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zeekay b832ba2c39 Initial Torus commit 
Forked from upstream concrete (BSD-3-Clause-Clear, © 2024 ZAMA) at HEAD
ecb729bb. Modifications copyright © 2026 Lux Industries Inc.

Rebranding scope:
  - Python module concrete → torus (across frontends/torus-python)
  - Rust module concrete-* → torus-* (across frontends/torus-rust)
  - MLIR dialect concretelang → toruslang (across compilers/torus-compiler)
  - Compiler optimizer concrete-optimizer → torus-optimizer
  - Backend concrete-cpu / concrete-cuda → torus-cpu / torus-cuda
  - Wire protocol concrete-protocol → torus-protocol
  - Parameter-curves concrete-security-curves-* → torus-security-curves-*
  - Public symbols concretelib → toruslib, ConcreteLang → TorusLang
  - URLs github.com/zama-ai/concrete → github.com/luxfhe/torus
  - URLs docs.zama.ai/concrete → docs.luxfhe.com/torus

Legal compliance:
  - LICENSE.txt retains original Copyright © 2024 ZAMA verbatim (§1-§2)
  - LICENSE.txt adds modifications copyright © 2026 Lux Industries Inc.
  - §3 endorsement clause: Torus is marketed exclusively as a Lux product;
    no Zama name used in README, docs, or marketing
  - NOTICE file provides factual attribution per legal best practice
    (not endorsement; required by upstream BSD-3-Clause-Clear)

README + NOTICE rewritten from scratch with Lux brand:
  - Quick-start in Python (torus.fhe)
  - Architecture diagram showing the gen-1 vtbl integration path
    (luxcpp/gpu → lux-private/gpu-kernels for CUDA/Metal/WebGPU)
  - Scheme coverage table: TFHE (luxfi/fhe), CKKS/BGV/BFV (luxfi/lattice)
  - Lux FHE family table: Torus / TorusVM / TorusEVM / TorusML / TorusNet

Known limitations (phase-2A scope):
  - PyPI package torus-fhe not yet published; the torus Python module
    is renamed structurally but pip-installable distribution is a
    follow-up (Phase 2A.1)
  - MLIR dialect rename is text-level; the compiler-internal LLVM
    rebuild (concrete-compiler-internal-llvm-project submodule) is
    structural and works; tablegen files renamed concrete→torus but the
    generated .inc files in the source tree will regenerate at build
    time
  - backends/torus-cuda/implementation/ is an upstream submodule
    pointer to the tfhe-rs source (not fetched in the staging clone);
    the CUDA backend body is delivered out-of-tree
  - ~100 test-fixture variable names like concrete_encoded_sample
    retain "concrete" as a math term (vs symbolic); these are inside
    tests/, not the public API; cleanup is a follow-up commit
  - 295 Python `from concrete import ...` residuals in luxfhe/ml-sdk
    consumer remain; that repo's import update is Phase 2B

This commit is the seed for the luxfhe/torus repo. Push as the first
commit to a fresh GitHub repo; do not re-import upstream Zama git
history.
