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We denote by $A_V ({\\bf C}) $, the Weyl algebra of algebraic differential operators on $V$. Following J. Bernstein, the ideal constituted by polynomials $ b \\in {\\bf C} [s_1, \\ldots, s_p] $ such that : $$ \\; \\; b (s_1, \\ldots, s_p) \\, l_1^{s_1} \\ldots l_p^{s_p} \\in A_n ({\\bf C}) [s_1, \\ldots, s_p] \\, l_1^ {s_1 + 1} \\ldots l_p^{s_p + 1} \\; , $$ is not red"},"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":"1610.03356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-06T14:25:20Z","cross_cats_sorted":[],"title_canon_sha256":"63ceb043cbc4d7a26898d09ed2195c23ad2d086dc9dc94ab31f4006b0bd70358","abstract_canon_sha256":"638babf1313ccc1dede8fcd569504a77edd5cc6cd8388f35dccdd83e11f8afea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:31.707615Z","signature_b64":"2z0yGTg85EB55g7N7XXhqVoh5rcb41e9foImjDXRSlrsvguBrbvJmE+nJTg8lVVqH1vl+w/P3ztG32ftv47fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dea664e261a9ecdb3abb1cbb371d09018af68ffc0b9be19e1db1ca34b2839c27","last_reissued_at":"2026-05-18T01:02:31.706938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:31.706938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L'id\\'eal de Bernstein d'un arrangement libre d'hyperplans lin\\'eaires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Philippe Maisonobe","submitted_at":"2016-10-06T14:25:20Z","abstract_excerpt":"Let $ V $ a vector space of dimension $n$. A family $ \\{H_1, \\ldots, H_p \\} $ of vectorial hyperplans $V$ defines an arrangement $ {\\cal A} $ of $ V $. For $ i \\in \\{ 1, \\ldots, p \\} $, let $ l_i $ be a linear form on $V$ with $H_i$ as kernel. We denote by $A_V ({\\bf C}) $, the Weyl algebra of algebraic differential operators on $V$. Following J. Bernstein, the ideal constituted by polynomials $ b \\in {\\bf C} [s_1, \\ldots, s_p] $ such that : $$ \\; \\; b (s_1, \\ldots, s_p) \\, l_1^{s_1} \\ldots l_p^{s_p} \\in A_n ({\\bf C}) [s_1, \\ldots, s_p] \\, l_1^ {s_1 + 1} \\ldots l_p^{s_p + 1} \\; , $$ is not red"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03356","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":""},"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":"1610.03356","created_at":"2026-05-18T01:02:31.707045+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.03356v1","created_at":"2026-05-18T01:02:31.707045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03356","created_at":"2026-05-18T01:02:31.707045+00:00"},{"alias_kind":"pith_short_12","alias_value":"32TGJYTBVHWN","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"32TGJYTBVHWNWOV3","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"32TGJYTB","created_at":"2026-05-18T12:29:55.572404+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/32TGJYTBVHWNWOV3DS5TOHIJAG","json":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG.json","graph_json":"https://pith.science/api/pith-number/32TGJYTBVHWNWOV3DS5TOHIJAG/graph.json","events_json":"https://pith.science/api/pith-number/32TGJYTBVHWNWOV3DS5TOHIJAG/events.json","paper":"https://pith.science/paper/32TGJYTB"},"agent_actions":{"view_html":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG","download_json":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG.json","view_paper":"https://pith.science/paper/32TGJYTB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.03356&json=true","fetch_graph":"https://pith.science/api/pith-number/32TGJYTBVHWNWOV3DS5TOHIJAG/graph.json","fetch_events":"https://pith.science/api/pith-number/32TGJYTBVHWNWOV3DS5TOHIJAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG/action/storage_attestation","attest_author":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG/action/author_attestation","sign_citation":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG/action/citation_signature","submit_replication":"https://pith.science/pith/32TGJYTBVHWNWOV3DS5TOHIJAG/action/replication_record"}},"created_at":"2026-05-18T01:02:31.707045+00:00","updated_at":"2026-05-18T01:02:31.707045+00:00"}