{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UPW6WTV77UDHZIQPJQQAT5JE55","short_pith_number":"pith:UPW6WTV7","canonical_record":{"source":{"id":"1106.1083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-06T14:54:33Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"30161031e4dc0b5294ee470cccc8b3bff27b3e7506c6ed2fec09b0f9617182b8","abstract_canon_sha256":"3595777d6709e32eb649db71e68ef9a8360049c43717fa4d5cce6597d804820a"},"schema_version":"1.0"},"canonical_sha256":"a3edeb4ebffd067ca20f4c2009f524ef6e6b07b8988bafd1f31ef64c157f8f44","source":{"kind":"arxiv","id":"1106.1083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1083","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1083v1","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1083","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"UPW6WTV77UDH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UPW6WTV77UDHZIQP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UPW6WTV7","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UPW6WTV77UDHZIQPJQQAT5JE55","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-06T14:54:33Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"30161031e4dc0b5294ee470cccc8b3bff27b3e7506c6ed2fec09b0f9617182b8","abstract_canon_sha256":"3595777d6709e32eb649db71e68ef9a8360049c43717fa4d5cce6597d804820a"},"schema_version":"1.0"},"canonical_sha256":"a3edeb4ebffd067ca20f4c2009f524ef6e6b07b8988bafd1f31ef64c157f8f44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:13.571418Z","signature_b64":"r91GQyROQcQAb1Kv2oDdeg5O9G+JJwTqb8OWVLOoLlC3mNO3m5XA8GvDBJMiQPTEV6WUYCeGPnd5NOX99w5pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3edeb4ebffd067ca20f4c2009f524ef6e6b07b8988bafd1f31ef64c157f8f44","last_reissued_at":"2026-05-18T04:02:13.570359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:13.570359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1083","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":"2026-05-18T04:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XX5qdulTwIf1nCwR3NQaQsZGuddxjE8axizplIb2QMdLNA1KPE6INBEmY8NFBhhhbbZ72nFBLrIztyHBqE0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:47:26.429697Z"},"content_sha256":"0930cafc509cabe48f74b0aa7a2cecaa2f23afb0dfe46ba984f93596d3b9d71b","schema_version":"1.0","event_id":"sha256:0930cafc509cabe48f74b0aa7a2cecaa2f23afb0dfe46ba984f93596d3b9d71b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UPW6WTV77UDHZIQPJQQAT5JE55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The su(2)_{\\alpha} Hahn oscillator and a discrete Hahn-Fourier transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"E.I. Jafarov, J. Van der Jeugt, N.I. Stoilova","submitted_at":"2011-06-06T14:54:33Z","abstract_excerpt":"We define the quadratic algebra su(2)_{\\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)_{\\alpha}. We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2)_{\\alpha}. It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1083","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":"2026-05-18T04:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+8kE/laQvNhjVFVBPWvwsrZN5K0sxXAvnIcRkZ9wvQAcB/aX2gpHqjU/5tb5WpnVAp07nYjAtSVXtAF2rK2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:47:26.430365Z"},"content_sha256":"1b3dc217294ae81dc106484d8d687b6d104604035db8e43f8052f13bb26f1fea","schema_version":"1.0","event_id":"sha256:1b3dc217294ae81dc106484d8d687b6d104604035db8e43f8052f13bb26f1fea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPW6WTV77UDHZIQPJQQAT5JE55/bundle.json","state_url":"https://pith.science/pith/UPW6WTV77UDHZIQPJQQAT5JE55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPW6WTV77UDHZIQPJQQAT5JE55/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":"2026-05-30T10:47:26Z","links":{"resolver":"https://pith.science/pith/UPW6WTV77UDHZIQPJQQAT5JE55","bundle":"https://pith.science/pith/UPW6WTV77UDHZIQPJQQAT5JE55/bundle.json","state":"https://pith.science/pith/UPW6WTV77UDHZIQPJQQAT5JE55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPW6WTV77UDHZIQPJQQAT5JE55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UPW6WTV77UDHZIQPJQQAT5JE55","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":"3595777d6709e32eb649db71e68ef9a8360049c43717fa4d5cce6597d804820a","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-06T14:54:33Z","title_canon_sha256":"30161031e4dc0b5294ee470cccc8b3bff27b3e7506c6ed2fec09b0f9617182b8"},"schema_version":"1.0","source":{"id":"1106.1083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1083","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1083v1","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1083","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"UPW6WTV77UDH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UPW6WTV77UDHZIQP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UPW6WTV7","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:1b3dc217294ae81dc106484d8d687b6d104604035db8e43f8052f13bb26f1fea","target":"graph","created_at":"2026-05-18T04:02:13Z","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 define the quadratic algebra su(2)_{\\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)_{\\alpha}. We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2)_{\\alpha}. It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn ","authors_text":"E.I. Jafarov, J. Van der Jeugt, N.I. Stoilova","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-06T14:54:33Z","title":"The su(2)_{\\alpha} Hahn oscillator and a discrete Hahn-Fourier transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1083","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":"sha256:0930cafc509cabe48f74b0aa7a2cecaa2f23afb0dfe46ba984f93596d3b9d71b","target":"record","created_at":"2026-05-18T04:02:13Z","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":"3595777d6709e32eb649db71e68ef9a8360049c43717fa4d5cce6597d804820a","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-06T14:54:33Z","title_canon_sha256":"30161031e4dc0b5294ee470cccc8b3bff27b3e7506c6ed2fec09b0f9617182b8"},"schema_version":"1.0","source":{"id":"1106.1083","kind":"arxiv","version":1}},"canonical_sha256":"a3edeb4ebffd067ca20f4c2009f524ef6e6b07b8988bafd1f31ef64c157f8f44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3edeb4ebffd067ca20f4c2009f524ef6e6b07b8988bafd1f31ef64c157f8f44","first_computed_at":"2026-05-18T04:02:13.570359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:13.570359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r91GQyROQcQAb1Kv2oDdeg5O9G+JJwTqb8OWVLOoLlC3mNO3m5XA8GvDBJMiQPTEV6WUYCeGPnd5NOX99w5pCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:13.571418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0930cafc509cabe48f74b0aa7a2cecaa2f23afb0dfe46ba984f93596d3b9d71b","sha256:1b3dc217294ae81dc106484d8d687b6d104604035db8e43f8052f13bb26f1fea"],"state_sha256":"70dbbc35b2761e4ee2b4eba98cfc685fa1d7485829cf9edcc0bb7142e9ed8542"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBBd2AxCQTSgcMXocfRBkjZZKciwgG+dZn42YQhLZvy/sL1+ldkuDRyCw4AmE4ERWuVWEzUnjx6RmZOb7ApDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:47:26.433649Z","bundle_sha256":"ddfcfcb275c4a0f53df058e604d7c9802d2902f4e44ab1ed3b5cd04903065094"}}