2026-05-29 14:16:47 -07:00

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security level: 128
target p_error: 6.3e-5
per precision and log norm2:
- 1: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 8, 582, 1, 15, 3, 3, 29, 5.3e-5
- 1 : 5, 8, 586, 1, 15, 3, 3, 29, 5.6e-5
- 2 : 5, 8, 620, 1, 15, 3, 3, 31, 6.2e-5
- 3 : 6, 8, 588, 1, 18, 3, 3, 36, 5.9e-5
- 4 : 6, 8, 591, 1, 18, 3, 3, 36, 6.3e-5
- 5 : 6, 8, 614, 1, 18, 3, 3, 37, 5.9e-5
- 6 : 5, 8, 589, 2, 10, 3, 3, 42, 6.0e-5
- 7 : 5, 8, 619, 2, 10, 6, 2, 49, 6.2e-5
- 8 : 4, 9, 597, 1, 23, 3, 3, 51, 5.5e-5
- 9 : 4, 9, 601, 1, 23, 3, 3, 51, 6.3e-5
- 10: 6, 8, 593, 2, 12, 3, 3, 52, 5.6e-5
- 11: 6, 8, 582, 2, 12, 5, 2, 55, 5.9e-5
- 12: 6, 8, 589, 3, 9, 3, 3, 68, 5.4e-5
- 13: 6, 8, 594, 3, 9, 3, 3, 69, 5.9e-5
- 14: 6, 8, 592, 3, 9, 5, 2, 72, 6.0e-5
- 15: 4, 9, 596, 2, 16, 3, 3, 73, 5.8e-5
- 16: 4, 9, 598, 2, 16, 3, 3, 73, 6.2e-5
- 17: 4, 9, 611, 2, 16, 3, 3, 74, 5.8e-5
- 18: 4, 9, 565, 3, 12, 5, 2, 94, 5.8e-5
- 19: 4, 9, 596, 3, 12, 3, 3, 95, 6.2e-5
- 20: 4, 9, 568, 3, 12, 5, 2, 95, 5.6e-5
- 21: 4, 9, 580, 3, 12, 5, 2, 97, 6.0e-5
- 22: 4, 9, 569, 4, 10, 5, 2, 116, 5.4e-5
- 23: 4, 9, 586, 4, 10, 5, 2, 119, 6.2e-5
- 24: 4, 9, 570, 5, 8, 5, 2, 137, 5.8e-5
- 25: 4, 9, 600, 5, 8, 5, 2, 144, 5.9e-5
- 26: 4, 9, 609, 6, 7, 6, 2, 170, 6.2e-5
- 27: 4, 9, 599, 8, 5, 5, 2, 209, 6.1e-5
- 28: 4, 9, 578, 11, 4, 5, 2, 266, 5.5e-5
- 29: 4, 9, 585, 15, 3, 5, 2, 355, 5.6e-5
- 30: 4, 9, 601, 22, 2, 11, 1, 532, 6.1e-5
# no solution starting from log norm2 = 31
- 2: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 8, 670, 1, 15, 3, 4, 33, 5.6e-5
- 1 : 4, 8, 668, 2, 8, 4, 3, 39, 6.2e-5
- 2 : 6, 8, 668, 1, 18, 3, 4, 40, 5.7e-5
- 3 : 6, 8, 673, 1, 18, 3, 4, 40, 5.7e-5
- 4 : 6, 8, 689, 1, 18, 4, 3, 43, 6.3e-5
- 5 : 5, 8, 644, 2, 10, 4, 3, 48, 5.9e-5
- 6 : 4, 9, 662, 1, 23, 3, 4, 56, 5.5e-5
- 7 : 4, 9, 663, 1, 23, 3, 4, 56, 5.3e-5
- 8 : 4, 9, 667, 1, 23, 3, 4, 56, 5.1e-5
- 9 : 4, 9, 693, 1, 23, 3, 4, 58, 6.2e-5
- 10: 3, 9, 653, 2, 12, 4, 3, 62, 6.1e-5
- 11: 6, 8, 638, 3, 9, 4, 3, 75, 6.1e-5
- 12: 6, 8, 646, 3, 9, 4, 3, 76, 5.7e-5
- 13: 4, 9, 632, 2, 16, 4, 3, 79, 6.3e-5
- 14: 4, 9, 633, 2, 16, 4, 3, 79, 5.4e-5
- 15: 4, 9, 635, 2, 16, 4, 3, 79, 5.2e-5
- 16: 4, 9, 643, 2, 16, 4, 3, 80, 6.2e-5
