{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OIT2XHR7UZBYXFPXSKUETOHQSW","short_pith_number":"pith:OIT2XHR7","canonical_record":{"source":{"id":"1506.06361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-21T13:08:26Z","cross_cats_sorted":[],"title_canon_sha256":"27592a2aed05c779bc760c7b1dcc8b92a46a0ba93a3e3bb865e36da79d5d1624","abstract_canon_sha256":"813938d9a8f76bce0a9ef0c1d1ffdc3276e7283e109fed0a406896183c57d7e9"},"schema_version":"1.0"},"canonical_sha256":"7227ab9e3fa6438b95f792a849b8f095920a238c464027ba94e5d7fa3b5215e7","source":{"kind":"arxiv","id":"1506.06361","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06361","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06361v3","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06361","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"OIT2XHR7UZBY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIT2XHR7UZBYXFPX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIT2XHR7","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OIT2XHR7UZBYXFPXSKUETOHQSW","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-21T13:08:26Z","cross_cats_sorted":[],"title_canon_sha256":"27592a2aed05c779bc760c7b1dcc8b92a46a0ba93a3e3bb865e36da79d5d1624","abstract_canon_sha256":"813938d9a8f76bce0a9ef0c1d1ffdc3276e7283e109fed0a406896183c57d7e9"},"schema_version":"1.0"},"canonical_sha256":"7227ab9e3fa6438b95f792a849b8f095920a238c464027ba94e5d7fa3b5215e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:49.825872Z","signature_b64":"HSuMmHn9WGwF1rxNCikP+PgdrEEufY36tA0t9id/IQjvxJrb88hrpgLsb+C7AlHOVvapCv+hH62pntTbZA46DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7227ab9e3fa6438b95f792a849b8f095920a238c464027ba94e5d7fa3b5215e7","last_reissued_at":"2026-05-17T23:51:49.825306Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:49.825306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06361","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":"2026-05-17T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSLasgSBz5s/JUpzNvIZg5v4vdwAVlyjirE0SPj0EdYypEOfJ7W91jrhGgUD5b+Lb0An0cp5I3w8D9kx9CjNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:33.107930Z"},"content_sha256":"2336961ded856d0b84c86d7813dba2bc4a8a46ddeef40537e33d453c29d176f9","schema_version":"1.0","event_id":"sha256:2336961ded856d0b84c86d7813dba2bc4a8a46ddeef40537e33d453c29d176f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OIT2XHR7UZBYXFPXSKUETOHQSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of Jack characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Piotr \\'Sniady","submitted_at":"2015-06-21T13:08:26Z","abstract_excerpt":"Jack characters are a one-parameter deformation of the characters of the symmetric groups; a deformation given by the coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. We study Jack characters from the viewpoint of the asymptotic representation theory. In particular, we give explicit formulas for their asymptotically top-degree part, in terms of bicolored oriented maps with an arbitrary face structure. We also study their multiplicative structure and their structure constants and we prove that they fulfill approximate factorization propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06361","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":"2026-05-17T23:51:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ndI2U+H507JmcOTYZj3QvRDhf758790qJHuL6+dtFu+p9TBH9IyZAlHXsQfcxDnJYLMtOqAp8Qhn4N0t3mtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:33.108270Z"},"content_sha256":"542a73f8d0d522fed320a6df80956d2dc299ef02807fc00f77c7c45d7291adf4","schema_version":"1.0","event_id":"sha256:542a73f8d0d522fed320a6df80956d2dc299ef02807fc00f77c7c45d7291adf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/bundle.json","state_url":"https://pith.science/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/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":"2026-06-03T00:22:33Z","links":{"resolver":"https://pith.science/pith/OIT2XHR7UZBYXFPXSKUETOHQSW","bundle":"https://pith.science/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/bundle.json","state":"https://pith.science/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIT2XHR7UZBYXFPXSKUETOHQSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OIT2XHR7UZBYXFPXSKUETOHQSW","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":"813938d9a8f76bce0a9ef0c1d1ffdc3276e7283e109fed0a406896183c57d7e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-21T13:08:26Z","title_canon_sha256":"27592a2aed05c779bc760c7b1dcc8b92a46a0ba93a3e3bb865e36da79d5d1624"},"schema_version":"1.0","source":{"id":"1506.06361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06361","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06361v3","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06361","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"OIT2XHR7UZBY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIT2XHR7UZBYXFPX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIT2XHR7","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:542a73f8d0d522fed320a6df80956d2dc299ef02807fc00f77c7c45d7291adf4","target":"graph","created_at":"2026-05-17T23:51:49Z","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":"Jack characters are a one-parameter deformation of the characters of the symmetric groups; a deformation given by the coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. We study Jack characters from the viewpoint of the asymptotic representation theory. In particular, we give explicit formulas for their asymptotically top-degree part, in terms of bicolored oriented maps with an arbitrary face structure. We also study their multiplicative structure and their structure constants and we prove that they fulfill approximate factorization propert","authors_text":"Piotr \\'Sniady","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-21T13:08:26Z","title":"Asymptotics of Jack characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06361","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":"sha256:2336961ded856d0b84c86d7813dba2bc4a8a46ddeef40537e33d453c29d176f9","target":"record","created_at":"2026-05-17T23:51:49Z","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":"813938d9a8f76bce0a9ef0c1d1ffdc3276e7283e109fed0a406896183c57d7e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-21T13:08:26Z","title_canon_sha256":"27592a2aed05c779bc760c7b1dcc8b92a46a0ba93a3e3bb865e36da79d5d1624"},"schema_version":"1.0","source":{"id":"1506.06361","kind":"arxiv","version":3}},"canonical_sha256":"7227ab9e3fa6438b95f792a849b8f095920a238c464027ba94e5d7fa3b5215e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7227ab9e3fa6438b95f792a849b8f095920a238c464027ba94e5d7fa3b5215e7","first_computed_at":"2026-05-17T23:51:49.825306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:49.825306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HSuMmHn9WGwF1rxNCikP+PgdrEEufY36tA0t9id/IQjvxJrb88hrpgLsb+C7AlHOVvapCv+hH62pntTbZA46DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:49.825872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2336961ded856d0b84c86d7813dba2bc4a8a46ddeef40537e33d453c29d176f9","sha256:542a73f8d0d522fed320a6df80956d2dc299ef02807fc00f77c7c45d7291adf4"],"state_sha256":"f850a3ab193db4761941db818016d330bd04ef6c52431846c7e1dd017312a8f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORgSXB+f2JLaXKrLdeg9ib5c/2zGuATgmwXNBKS/gfjNvd8xsv8kPrweYSYWBupKpVGhLe2Txm4xFGFq/dYtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:22:33.110271Z","bundle_sha256":"0e1a23acad3ee2b9708b5e1718873591d1278b5a3f85851b657f9305835f2951"}}