{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NJLXAEYAO2VLGW3NHKR6KWXJMV","short_pith_number":"pith:NJLXAEYA","schema_version":"1.0","canonical_sha256":"6a5770130076aab35b6d3aa3e55ae96542e6171afb2f0da150b0612c411acbd5","source":{"kind":"arxiv","id":"2607.19013","version":1},"attestation_state":"computed","paper":{"title":"Topology of higher Albanese maps and aspherical varieties with nilpotent fundamental group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Vasily Rogov","submitted_at":"2026-07-21T11:54:39Z","abstract_excerpt":"Let $X$ be a normal complex algebraic variety. Let $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ be the maximal torsion free nilpotent quotient of $\\pi_1(X)$ of nilpotency class at most $s$. Let $F^{\\bullet}\\mathfrak{g}^s$ be the Morgan--Hain Hodge filtration on the Lie algebra of the $s$-th lower central quotient of the complex Malcev completion of $\\pi_1(X)$. We show that the natural map $H^k(\\mathcal{G}^s_{\\mathbb{Z}}(X), \\mathbb{Z}) \\to H^k(X, \\mathbb{Z})$ vanishes for $k > \\dim F^1\\mathfrak{g}^s$. If $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ is of nilpotency class greater than two, this includes the top nonvanis"},"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":"2607.19013","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-07-21T11:54:39Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d9179735332570e2f30897fc5c700293c9e5acaee3df96fe080f768b3194d172","abstract_canon_sha256":"c89533f8a8f9308544fa9a821e01df0029c026643f15ca8142d56fe6281ee1da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:24:04.412505Z","signature_b64":"BvNJqbqbrYfam+N4cas+2JQ8UKpjioQGReeE5DmwC2UZ6J+yAUt0pjQuG03TKngx4/W+LAkOWVYTmKaod36qCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a5770130076aab35b6d3aa3e55ae96542e6171afb2f0da150b0612c411acbd5","last_reissued_at":"2026-07-22T01:24:04.411728Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:24:04.411728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology of higher Albanese maps and aspherical varieties with nilpotent fundamental group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Vasily Rogov","submitted_at":"2026-07-21T11:54:39Z","abstract_excerpt":"Let $X$ be a normal complex algebraic variety. Let $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ be the maximal torsion free nilpotent quotient of $\\pi_1(X)$ of nilpotency class at most $s$. Let $F^{\\bullet}\\mathfrak{g}^s$ be the Morgan--Hain Hodge filtration on the Lie algebra of the $s$-th lower central quotient of the complex Malcev completion of $\\pi_1(X)$. We show that the natural map $H^k(\\mathcal{G}^s_{\\mathbb{Z}}(X), \\mathbb{Z}) \\to H^k(X, \\mathbb{Z})$ vanishes for $k > \\dim F^1\\mathfrak{g}^s$. If $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ is of nilpotency class greater than two, this includes the top nonvanis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19013","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/2607.19013/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":"2607.19013","created_at":"2026-07-22T01:24:04.412143+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.19013v1","created_at":"2026-07-22T01:24:04.412143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19013","created_at":"2026-07-22T01:24:04.412143+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJLXAEYAO2VL","created_at":"2026-07-22T01:24:04.412143+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJLXAEYAO2VLGW3N","created_at":"2026-07-22T01:24:04.412143+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJLXAEYA","created_at":"2026-07-22T01:24:04.412143+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/NJLXAEYAO2VLGW3NHKR6KWXJMV","json":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV.json","graph_json":"https://pith.science/api/pith-number/NJLXAEYAO2VLGW3NHKR6KWXJMV/graph.json","events_json":"https://pith.science/api/pith-number/NJLXAEYAO2VLGW3NHKR6KWXJMV/events.json","paper":"https://pith.science/paper/NJLXAEYA"},"agent_actions":{"view_html":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV","download_json":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV.json","view_paper":"https://pith.science/paper/NJLXAEYA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.19013&json=true","fetch_graph":"https://pith.science/api/pith-number/NJLXAEYAO2VLGW3NHKR6KWXJMV/graph.json","fetch_events":"https://pith.science/api/pith-number/NJLXAEYAO2VLGW3NHKR6KWXJMV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV/action/storage_attestation","attest_author":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV/action/author_attestation","sign_citation":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV/action/citation_signature","submit_replication":"https://pith.science/pith/NJLXAEYAO2VLGW3NHKR6KWXJMV/action/replication_record"}},"created_at":"2026-07-22T01:24:04.412143+00:00","updated_at":"2026-07-22T01:24:04.412143+00:00"}