- 17: 4, 9, 615, 3, 12, 5, 2, 102, 6.1e-5
- 18: 4, 9, 616, 3, 12, 5, 2, 102, 6.1e-5
- 19: 4, 9, 636, 3, 12, 4, 3, 103, 5.4e-5
- 20: 4, 9, 651, 3, 12, 4, 3, 105, 5.7e-5
- 21: 4, 9, 622, 4, 10, 5, 2, 126, 6.0e-5
- 22: 4, 9, 659, 4, 10, 4, 3, 130, 6.1e-5
- 23: 4, 9, 614, 5, 8, 6, 2, 149, 5.2e-5
- 24: 4, 9, 652, 5, 8, 6, 2, 158, 6.1e-5
- 25: 4, 9, 616, 7, 6, 6, 2, 195, 6.0e-5
- 26: 4, 9, 651, 8, 5, 6, 2, 229, 6.2e-5
- 27: 4, 9, 622, 11, 4, 6, 2, 288, 6.2e-5
- 28: 4, 9, 631, 15, 3, 6, 2, 384, 5.7e-5
- 29: 4, 9, 658, 23, 2, 13, 1, 611, 6.3e-5
# no solution starting from log norm2 = 30
- 3: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 3, 9, 708, 1, 18, 3, 4, 45, 6.2e-5
- 1 : 3, 9, 710, 1, 18, 3, 4, 45, 5.7e-5
- 2 : 3, 9, 716, 1, 18, 3, 4, 45, 6.2e-5
- 3 : 4, 9, 717, 1, 23, 3, 4, 60, 6.2e-5
- 4 : 4, 9, 717, 1, 23, 3, 4, 60, 6.3e-5
- 5 : 4, 9, 718, 1, 23, 3, 4, 60, 5.8e-5
- 6 : 4, 9, 720, 1, 23, 3, 4, 60, 5.8e-5
- 7 : 4, 9, 730, 1, 23, 3, 4, 61, 5.9e-5
- 8 : 3, 9, 688, 2, 12, 4, 3, 65, 6.0e-5
- 9 : 3, 9, 678, 3, 9, 4, 3, 82, 6.1e-5
- 10: 3, 9, 680, 3, 9, 4, 3, 83, 6.2e-5
- 11: 3, 9, 691, 3, 9, 4, 3, 84, 6.1e-5
- 12: 4, 9, 687, 2, 16, 4, 3, 85, 6.1e-5
- 13: 4, 9, 688, 2, 16, 4, 3, 85, 6.0e-5
- 14: 4, 9, 692, 2, 16, 4, 3, 86, 6.1e-5
- 15: 4, 9, 725, 2, 16, 4, 3, 90, 6.2e-5
- 16: 4, 9, 687, 3, 12, 4, 3, 111, 6.2e-5
- 17: 4, 9, 689, 3, 12, 4, 3, 111, 5.7e-5
- 18: 4, 9, 695, 3, 12, 4, 3, 112, 6.0e-5
- 19: 4, 9, 689, 4, 10, 4, 3, 136, 6.1e-5
- 20: 4, 9, 697, 4, 10, 4, 3, 138, 6.3e-5
- 21: 4, 9, 664, 5, 8, 6, 2, 161, 6.3e-5
- 22: 4, 9, 675, 5, 8, 6, 2, 163, 6.2e-5
- 23: 4, 9, 678, 6, 7, 6, 2, 189, 6.3e-5
- 24: 4, 9, 684, 7, 6, 6, 2, 216, 6.0e-5
- 25: 4, 9, 686, 9, 5, 7, 2, 269, 6.3e-5
- 26: 4, 9, 701, 11, 4, 7, 2, 326, 6.2e-5
- 27: 4, 9, 679, 22, 2, 6, 2, 587, 6.3e-5
- 28: 4, 9, 696, 45, 1, 14, 1, 1210, 6.2e-5
# no solution starting from log norm2 = 29
- 4: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 2, 10, 784, 1, 23, 3, 4, 74, 6.1e-5
- 1 : 2, 10, 784, 1, 23, 3, 4, 74, 6.1e-5
- 2 : 2, 10, 784, 1, 23, 3, 4, 74, 6.1e-5
- 3 : 2, 10, 784, 1, 23, 3, 4, 74, 6.3e-5
- 4 : 2, 10, 787, 1, 23, 3, 4, 74, 6.1e-5
- 5 : 2, 10, 794, 1, 23, 3, 5, 75, 6.0e-5
- 6 : 2, 10, 810, 1, 23, 3, 5, 76, 6.1e-5
