File size: 5,522 Bytes
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"kernel": "run_sabrina_cdqs_amplification_singleton_obstruction",
"role": "post-computation assertion only",
"schema": "ouroboros_scientific_reference_assertion_v1",
"scientific_payload": {
"claim_boundary": {
"amplification_impossible_by_all_methods": false,
"capabilities_removed": [],
"cdqs_amplification_theorem_disproved": false,
"corrected_amplification_constructed": false,
"external_primary_source_locally_hash_pinned": false
},
"exact_checks": {
"arbitrary_error_claim_present": true,
"archive_hash_matches": true,
"base_error_exceeds_feasible_critical_value": true,
"base_error_present": true,
"chosen_alpha_repeated_consistently": true,
"chosen_beta_present": true,
"chosen_code_violates_singleton": true,
"claimed_gamma_present": true,
"dense_feasible_interval_all_positive": true,
"endpoint_sign_reduced_exactly": true,
"feasible_endpoint_exponent_positive": true,
"formal_chosen_exponent_is_negative": true,
"iid_threshold_has_nonempty_feasible_overlap": true,
"member_hash_matches": true,
"source_blocks_match": true
},
"obstruction_certificate": {
"iid_bound_exponent": {
"base_error_above_critical": true,
"chosen_alpha_exponent": "log((16069380442589902755419620923411626025222029937827928353013760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*exp(99)/342243006754497214485443249645813990751059732070716568543936815868940301575034686735225336447729307468584115174245740122709611535009385886402561100780239308476935874720288061945977461246662053274637340836487355792890658595154376799029579756193350955933659009857590063321243470034670724972781837355257414191)**(1/(200*log(2))))",
"chosen_alpha_would_decay": true,
"concavity_argument": "q is concave, q(0)=0, and q(1/4)>0, so q(alpha)>0 throughout 0<alpha<=1/4",
"critical_base_error_at_zero_rate_boundary": "27*exp(-1)/256",
"critical_base_error_decimal": "0.0387997848110",
"definition": "q_epsilon(alpha)=H2(alpha)+alpha log2(e epsilon); exponential decay from the cited estimate requires q_epsilon(alpha)<0",
"endpoint_exponent": "(log(64/75) + 1)/(4*log(2))",
"endpoint_positive": true,
"endpoint_sign_equivalent_to_256e_gt_300": true,
"singleton_feasible_interval": "0<alpha<=1/4"
},
"quantum_singleton": {
"chosen_alpha": "99/200",
"chosen_parameters_impossible": true,
"claimed_beta": "log((369729637649726772657187905628805440595668764281741102430259972423552570455277523421410650010128232727940978889548326540119429996769494359451621570193644014418071060667659301384999779999159200499899/88817841970012523233890533447265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)**(1/(50*log(2))))",
"claimed_beta_decimal": "0.838413728208",
"primary_reference": "https://arxiv.org/abs/2010.07902",
"singleton_rate_ceiling": "-49/50",
"statement": "for an [[m,k,d]] code, k+2(d-1)<=m; correcting arbitrary t-qubit errors needs d>=2t+1, hence k<=m-4t"
},
"rational_feasible_witness_count": 250,
"rational_feasible_witness_failures": [],
"threshold_applicable_witness_count": 168
},
"paper": {
"arxiv_id": "2404.14491",
"title": "Conditional disclosure of secrets with quantum resources"
},
"result": {
"exponent_obstruction": "after enforcing alpha<=1/4, the cited i.i.d. bound has positive rather than negative asymptotic exponent at epsilon=0.09",
"repair_classes": [
"first reduce the one-qubit base error below the feasible coding threshold",
"replace the cited arbitrary-error code/i.i.d. estimate with a compatible threshold theorem",
"supply a different amplification construction not requiring the inconsistent parameters"
],
"singleton_obstruction": "the alpha=0.495, beta approximately 0.838 code used in the proof cannot correct arbitrary t-qubit errors"
},
"result_version": "sabrina_cdqs_amplification_singleton_obstruction_v1",
"source_evidence": {
"archive_sha256": "cbeaadef653abc7c51e2c763ac8c01ae7628c881c294903e367361e2704ac3c8",
"block_hashes": {
"cdqs_amplification_statement": "605c5df3fe268dcc4550521c2355e154c88ce950d1e19861e9d3ee589f7aafc9",
"discussion_scope": "d1ccd56634eb89812a8c42d9c36ddda4de7f5cb6047be60e9d78048aadb5f48b",
"good_code_claim": "69d0d37947b1286a3d03d6d4fb907b51ffd7c81748e2152a3fdfa37ee991873f",
"routing_amplification_proof": "7a1fc06464b25f40ce6c5a4414c75cf0edcd20527c10937c07b5143746abed85"
},
"checks": {
"arbitrary_error_claim_present": true,
"archive_hash_matches": true,
"base_error_present": true,
"chosen_alpha_repeated_consistently": true,
"chosen_beta_present": true,
"claimed_gamma_present": true,
"member_hash_matches": true,
"source_blocks_match": true
},
"member_sha256": "8e992c4195a75419859c17fadfa62b8e646a9056de804fc2e0334ac21d0a1ac0"
},
"status": "complete"
},
"scientific_payload_sha256": "030824c1879fcf5639d3fb849067dcd70eb43ab728bad7d3961c5fe44ac5f1b5"
}
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