{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:KIJGSTQPCDAMHIEPG44NBMN7RO","short_pith_number":"pith:KIJGSTQP","schema_version":"1.0","canonical_sha256":"5212694e0f10c0c3a08f3738d0b1bf8b887850d5e57a83d3a595313a00681879","source":{"kind":"arxiv","id":"math/0606352","version":2},"attestation_state":"computed","paper":{"title":"Characteristic classes of proalgebraic varieties and motivic measures","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Shoji Yokura","submitted_at":"2006-06-15T06:17:21Z","abstract_excerpt":"Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry\", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In this paper we introduce characteristic classes of proalgebraic varieties, using Grothendieck transformations of Fulton--MacPherson's Bivariant Theory, modeled on the construction of MacPherson's Chern class transformation of proalgebraic varieties. We show that a proalgebraic version of the Euler--Poincar\\'e characteristic with values in the Grothendieck rin"},"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/0606352","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-06-15T06:17:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"9a9659df111f96134207a61d936762f555e1c14225b2ff017b4a3aca90d114ba","abstract_canon_sha256":"ef55ce6043c66209f2c9c687d3350593df6e240016a9dcd56414f9f385f04945"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:21.010586Z","signature_b64":"ovzA8Fp8NVn79v9bNski0c7/83tUjnbCcSWgSjwuArZv+O5HCFpFSHo0pR1rgNkyeLoWm3oNMBvTGXJ5LNgMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5212694e0f10c0c3a08f3738d0b1bf8b887850d5e57a83d3a595313a00681879","last_reissued_at":"2026-05-18T03:20:21.010067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:21.010067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characteristic classes of proalgebraic varieties and motivic measures","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Shoji Yokura","submitted_at":"2006-06-15T06:17:21Z","abstract_excerpt":"Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry\", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In this paper we introduce characteristic classes of proalgebraic varieties, using Grothendieck transformations of Fulton--MacPherson's Bivariant Theory, modeled on the construction of MacPherson's Chern class transformation of proalgebraic varieties. We show that a proalgebraic version of the Euler--Poincar\\'e characteristic with values in the Grothendieck rin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606352","kind":"arxiv","version":2},"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/0606352","created_at":"2026-05-18T03:20:21.010146+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0606352v2","created_at":"2026-05-18T03:20:21.010146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606352","created_at":"2026-05-18T03:20:21.010146+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIJGSTQPCDAM","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIJGSTQPCDAMHIEP","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIJGSTQP","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/KIJGSTQPCDAMHIEPG44NBMN7RO","json":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO.json","graph_json":"https://pith.science/api/pith-number/KIJGSTQPCDAMHIEPG44NBMN7RO/graph.json","events_json":"https://pith.science/api/pith-number/KIJGSTQPCDAMHIEPG44NBMN7RO/events.json","paper":"https://pith.science/paper/KIJGSTQP"},"agent_actions":{"view_html":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO","download_json":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO.json","view_paper":"https://pith.science/paper/KIJGSTQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0606352&json=true","fetch_graph":"https://pith.science/api/pith-number/KIJGSTQPCDAMHIEPG44NBMN7RO/graph.json","fetch_events":"https://pith.science/api/pith-number/KIJGSTQPCDAMHIEPG44NBMN7RO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO/action/storage_attestation","attest_author":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO/action/author_attestation","sign_citation":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO/action/citation_signature","submit_replication":"https://pith.science/pith/KIJGSTQPCDAMHIEPG44NBMN7RO/action/replication_record"}},"created_at":"2026-05-18T03:20:21.010146+00:00","updated_at":"2026-05-18T03:20:21.010146+00:00"}