{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FPNYV6JB7SGK44YM2XTRFCYRPW","short_pith_number":"pith:FPNYV6JB","schema_version":"1.0","canonical_sha256":"2bdb8af921fc8cae730cd5e7128b117d9a94d719fbafc81ad5d2d03577cc788b","source":{"kind":"arxiv","id":"2602.07302","version":2},"attestation_state":"computed","paper":{"title":"Failure of the invariant cycle theorem over $\\mathbb Z$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Donu Arapura, Fran\\c{c}ois Greer, Yilong Zhang","submitted_at":"2026-02-07T01:29:50Z","abstract_excerpt":"We initiate a study of the local invariant cycle theorem with integral coefficients for 1-parameter semistable families of varieties. We show that it always holds for $H^1$, and it holds for $H^2$ if the general fiber has trivial Albanese variety. The latter generalizes results of Friedman, Griffiths, and Scattone on K3 surfaces and I-surfaces. We construct the first example of a semistable family which fails the local (and global) invariant cycle theorems with integral coefficients. The family has constant period map associated to $H^2$, and its smooth fibers are algebraic surfaces with $p_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":"2602.07302","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-02-07T01:29:50Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"2336dfff164eeb36f2d818b0935382f81a38f0624b366e22fb54b4a86262d995","abstract_canon_sha256":"cac04ec6d7b6bcd1b51a7450770ea42ed26895f96a549afca560c9af49689476"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:33.826816Z","signature_b64":"O8wcaHNvCWShjx4smca8i5N8xMrPV6U7ydQ6ohWfbAAMZHIO6RTihpK/hP4ks7FReXGtgNAiBbX/1g0CC87TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bdb8af921fc8cae730cd5e7128b117d9a94d719fbafc81ad5d2d03577cc788b","last_reissued_at":"2026-05-20T00:00:33.826110Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:33.826110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Failure of the invariant cycle theorem over $\\mathbb Z$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Donu Arapura, Fran\\c{c}ois Greer, Yilong Zhang","submitted_at":"2026-02-07T01:29:50Z","abstract_excerpt":"We initiate a study of the local invariant cycle theorem with integral coefficients for 1-parameter semistable families of varieties. We show that it always holds for $H^1$, and it holds for $H^2$ if the general fiber has trivial Albanese variety. The latter generalizes results of Friedman, Griffiths, and Scattone on K3 surfaces and I-surfaces. We construct the first example of a semistable family which fails the local (and global) invariant cycle theorems with integral coefficients. The family has constant period map associated to $H^2$, and its smooth fibers are algebraic surfaces with $p_g="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.07302","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.07302/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":"2602.07302","created_at":"2026-05-20T00:00:33.826245+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.07302v2","created_at":"2026-05-20T00:00:33.826245+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.07302","created_at":"2026-05-20T00:00:33.826245+00:00"},{"alias_kind":"pith_short_12","alias_value":"FPNYV6JB7SGK","created_at":"2026-05-20T00:00:33.826245+00:00"},{"alias_kind":"pith_short_16","alias_value":"FPNYV6JB7SGK44YM","created_at":"2026-05-20T00:00:33.826245+00:00"},{"alias_kind":"pith_short_8","alias_value":"FPNYV6JB","created_at":"2026-05-20T00:00:33.826245+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/FPNYV6JB7SGK44YM2XTRFCYRPW","json":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW.json","graph_json":"https://pith.science/api/pith-number/FPNYV6JB7SGK44YM2XTRFCYRPW/graph.json","events_json":"https://pith.science/api/pith-number/FPNYV6JB7SGK44YM2XTRFCYRPW/events.json","paper":"https://pith.science/paper/FPNYV6JB"},"agent_actions":{"view_html":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW","download_json":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW.json","view_paper":"https://pith.science/paper/FPNYV6JB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.07302&json=true","fetch_graph":"https://pith.science/api/pith-number/FPNYV6JB7SGK44YM2XTRFCYRPW/graph.json","fetch_events":"https://pith.science/api/pith-number/FPNYV6JB7SGK44YM2XTRFCYRPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW/action/storage_attestation","attest_author":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW/action/author_attestation","sign_citation":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW/action/citation_signature","submit_replication":"https://pith.science/pith/FPNYV6JB7SGK44YM2XTRFCYRPW/action/replication_record"}},"created_at":"2026-05-20T00:00:33.826245+00:00","updated_at":"2026-05-20T00:00:33.826245+00:00"}