{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:VARCJU5G7NGD5ARFLGCODYISBW","short_pith_number":"pith:VARCJU5G","schema_version":"1.0","canonical_sha256":"a82224d3a6fb4c3e82255984e1e1120d8ff84a83334ec3835fb2b36a5de36d83","source":{"kind":"arxiv","id":"2109.09800","version":1},"attestation_state":"computed","paper":{"title":"A motivic change of variables formula for Artin stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine, Matthew Satriano","submitted_at":"2021-09-20T19:17:37Z","abstract_excerpt":"Let $\\mathcal{X} \\to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\\mathcal{X}$. With a view toward the study of stringy Hodge numbers, this change of variables formula leads to a new notion of crepantness for the map $\\mathcal{X} \\to Y$ that coincides with the usual notion in the special case that $\\mathcal{X}$ is a scheme."},"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":"2109.09800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-20T19:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"82fe35d784e97329018d6246328c07b5a8822708fccae42303e4fe5a89e67df2","abstract_canon_sha256":"2c1f1ed0dbf38e114b18417f633fad6ef9b254aff655b3acc50671edd46af38c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:15:54.705558Z","signature_b64":"YaQMGM+pEnPrkjtHjZAWb5z8k9RaM3FglnwqCMUPREOvQ/Vt5hpkrw/2JmzUgC/oRXwF+CVM9EMauFdd8XpEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a82224d3a6fb4c3e82255984e1e1120d8ff84a83334ec3835fb2b36a5de36d83","last_reissued_at":"2026-07-05T03:15:54.705068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:15:54.705068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A motivic change of variables formula for Artin stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine, Matthew Satriano","submitted_at":"2021-09-20T19:17:37Z","abstract_excerpt":"Let $\\mathcal{X} \\to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\\mathcal{X}$. With a view toward the study of stringy Hodge numbers, this change of variables formula leads to a new notion of crepantness for the map $\\mathcal{X} \\to Y$ that coincides with the usual notion in the special case that $\\mathcal{X}$ is a scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.09800","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.09800/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2109.09800","created_at":"2026-07-05T03:15:54.705132+00:00"},{"alias_kind":"arxiv_version","alias_value":"2109.09800v1","created_at":"2026-07-05T03:15:54.705132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.09800","created_at":"2026-07-05T03:15:54.705132+00:00"},{"alias_kind":"pith_short_12","alias_value":"VARCJU5G7NGD","created_at":"2026-07-05T03:15:54.705132+00:00"},{"alias_kind":"pith_short_16","alias_value":"VARCJU5G7NGD5ARF","created_at":"2026-07-05T03:15:54.705132+00:00"},{"alias_kind":"pith_short_8","alias_value":"VARCJU5G","created_at":"2026-07-05T03:15:54.705132+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2112.06361","citing_title":"Logarithmic resolution via multi-weighted blow-ups","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW","json":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW.json","graph_json":"https://pith.science/api/pith-number/VARCJU5G7NGD5ARFLGCODYISBW/graph.json","events_json":"https://pith.science/api/pith-number/VARCJU5G7NGD5ARFLGCODYISBW/events.json","paper":"https://pith.science/paper/VARCJU5G"},"agent_actions":{"view_html":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW","download_json":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW.json","view_paper":"https://pith.science/paper/VARCJU5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2109.09800&json=true","fetch_graph":"https://pith.science/api/pith-number/VARCJU5G7NGD5ARFLGCODYISBW/graph.json","fetch_events":"https://pith.science/api/pith-number/VARCJU5G7NGD5ARFLGCODYISBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW/action/storage_attestation","attest_author":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW/action/author_attestation","sign_citation":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW/action/citation_signature","submit_replication":"https://pith.science/pith/VARCJU5G7NGD5ARFLGCODYISBW/action/replication_record"}},"created_at":"2026-07-05T03:15:54.705132+00:00","updated_at":"2026-07-05T03:15:54.705132+00:00"}