{"paper":{"title":"Double-Exponential Quasi-Orthogonality: The Geometry of Decoherence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"In high-dimensional Hilbert spaces almost all state vectors are nearly orthogonal, supplying an exponentially large reservoir of mutually quasi-orthogonal environmental records that prevents visible interference between macroscopic quantum ","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Karl Svozil","submitted_at":"2026-05-05T14:31:58Z","abstract_excerpt":"A composite system of N local q-level factors has dimension D=q^N. Although at most D vectors can be exactly orthogonal, a fixed squared-overlap tolerance \\eps permits M_\\eps(D)\\gtrsim\\exp(c_\\eps D) mutually quasi-orthogonal directions. Consequently M_\\eps(q^N)\\gtrsim\\exp(c_\\eps q^N): the dimension grows exponentially in N, but its quasi-orthogonal capacity grows doubly exponentially. L\\'evy's lemma explains the accompanying concentration of regular observables, and Johnson--Lindenstrauss scaling gives the complementary finite-set account of exponential capacity. For Haar-random pure states th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of mutually quasi-orthogonal environmental records. This geometry explains why macroscopic alternatives fail to exhibit visible interference once such records are populated.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the system's Hamiltonian and the environment's degrees of freedom will actually populate these typical quasi-orthogonal records rather than atypical ones; the paper explicitly notes that geometry alone does not guarantee the dynamics drive the system into the typical region of the accessible subspace.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In high-dimensional Hilbert spaces, near-orthogonality of almost all vectors supplies an exponentially large reservoir of mutually quasi-orthogonal environmental records that makes decoherence overwhelmingly effective for macroscopic systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In high-dimensional Hilbert spaces almost all state vectors are nearly orthogonal, supplying an exponentially large reservoir of mutually quasi-orthogonal environmental records that prevents visible interference between macroscopic quantum ","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bab603981042107721cb3285478f620e8beee3724fdc2c2c793718aa21560ebc"},"source":{"id":"2605.03807","kind":"arxiv","version":2},"verdict":{"id":"1ecd27a3-0066-4169-8fcc-ea7f110dd643","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T04:14:44.538889Z","strongest_claim":"In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of mutually quasi-orthogonal environmental records. This geometry explains why macroscopic alternatives fail to exhibit visible interference once such records are populated.","one_line_summary":"In high-dimensional Hilbert spaces, near-orthogonality of almost all vectors supplies an exponentially large reservoir of mutually quasi-orthogonal environmental records that makes decoherence overwhelmingly effective for macroscopic systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the system's Hamiltonian and the environment's degrees of freedom will actually populate these typical quasi-orthogonal records rather than atypical ones; the paper explicitly notes that geometry alone does not guarantee the dynamics drive the system into the typical region of the accessible subspace.","pith_extraction_headline":"In high-dimensional Hilbert spaces almost all state vectors are nearly orthogonal, supplying an exponentially large reservoir of mutually quasi-orthogonal environmental records that prevents visible interference between macroscopic quantum "},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03807/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T13:33:44.651568Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:31:20.977928Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:01:55.817408Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a74a75d93b8eb17a7045280bde4afef3f35e2ca790de6d34c90aa1f41045dbe7"},"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"}