{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ZYXM5XWBLJFMXDMCQYHA5L2WJN","short_pith_number":"pith:ZYXM5XWB","schema_version":"1.0","canonical_sha256":"ce2ecedec15a4acb8d82860e0eaf564b7bf8026a0e68349ef0f5b82b3653597c","source":{"kind":"arxiv","id":"2307.04395","version":3},"attestation_state":"computed","paper":{"title":"Generalized Brieskorn Modules I: Convergent (a,b)-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Generalized Brieskorn modules receive a full description through convergent asymptotic expansions of Nilsson class.","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Barlet (IUF, IECL), UL","submitted_at":"2023-07-10T07:57:24Z","abstract_excerpt":"This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribution |f|2$\\lambda$ with an hypothesis on a Higher Bernstein Polynomial of the (a,b)-module generated by the germ $\\omega$$\\in$$\\Omega$n+1 0 of a given holomorphic volum form. Note that, even for the existence of a simple pole this converse is already new. One difficulty to prove such a result comes from the use of the formal completion in f of the Brieskorn module of the holomorphic germ f\\,: (Cn+1 ,0) $\\rightarrow$("},"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":"2307.04395","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-07-10T07:57:24Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"150b4e99ddd47326421514a255e84d983c3a38ba4cb736fe495bdec27e7b6b32","abstract_canon_sha256":"440a13fb969e85e3640dae1016c996909550b5118e37c01407c8b8767a57aca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:31.881299Z","signature_b64":"DSaoGrrbjpMO5sQQDMM4iS2SPvJEpW0h7o3F/xjOPud+9eJplDVdT36QmItvSWMw2VyvwfH00pXGZssyolKUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2ecedec15a4acb8d82860e0eaf564b7bf8026a0e68349ef0f5b82b3653597c","last_reissued_at":"2026-05-27T01:05:31.880736Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:31.880736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Brieskorn Modules I: Convergent (a,b)-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Generalized Brieskorn modules receive a full description through convergent asymptotic expansions of Nilsson class.","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Barlet (IUF, IECL), UL","submitted_at":"2023-07-10T07:57:24Z","abstract_excerpt":"This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribution |f|2$\\lambda$ with an hypothesis on a Higher Bernstein Polynomial of the (a,b)-module generated by the germ $\\omega$$\\in$$\\Omega$n+1 0 of a given holomorphic volum form. Note that, even for the existence of a simple pole this converse is already new. One difficulty to prove such a result comes from the use of the formal completion in f of the Brieskorn module of the holomorphic germ f\\,: (Cn+1 ,0) $\\rightarrow$("},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We obtain a full description of generalized Brieskorn-modules in terms of (convergent) asymptotics expansions of Nilsson class which will be used as a starting point in part II.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The formal completion in f of the Brieskorn module does not give access to the cohomology of the Milnor fiber of f, which by definition is outside the zero set of f; this necessitates the introduction of generalized Brieskorn modules.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Develops the theory of convergent generalized Brieskorn modules, including semi-simple filtration, with a full description via convergent asymptotic expansions of Nilsson class and explicit relation to the nilpotent filtration of monodromy.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Generalized Brieskorn modules receive a full description through convergent asymptotic expansions of Nilsson class.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f2f3c87ba8c4493ad7d2bf0587cfdb4976c3a393ef15c14025b9d04153943571"},"source":{"id":"2307.04395","kind":"arxiv","version":3},"verdict":{"id":"ad5d951f-e3f5-413b-8a05-69d1ef9f3b1c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T07:26:52.417385Z","strongest_claim":"We obtain a full description of generalized Brieskorn-modules in terms of (convergent) asymptotics expansions of Nilsson class which will be used as a starting point in part II.","one_line_summary":"Develops the theory of convergent generalized Brieskorn modules, including semi-simple filtration, with a full description via convergent asymptotic expansions of Nilsson class and explicit relation to the nilpotent filtration of monodromy.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The formal completion in f of the Brieskorn module does not give access to the cohomology of the Milnor fiber of f, which by definition is outside the zero set of f; this necessitates the introduction of generalized Brieskorn modules.","pith_extraction_headline":"Generalized Brieskorn modules receive a full description through convergent asymptotic expansions of Nilsson class."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.04395/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":"2307.04395","created_at":"2026-05-27T01:05:31.880809+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.04395v3","created_at":"2026-05-27T01:05:31.880809+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.04395","created_at":"2026-05-27T01:05:31.880809+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYXM5XWBLJFM","created_at":"2026-05-27T01:05:31.880809+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYXM5XWBLJFMXDMC","created_at":"2026-05-27T01:05:31.880809+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYXM5XWB","created_at":"2026-05-27T01:05:31.880809+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/ZYXM5XWBLJFMXDMCQYHA5L2WJN","json":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN.json","graph_json":"https://pith.science/api/pith-number/ZYXM5XWBLJFMXDMCQYHA5L2WJN/graph.json","events_json":"https://pith.science/api/pith-number/ZYXM5XWBLJFMXDMCQYHA5L2WJN/events.json","paper":"https://pith.science/paper/ZYXM5XWB"},"agent_actions":{"view_html":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN","download_json":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN.json","view_paper":"https://pith.science/paper/ZYXM5XWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.04395&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYXM5XWBLJFMXDMCQYHA5L2WJN/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYXM5XWBLJFMXDMCQYHA5L2WJN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN/action/storage_attestation","attest_author":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN/action/author_attestation","sign_citation":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN/action/citation_signature","submit_replication":"https://pith.science/pith/ZYXM5XWBLJFMXDMCQYHA5L2WJN/action/replication_record"}},"created_at":"2026-05-27T01:05:31.880809+00:00","updated_at":"2026-05-27T01:05:31.880809+00:00"}