{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FWQCY6U5XTPPJNQCVKRTJDRD2O","short_pith_number":"pith:FWQCY6U5","canonical_record":{"source":{"id":"2508.06657","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-08T19:15:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6e6671e7e7c8174a696c84cfd6d5761687510faed32a345c91120bcc5ed26f55","abstract_canon_sha256":"5e01e3dc5218e19fffbcef809d2f89d4211f5cbc3663520810a95816d1b4d3c8"},"schema_version":"1.0"},"canonical_sha256":"2da02c7a9dbcdef4b602aaa3348e23d396fdba60ecb1da96213c946d9b5c44f3","source":{"kind":"arxiv","id":"2508.06657","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.06657","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"2508.06657v3","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.06657","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"FWQCY6U5XTPP","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_16","alias_value":"FWQCY6U5XTPPJNQC","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_8","alias_value":"FWQCY6U5","created_at":"2026-05-29T02:05:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FWQCY6U5XTPPJNQCVKRTJDRD2O","target":"record","payload":{"canonical_record":{"source":{"id":"2508.06657","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-08T19:15:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6e6671e7e7c8174a696c84cfd6d5761687510faed32a345c91120bcc5ed26f55","abstract_canon_sha256":"5e01e3dc5218e19fffbcef809d2f89d4211f5cbc3663520810a95816d1b4d3c8"},"schema_version":"1.0"},"canonical_sha256":"2da02c7a9dbcdef4b602aaa3348e23d396fdba60ecb1da96213c946d9b5c44f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:35.716393Z","signature_b64":"UOIeEJ3scVvfQqMWRPOoUvY57HgnSaWzwpvZfBU58jprkj/HlHnekKVX5y6Vl1Fo4w/YoKptpRHk+Frelni2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2da02c7a9dbcdef4b602aaa3348e23d396fdba60ecb1da96213c946d9b5c44f3","last_reissued_at":"2026-05-29T02:05:35.715716Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:35.715716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.06657","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUn3gXPsOSuPf5bIiQWGzGAV5G6njIEd6NfJwhr6KUG3cSaor4MECNbPQ4qDNaH2N0QyiQaSp2enpx/e3HSCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:35:39.493576Z"},"content_sha256":"a46f1d9c65c6f1f68c1d82c8944034f722447cc29b8a782f4794df51eaad7c06","schema_version":"1.0","event_id":"sha256:a46f1d9c65c6f1f68c1d82c8944034f722447cc29b8a782f4794df51eaad7c06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FWQCY6U5XTPPJNQCVKRTJDRD2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Corrigendum to \"Modular Gelfand pairs and multiplicity-free representations\"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Patrick Allen, Preston Wake, Robin Zhang","submitted_at":"2025-08-08T19:15:00Z","abstract_excerpt":"Some of the multiplicity-freeness results in ``Modular Gelfand pairs and multiplicity-free representations'' are stated in overly broad generality. We provide counterexamples and partial corrections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.06657","kind":"arxiv","version":3},"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/2508.06657/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":"2026-05-29T02:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKBvjWXcLPWduFXF0YHCRGbhA4ric/J4mMy8jBVlGjkGfUnXJqR5R73lXQcYoiStoRl5ww+GSCO9km0oEt1dAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:35:39.494516Z"},"content_sha256":"79a7c69e9c38a6c2c7f7d79f1869afa1977645acb6b57520e408f060459d7efe","schema_version":"1.0","event_id":"sha256:79a7c69e9c38a6c2c7f7d79f1869afa1977645acb6b57520e408f060459d7efe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/bundle.json","state_url":"https://pith.science/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/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":"2026-06-09T16:35:39Z","links":{"resolver":"https://pith.science/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O","bundle":"https://pith.science/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/bundle.json","state":"https://pith.science/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWQCY6U5XTPPJNQCVKRTJDRD2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FWQCY6U5XTPPJNQCVKRTJDRD2O","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":"5e01e3dc5218e19fffbcef809d2f89d4211f5cbc3663520810a95816d1b4d3c8","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-08T19:15:00Z","title_canon_sha256":"6e6671e7e7c8174a696c84cfd6d5761687510faed32a345c91120bcc5ed26f55"},"schema_version":"1.0","source":{"id":"2508.06657","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.06657","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"2508.06657v3","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.06657","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"FWQCY6U5XTPP","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_16","alias_value":"FWQCY6U5XTPPJNQC","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_8","alias_value":"FWQCY6U5","created_at":"2026-05-29T02:05:35Z"}],"graph_snapshots":[{"event_id":"sha256:79a7c69e9c38a6c2c7f7d79f1869afa1977645acb6b57520e408f060459d7efe","target":"graph","created_at":"2026-05-29T02:05:35Z","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/2508.06657/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Some of the multiplicity-freeness results in ``Modular Gelfand pairs and multiplicity-free representations'' are stated in overly broad generality. We provide counterexamples and partial corrections.","authors_text":"Patrick Allen, Preston Wake, Robin Zhang","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-08T19:15:00Z","title":"Corrigendum to \"Modular Gelfand pairs and multiplicity-free representations\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.06657","kind":"arxiv","version":3},"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:a46f1d9c65c6f1f68c1d82c8944034f722447cc29b8a782f4794df51eaad7c06","target":"record","created_at":"2026-05-29T02:05:35Z","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":"5e01e3dc5218e19fffbcef809d2f89d4211f5cbc3663520810a95816d1b4d3c8","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RT","submitted_at":"2025-08-08T19:15:00Z","title_canon_sha256":"6e6671e7e7c8174a696c84cfd6d5761687510faed32a345c91120bcc5ed26f55"},"schema_version":"1.0","source":{"id":"2508.06657","kind":"arxiv","version":3}},"canonical_sha256":"2da02c7a9dbcdef4b602aaa3348e23d396fdba60ecb1da96213c946d9b5c44f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2da02c7a9dbcdef4b602aaa3348e23d396fdba60ecb1da96213c946d9b5c44f3","first_computed_at":"2026-05-29T02:05:35.715716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:35.715716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOIeEJ3scVvfQqMWRPOoUvY57HgnSaWzwpvZfBU58jprkj/HlHnekKVX5y6Vl1Fo4w/YoKptpRHk+Frelni2CA==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:35.716393Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.06657","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a46f1d9c65c6f1f68c1d82c8944034f722447cc29b8a782f4794df51eaad7c06","sha256:79a7c69e9c38a6c2c7f7d79f1869afa1977645acb6b57520e408f060459d7efe"],"state_sha256":"152d92a6f2ef4ca7accbb7dd832859844a5517b1d2d03624b095bb09013ad8f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/SQoJOUjDaYioJHG5RIyAAtjEME8J0E7JhDhF9IFxPSKorbTaEShA2D03J0C/hlOYwZ672hyyxe7CC1EBbGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:35:39.498169Z","bundle_sha256":"6d355b9ac28e333107d85eecb7dca5a025ad2f5b76e66343f3c62fb901a3cd41"}}