{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2H5AJA2CODNDVEU4QLXJW67AQE","short_pith_number":"pith:2H5AJA2C","canonical_record":{"source":{"id":"2508.04624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-08-06T16:51:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"15a5e2cfcbb2ee9a9999c8120904899ba1530666e87c2aa740e8e6d8c4e258fd","abstract_canon_sha256":"813578ce2ff5c827d2a97b5cb8f7f6225fc3c02004a15bdbb5685c9a576123ce"},"schema_version":"1.0"},"canonical_sha256":"d1fa04834270da3a929c82ee9b7be081108647ce4d32ebf4df9104982837a37f","source":{"kind":"arxiv","id":"2508.04624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.04624","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"2508.04624v1","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.04624","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"2H5AJA2CODND","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_16","alias_value":"2H5AJA2CODNDVEU4","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_8","alias_value":"2H5AJA2C","created_at":"2026-07-05T11:49:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2H5AJA2CODNDVEU4QLXJW67AQE","target":"record","payload":{"canonical_record":{"source":{"id":"2508.04624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-08-06T16:51:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"15a5e2cfcbb2ee9a9999c8120904899ba1530666e87c2aa740e8e6d8c4e258fd","abstract_canon_sha256":"813578ce2ff5c827d2a97b5cb8f7f6225fc3c02004a15bdbb5685c9a576123ce"},"schema_version":"1.0"},"canonical_sha256":"d1fa04834270da3a929c82ee9b7be081108647ce4d32ebf4df9104982837a37f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:49:40.633069Z","signature_b64":"amRLYIAgS7a7tMewWqoujEgSZyNzKM2307blo/DmlMUKzQDQAX5bUpw9l5oWMfcSwqMsBkNhylxmxLmqeDldCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1fa04834270da3a929c82ee9b7be081108647ce4d32ebf4df9104982837a37f","last_reissued_at":"2026-07-05T11:49:40.632644Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:49:40.632644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.04624","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":"2026-07-05T11:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSdycfZUWv1fMx5ivVk663HKXAxOMNIzRK9OmVmwJQRm72m91A5k8Pz2Ur4zcIWjkv4OEMzdpAtpmluLA3kxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:04:50.019406Z"},"content_sha256":"d6c13736b7e77227773f8d355de277494aa07dbbe5dd34ddb0501fda61c1cc84","schema_version":"1.0","event_id":"sha256:d6c13736b7e77227773f8d355de277494aa07dbbe5dd34ddb0501fda61c1cc84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2H5AJA2CODNDVEU4QLXJW67AQE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric modules over the infinite polynomial ring I: nilpotent quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Andrew Snowden, Rohit Nagpal, Teresa Yu","submitted_at":"2025-08-06T16:51:07Z","abstract_excerpt":"Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\\mathfrak{S}$. The first two authors began a program to understand the $\\mathfrak{S}$-equivariant algebra of $R$ in detail. In previous work, they classified the $\\mathfrak{S}$-prime ideals of $R$. An important example of an $\\mathfrak{S}$-prime is the ideal $\\mathfrak{h}_s$ generated by $(s+1)$st powers of the variables. In this paper, we study the category of $R/\\mathfrak{h}_s$-modules. We obtain a number of results, and mention just three he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04624","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/2508.04624/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":"2026-07-05T11:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iGnoAa38PCs1H53OLnvRrhmQY4pLvtdCC8Wm0AYqUN15TpghrfYhr2Jk2kPHMstxfPBPDdPrkG4El7P22I4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:04:50.019917Z"},"content_sha256":"89ddd3c424aeea57c08c05e9cb4fea808752a186cc6231ddd6a450351b946ca9","schema_version":"1.0","event_id":"sha256:89ddd3c424aeea57c08c05e9cb4fea808752a186cc6231ddd6a450351b946ca9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2H5AJA2CODNDVEU4QLXJW67AQE/bundle.json","state_url