Datasets:
Formats:
csv
Languages:
English
Size:
1K - 10K
Tags:
mathematics
inverse-problems
observability
noncommutative-algebra
symbolic-computation
calibration-rigidity
| #!/usr/bin/env python3 | |
| """Generate exact V3 data; no plotted or simulated physical measurements.""" | |
| import csv,json,sys | |
| from pathlib import Path | |
| from math import comb,ceil | |
| ROOT=Path(__file__).resolve().parents[1] | |
| sys.path.insert(0,str(ROOT/'src')) | |
| from noulith.third import (example_point,predicted_rank,direct_block_rank,optimal_calibration_subfamily, | |
| calibration_classes,certify_scalar,component_equations,all_components) | |
| from noulith.algebra import TwistedAlgebra | |
| def table(name,fields,rows): | |
| with (ROOT/'data'/name).open('w',newline='') as f: | |
| w=csv.DictWriter(f,fieldnames=fields);w.writeheader();w.writerows(rows) | |
| def main(): | |
| rows=[] | |
| for m in range(6,31): | |
| E=optimal_calibration_subfamily(m) | |
| rows.append(dict(m=m,edge_parameters=comb(m,2),star_components=m,triangle_components=comb(m,3), | |
| twin_components=comb(m,2),total_components=m+comb(m+1,3), | |
| minimum_calibration_constraints=len(E),remaining_scale_classes=len(calibration_classes(m,E)))) | |
| table('v3_component_and_budget_counts.csv',list(rows[0]),rows) | |
| kinds=['origin','star','triangle','twin','uniform_star','star_twin','edge','double_star','generic'] | |
| rows=[] | |
| for m in [6,7,8]: | |
| for kind in kinds: | |
| q=example_point(m,kind);r=direct_block_rank(m,q,m-3) | |
| assert r==predicted_rank(m,q) | |
| rows.append(dict(m=m,stratum=kind,state_dimension=2**m,rank=r,nullity=2**m-r)) | |
| table('v3_exact_rank_strata.csv',list(rows[0]),rows) | |
| components=[] | |
| for c in all_components(6): | |
| M=component_equations(6,c) | |
| components.append({'type':c[0],'labels_zero_based':c[1],'dimension':15-M.rank(), | |
| 'linear_equations_ascending_edges':[[int(x) for x in M.row(i)] for i in range(M.rows)]}) | |
| (ROOT/'data/v3_components_m6.json').write_text(json.dumps(components,indent=2)+'\n') | |
| certs=[] | |
| for kind in kinds: | |
| q=example_point(6,kind);c=certify_scalar(6,q) | |
| entry={'stratum':kind,'visible':c.visible,'motif':c.motif, | |
| 'normalized_response':str(c.normalized_response),'containing_components':c.components} | |
| if c.visible: | |
| alg=TwistedAlgebra(6,q);b=c.full_partition(6);raw=alg.isolated_response(b) | |
| assert raw==alg.isolated_unit(b)*c.normalized_response | |
| entry['raw_word_response']=str(raw);entry['partition_masks']=b | |
| certs.append(entry) | |
| (ROOT/'data/v3_visibility_certificates.json').write_text(json.dumps(certs,indent=2)+'\n') | |
| print('Generated component counts, exact rank strata, linear equations, and raw-word certificates.') | |
| if __name__=='__main__':main() | |