{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QTPE5JW2KMBXVVILSCUF7T6JFU","short_pith_number":"pith:QTPE5JW2","schema_version":"1.0","canonical_sha256":"84de4ea6da53037ad50b90a85fcfc92d105871b5803fcb5e53c33d0421900798","source":{"kind":"arxiv","id":"1805.08372","version":1},"attestation_state":"computed","paper":{"title":"Motivic Volumes of Fibers of Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine","submitted_at":"2018-05-22T03:09:19Z","abstract_excerpt":"Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$-toric variety such that $U = X \\cap T$ is not empty, and let $\\mathscr{L}(X)$ be the arc scheme of $X$. We define a tropicalization map on $\\mathscr{L}(X) \\setminus \\mathscr{L}(X \\setminus U)$, the set of arcs of $X$ that do not factor through $X \\setminus U$. We show that each fiber of this tropicalization map is a constructible subset of $\\mathscr{L}(X)$ and therefore has a motivic volume. We prove that if $U$ has a compactification with simple normal crossing boundary, then the 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":"1805.08372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-22T03:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"5edac57c661ccef9cf4c42ab31d6332c3587c1f85a5b75204a2bb6cd7f0066b3","abstract_canon_sha256":"7d6f6ccfcf48705bd8a724f8213d6a39dbabf6754f81e504893ab82594d3b44e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:26.714475Z","signature_b64":"+XSHsjGF3jO6JISbwr4IAg3AyPBRNs3nLaXdUV7S1USsgR1YdfcvgPvScR40u/lY8Ducqo1p9z1+0fKV0Ex/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84de4ea6da53037ad50b90a85fcfc92d105871b5803fcb5e53c33d0421900798","last_reissued_at":"2026-05-18T00:15:26.713716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:26.713716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Motivic Volumes of Fibers of Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine","submitted_at":"2018-05-22T03:09:19Z","abstract_excerpt":"Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$-toric variety such that $U = X \\cap T$ is not empty, and let $\\mathscr{L}(X)$ be the arc scheme of $X$. We define a tropicalization map on $\\mathscr{L}(X) \\setminus \\mathscr{L}(X \\setminus U)$, the set of arcs of $X$ that do not factor through $X \\setminus U$. We show that each fiber of this tropicalization map is a constructible subset of $\\mathscr{L}(X)$ and therefore has a motivic volume. We prove that if $U$ has a compactification with simple normal crossing boundary, then the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08372","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":"1805.08372","created_at":"2026-05-18T00:15:26.713842+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.08372v1","created_at":"2026-05-18T00:15:26.713842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08372","created_at":"2026-05-18T00:15:26.713842+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTPE5JW2KMBX","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTPE5JW2KMBXVVIL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTPE5JW2","created_at":"2026-05-18T12:32:46.962924+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/QTPE5JW2KMBXVVILSCUF7T6JFU","json":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU.json","graph_json":"https://pith.science/api/pith-number/QTPE5JW2KMBXVVILSCUF7T6JFU/graph.json","events_json":"https://pith.science/api/pith-number/QTPE5JW2KMBXVVILSCUF7T6JFU/events.json","paper":"https://pith.science/paper/QTPE5JW2"},"agent_actions":{"view_html":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU","download_json":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU.json","view_paper":"https://pith.science/paper/QTPE5JW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.08372&json=true","fetch_graph":"https://pith.science/api/pith-number/QTPE5JW2KMBXVVILSCUF7T6JFU/graph.json","fetch_events":"https://pith.science/api/pith-number/QTPE5JW2KMBXVVILSCUF7T6JFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU/action/storage_attestation","attest_author":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU/action/author_attestation","sign_citation":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU/action/citation_signature","submit_replication":"https://pith.science/pith/QTPE5JW2KMBXVVILSCUF7T6JFU/action/replication_record"}},"created_at":"2026-05-18T00:15:26.713842+00:00","updated_at":"2026-05-18T00:15:26.713842+00:00"}