{ "benchmark_version": "v1", "cases": [ { "benchmark": "ckks-depth-aware-single-operations", "category": "Single operations", "comparison": { "axis": [ "operation", "entry_level" ], "portal_highlight": { "entry_level": 0, "label": "CT × CT multiply · level 0", "metric": "depth-aware-ckks-operation-latency", "operation": "multiply" } }, "failure": null, "finished_at": "2026-08-14T14:52:57.298183+00:00", "id": "ckks-depth-aware-single-operations", "parameters": { "ciphertext_modulus_basis": "Q", "include_raw_samples": true, "levels": [ 0, 1, 2, 3, 4, 5, 6 ], "logN": 14, "nonce": 0, "ntt_backend": "radix2_indexed", "num_p_primes": 1, "num_scale_primes": 7, "operations": [ "encrypt", "decrypt", "coefficient_domain_to_ntt_domain", "ntt_domain_to_coefficient_domain", "add", "add_plaintext", "multiply_plaintext", "multiply", "relinearize", "rotate_with_key", "rescale_to_next_level", "mod_switch_to_next_level" ], "preset": "slots8192-scale40-levels7-int64", "rescale_rounding": "nearest", "rotation_step": 1, "runs": 3, "scale_bits": 40, "seed": 20260807, "warmup": 1 }, "profile": "core", "requirements": { "native_backends_any": [ "cpu", "cuda" ] }, "result": { "benchmark": "ckks-depth-aware-single-operations", "correctness": [ { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.634564257476506e-06, "rms_error": 5.480023228682282e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-0-semantic-error", "observed": 2.5928562484449522e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 0, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 0, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.6582367919934425e-06, "rms_error": 5.508014218088745e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-0-semantic-error", "observed": 2.6091945005486113e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": 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"name": "coefficient_domain_to_ntt_domain-level-0-semantic-error", "observed": 2.6091945005486113e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.6582367919934425e-06, "rms_error": 5.508014218088745e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-0-semantic-error", "observed": 2.6091945005486113e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.04451444967053e-06, "rms_error": 8.91086824113455e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-0-semantic-error", "observed": 5.204867540006415e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.736257362498796e-06, "rms_error": 5.508018443732958e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-0-semantic-error", "observed": 2.6092304817552005e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.85115757502978e-06, "rms_error": 5.16688664858223e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-0-semantic-error", "observed": 2.660831338531045e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, 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"value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.324116476923094e-06, "rms_error": 8.865876983101977e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-0-semantic-error", "observed": 5.013799912497439e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 0, "limb_count": 8, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 0, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.03959061594972e-06, "rms_error": 5.958936397073727e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-0-semantic-error", "observed": 2.6065143133155465e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 0, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-0-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, 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"component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 1, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 1, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.665025972535393e-06, "rms_error": 5.5160419128204766e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-1-semantic-error", "observed": 2.5668180061209114e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.665025972535393e-06, "rms_error": 5.5160419128204766e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-1-semantic-error", "observed": 2.5668180061209114e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.665025972535393e-06, "rms_error": 5.5160419128204766e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-1-semantic-error", "observed": 2.5668180061209114e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.013629992193045e-06, "rms_error": 8.865338143792186e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-1-semantic-error", "observed": 5.100981524848808e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "add_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "add_plaintext-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "add_plaintext", "relative_l2_error": 3.7416652490720547e-06, "rms_error": 5.515990790414986e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add_plaintext-level-1-semantic-error", "observed": 2.5668144331845213e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.883633522608103e-06, "rms_error": 5.201476236190394e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-1-semantic-error", "observed": 2.6176784855011763e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "multiply", "relative_l2_error": 8.35877102545119e-06, "rms_error": 8.902786962077729e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-1-semantic-error", "observed": 4.9545511067118664e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.358771025548065e-06, "rms_error": 8.902786962180911e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-1-semantic-error", "observed": 4.9545511068605485e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 1, "limb_count": 7, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 1, 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.016238356541062e-06, "rms_error": 5.931324108864493e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-1-semantic-error", "observed": 2.5613119457871235e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.665025972535393e-06, "rms_error": 5.5160419128204766e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-1-semantic-error", "observed": 2.5668180061209114e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 1, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-1-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 1, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.665025972535393e-06, "rms_error": 5.5160419128204766e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-1-semantic-error", "observed": 2.5668180061209114e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.638173875130122e-06, "rms_error": 5.4842913297354866e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-2-semantic-error", "observed": 2.579241101198864e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], 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"coefficient_domain_to_ntt_domain-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "ntt_domain_to_coefficient_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", 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rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "add", "relative_l2_error": 6.017200065412184e-06, "rms_error": 8.870601172333494e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "add-level-2-semantic-error", "observed": 5.178809868304639e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" 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"add_plaintext-level-2-semantic-error", "observed": 2.6012490067965907e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.836437177765644e-06, "rms_error": 5.151208200106882e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-2-semantic-error", "observed": 2.6527967430342666e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply", "predicted_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and 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5.034556776265643e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 2, "limb_count": 6, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 2, 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.003580306317125e-06, "rms_error": 