{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4IXPECG4PDK2L3BIVVPNNMQLXV","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":"f9df91e675c1a384dd583f3f4706e99ed85da72d57a5813214ed7d88813fe916","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-01-15T08:52:41Z","title_canon_sha256":"9aeac8f19d3b349444fabf45597856eee343a9892b6bdbe1025ca18c09008f71"},"schema_version":"1.0","source":{"id":"1201.3069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3069","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3069v1","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3069","created_at":"2026-05-18T04:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"4IXPECG4PDK2","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4IXPECG4PDK2L3BI","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4IXPECG4","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:7fe5f63c611af2f0cd69a84db2b8daec097179acf13b5317bbb184738db3894e","target":"graph","created_at":"2026-05-18T04:04:32Z","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 show that the relation between the Schr\\\"odinger equation and diffusion processes has an algebraic nature and can be revealed via the structure of \"duplex numbers.\" This helps one to clarify that quantum mechanics cannot be reduced to diffusion theory. Also, a generalized version of quantum mechanics where $\\C$ is replaced by a normed algebra with a unit is proposed.","authors_text":"Jerzy Kocik","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-01-15T08:52:41Z","title":"Duplex numbers, diffusion systems, and generalized quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3069","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:f38ca6387f13f0428701656a7ab8623e85ff52d4d45d49d2470079556d78a413","target":"record","created_at":"2026-05-18T04:04:32Z","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":"f9df91e675c1a384dd583f3f4706e99ed85da72d57a5813214ed7d88813fe916","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-01-15T08:52:41Z","title_canon_sha256":"9aeac8f19d3b349444fabf45597856eee343a9892b6bdbe1025ca18c09008f71"},"schema_version":"1.0","source":{"id":"1201.3069","kind":"arxiv","version":1}},"canonical_sha256":"e22ef208dc78d5a5ec28ad5ed6b20bbd762d2e73b14e355464e023eac2aa3940","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e22ef208dc78d5a5ec28ad5ed6b20bbd762d2e73b14e355464e023eac2aa3940","first_computed_at":"2026-05-18T04:04:32.330232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:32.330232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEHKCsL5waTQmF6qOlI4h7LasQ9Zow19innq/opqiLatrOSUK7vLlZ1Dg71zLpMYWxB+Td1nVz5iafaIMSdcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:32.330756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f38ca6387f13f0428701656a7ab8623e85ff52d4d45d49d2470079556d78a413","sha256:7fe5f63c611af2f0cd69a84db2b8daec097179acf13b5317bbb184738db3894e"],"state_sha256":"b39b8e9299c4d4c4200b3096b0f76029990328b95457630d0518d0dcfe1a214f"}