- 7 : 2, 10, 728, 2, 15, 5, 3, 105, 5.6e-5
- 8 : 2, 10, 728, 2, 15, 5, 3, 105, 5.6e-5
- 9 : 2, 10, 728, 2, 15, 5, 3, 105, 5.6e-5
- 10: 2, 10, 728, 2, 15, 5, 3, 105, 5.7e-5
- 11: 2, 10, 728, 2, 15, 5, 3, 105, 6.1e-5
- 12: 2, 10, 730, 2, 15, 5, 3, 105, 5.9e-5
- 13: 2, 10, 739, 2, 15, 5, 3, 106, 5.8e-5
- 14: 2, 10, 728, 3, 12, 5, 3, 135, 5.8e-5
- 15: 2, 10, 729, 3, 12, 5, 3, 135, 5.6e-5
- 16: 2, 10, 732, 3, 12, 5, 3, 135, 5.8e-5
- 17: 2, 10, 751, 3, 12, 5, 3, 139, 6.2e-5
- 18: 2, 10, 704, 4, 9, 7, 2, 165, 6.3e-5
- 19: 2, 10, 716, 4, 9, 7, 2, 168, 6.0e-5
- 20: 2, 10, 708, 5, 8, 7, 2, 195, 6.2e-5
- 21: 2, 10, 710, 6, 7, 7, 2, 225, 5.9e-5
- 22: 2, 10, 712, 7, 6, 7, 2, 254, 5.8e-5
- 23: 2, 10, 726, 8, 5, 7, 2, 289, 6.3e-5
- 24: 2, 10, 720, 11, 4, 7, 2, 375, 6.1e-5
- 25: 2, 10, 734, 15, 3, 7, 2, 503, 6.1e-5
- 26: 2, 10, 725, 43, 1, 14, 1, 1349, 6.1e-5
# no solution starting from log norm2 = 27
- 5: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 11, 768, 1, 23, 5, 3, 101, 5.6e-5
- 1 : 1, 11, 768, 1, 23, 5, 3, 101, 5.6e-5
- 2 : 1, 11, 768, 1, 23, 5, 3, 101, 5.8e-5
- 3 : 1, 11, 769, 1, 23, 5, 3, 101, 5.9e-5
- 4 : 1, 11, 774, 1, 23, 5, 3, 101, 5.9e-5
- 5 : 1, 11, 790, 1, 23, 8, 2, 112, 6.2e-5
- 6 : 1, 11, 768, 2, 15, 5, 3, 143, 5.6e-5
- 7 : 1, 11, 768, 2, 15, 5, 3, 143, 5.6e-5
- 8 : 1, 11, 768, 2, 15, 5, 3, 143, 5.6e-5
- 9 : 1, 11, 768, 2, 15, 5, 3, 143, 5.7e-5
- 10: 1, 11, 769, 2, 15, 5, 3, 143, 5.5e-5
- 11: 1, 11, 772, 2, 15, 5, 3, 143, 5.7e-5
- 12: 1, 11, 791, 2, 15, 5, 3, 147, 6.0e-5
- 13: 1, 11, 768, 3, 11, 5, 3, 185, 6.1e-5
- 14: 1, 11, 770, 3, 11, 5, 3, 185, 6.1e-5
- 15: 1, 11, 781, 3, 11, 5, 3, 188, 5.9e-5
- 16: 1, 11, 746, 4, 9, 7, 2, 226, 5.9e-5
- 17: 1, 11, 751, 4, 9, 7, 2, 228, 6.1e-5
- 18: 1, 11, 790, 4, 9, 8, 2, 242, 6.2e-5
- 19: 1, 11, 773, 5, 8, 8, 2, 279, 6.1e-5
- 20: 1, 11, 790, 6, 7, 8, 2, 328, 6.3e-5
- 21: 1, 11, 757, 8, 5, 7, 2, 395, 6.2e-5
- 22: 1, 11, 767, 10, 4, 8, 2, 487, 6.2e-5
- 23: 1, 11, 763, 14, 3, 8, 2, 651, 6.1e-5
- 24: 1, 11, 782, 22, 2, 8, 2, 1009, 6.2e-5
# no solution starting from log norm2 = 25
- 6: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 12, 860, 1, 22, 4, 4, 231, 6.2e-5
- 1 : 1, 12, 862, 1, 22, 4, 4, 231, 5.7e-5
- 2 : 1, 12, 867, 1, 22, 4, 4, 232, 6.1e-5
- 3 : 1, 12, 886, 1, 22, 6, 3, 251, 6.3e-5
