{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OL3V7YXRIBGTGXKMDC5DXV6S4S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"59fbfa0c8d356509cae7953e9e65a6927759e43cbb18220dd752a00daee6785b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-05-09T20:06:36Z","title_canon_sha256":"c59531a243fc4920ba1e92b266fd76ff28bd2d48ef58a73ec88435d179a61301"},"schema_version":"1.0","source":{"id":"1405.2343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2343","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2343v1","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2343","created_at":"2026-05-18T01:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"OL3V7YXRIBGT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OL3V7YXRIBGTGXKM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OL3V7YXR","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6503491c762207661e14bc9b5ea60d6fd7a2c49936864a80b9a459fcab9db400","target":"graph","created_at":"2026-05-18T01:02:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $f:\\CN \\rightarrow \\C $ be a polynomial map, which is transversal at infinity. Using Sabbah's specialization complex, we give a new description of the Alexander modules of the hypersurface complement $\\CN\\setminus f^{-1}(0)$, and obtain a general divisibility result for the associated Alexander polynomials. As a byproduct, we prove a conjecture of Maxim on the decomposition of the Cappell-Shaneson peripheral complex of the hypersurface. Moreover, as an application, we use nearby cycles to recover the mixed Hodge structure on the torsion Alexander modules, as defined by Dimca and Libgober. ","authors_text":"Yongqiang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-05-09T20:06:36Z","title":"Nearby Cycles and Alexander Modules of Hypersurface Complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2343","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4c12eb168ffd635dec511421a10d42b0099e2b8a5bf940378a920be2eee96440","target":"record","created_at":"2026-05-18T01:02:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"59fbfa0c8d356509cae7953e9e65a6927759e43cbb18220dd752a00daee6785b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-05-09T20:06:36Z","title_canon_sha256":"c59531a243fc4920ba1e92b266fd76ff28bd2d48ef58a73ec88435d179a61301"},"schema_version":"1.0","source":{"id":"1405.2343","kind":"arxiv","version":1}},"canonical_sha256":"72f75fe2f1404d335d4c18ba3bd7d2e4b8cd798b27f60cd9484a93c803cf7c63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72f75fe2f1404d335d4c18ba3bd7d2e4b8cd798b27f60cd9484a93c803cf7c63","first_computed_at":"2026-05-18T01:02:46.082891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:46.082891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVK9jbEy982vtIzrpO51GMSLAgLNJ1f0U2vm/OUk2gFYUOKsH3p65Kuhc6TNDMyZQvmg8wvluJw2R5AuwSAQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:46.083344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c12eb168ffd635dec511421a10d42b0099e2b8a5bf940378a920be2eee96440","sha256:6503491c762207661e14bc9b5ea60d6fd7a2c49936864a80b9a459fcab9db400"],"state_sha256":"a7af9859c5145d75140a523dd608ab7db90e3396ce359f056691c9778a1c2f11"}