{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:W64DFYKRTBDQMGV3HTL6LG2IY6","short_pith_number":"pith:W64DFYKR","schema_version":"1.0","canonical_sha256":"b7b832e1519847061abb3cd7e59b48c78f8d4439bfcff045296007a46b967479","source":{"kind":"arxiv","id":"1108.2194","version":1},"attestation_state":"computed","paper":{"title":"On hyperbolic interferences in the quantum--like representation algorithm for the case of triple-valued observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter Nyman","submitted_at":"2011-08-10T14:50:07Z","abstract_excerpt":"The quantum-like representation algorithm (QLRA) was introduced by A. Khrennikov \\cite{K1,K2,K3,K4,K5} to solve the \"inverse Born's rule problem\", i.e. to construct a representation of probabilistic data - measured in any context of science - and represent this data by a complex or more general (A Clifford algebra is introduced for this more general representation) probability amplitude which matches a generalization of Born's rule. The outcome from QLRA will introduce the formula of total probability with an additional term of trigonometric, hyperbolic or hyper-trigonometric interference and "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.2194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-10T14:50:07Z","cross_cats_sorted":[],"title_canon_sha256":"a3af75ce12e85aa7fd75d2c39d324d4f888a9eaabaa5847d451dad71156e8684","abstract_canon_sha256":"1f5c95a73d572ec4ed4b684df426719f16727f849efdfd324bbf1feb86152f37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:49.125561Z","signature_b64":"GRh/M+T40sFA+TJVt3QfnfDQNxSLorEsZnRnqdWmKYRsYzETiSaD6+E66Tu/PXoD4vE2PcL4QeUODyshcKgmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7b832e1519847061abb3cd7e59b48c78f8d4439bfcff045296007a46b967479","last_reissued_at":"2026-05-18T04:15:49.124972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:49.124972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On hyperbolic interferences in the quantum--like representation algorithm for the case of triple-valued observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Peter Nyman","submitted_at":"2011-08-10T14:50:07Z","abstract_excerpt":"The quantum-like representation algorithm (QLRA) was introduced by A. Khrennikov \\cite{K1,K2,K3,K4,K5} to solve the \"inverse Born's rule problem\", i.e. to construct a representation of probabilistic data - measured in any context of science - and represent this data by a complex or more general (A Clifford algebra is introduced for this more general representation) probability amplitude which matches a generalization of Born's rule. The outcome from QLRA will introduce the formula of total probability with an additional term of trigonometric, hyperbolic or hyper-trigonometric interference and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2194","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.2194","created_at":"2026-05-18T04:15:49.125087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2194v1","created_at":"2026-05-18T04:15:49.125087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2194","created_at":"2026-05-18T04:15:49.125087+00:00"},{"alias_kind":"pith_short_12","alias_value":"W64DFYKRTBDQ","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"W64DFYKRTBDQMGV3","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"W64DFYKR","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6","json":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6.json","graph_json":"https://pith.science/api/pith-number/W64DFYKRTBDQMGV3HTL6LG2IY6/graph.json","events_json":"https://pith.science/api/pith-number/W64DFYKRTBDQMGV3HTL6LG2IY6/events.json","paper":"https://pith.science/paper/W64DFYKR"},"agent_actions":{"view_html":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6","download_json":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6.json","view_paper":"https://pith.science/paper/W64DFYKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2194&json=true","fetch_graph":"https://pith.science/api/pith-number/W64DFYKRTBDQMGV3HTL6LG2IY6/graph.json","fetch_events":"https://pith.science/api/pith-number/W64DFYKRTBDQMGV3HTL6LG2IY6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6/action/storage_attestation","attest_author":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6/action/author_attestation","sign_citation":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6/action/citation_signature","submit_replication":"https://pith.science/pith/W64DFYKRTBDQMGV3HTL6LG2IY6/action/replication_record"}},"created_at":"2026-05-18T04:15:49.125087+00:00","updated_at":"2026-05-18T04:15:49.125087+00:00"}