- 4 : 1, 12, 838, 2, 15, 5, 3, 330, 6.0e-5
- 5 : 1, 12, 838, 2, 15, 5, 3, 330, 6.0e-5
- 6 : 1, 12, 838, 2, 15, 5, 3, 330, 6.0e-5
- 7 : 1, 12, 838, 2, 15, 5, 3, 330, 6.2e-5
- 8 : 1, 12, 839, 2, 15, 5, 3, 330, 6.2e-5
- 9 : 1, 12, 844, 2, 15, 5, 3, 332, 6.0e-5
- 10: 1, 12, 884, 2, 15, 4, 4, 340, 6.1e-5
- 11: 1, 12, 839, 3, 11, 5, 3, 429, 5.9e-5
- 12: 1, 12, 841, 3, 11, 5, 3, 429, 6.1e-5
- 13: 1, 12, 813, 3, 11, 8, 2, 435, 6.1e-5
- 14: 1, 12, 806, 4, 9, 8, 2, 526, 5.6e-5
- 15: 1, 12, 810, 4, 9, 8, 2, 528, 6.1e-5
- 16: 1, 12, 848, 4, 9, 9, 2, 559, 6.2e-5
- 17: 1, 12, 848, 5, 8, 9, 2, 658, 6.3e-5
- 18: 1, 12, 813, 7, 6, 8, 2, 816, 6.1e-5
- 19: 1, 12, 816, 8, 5, 8, 2, 914, 6.3e-5
- 20: 1, 12, 828, 10, 4, 8, 2, 1122, 6.1e-5
- 21: 1, 12, 831, 14, 3, 8, 2, 1515, 6.2e-5
- 22: 1, 12, 854, 22, 2, 18, 1, 2424, 6.3e-5
# no solution starting from log norm2 = 23
- 7: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 13, 894, 1, 22, 6, 3, 535, 6.3e-5
- 1 : 1, 13, 915, 1, 22, 6, 3, 546, 6.3e-5
- 2 : 1, 13, 890, 2, 15, 6, 3, 755, 6.2e-5
- 3 : 1, 13, 890, 2, 15, 6, 3, 755, 6.2e-5
- 4 : 1, 13, 890, 2, 15, 6, 3, 755, 6.2e-5
- 5 : 1, 13, 890, 2, 15, 6, 3, 755, 6.3e-5
- 6 : 1, 13, 891, 2, 15, 6, 3, 756, 6.0e-5
- 7 : 1, 13, 894, 2, 15, 6, 3, 758, 5.9e-5
- 8 : 1, 13, 909, 2, 15, 6, 3, 770, 6.1e-5
- 9 : 1, 13, 891, 3, 11, 6, 3, 978, 5.8e-5
- 10: 1, 13, 892, 3, 11, 6, 3, 979, 6.0e-5
- 11: 1, 13, 898, 3, 11, 6, 3, 986, 5.9e-5
- 12: 1, 13, 892, 4, 9, 6, 3, 1202, 5.8e-5
- 13: 1, 13, 897, 4, 9, 6, 3, 1209, 6.0e-5
- 14: 1, 13, 920, 4, 9, 10, 2, 1297, 6.3e-5
- 15: 1, 13, 874, 6, 7, 9, 2, 1657, 5.8e-5
- 16: 1, 13, 875, 7, 6, 9, 2, 1877, 6.2e-5
- 17: 1, 13, 878, 8, 5, 9, 2, 2103, 6.2e-5
- 18: 1, 13, 887, 10, 4, 9, 2, 2568, 6.2e-5
- 19: 1, 13, 897, 14, 3, 9, 2, 3494, 6.2e-5
- 20: 1, 13, 876, 42, 1, 18, 1, 9668, 6.2e-5
# no solution starting from log norm2 = 21
- 8: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 14, 982, 2, 15, 5, 4, 1721, 6.2e-5
- 1 : 1, 14, 982, 2, 15, 5, 4, 1721, 6.2e-5
- 2 : 1, 14, 982, 2, 15, 5, 4, 1721, 6.2e-5
- 3 : 1, 14, 965, 2, 15, 6, 3, 1722, 6.2e-5
- 4 : 1, 14, 983, 2, 15, 5, 4, 1723, 6.2e-5
- 5 : 1, 14, 986, 2, 15, 5, 4, 1728, 6.2e-5
- 6 : 1, 14, 1005, 2, 15, 5, 4, 1760, 6.3e-5
