#!/usr/bin/env python3
"""Create and actually execute a small self-contained demonstration notebook."""
from __future__ import annotations
import json
import time
from pathlib import Path
import nbformat as nbf
from nbclient import NotebookClient

ROOT=Path(__file__).resolve().parents[1]


def main() -> None:
    nb=nbf.v4.new_notebook()
    nb.metadata.kernelspec={'display_name':'Python 3','language':'python','name':'python3'}
    md=nbf.v4.new_markdown_cell; code=nbf.v4.new_code_cell
    nb.cells=[
      md('# AELYRION–NOÛLITH III: retained foundations walkthrough\n\nThis notebook executes finite examples from the manuscript. It does not certify all-size theorems or worldwide originality. All algebraic outputs below are exact.'),
      code('''from pathlib import Path
import sys
root=Path.cwd()
if not (root/'src').exists():
    root=root.parent
assert (root/'src'/'noulith').exists(), "Run from the package or notebooks directory."
sys.path.insert(0,str(root/'src'))
import sympy as sp
from noulith import TwistedAlgebra
from noulith.ideals import universal_algebra,equal_polynomial_ideals
from noulith.protocols import ideal_generators,root_profile,normalized_measurement_matrix
from noulith.geometry import resonance_group,flat_edge,line_arrangement_generators,branch_carriers,perfect_slice_matrix
sp.init_printing()
a,b=sp.symbols('a b')'''),
      md('## 1. Two analytically inequivalent three-channel observations\n\nThe penultimate block ideal realizes $(a^2,b^2)$ or $(a^2,ab,b^2)$. Their arc orders agree, but only the second synthesizes the target $ab$ analytically.'),
      code('''J=universal_algebra([a**2,b**2],m=3)
K=universal_algebra([a**2,b**2,a*b],m=3)
PJ,PK=J.shuffle_table(),K.shuffle_table()
GJ=ideal_generators(PJ,7,2)
GK=ideal_generators(PK,7,2)
assert equal_polynomial_ideals(GJ,[a*a,b*b],(a,b))
assert equal_polynomial_ideals(GK,[a*a,a*b,b*b],(a,b))
remainder_J=sp.groebner(GJ,a,b).reduce(a*b)[1]
remainder_K=sp.groebner(GK,a,b).reduce(a*b)[1]
assert remainder_J==a*b and remainder_K==0
{'target_remainder_for_J':remainder_J,'target_remainder_for_K':remainder_K}'''),
      md('## 2. Triangle cancellation forces a known formal-group law\n\nThe new candidate is its role in the observation ideal, not the formal-group operation itself.'),
      code('''x,y,z=sp.symbols('x y z')
F=resonance_group
assert sp.cancel(F(F(x,y),z)-F(x,F(y,z)))==0
A,B,C=sp.symbols('A B C')
triple=TwistedAlgebra(3,{(0,1):-1+A,(0,2):-1+B,(1,2):-1+C}).shuffle_table()[7]
assert sp.cancel(triple.subs(B,F(A,C)))==0
{'triple_shuffle':sp.factor(triple),'law':F(x,y),'flat_edge':flat_edge(x,y)}'''),
      md('## 3. A known elliptic singularity and its gluing carriers\n\nAfter the logarithmic coordinate change the scalar critical curve is three axes and one diagonal, not the full-state rank-failure set. This is the known elliptic four-fold point, credited to Smyth and Stevens in the manuscript; its discovery is not claimed.'),
      code('''variables=(x,y,z)
relations=line_arrangement_generators(variables)
assert equal_polynomial_ideals(relations,[x*y-x*z,x*y-y*z],variables)
carriers=branch_carriers(variables)
t=sp.symbols('t')
branches=[(t,0,0),(0,t,0),(0,0,t),(t,t,t)]
R=sp.Matrix([[sp.expand(f.subs(dict(zip(variables,branch)),simultaneous=True)) for f in carriers] for branch in branches])
assert R==t*t*sp.eye(4)
{'relations':relations,'branch_carriers':carriers,'restriction_matrix':R,'slice_pairing':perfect_slice_matrix(3)}'''),
      md('## 4. Full four-channel rank strata from actual matrices'),
      code('''from itertools import combinations
pairs=list(combinations(range(4),2))
def actual_rank(f):
    model=TwistedAlgebra(4,{p:-1+f.get(p,0) for p in pairs})
    return normalized_measurement_matrix(model.shuffle_table(),2).rank()
zero={p:sp.S.Zero for p in pairs}
star=zero | {(0,1):sp.Rational(1,20),(0,2):sp.Rational(2,20),(0,3):sp.Rational(3,20)}
outlier=zero | {p:sp.Rational(1,20) for p in pairs if 0 in p}
two=zero | {(0,1):sp.Rational(1,20)}
generic={p:sp.Rational(i+1,100) for i,p in enumerate(pairs)}
ranks=[actual_rank(f) for f in (generic,star,outlier,two,zero)]
assert ranks==[16,15,14,14,11]
dict(zip(['generic','single_star','outlier','two_stars','origin'],ranks))'''),
      md('## 5. Root-of-unity block budgets\n\nThese exact exponents concern the specified transverse detuning, not arbitrary multivariate perturbations.'),
      code('''profiles={r:[root_profile(d,r,3) for d in range(13)] for r in range(1,5)}
assert profiles[1][6]==2 and profiles[2][6]==1 and profiles[3][6]==0
profiles'''),
      md('## Scope\n\nThe formal group, quantum complete intersections, local ideals, Fitting invariants, and Smith theory have established antecedents. The package proposes their exact restricted-observation integration and proves the stated results within its hypotheses. No hardware, empirical performance, or independent priority certification is supplied.')
    ]
    start=time.perf_counter()
    NotebookClient(nb,timeout=120,kernel_name='python3',resources={'metadata':{'path':str(ROOT)}}).execute()
    path=ROOT/'notebooks'/'01_exact_walkthrough.ipynb'
    nbf.write(nb,path)
    code_cells=[c for c in nb.cells if c.cell_type=='code']
    errors=[o for c in code_cells for o in c.get('outputs',[]) if o.get('output_type')=='error']
    report={'notebook':str(path.relative_to(ROOT)),'executed_code_cells':len(code_cells),
        'errors':len(errors),'elapsed_seconds':round(time.perf_counter()-start,3)}
    (ROOT/'validation/notebook_report.json').write_text(json.dumps(report,indent=2)+'\n')
    if errors: raise SystemExit('Notebook execution reported errors.')
    print(f'Executed {len(code_cells)} notebook code cells without errors.')

if __name__=='__main__': main()