{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4JKS5HLWANXL36DWHBRL4ZEMP3","short_pith_number":"pith:4JKS5HLW","canonical_record":{"source":{"id":"1409.6663","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-23T16:45:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f83d827dd9c58bd0328c1d61b63b5758eb882c82f81da421b3dc20a3a4c9a931","abstract_canon_sha256":"5f48613543283021d08e3728e059dfb2f6db6ad9c281953f49b39a0434da7a04"},"schema_version":"1.0"},"canonical_sha256":"e2552e9d76036ebdf8763862be648c7ef5729ac9408ec4b886d0243d768ab619","source":{"kind":"arxiv","id":"1409.6663","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6663","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6663v3","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6663","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"4JKS5HLWANXL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4JKS5HLWANXL36DW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4JKS5HLW","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4JKS5HLWANXL36DWHBRL4ZEMP3","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6663","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-23T16:45:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f83d827dd9c58bd0328c1d61b63b5758eb882c82f81da421b3dc20a3a4c9a931","abstract_canon_sha256":"5f48613543283021d08e3728e059dfb2f6db6ad9c281953f49b39a0434da7a04"},"schema_version":"1.0"},"canonical_sha256":"e2552e9d76036ebdf8763862be648c7ef5729ac9408ec4b886d0243d768ab619","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:46.949878Z","signature_b64":"VpQX/j6m/+4xrBDRx9BeSPICEHX2WB8hv9W/eWlZ06LHVFqLI6M366iY5yYyIWt2i0RdjwawNXElhtEjAxG7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2552e9d76036ebdf8763862be648c7ef5729ac9408ec4b886d0243d768ab619","last_reissued_at":"2026-05-18T02:30:46.949255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:46.949255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6663","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":"2026-05-18T02:30:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLRSHFp4MGzsgasakC+vpF02BL+TOPEdDAAqXK4EApDIHlprdjQHaGKiJHkVF2SigBZGuAT2DSWyKFfirYWIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:22:40.938504Z"},"content_sha256":"638294062d8caa5e7ad60ab12556abc941b39ca0fea773568bcca931b3783505","schema_version":"1.0","event_id":"sha256:638294062d8caa5e7ad60ab12556abc941b39ca0fea773568bcca931b3783505"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4JKS5HLWANXL36DWHBRL4ZEMP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signatures of representations of Hecke algebras and rational Cherednik algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Vidya Venkateswaran","submitted_at":"2014-09-23T16:45:05Z","abstract_excerpt":"Determining whether an irreducible representation of a group (or $*$-algebra) admits a non-degenerate invariant, positive-definite Hermitian form is an important problem in representation theory. In this paper, we study a related notion: that of signatures. We study representations $S^{\\lambda}(q)$ of $\\mathcal{H}_{n}(q)$, the Hecke algebra of type $A$ ($|q| = 1$), and representations $M_{c}(\\lambda)$ of $\\mathbb{H}_{c}$, the rational Cherednik algebra of type $A$ ($c \\in \\mathbb{R}$), which have unique (up to scaling) invariant Hermitian forms (here $\\lambda$ is a partition of $n$). The signa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6663","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":""},"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":"2026-05-18T02:30:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iMmi8SvgJTl1V/GtWQaSYGgjgYoHDbp3gqxDktxeNGTKX+w/NwuSvZ4f8jKNvfmP2seV+SbcWk/2GbAMYesGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:22:40.939149Z"},"content_sha256":"4e71a09dbfb497aab920cfd833422debe127d36d9138bff2e5196f6720ce945c","schema_version":"1.0","event_id":"sha256:4e71a09dbfb497aab920cfd833422debe127d36d9138bff2e5196f6720ce945c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/bundle.json","state_url":"https://pith.science/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/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":"2026-06-07T09:22:40Z","links":{"resolver":"https://pith.science/pith/4JKS5HLWANXL36DWHBRL4ZEMP3","bundle":"https://pith.science/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/bundle.json","state":"https://pith.science/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JKS5HLWANXL36DWHBRL4ZEMP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4JKS5HLWANXL36DWHBRL4ZEMP3","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":"5f48613543283021d08e3728e059dfb2f6db6ad9c281953f49b39a0434da7a04","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-23T16:45:05Z","title_canon_sha256":"f83d827dd9c58bd0328c1d61b63b5758eb882c82f81da421b3dc20a3a4c9a931"},"schema_version":"1.0","source":{"id":"1409.6663","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6663","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6663v3","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6663","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"4JKS5HLWANXL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4JKS5HLWANXL36DW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4JKS5HLW","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:4e71a09dbfb497aab920cfd833422debe127d36d9138bff2e5196f6720ce945c","target":"graph","created_at":"2026-05-18T02:30:46Z","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":"Determining whether an irreducible representation of a group (or $*$-algebra) admits a non-degenerate invariant, positive-definite Hermitian form is an important problem in representation theory. In this paper, we study a related notion: that of signatures. We study representations $S^{\\lambda}(q)$ of $\\mathcal{H}_{n}(q)$, the Hecke algebra of type $A$ ($|q| = 1$), and representations $M_{c}(\\lambda)$ of $\\mathbb{H}_{c}$, the rational Cherednik algebra of type $A$ ($c \\in \\mathbb{R}$), which have unique (up to scaling) invariant Hermitian forms (here $\\lambda$ is a partition of $n$). The signa","authors_text":"Vidya Venkateswaran","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-23T16:45:05Z","title":"Signatures of representations of Hecke algebras and rational Cherednik algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6663","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":"sha256:638294062d8caa5e7ad60ab12556abc941b39ca0fea773568bcca931b3783505","target":"record","created_at":"2026-05-18T02:30:46Z","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":"5f48613543283021d08e3728e059dfb2f6db6ad9c281953f49b39a0434da7a04","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-23T16:45:05Z","title_canon_sha256":"f83d827dd9c58bd0328c1d61b63b5758eb882c82f81da421b3dc20a3a4c9a931"},"schema_version":"1.0","source":{"id":"1409.6663","kind":"arxiv","version":3}},"canonical_sha256":"e2552e9d76036ebdf8763862be648c7ef5729ac9408ec4b886d0243d768ab619","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2552e9d76036ebdf8763862be648c7ef5729ac9408ec4b886d0243d768ab619","first_computed_at":"2026-05-18T02:30:46.949255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:46.949255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpQX/j6m/+4xrBDRx9BeSPICEHX2WB8hv9W/eWlZ06LHVFqLI6M366iY5yYyIWt2i0RdjwawNXElhtEjAxG7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:46.949878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6663","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:638294062d8caa5e7ad60ab12556abc941b39ca0fea773568bcca931b3783505","sha256:4e71a09dbfb497aab920cfd833422debe127d36d9138bff2e5196f6720ce945c"],"state_sha256":"e3174ad2216d257f2ec6b9f82574c70c5f81edd2bc25bc48b96f89800bf1d9e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGOIiw0R1DGsYb/OfK6e6+rk7lngEkfEXj59SdNhYxE2aXTFw+lU3EMF6+xthfxy5ZWpB7cexdocNuppTMrbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:22:40.941865Z","bundle_sha256":"30fb56c3068abdb308454c07a5cd26da08ff4c6c846ee05a1d0d1be5199a4068"}}