{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IOKKE7YMJYHWRBY4TAARIBJGRQ","short_pith_number":"pith:IOKKE7YM","canonical_record":{"source":{"id":"1309.6012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-24T00:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"a07ca13598001308d10f426e8c9a570cac9477a7f64019dd790940899f62a682","abstract_canon_sha256":"6fba5456f696ae4a22602706412659b2e35e3b971dc4d0245b171edfc07d0c5b"},"schema_version":"1.0"},"canonical_sha256":"4394a27f0c4e0f68871c98011405268c2415f097aed11056a5e4b5533725f4a7","source":{"kind":"arxiv","id":"1309.6012","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6012","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6012v2","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6012","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"IOKKE7YMJYHW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IOKKE7YMJYHWRBY4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IOKKE7YM","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IOKKE7YMJYHWRBY4TAARIBJGRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-24T00:21:35Z","cross_cats_sorted":[],"title_canon_sha256":"a07ca13598001308d10f426e8c9a570cac9477a7f64019dd790940899f62a682","abstract_canon_sha256":"6fba5456f696ae4a22602706412659b2e35e3b971dc4d0245b171edfc07d0c5b"},"schema_version":"1.0"},"canonical_sha256":"4394a27f0c4e0f68871c98011405268c2415f097aed11056a5e4b5533725f4a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:17.033765Z","signature_b64":"Ot41RnJlnLDj++Ckpb4md8STIqqaHE3clP001SIo2d1Bu+Z6Ebc7XAu7Rttr6fnxlH7VcX4QUM20U1kjCtB6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4394a27f0c4e0f68871c98011405268c2415f097aed11056a5e4b5533725f4a7","last_reissued_at":"2026-05-18T02:38:17.033084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:17.033084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6012","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weEi/vUdL85Ss+nwu9NF1G3V3sBnt3TvOod8M2LToMlsUa3KQWnWEvgM2JGQOT3JXAHDfbJLnfXUKTy2dIFzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:07:49.252142Z"},"content_sha256":"f683fd2ca2a21d01bb8cb3b0e2f7984cc8504ea59b3e3de50006b2491a333ed7","schema_version":"1.0","event_id":"sha256:f683fd2ca2a21d01bb8cb3b0e2f7984cc8504ea59b3e3de50006b2491a333ed7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IOKKE7YMJYHWRBY4TAARIBJGRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separating Invariants and Local Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Emilie Dufresne, Jack Jeffries","submitted_at":"2013-09-24T00:21:35Z","abstract_excerpt":"The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6012","kind":"arxiv","version":2},"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":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mck3j+VmScTHJTbVZu8/KxsLQWoxNxX68AUDuc9+Vcpj7Qf0ARCIFd9fxUvnqIEfFDXcg1VWX3HYAdkQ4O81Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:07:49.252797Z"},"content_sha256":"b9fd1874f32122175b5a12d5bc66e020c05d710f069f88caeebf998c6722d245","schema_version":"1.0","event_id":"sha256:b9fd1874f32122175b5a12d5bc66e020c05d710f069f88caeebf998c6722d245"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/bundle.json","state_url":"https://pith.science/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/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":"2026-06-06T20:07:49Z","links":{"resolver":"https://pith.science/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ","bundle":"https://pith.science/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/bundle.json","state":"https://pith.science/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOKKE7YMJYHWRBY4TAARIBJGRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IOKKE7YMJYHWRBY4TAARIBJGRQ","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":"6fba5456f696ae4a22602706412659b2e35e3b971dc4d0245b171edfc07d0c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-24T00:21:35Z","title_canon_sha256":"a07ca13598001308d10f426e8c9a570cac9477a7f64019dd790940899f62a682"},"schema_version":"1.0","source":{"id":"1309.6012","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6012","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6012v2","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6012","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"IOKKE7YMJYHW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IOKKE7YMJYHWRBY4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IOKKE7YM","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:b9fd1874f32122175b5a12d5bc66e020c05d710f069f88caeebf998c6722d245","target":"graph","created_at":"2026-05-18T02:38:17Z","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":"The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find","authors_text":"Emilie Dufresne, Jack Jeffries","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-24T00:21:35Z","title":"Separating Invariants and Local Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6012","kind":"arxiv","version":2},"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:f683fd2ca2a21d01bb8cb3b0e2f7984cc8504ea59b3e3de50006b2491a333ed7","target":"record","created_at":"2026-05-18T02:38:17Z","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":"6fba5456f696ae4a22602706412659b2e35e3b971dc4d0245b171edfc07d0c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-24T00:21:35Z","title_canon_sha256":"a07ca13598001308d10f426e8c9a570cac9477a7f64019dd790940899f62a682"},"schema_version":"1.0","source":{"id":"1309.6012","kind":"arxiv","version":2}},"canonical_sha256":"4394a27f0c4e0f68871c98011405268c2415f097aed11056a5e4b5533725f4a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4394a27f0c4e0f68871c98011405268c2415f097aed11056a5e4b5533725f4a7","first_computed_at":"2026-05-18T02:38:17.033084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.033084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ot41RnJlnLDj++Ckpb4md8STIqqaHE3clP001SIo2d1Bu+Z6Ebc7XAu7Rttr6fnxlH7VcX4QUM20U1kjCtB6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.033765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6012","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f683fd2ca2a21d01bb8cb3b0e2f7984cc8504ea59b3e3de50006b2491a333ed7","sha256:b9fd1874f32122175b5a12d5bc66e020c05d710f069f88caeebf998c6722d245"],"state_sha256":"c847236454d1ede6c9a7f6c16041d097e29d395824296e5f232095ee2e8a8c34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/97Kgm/20GUdGG38kSPChJogQ3DAdLDdOOl9GWE2NDl5NYCdig4B8kn4tZoZ1sBHXkE3YknDDnvrWI7/1U8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:07:49.256568Z","bundle_sha256":"111e2d9e9486f21cb231597b01779963d89adf0988fdcec141a701ab56448de7"}}