Datasets:
Formats:
csv
Languages:
English
Size:
1K - 10K
Tags:
mathematics
inverse-problems
observability
noncommutative-algebra
symbolic-computation
calibration-rigidity
| #!/usr/bin/env python3 | |
| """Run exact channel, rank, and witness examples without network access.""" | |
| from __future__ import annotations | |
| import argparse,json,sys | |
| from collections import Counter | |
| from pathlib import Path | |
| sys.path.insert(0,str(Path(__file__).resolve().parents[1]/"src")) | |
| from noulith.third import ( | |
| all_components, example_point, certify_scalar, predicted_rank, direct_block_rank, | |
| optimal_calibration_subfamily, calibration_classes, | |
| ) | |
| from noulith.algebra import TwistedAlgebra | |
| def main(): | |
| parser=argparse.ArgumentParser(description=__doc__) | |
| parser.add_argument("--m",type=int,default=6) | |
| args=parser.parse_args() | |
| if args.m<6:parser.error("The third-deficit recipe requires m >= 6.") | |
| m=args.m;q=example_point(m,"twin");cert=certify_scalar(m,q) | |
| rank=predicted_rank(m,q) | |
| independent=direct_block_rank(m,q,m-3) if m<=8 else None | |
| if independent is not None and independent!=rank:raise AssertionError("Independent rank disagrees") | |
| selected=optimal_calibration_subfamily(m) | |
| classes=calibration_classes(m,selected) | |
| visible_q=example_point(m,"generic");visible=certify_scalar(m,visible_q) | |
| assert visible.visible | |
| algebra=TwistedAlgebra(m,visible_q);blocks=visible.full_partition(m) | |
| raw=algebra.isolated_response(blocks) | |
| assert len(blocks)==m-3 | |
| assert raw==algebra.isolated_unit(blocks)*visible.normalized_response and raw!=0 | |
| print(json.dumps({ | |
| "channels":m,"blocks":m-3,"component_count":len(all_components(m)), | |
| "components_by_kind":dict(Counter(c[0] for c in all_components(m))), | |
| "twin_visible":cert.visible,"twin_predicted_rank":rank,"twin_independent_rank":independent, | |
| "independent_rank_note":"Computed through m=8; omitted above eight because the route is exponential", | |
| "state_dimension":2**m,"selected_twin_constraints":selected,"selected_count":len(selected), | |
| "remaining_scale_classes":len(classes),"generic_witness_verified_in_original_algebra":True, | |
| "generic_witness_raw_response":str(raw), | |
| "scope":"Exact examples in the manuscript's abstract model" | |
| },indent=2)) | |
| return 0 | |
| if __name__=="__main__":raise SystemExit(main()) | |