{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JTU5PNPRKW3LH3X2CLSDOWY6EW","short_pith_number":"pith:JTU5PNPR","canonical_record":{"source":{"id":"2309.16847","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-09-28T20:56:32Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"5e4469f9d4b50281b686ee1e58c160bdd44c29e96647edb5e32f9288548a5452","abstract_canon_sha256":"42fb66f9e2c1f3599b30a2c23de705017558f0869031a773924e91aefb862965"},"schema_version":"1.0"},"canonical_sha256":"4ce9d7b5f155b6b3eefa12e4375b1e25a27fc54574952aa2238261e90859b9e4","source":{"kind":"arxiv","id":"2309.16847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16847","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16847v1","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16847","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"JTU5PNPRKW3L","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_16","alias_value":"JTU5PNPRKW3LH3X2","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_8","alias_value":"JTU5PNPR","created_at":"2026-07-05T06:55:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JTU5PNPRKW3LH3X2CLSDOWY6EW","target":"record","payload":{"canonical_record":{"source":{"id":"2309.16847","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-09-28T20:56:32Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"5e4469f9d4b50281b686ee1e58c160bdd44c29e96647edb5e32f9288548a5452","abstract_canon_sha256":"42fb66f9e2c1f3599b30a2c23de705017558f0869031a773924e91aefb862965"},"schema_version":"1.0"},"canonical_sha256":"4ce9d7b5f155b6b3eefa12e4375b1e25a27fc54574952aa2238261e90859b9e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:55:28.296070Z","signature_b64":"/fKqWugiQ8BIjT900rLtLMuKwgSkEsauebbcHaxbz6Nu9VcJBFwVV4NuOiliPs4DZ6UNCyGmh2hBq/EjqXa8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ce9d7b5f155b6b3eefa12e4375b1e25a27fc54574952aa2238261e90859b9e4","last_reissued_at":"2026-07-05T06:55:28.295616Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:55:28.295616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.16847","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoVmnqp9Eg/8tEIPGdMV3EXIZa1ZZyERnMOglGeY9hdjoyKm9CcM5mvcfjeniJjoE5OdiX6lnjTh+iGYAlHsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T02:50:09.231027Z"},"content_sha256":"a28b47eb9054c8d97c57e6b15e916cd6559151af83352a1546d153f08acef3a8","schema_version":"1.0","event_id":"sha256:a28b47eb9054c8d97c57e6b15e916cd6559151af83352a1546d153f08acef3a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JTU5PNPRKW3LH3X2CLSDOWY6EW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small ideals in polynomial rings and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Amichai Lampert","submitted_at":"2023-09-28T20:56:32Z","abstract_excerpt":"Let $\\mathbf{k}$ be a field which is either finite or algebraically closed and let $R = \\mathbf{k}[x_1,\\ldots,x_n].$ We prove that any $g_1,\\ldots,g_s\\in R$ homogeneous of positive degrees $\\le d$ are contained in an ideal generated by an $R_t$-sequence of $\\le A(d)(s+t)^{B(d)}$ homogeneous polynomials of degree $\\le d,$ subject to some restrictions on the characteristic of $\\mathbf{k}.$ This yields effective bounds for new cases of Ananyan and Hochster's theorem A in arXiv:1610.09268 on strength and the codimension of the singular locus. It also implies effective bounds when $d$ equals the ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16847","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/2309.16847/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjAqhPMotTKmyBwcripprG0JmPznsUiG/Pz1CKGSIIv6WZxwrO21wHIcCWKF5v7frAo0fwBOY9NpUJBcl2BGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T02:50:09.231688Z"},"content_sha256":"6207a6859bf41e48f54405cfed261a53b00bab2371c9a89c9a649f10c8a5c9d9","schema_version":"1.0","event_id":"sha256:6207a6859bf41e48f54405cfed261a53b00bab2371c9a89c9a649f10c8a5c9d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/bundle.json","state_url":"https://pith.science/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T02:50:09Z","links":{"resolver":"https://pith.science/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW","bundle":"https://pith.science/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/bundle.json","state":"https://pith.science/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTU5PNPRKW3LH3X2CLSDOWY6EW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JTU5PNPRKW3LH3X2CLSDOWY6EW","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":"42fb66f9e2c1f3599b30a2c23de705017558f0869031a773924e91aefb862965","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-09-28T20:56:32Z","title_canon_sha256":"5e4469f9d4b50281b686ee1e58c160bdd44c29e96647edb5e32f9288548a5452"},"schema_version":"1.0","source":{"id":"2309.16847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16847","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16847v1","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16847","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"JTU5PNPRKW3L","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_16","alias_value":"JTU5PNPRKW3LH3X2","created_at":"2026-07-05T06:55:28Z"},{"alias_kind":"pith_short_8","alias_value":"JTU5PNPR","created_at":"2026-07-05T06:55:28Z"}],"graph_snapshots":[{"event_id":"sha256:6207a6859bf41e48f54405cfed261a53b00bab2371c9a89c9a649f10c8a5c9d9","target":"graph","created_at":"2026-07-05T06:55:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.16847/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbf{k}$ be a field which is either finite or algebraically closed and let $R = \\mathbf{k}[x_1,\\ldots,x_n].$ We prove that any $g_1,\\ldots,g_s\\in R$ homogeneous of positive degrees $\\le d$ are contained in an ideal generated by an $R_t$-sequence of $\\le A(d)(s+t)^{B(d)}$ homogeneous polynomials of degree $\\le d,$ subject to some restrictions on the characteristic of $\\mathbf{k}.$ This yields effective bounds for new cases of Ananyan and Hochster's theorem A in arXiv:1610.09268 on strength and the codimension of the singular locus. It also implies effective bounds when $d$ equals the ch","authors_text":"Amichai Lampert","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-09-28T20:56:32Z","title":"Small ideals in polynomial rings and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16847","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:a28b47eb9054c8d97c57e6b15e916cd6559151af83352a1546d153f08acef3a8","target":"record","created_at":"2026-07-05T06:55:28Z","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":"42fb66f9e2c1f3599b30a2c23de705017558f0869031a773924e91aefb862965","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-09-28T20:56:32Z","title_canon_sha256":"5e4469f9d4b50281b686ee1e58c160bdd44c29e96647edb5e32f9288548a5452"},"schema_version":"1.0","source":{"id":"2309.16847","kind":"arxiv","version":1}},"canonical_sha256":"4ce9d7b5f155b6b3eefa12e4375b1e25a27fc54574952aa2238261e90859b9e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ce9d7b5f155b6b3eefa12e4375b1e25a27fc54574952aa2238261e90859b9e4","first_computed_at":"2026-07-05T06:55:28.295616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:55:28.295616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fKqWugiQ8BIjT900rLtLMuKwgSkEsauebbcHaxbz6Nu9VcJBFwVV4NuOiliPs4DZ6UNCyGmh2hBq/EjqXa8DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:55:28.296070Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.16847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a28b47eb9054c8d97c57e6b15e916cd6559151af83352a1546d153f08acef3a8","sha256:6207a6859bf41e48f54405cfed261a53b00bab2371c9a89c9a649f10c8a5c9d9"],"state_sha256":"111b56d2bd58e13e0a331aad076ef0ddc4633a4c75ef77b2d0927b9911b2eeb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRjIFxyhaWO7sIlt5/xz/UP+hoNgX/VhqXTq3kRba+/mgIH0rOukjc6f/NSrXflTVt2r+7vHFXoeInZB14X2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T02:50:09.237998Z","bundle_sha256":"743ba2df49e2b8c1933cbe82819727a1872a8eb9e5d4c7926d5a3b34d1d38297"}}