{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4RYBWGN6RNRQDQOMU5FBMYBATR","short_pith_number":"pith:4RYBWGN6","canonical_record":{"source":{"id":"2507.03309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-04T05:36:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e6be546d676abe6259e3283d5b6b01eb341af9df150bcfbdd8827452c1b165ea","abstract_canon_sha256":"f4e2f68754d763f442110dd534fd0bfba439268e51b6b037e0a574a4e511779b"},"schema_version":"1.0"},"canonical_sha256":"e4701b19be8b6301c1cca74a1660209c56f9eb1da791db65b0f722e13c0a01a4","source":{"kind":"arxiv","id":"2507.03309","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03309","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03309v2","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03309","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"4RYBWGN6RNRQ","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_16","alias_value":"4RYBWGN6RNRQDQOM","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_8","alias_value":"4RYBWGN6","created_at":"2026-05-20T00:00:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4RYBWGN6RNRQDQOMU5FBMYBATR","target":"record","payload":{"canonical_record":{"source":{"id":"2507.03309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-04T05:36:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e6be546d676abe6259e3283d5b6b01eb341af9df150bcfbdd8827452c1b165ea","abstract_canon_sha256":"f4e2f68754d763f442110dd534fd0bfba439268e51b6b037e0a574a4e511779b"},"schema_version":"1.0"},"canonical_sha256":"e4701b19be8b6301c1cca74a1660209c56f9eb1da791db65b0f722e13c0a01a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:21.945828Z","signature_b64":"OvkBBGty5E8V6gM6kM8kstYfgj447UrLHHCM4FUUi6AlpZZw3Ay9DdldcLvVfeq7RVZyH+mvke8D0Aa8djeBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4701b19be8b6301c1cca74a1660209c56f9eb1da791db65b0f722e13c0a01a4","last_reissued_at":"2026-05-20T00:00:21.944978Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:21.944978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.03309","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":"2026-05-20T00:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aWFaAsXyShg21G5X6o5TagmYBECOe4Ve46lcEScGDCuS2f3/20tLmBrf66idpjDQERdf1j5MR7+KauZOT061Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:22:21.016063Z"},"content_sha256":"c7ea951302f99bf6428a2c634e7f7f9210b3f4b60ba58d99bb42a96aaed41843","schema_version":"1.0","event_id":"sha256:c7ea951302f99bf6428a2c634e7f7f9210b3f4b60ba58d99bb42a96aaed41843"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4RYBWGN6RNRQDQOMU5FBMYBATR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A special class of prime ideals for infinite symmetric group algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Kevin Coulembier","submitted_at":"2025-07-04T05:36:30Z","abstract_excerpt":"We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical representations of (the Gelfand pair corresponding to) the infinite symmetric group. In positive characteristic, we investigate a close connection with the structure theory of symmetric tensor categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03309","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.03309/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":"2026-05-20T00:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3kOB9DmsRo0zjm0od6ajRFksQtgF9Bn+p8VGJ9p5UxuuV4LYIStQPmHAknqWI6s2UqHjSAFUPoiq9hHxLMHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:22:21.016854Z"},"content_sha256":"9d641c6596d54759a6466cae4537115db406875a3dda675884571a34c2bc8035","schema_version":"1.0","event_id":"sha256:9d641c6596d54759a6466cae4537115db406875a3dda675884571a34c2bc8035"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/bundle.json","state_url":"https://pith.science/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/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":"2026-06-06T23:22:21Z","links":{"resolver":"https://pith.science/pith/4RYBWGN6RNRQDQOMU5FBMYBATR","bundle":"https://pith.science/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/bundle.json","state":"https://pith.science/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4RYBWGN6RNRQDQOMU5FBMYBATR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4RYBWGN6RNRQDQOMU5FBMYBATR","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":"f4e2f68754d763f442110dd534fd0bfba439268e51b6b037e0a574a4e511779b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-04T05:36:30Z","title_canon_sha256":"e6be546d676abe6259e3283d5b6b01eb341af9df150bcfbdd8827452c1b165ea"},"schema_version":"1.0","source":{"id":"2507.03309","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03309","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03309v2","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03309","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"4RYBWGN6RNRQ","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_16","alias_value":"4RYBWGN6RNRQDQOM","created_at":"2026-05-20T00:00:21Z"},{"alias_kind":"pith_short_8","alias_value":"4RYBWGN6","created_at":"2026-05-20T00:00:21Z"}],"graph_snapshots":[{"event_id":"sha256:9d641c6596d54759a6466cae4537115db406875a3dda675884571a34c2bc8035","target":"graph","created_at":"2026-05-20T00:00:21Z","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/2507.03309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical representations of (the Gelfand pair corresponding to) the infinite symmetric group. In positive characteristic, we investigate a close connection with the structure theory of symmetric tensor categories.","authors_text":"Kevin Coulembier","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-04T05:36:30Z","title":"A special class of prime ideals for infinite symmetric group algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03309","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:c7ea951302f99bf6428a2c634e7f7f9210b3f4b60ba58d99bb42a96aaed41843","target":"record","created_at":"2026-05-20T00:00:21Z","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":"f4e2f68754d763f442110dd534fd0bfba439268e51b6b037e0a574a4e511779b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-04T05:36:30Z","title_canon_sha256":"e6be546d676abe6259e3283d5b6b01eb341af9df150bcfbdd8827452c1b165ea"},"schema_version":"1.0","source":{"id":"2507.03309","kind":"arxiv","version":2}},"canonical_sha256":"e4701b19be8b6301c1cca74a1660209c56f9eb1da791db65b0f722e13c0a01a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4701b19be8b6301c1cca74a1660209c56f9eb1da791db65b0f722e13c0a01a4","first_computed_at":"2026-05-20T00:00:21.944978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:21.944978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OvkBBGty5E8V6gM6kM8kstYfgj447UrLHHCM4FUUi6AlpZZw3Ay9DdldcLvVfeq7RVZyH+mvke8D0Aa8djeBBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:21.945828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.03309","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7ea951302f99bf6428a2c634e7f7f9210b3f4b60ba58d99bb42a96aaed41843","sha256:9d641c6596d54759a6466cae4537115db406875a3dda675884571a34c2bc8035"],"state_sha256":"2cf79d938a15f61f7e667861391e63505cdeabfd377386b51860b2eaec685d83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+2FmHhXg6vr5b/kO8e/oPx9tCoFKy5yV9AOMLI4EjLfeKe31wgOnQn2Q5kxcivF3AalkYVvh37e2WoLUfTDqBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:22:21.021058Z","bundle_sha256":"69f394c0dbbe3f6324cafd60f4142527c3afb6c9b8f741dd04ec0a8cf5c6ccae"}}