{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KA6TCTH4YCOMK2P5C3ZV2QNZEH","short_pith_number":"pith:KA6TCTH4","canonical_record":{"source":{"id":"1309.1098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dd44d5376f12e011797c5c0457e55165d347380b4d304b95acc2f5ed3019bc16","abstract_canon_sha256":"fbd4d5635355f0dacb49ea4c09b97f7e54dd276761a143468a53bab27ada0858"},"schema_version":"1.0"},"canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","source":{"kind":"arxiv","id":"1309.1098","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1098","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1098v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1098","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"KA6TCTH4YCOM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KA6TCTH4YCOMK2P5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KA6TCTH4","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KA6TCTH4YCOMK2P5C3ZV2QNZEH","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dd44d5376f12e011797c5c0457e55165d347380b4d304b95acc2f5ed3019bc16","abstract_canon_sha256":"fbd4d5635355f0dacb49ea4c09b97f7e54dd276761a143468a53bab27ada0858"},"schema_version":"1.0"},"canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:09.099917Z","signature_b64":"RlxkVxGkwG+FF6cWTHzTUuEIkDkawPL9V2RGB37X1ufXGkeUaYCZdwetaOgtzrB71jkgnH1bZMrYSGWItRNWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","last_reissued_at":"2026-05-18T03:14:09.099253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:09.099253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1098","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":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5XjNmol5gb9NZY5ycTnkig+/My89Ke+DM4SnEF7j8kYEtHjYAJrGpeiVNwsL93lJ/iqorcahD/rWUY7ncF4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:01.196570Z"},"content_sha256":"dd92ba896c385bf0da22507b3215919172e0033c3d36974de7da1f3a5534b55c","schema_version":"1.0","event_id":"sha256:dd92ba896c385bf0da22507b3215919172e0033c3d36974de7da1f3a5534b55c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KA6TCTH4YCOMK2P5C3ZV2QNZEH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prime ideals and regular sequences of symmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Neeraj Kumar","submitted_at":"2013-09-04T16:47:23Z","abstract_excerpt":"Let S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \\subset \\mathbb{N}$ such that the set of polynomials $p_a$ with $a \\in A$ generate a prime ideal in S or the set of polynomials $p_a$ with $a \\in A$ is a regular sequence in S. We produce a large families of prime ideals by exploiting Serre's criterion for normality [4, Theorem 18.15] with the help of arithmetic considerations, vanishing sums of roots of unity [9]. We also deduce several other results concerning regular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1098","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBrYbOeYNq0KB/4iIga49SDwp3lekA3nREfPwyRq78XyMaxIRLGZF8NATcF1K6rmU7YVJeN+4H2oeyR138G+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:01.197282Z"},"content_sha256":"17168912a82e5dd539d85b0257ef96f261c6bb42d6cb34fe9d0388c13e1e6f8b","schema_version":"1.0","event_id":"sha256:17168912a82e5dd539d85b0257ef96f261c6bb42d6cb34fe9d0388c13e1e6f8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/bundle.json","state_url":"https://pith.science/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/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":"2026-06-11T03:59:01Z","links":{"resolver":"https://pith.science/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH","bundle":"https://pith.science/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/bundle.json","state":"https://pith.science/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KA6TCTH4YCOMK2P5C3ZV2QNZEH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KA6TCTH4YCOMK2P5C3ZV2QNZEH","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":"fbd4d5635355f0dacb49ea4c09b97f7e54dd276761a143468a53bab27ada0858","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","title_canon_sha256":"dd44d5376f12e011797c5c0457e55165d347380b4d304b95acc2f5ed3019bc16"},"schema_version":"1.0","source":{"id":"1309.1098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1098","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1098v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1098","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"KA6TCTH4YCOM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KA6TCTH4YCOMK2P5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KA6TCTH4","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:17168912a82e5dd539d85b0257ef96f261c6bb42d6cb34fe9d0388c13e1e6f8b","target":"graph","created_at":"2026-05-18T03:14:09Z","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 S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \\subset \\mathbb{N}$ such that the set of polynomials $p_a$ with $a \\in A$ generate a prime ideal in S or the set of polynomials $p_a$ with $a \\in A$ is a regular sequence in S. We produce a large families of prime ideals by exploiting Serre's criterion for normality [4, Theorem 18.15] with the help of arithmetic considerations, vanishing sums of roots of unity [9]. We also deduce several other results concerning regular ","authors_text":"Neeraj Kumar","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","title":"Prime ideals and regular sequences of symmetric polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1098","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:dd92ba896c385bf0da22507b3215919172e0033c3d36974de7da1f3a5534b55c","target":"record","created_at":"2026-05-18T03:14:09Z","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":"fbd4d5635355f0dacb49ea4c09b97f7e54dd276761a143468a53bab27ada0858","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","title_canon_sha256":"dd44d5376f12e011797c5c0457e55165d347380b4d304b95acc2f5ed3019bc16"},"schema_version":"1.0","source":{"id":"1309.1098","kind":"arxiv","version":1}},"canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","first_computed_at":"2026-05-18T03:14:09.099253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:09.099253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RlxkVxGkwG+FF6cWTHzTUuEIkDkawPL9V2RGB37X1ufXGkeUaYCZdwetaOgtzrB71jkgnH1bZMrYSGWItRNWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:09.099917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd92ba896c385bf0da22507b3215919172e0033c3d36974de7da1f3a5534b55c","sha256:17168912a82e5dd539d85b0257ef96f261c6bb42d6cb34fe9d0388c13e1e6f8b"],"state_sha256":"03ccdb7c30fff41cc7bc6b13c0215a4513c2c4a9131402c9f6b33d157fe9529a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQHmAQ/cqVO7vb3/j2jVK7ST+WghokYGPOqc66BcpTMGvDof9XJIB09L9oIpDlap8ju1BTFEL9U7fPplw+aSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:59:01.201274Z","bundle_sha256":"426aaeba12c8c38735b2730ee49b97dc725764cbfbd7a151f83f1ad03c21995d"}}