{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4BMOH2KABRRU2RHL4DXOGTIXWA","short_pith_number":"pith:4BMOH2KA","canonical_record":{"source":{"id":"1802.06735","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T18:00:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6b8c7198e66eeba7f4f4d3d0f41164af559d75516695122a1f47bad10f705ab5","abstract_canon_sha256":"8d8d00ff4494d45e287c7d4065c7feaecc5372eb4dfd3cdcb141dd98bb46a1fd"},"schema_version":"1.0"},"canonical_sha256":"e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1","source":{"kind":"arxiv","id":"1802.06735","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06735","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06735v5","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06735","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"4BMOH2KABRRU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BMOH2KABRRU2RHL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BMOH2KA","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4BMOH2KABRRU2RHL4DXOGTIXWA","target":"record","payload":{"canonical_record":{"source":{"id":"1802.06735","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T18:00:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6b8c7198e66eeba7f4f4d3d0f41164af559d75516695122a1f47bad10f705ab5","abstract_canon_sha256":"8d8d00ff4494d45e287c7d4065c7feaecc5372eb4dfd3cdcb141dd98bb46a1fd"},"schema_version":"1.0"},"canonical_sha256":"e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:30.083110Z","signature_b64":"YTqyxPOmg7fZxCH4Ov2266jfFclzQT8qyU338N23avT0ll2aYiNM4543Xgmha0k/UqAKoSr+7X8gACNPe9EjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1","last_reissued_at":"2026-05-18T00:01:30.082678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:30.082678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.06735","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8xd9G7sMISL7fbQXtB3E+xQB+PMGs/JYcZwUe63LkFIXIzOqqwlya6jj85aWUp7uzkApMC9aL5F+T3CinxuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:02:34.162699Z"},"content_sha256":"05305178df2e49dec802b6fdc66c419cffcf623af822bf0a9efb3807b6ba570d","schema_version":"1.0","event_id":"sha256:05305178df2e49dec802b6fdc66c419cffcf623af822bf0a9efb3807b6ba570d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4BMOH2KABRRU2RHL4DXOGTIXWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When are permutation invariants Cohen-Macaulay over all fields?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ben Blum-Smith, Sophie Marques","submitted_at":"2018-02-19T18:00:36Z","abstract_excerpt":"We prove that the polynomial invariants of a permutation group are Cohen-Macaulay for any choice of coefficient field if and only if the group is generated by transpositions, double transpositions, and 3-cycles. This unites and generalizes several previously known results. The \"if\" direction of the argument uses Stanley-Reisner theory and a recent result of Christian Lange in orbifold theory. The \"only-if\" direction uses a local-global result based on a theorem of Raynaud to reduce the problem to an analysis of inertia groups, and a combinatorial argument to identify inertia groups that obstru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06735","kind":"arxiv","version":5},"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":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B1iazyyWIOAJjA6IphDGS0oEN/Hzt4fD1RoutJzOlov7oiSQE9Pro/424MnCOGUOVL+/I2s5PvOhBqbYA5k1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:02:34.163245Z"},"content_sha256":"7f24a7f44560909a67414dbbd19131c853419c4964792a12066ef82b36c209eb","schema_version":"1.0","event_id":"sha256:7f24a7f44560909a67414dbbd19131c853419c4964792a12066ef82b36c209eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/bundle.json","state_url":"https://pith.science/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/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":"2026-05-22T08:02:34Z","links":{"resolver":"https://pith.science/pith/4BMOH2KABRRU2RHL4DXOGTIXWA","bundle":"https://pith.science/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/bundle.json","state":"https://pith.science/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BMOH2KABRRU2RHL4DXOGTIXWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4BMOH2KABRRU2RHL4DXOGTIXWA","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":"8d8d00ff4494d45e287c7d4065c7feaecc5372eb4dfd3cdcb141dd98bb46a1fd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T18:00:36Z","title_canon_sha256":"6b8c7198e66eeba7f4f4d3d0f41164af559d75516695122a1f47bad10f705ab5"},"schema_version":"1.0","source":{"id":"1802.06735","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06735","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06735v5","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06735","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"4BMOH2KABRRU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BMOH2KABRRU2RHL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BMOH2KA","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:7f24a7f44560909a67414dbbd19131c853419c4964792a12066ef82b36c209eb","target":"graph","created_at":"2026-05-18T00:01:30Z","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":"We prove that the polynomial invariants of a permutation group are Cohen-Macaulay for any choice of coefficient field if and only if the group is generated by transpositions, double transpositions, and 3-cycles. This unites and generalizes several previously known results. The \"if\" direction of the argument uses Stanley-Reisner theory and a recent result of Christian Lange in orbifold theory. The \"only-if\" direction uses a local-global result based on a theorem of Raynaud to reduce the problem to an analysis of inertia groups, and a combinatorial argument to identify inertia groups that obstru","authors_text":"Ben Blum-Smith, Sophie Marques","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T18:00:36Z","title":"When are permutation invariants Cohen-Macaulay over all fields?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06735","kind":"arxiv","version":5},"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":"sha256:05305178df2e49dec802b6fdc66c419cffcf623af822bf0a9efb3807b6ba570d","target":"record","created_at":"2026-05-18T00:01:30Z","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":"8d8d00ff4494d45e287c7d4065c7feaecc5372eb4dfd3cdcb141dd98bb46a1fd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T18:00:36Z","title_canon_sha256":"6b8c7198e66eeba7f4f4d3d0f41164af559d75516695122a1f47bad10f705ab5"},"schema_version":"1.0","source":{"id":"1802.06735","kind":"arxiv","version":5}},"canonical_sha256":"e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1","first_computed_at":"2026-05-18T00:01:30.082678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:30.082678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTqyxPOmg7fZxCH4Ov2266jfFclzQT8qyU338N23avT0ll2aYiNM4543Xgmha0k/UqAKoSr+7X8gACNPe9EjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:30.083110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06735","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05305178df2e49dec802b6fdc66c419cffcf623af822bf0a9efb3807b6ba570d","sha256:7f24a7f44560909a67414dbbd19131c853419c4964792a12066ef82b36c209eb"],"state_sha256":"b3af960d92b557aff18fe4a177e73b0e787018db00a58c206bc211d513686831"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6Pgv/OsTJfk0CHJVdPA+QVppKtPU8fWWJ06xNrgnUSh/NeDARiAP6SdN9WQydpaRiuELO9F8xdokyDrHk2nAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T08:02:34.165495Z","bundle_sha256":"f0666dbb46ab3df8df1c2d65b2a280284470c41b865d55b2675f48d0359095ae"}}