{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BEHKJIZXIYXQZB7JPFAZJJHJEC","short_pith_number":"pith:BEHKJIZX","canonical_record":{"source":{"id":"1206.4737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-20T23:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"f6c5dade27263c8b6775fb6b75f1911ad917f22c0fa6ab3fc01bae7759072035","abstract_canon_sha256":"711c5307b92dd803fce754b84843de251ca4aecd05dd0cc69c3756b5275e6392"},"schema_version":"1.0"},"canonical_sha256":"090ea4a337462f0c87e9794194a4e9209870523db132ade4d7fc138a1b5893d4","source":{"kind":"arxiv","id":"1206.4737","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4737","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4737v1","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4737","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"BEHKJIZXIYXQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BEHKJIZXIYXQZB7J","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BEHKJIZX","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BEHKJIZXIYXQZB7JPFAZJJHJEC","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-20T23:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"f6c5dade27263c8b6775fb6b75f1911ad917f22c0fa6ab3fc01bae7759072035","abstract_canon_sha256":"711c5307b92dd803fce754b84843de251ca4aecd05dd0cc69c3756b5275e6392"},"schema_version":"1.0"},"canonical_sha256":"090ea4a337462f0c87e9794194a4e9209870523db132ade4d7fc138a1b5893d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:03.872241Z","signature_b64":"hTahOFCBx6uSTUsTgd6eZDcNJIUa7ahdYTrhuyA+RhxGsVc1hQBslyE+h7rGqW7rF/QKv8thKGFGI2SbuzG9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"090ea4a337462f0c87e9794194a4e9209870523db132ade4d7fc138a1b5893d4","last_reissued_at":"2026-05-18T03:53:03.871432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:03.871432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4737","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":"2026-05-18T03:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQ5/BQyI0+T+qKwtOtFruMDJf7BXO/vFZp+hfLV+gUKdDcRyQ4xAe8zipPBs/8UALjOlJfrFsEw13WoGNwEqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:39:35.122007Z"},"content_sha256":"8b16c3dfb1367b7a8999c64fcae53b7721e449ccc6d2a9fce91413124bc2de2f","schema_version":"1.0","event_id":"sha256:8b16c3dfb1367b7a8999c64fcae53b7721e449ccc6d2a9fce91413124bc2de2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BEHKJIZXIYXQZB7JPFAZJJHJEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mourad E. H. Ismail, Xin Li","submitted_at":"2012-06-20T23:15:46Z","abstract_excerpt":"We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q^{-1}-Hermite polynomials of Askey, Ismail and Masson, q-Laguerre polynomials, and the Stieltjes-Wigert polynomials. We also introduce a one parameter family of solutions to the q-difference equation of the Ramanujan function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4737","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":"2026-05-18T03:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GwB85cCYxIyC5g+Jfj2MLFExn+JTmvB8Yu4V57U2byrlxpowIHY3MA1Vcn8zlMimaMr6YAGp5W5/UFb1JC/UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:39:35.122372Z"},"content_sha256":"86907f75cab52e05cd6d8c13bb8e907a63d536b4fa245acccafe99bb4454c6f7","schema_version":"1.0","event_id":"sha256:86907f75cab52e05cd6d8c13bb8e907a63d536b4fa245acccafe99bb4454c6f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/bundle.json","state_url":"https://pith.science/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/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":"2026-06-23T23:39:35Z","links":{"resolver":"https://pith.science/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC","bundle":"https://pith.science/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/bundle.json","state":"https://pith.science/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEHKJIZXIYXQZB7JPFAZJJHJEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BEHKJIZXIYXQZB7JPFAZJJHJEC","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":"711c5307b92dd803fce754b84843de251ca4aecd05dd0cc69c3756b5275e6392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-20T23:15:46Z","title_canon_sha256":"f6c5dade27263c8b6775fb6b75f1911ad917f22c0fa6ab3fc01bae7759072035"},"schema_version":"1.0","source":{"id":"1206.4737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4737","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4737v1","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4737","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"BEHKJIZXIYXQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BEHKJIZXIYXQZB7J","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BEHKJIZX","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:86907f75cab52e05cd6d8c13bb8e907a63d536b4fa245acccafe99bb4454c6f7","target":"graph","created_at":"2026-05-18T03:53:03Z","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":"We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q^{-1}-Hermite polynomials of Askey, Ismail and Masson, q-Laguerre polynomials, and the Stieltjes-Wigert polynomials. We also introduce a one parameter family of solutions to the q-difference equation of the Ramanujan function.","authors_text":"Mourad E. H. Ismail, Xin Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-20T23:15:46Z","title":"Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4737","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":"sha256:8b16c3dfb1367b7a8999c64fcae53b7721e449ccc6d2a9fce91413124bc2de2f","target":"record","created_at":"2026-05-18T03:53:03Z","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":"711c5307b92dd803fce754b84843de251ca4aecd05dd0cc69c3756b5275e6392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-20T23:15:46Z","title_canon_sha256":"f6c5dade27263c8b6775fb6b75f1911ad917f22c0fa6ab3fc01bae7759072035"},"schema_version":"1.0","source":{"id":"1206.4737","kind":"arxiv","version":1}},"canonical_sha256":"090ea4a337462f0c87e9794194a4e9209870523db132ade4d7fc138a1b5893d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"090ea4a337462f0c87e9794194a4e9209870523db132ade4d7fc138a1b5893d4","first_computed_at":"2026-05-18T03:53:03.871432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:03.871432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTahOFCBx6uSTUsTgd6eZDcNJIUa7ahdYTrhuyA+RhxGsVc1hQBslyE+h7rGqW7rF/QKv8thKGFGI2SbuzG9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:03.872241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b16c3dfb1367b7a8999c64fcae53b7721e449ccc6d2a9fce91413124bc2de2f","sha256:86907f75cab52e05cd6d8c13bb8e907a63d536b4fa245acccafe99bb4454c6f7"],"state_sha256":"46d43d8a25fce43e167b7d0116fcbff3f2d2c727e67c5a21397c4db6e258bb5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxJpHaCzlj4LK5qu1Fxdd5GDpFLMoQup2rbPbgqvmbunqibAa5yxQ5OB2aoA//NRpWQEpOworysO+YXN3lCBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:39:35.124384Z","bundle_sha256":"af837c35d56a3df39713569ee4c65043029fccd0d62eae65b196e16d0b31d381"}}