5.916356917688941e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-2-semantic-error", "observed": 2.6135831632193365e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.644382992316369e-06, "rms_error": 5.491633143230755e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 2, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-2-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 2, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.644382992316369e-06, "rms_error": 5.491633143230755e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-2-semantic-error", "observed": 2.6012627146301705e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.6260341949064764e-06, "rms_error": 5.4699370720494455e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-3-semantic-error", "observed": 2.5937933014869438e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 3, "limb_count": null, 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3, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.658091131697721e-06, "rms_error": 5.5078419857580006e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", 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"state_mismatch_count", "name": "ntt_domain_to_coefficient_domain-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "ntt_domain_to_coefficient_domain", "relative_l2_error": 4.658091131697721e-06, "rms_error": 5.5078419857580006e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "ntt_domain_to_coefficient_domain-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 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canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "multiply_plaintext", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "multiply_plaintext-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "multiply_plaintext", "relative_l2_error": 4.846581814431461e-06, "rms_error": 5.162013082639071e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply_plaintext-level-3-semantic-error", "observed": 2.6523402668704114e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 3, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "ntt", 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"relative_l2_error": 8.286106343790282e-06, "rms_error": 8.825393027188921e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "multiply-level-3-semantic-error", "observed": 4.953342259691456e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" }, "operation": "relinearize", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1.2089258196146292e+24, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "relinearize-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.286106343891724e-06, "rms_error": 8.825393027296959e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-3-semantic-error", "observed": 4.953342259840304e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rotate_with_key", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 3, "limb_count": 5, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 3, 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rotate_with_key-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "rotate_with_key", "relative_l2_error": 5.043410042578997e-06, "rms_error": 5.963452581440987e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "rotate_with_key-level-3-semantic-error", "observed": 2.594380339906795e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-3-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 3, "nonfinite_count": 0, "operation": "rescale_to_next_level", "relative_l2_error": 4.658091131697721e-06, "rms_error": 5.5078419857580006e-08 }, "limit": 3e-05, "metric": "max_abs_error", "name": "rescale_to_next_level-level-3-semantic-error", "observed": 2.600835732805084e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 3, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", 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"==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "encrypt-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "encrypt", "relative_l2_error": 4.617473907040801e-06, "rms_error": 5.459815176280616e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "encrypt-level-4-semantic-error", "observed": 2.6068397104684956e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 4, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 4, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "decrypt", "relative_l2_error": 4.6350674769132685e-06, "rms_error": 5.480618247771326e-08 }, "limit": 1e-05, "metric": "max_abs_error", "name": "decrypt-level-4-semantic-error", "observed": 2.525191215776654e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "coefficient_domain_to_ntt_domain", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "ntt", "prime_ids": [ 4, 5, 6, 7 ], "representation": "rns", "residue_representation": "montgomery", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "coefficient_domain_to_ntt_domain-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "coefficient_domain_to_ntt_domain", "relative_l2_error": 4.6350674769132685e-06, "rms_error": 5.480618247771326e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "coefficient_domain_to_ntt_domain-level-4-semantic-error", "observed": 2.525191215776654e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, 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"name": "relinearize-level-4-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 4, "nonfinite_count": 0, "operation": "relinearize", "relative_l2_error": 8.234684930164154e-06, "rms_error": 8.770624941137946e-10 }, "limit": 3e-05, "metric": "max_abs_error", "name": "relinearize-level-4-semantic-error", "observed": 4.954851793154302e-08, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 4, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 4, "limb_count": 4, "modulus_basis": "Q", "polynomial_domain": "coefficient", 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"details": { "entry_level": 5, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "rescale_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "rescale_to_next_level-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions 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"scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "mod_switch_to_next_level", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "mod_switch_to_next_level-level-5-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, dtype, and device.", "passed": true, "unit": "fields" }, { "comparison": "<=", "details": { "entry_level": 5, "nonfinite_count": 0, "operation": "mod_switch_to_next_level", "relative_l2_error": 4.6297363961417774e-06, "rms_error": 5.4743146462159847e-08 }, "limit": 2e-05, "metric": "max_abs_error", "name": "mod_switch_to_next_level-level-5-semantic-error", "observed": 2.5789186345827985e-06, "oracle": "All decoded slots are compared with the fixed cleartext operation after untimed canonicalization.", "passed": true, "unit": "absolute" }, { "comparison": "==", "details": { "entry_level": 6, "mismatches": {}, "observed_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", "residue_representation": "standard", "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "ciphertext" }, "operation": "encrypt", "predicted_exit_state": { "batch_shape": [], "component_count": 2, "device": "cuda:0", "dtype": "torch.int64", "level": 6, "limb_count": 2, "modulus_basis": "Q", "polynomial_domain": "coefficient", "prime_ids": [ 6, 7 ], "representation": "rns", 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"component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" }, "operation": "decrypt", "predicted_exit_state": { "batch_shape": [], "component_count": null, "device": "cuda:0", "dtype": "torch.float64", "level": 6, "limb_count": null, "modulus_basis": null, "polynomial_domain": "coefficient", "prime_ids": [], "representation": "approximate_coefficients", "residue_representation": null, "ring_dimension": 16384, "scale": 1099511627776.0, "value_type": "plaintext" } }, "limit": 0, "metric": "state_mismatch_count", "name": "decrypt-level-6-exit-state", "observed": 0, "oracle": "Observed exit state satisfies the operation postconditions for level, actual scale, rows, components, domain, basis, representation, shape, 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