of singularities of $\\mathcal L X$ in the neighborhood of non-degenerate arcs, we show that a canonical \"basic function\" can be defined on the non-degenerate locus of $\\mathcal L X(k)$, which corresponds to the trace of Frobenius on the stalks of the intersection complex of any finite-dimensional model. We then proceed to compute this function when $X$ is an affine "},"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":"1412.6174","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-18T23:11:58Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"07af28be412633c1a9146a5e0e7c2c2f8f951a02ab0728d068326807be1f5f09","abstract_canon_sha256":"085b46f5838e7409b7f4a30a087363e0c123096ac15cd99267a02839698c7165"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:49.517176Z","signature_b64":"jdDTCjiaUxsWgAMvWumFotI3mRbE6I5/x+qvSvy0zYEew+6zJUdCTQ91N5kNKhjM/jdn5jsZxjVCi7zMF+gXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"977c803b16d106fb7c30fd0701b3468d8c4214a3d6e54a6d9a8550eef64e572a","last_reissued_at":"2026-05-18T01:01:49.516607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:49.516607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the formal arc space of a reductive monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Alexis Bouthier, Ngo Bao Chau, Yiannis Sakellaridis","submitted_at":"2014-12-18T23:11:58Z","abstract_excerpt":"Let $X$ be a scheme of finite type over a finite field $k$, and let $\\mathcal L X$ denote its arc space; in particular, $\\mathcal L X(k) = X(k[[t]])$. Using the theory of Grinberg, Kazhdan, and Drinfeld on the finite-dimensionality of singularities of $\\mathcal L X$ in the neighborhood of non-degenerate arcs, we show that a canonical \"basic function\" can be defined on the non-degenerate locus of $\\mathcal L X(k)$, which corresponds to the trace of Frobenius on the stalks of the intersection complex of any finite-dimensional model. We then proceed to compute this function when $X$ is an affine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6174","kind":"arxiv","version":4},"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":"1412.6174","created_at":"2026-05-18T01:01:49.516691+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.6174v4","created_at":"2026-05-18T01:01:49.516691+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6174","created_at":"2026-05-18T01:01:49.516691+00:00"},{"alias_kind":"pith_short_12","alias_value":"S56IAOYW2EDP","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"S56IAOYW2EDPW7BQ","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"S56IAOYW","created_at":"2026-05-18T12:28:49.207871+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/S56IAOYW2EDPW7BQ7UDQDM2GRW","json":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW.json","graph_json":"https://pith.science/api/pith-number/S56IAOYW2EDPW7BQ7UDQDM2GRW/graph.json","events_json":"https://pith.science/api/pith-number/S56IAOYW2EDPW7BQ7UDQDM2GRW/events.json","paper":"https://pith.science/paper/S56IAOYW"},"agent_actions":{"view_html":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW","download_json":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW.json","view_paper":"https://pith.science/paper/S56IAOYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.6174&json=true","fetch_graph":"https://pith.science/api/pith-number/S56IAOYW2EDPW7BQ7UDQDM2GRW/graph.json","fetch_events":"https://pith.science/api/pith-number/S56IAOYW2EDPW7BQ7UDQDM2GRW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW/action/storage_attestation","attest_author":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW/action/author_attestation","sign_citation":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW/action/citation_signature","submit_replication":"https://pith.science/pith/S56IAOYW2EDPW7BQ7UDQDM2GRW/action/replication_record"}},"created_at":"2026-05-18T01:01:49.516691+00:00","updated_at":"2026-05-18T01:01:49.516691+00:00"}