{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:22QPCC53JFMW4R6XDFVF5ROTBW","short_pith_number":"pith:22QPCC53","canonical_record":{"source":{"id":"1605.03493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-11T16:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"23218f0adc2d8047a24b3888b34ffd13bb6ba46c4222b0d36ce5b79eaa8a57fa","abstract_canon_sha256":"614e052b23b5b28d59d7d99af593d62644a948d94f21943ca9d5d17bdb432b64"},"schema_version":"1.0"},"canonical_sha256":"d6a0f10bbb49596e47d7196a5ec5d30d8777b12be9d1406f2ea350597089c23a","source":{"kind":"arxiv","id":"1605.03493","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03493","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03493v1","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03493","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"22QPCC53JFMW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"22QPCC53JFMW4R6X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"22QPCC53","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:22QPCC53JFMW4R6XDFVF5ROTBW","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-11T16:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"23218f0adc2d8047a24b3888b34ffd13bb6ba46c4222b0d36ce5b79eaa8a57fa","abstract_canon_sha256":"614e052b23b5b28d59d7d99af593d62644a948d94f21943ca9d5d17bdb432b64"},"schema_version":"1.0"},"canonical_sha256":"d6a0f10bbb49596e47d7196a5ec5d30d8777b12be9d1406f2ea350597089c23a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:05.284618Z","signature_b64":"K4t07mwmLnryp1auO53bJ6d0yXQx71W3va1L/cqWAIzmNPVDPq199Of+lzIf5iA1q+2cHy4h45LxSPTKhHmzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6a0f10bbb49596e47d7196a5ec5d30d8777b12be9d1406f2ea350597089c23a","last_reissued_at":"2026-05-18T01:15:05.283798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:05.283798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03493","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":"2026-05-18T01:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CplupHawndmx23fmbOFkcTXWQ8MvwU0K+f0ihCmm1qJ3/OGqV7e5p8nYuMBFYZ23v9yRjlrzPfZTEmuwMGcBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:09:32.314785Z"},"content_sha256":"cd85819c42293482f8f5ffebc00c287b1dad66691502648ac011a228bb42486c","schema_version":"1.0","event_id":"sha256:cd85819c42293482f8f5ffebc00c287b1dad66691502648ac011a228bb42486c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:22QPCC53JFMW4R6XDFVF5ROTBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cocenters and representations of pro-$p$ Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sian Nie, Xuhua He","submitted_at":"2016-05-11T16:03:40Z","abstract_excerpt":"In this paper, we study the relation between the cocenter and the representations of an affine pro-$p$ Hecke algebra. As a consequence, we obtain a new criterion on the supersingular representation: a (virtual) representation is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03493","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":""},"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":"2026-05-18T01:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QjWB5Mr72jM2pIajb5F6y6bYzv5bcdrQqJX1n3FP+UBXO/GQQPCsymrQ10c2Bbw/F+exxnjfcEi2Kdvy9a2wCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:09:32.315127Z"},"content_sha256":"44c38aa7381274ebb398ce96db4fddce9f9633c933c02afdbccd8278ae9bd175","schema_version":"1.0","event_id":"sha256:44c38aa7381274ebb398ce96db4fddce9f9633c933c02afdbccd8278ae9bd175"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22QPCC53JFMW4R6XDFVF5ROTBW/bundle.json","state_url":"https://pith.science/pith/22QPCC53JFMW4R6XDFVF5ROTBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22QPCC53JFMW4R6XDFVF5ROTBW/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":"2026-06-08T22:09:32Z","links":{"resolver":"https://pith.science/pith/22QPCC53JFMW4R6XDFVF5ROTBW","bundle":"https://pith.science/pith/22QPCC53JFMW4R6XDFVF5ROTBW/bundle.json","state":"https://pith.science/pith/22QPCC53JFMW4R6XDFVF5ROTBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22QPCC53JFMW4R6XDFVF5ROTBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:22QPCC53JFMW4R6XDFVF5ROTBW","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":"614e052b23b5b28d59d7d99af593d62644a948d94f21943ca9d5d17bdb432b64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-11T16:03:40Z","title_canon_sha256":"23218f0adc2d8047a24b3888b34ffd13bb6ba46c4222b0d36ce5b79eaa8a57fa"},"schema_version":"1.0","source":{"id":"1605.03493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03493","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03493v1","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03493","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"22QPCC53JFMW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"22QPCC53JFMW4R6X","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"22QPCC53","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:44c38aa7381274ebb398ce96db4fddce9f9633c933c02afdbccd8278ae9bd175","target":"graph","created_at":"2026-05-18T01:15:05Z","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":"In this paper, we study the relation between the cocenter and the representations of an affine pro-$p$ Hecke algebra. As a consequence, we obtain a new criterion on the supersingular representation: a (virtual) representation is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter.","authors_text":"Sian Nie, Xuhua He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-11T16:03:40Z","title":"Cocenters and representations of pro-$p$ Hecke algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03493","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:cd85819c42293482f8f5ffebc00c287b1dad66691502648ac011a228bb42486c","target":"record","created_at":"2026-05-18T01:15:05Z","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":"614e052b23b5b28d59d7d99af593d62644a948d94f21943ca9d5d17bdb432b64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-11T16:03:40Z","title_canon_sha256":"23218f0adc2d8047a24b3888b34ffd13bb6ba46c4222b0d36ce5b79eaa8a57fa"},"schema_version":"1.0","source":{"id":"1605.03493","kind":"arxiv","version":1}},"canonical_sha256":"d6a0f10bbb49596e47d7196a5ec5d30d8777b12be9d1406f2ea350597089c23a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6a0f10bbb49596e47d7196a5ec5d30d8777b12be9d1406f2ea350597089c23a","first_computed_at":"2026-05-18T01:15:05.283798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:05.283798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K4t07mwmLnryp1auO53bJ6d0yXQx71W3va1L/cqWAIzmNPVDPq199Of+lzIf5iA1q+2cHy4h45LxSPTKhHmzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:05.284618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd85819c42293482f8f5ffebc00c287b1dad66691502648ac011a228bb42486c","sha256:44c38aa7381274ebb398ce96db4fddce9f9633c933c02afdbccd8278ae9bd175"],"state_sha256":"e053158505280ffdf29a14656c467d74a7e7a0a3c2e7bfe54184544d82d6a63c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLttdDFx0U5BRt+XB3JtpEzbvlXUSNtN29NBoWGTZO3+8n/k3tlyYn1zIKTzD7jsZ1+9B+ImCk5Q1dV+kyaHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:09:32.317055Z","bundle_sha256":"60b2496e7955041fca51366a8eaac7839f1d9d1d2c9be59302291be5a9530d5c"}}