":"https://pith.science/pith/2H5AJA2CODNDVEU4QLXJW67AQE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2H5AJA2CODNDVEU4QLXJW67AQE/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":"2026-08-09T04:04:50Z","links":{"resolver":"https://pith.science/pith/2H5AJA2CODNDVEU4QLXJW67AQE","bundle":"https://pith.science/pith/2H5AJA2CODNDVEU4QLXJW67AQE/bundle.json","state":"https://pith.science/pith/2H5AJA2CODNDVEU4QLXJW67AQE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2H5AJA2CODNDVEU4QLXJW67AQE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2H5AJA2CODNDVEU4QLXJW67AQE","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":"813578ce2ff5c827d2a97b5cb8f7f6225fc3c02004a15bdbb5685c9a576123ce","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-08-06T16:51:07Z","title_canon_sha256":"15a5e2cfcbb2ee9a9999c8120904899ba1530666e87c2aa740e8e6d8c4e258fd"},"schema_version":"1.0","source":{"id":"2508.04624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.04624","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"2508.04624v1","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.04624","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"2H5AJA2CODND","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_16","alias_value":"2H5AJA2CODNDVEU4","created_at":"2026-07-05T11:49:40Z"},{"alias_kind":"pith_short_8","alias_value":"2H5AJA2C","created_at":"2026-07-05T11:49:40Z"}],"graph_snapshots":[{"event_id":"sha256:89ddd3c424aeea57c08c05e9cb4fea808752a186cc6231ddd6a450351b946ca9","target":"graph","created_at":"2026-07-05T11:49:40Z","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/2508.04624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\\mathfrak{S}$. The first two authors began a program to understand the $\\mathfrak{S}$-equivariant algebra of $R$ in detail. In previous work, they classified the $\\mathfrak{S}$-prime ideals of $R$. An important example of an $\\mathfrak{S}$-prime is the ideal $\\mathfrak{h}_s$ generated by $(s+1)$st powers of the variables. In this paper, we study the category of $R/\\mathfrak{h}_s$-modules. We obtain a number of results, and mention just three he","authors_text":"Andrew Snowden, Rohit Nagpal, Teresa Yu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-08-06T16:51:07Z","title":"Symmetric modules over the infinite polynomial ring I: nilpotent quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04624","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:d6c13736b7e77227773f8d355de277494aa07dbbe5dd34ddb0501fda61c1cc84","target":"record","created_at":"2026-07-05T11:49:40Z","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":"813578ce2ff5c827d2a97b5cb8f7f6225fc3c02004a15bdbb5685c9a576123ce","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-08-06T16:51:07Z","title_canon_sha256":"15a5e2cfcbb2ee9a9999c8120904899ba1530666e87c2aa740e8e6d8c4e258fd"},"schema_version":"1.0","source":{"id":"2508.04624","kind":"arxiv","version":1}},"canonical_sha256":"d1fa04834270da3a929c82ee9b7be081108647ce4d32ebf4df9104982837a37f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1fa04834270da3a929c82ee9b7be081108647ce4d32ebf4df9104982837a37f","first_computed_at":"2026-07-05T11:49:40.632644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:49:40.632644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"amRLYIAgS7a7tMewWqoujEgSZyNzKM2307blo/DmlMUKzQDQAX5bUpw9l5oWMfcSwqMsBkNhylxmxLmqeDldCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:49:40.633069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.04624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c13736b7e77227773f8d355de277494aa07dbbe5dd34ddb0501fda61c1cc84","sha256:89ddd3c424aeea57c08c05e9cb4fea808752a186cc6231ddd6a450351b946ca9"],"state_sha256":"e412a904f70ac351e9af0cde178b0625f928d1a8baaef0425f701437dc750bd7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSrfKQdX84sf+WwA90yTJQzS0BLJ8c6DdJWyhLNmd3QQPeld7lfrKgOTVdK+bN+OuDghAm6Kmyee3KMviOnkCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:04:50.023862Z","bundle_sha256":"7e7897c3026a6fbc182fe807a2e4cbe03954afca8d304915b1b1eb7b65ef9e53"}}