- 7 : 1, 14, 966, 3, 11, 6, 3, 2237, 6.0e-5
- 8 : 1, 14, 954, 3, 11, 7, 3, 2240, 6.0e-5
- 9 : 1, 14, 959, 3, 11, 7, 3, 2252, 6.1e-5
- 10: 1, 14, 977, 3, 11, 21, 1, 2721, 6.3e-5
- 11: 1, 14, 960, 4, 9, 7, 3, 2764, 5.9e-5
- 12: 1, 14, 934, 5, 8, 10, 2, 3275, 6.3e-5
- 13: 1, 14, 935, 6, 6, 10, 2, 3775, 6.3e-5
- 14: 1, 14, 939, 7, 6, 10, 2, 4289, 6.0e-5
- 15: 1, 14, 942, 8, 5, 10, 2, 4803, 6.1e-5
- 16: 1, 14, 951, 10, 4, 10, 2, 5859, 6.1e-5
- 17: 1, 14, 971, 14, 3, 10, 2, 8044, 6.3e-5
- 18: 1, 14, 955, 41, 1, 20, 1, 21910, 6.3e-5
# no solution starting from log norm2 = 19
- 9: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 15, 1013, 2, 15, 7, 3, 3864, 6.3e-5
- 1 : 1, 15, 1014, 2, 15, 7, 3, 3867, 5.8e-5
- 2 : 1, 15, 1014, 2, 15, 7, 3, 3867, 6.2e-5
- 3 : 1, 15, 1018, 2, 15, 7, 3, 3882, 5.9e-5
- 4 : 1, 15, 1040, 2, 15, 7, 3, 3963, 6.2e-5
- 5 : 1, 15, 1014, 3, 11, 7, 3, 5008, 5.9e-5
- 6 : 1, 15, 1015, 3, 11, 7, 3, 5013, 6.1e-5
- 7 : 1, 15, 1021, 3, 11, 7, 3, 5042, 6.1e-5
- 8 : 1, 15, 1015, 4, 9, 7, 3, 6155, 6.2e-5
- 9 : 1, 15, 1023, 4, 9, 7, 3, 6202, 6.0e-5
- 10: 1, 15, 1020, 5, 7, 7, 3, 7332, 6.2e-5
- 11: 1, 15, 1054, 5, 7, 12, 2, 7902, 6.3e-5
- 12: 1, 15, 1003, 7, 6, 11, 2, 9720, 6.3e-5
- 13: 1, 15, 1007, 8, 5, 11, 2, 10891, 6.3e-5
- 14: 1, 15, 1019, 10, 4, 11, 2, 13312, 6.2e-5
- 15: 1, 15, 1003, 20, 2, 11, 2, 24389, 6.3e-5
- 16: 1, 15, 1018, 41, 1, 22, 1, 49503, 6.3e-5
# no solution starting from log norm2 = 17
- 10: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 16, 1107, 2, 14, 6, 4, 8697, 6.2e-5
- 1 : 1, 16, 1110, 2, 14, 6, 4, 8720, 6.2e-5
- 2 : 1, 16, 1128, 2, 14, 6, 4, 8858, 6.2e-5
- 3 : 1, 16, 1076, 3, 11, 8, 3, 11286, 5.9e-5
- 4 : 1, 16, 1077, 3, 11, 8, 3, 11296, 6.1e-5
- 5 : 1, 16, 1083, 3, 11, 8, 3, 11358, 6.3e-5
- 6 : 1, 16, 1078, 4, 9, 8, 3, 13867, 5.9e-5
- 7 : 1, 16, 1086, 4, 9, 8, 3, 13968, 6.2e-5
- 8 : 1, 16, 1081, 5, 7, 8, 3, 16472, 6.0e-5
- 9 : 1, 16, 1117, 5, 7, 8, 3, 17012, 6.3e-5
- 10: 1, 16, 1094, 6, 6, 12, 2, 19813, 6.3e-5
- 11: 1, 16, 1076, 8, 5, 12, 2, 24602, 6.2e-5
- 12: 1, 16, 1099, 10, 4, 12, 2, 30343, 6.3e-5
- 13: 1, 16, 1066, 20, 2, 12, 2, 54757, 6.1e-5
- 14: 1, 16, 1090, 42, 1, 24, 1, 114574, 6.3e-5
# no solution starting from log norm2 = 15
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