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4007 bytes, as of the version from 2026-10-30 06:50 (current). Recorded here, not run.
"""Read stored T616 entries and test their intervals against checked identities.
Run: sage -python readback_checks.py, with NUMBERDB_API_KEY set for draft reads.
The default reads the live database. READBACK_DOCUMENT may select a downloaded
API document for an offline repeat of exactly the same interval tests.
Requires numerical-evidence.json beside this script. All selected rows, exact
anchors, companion radius/mass/concentration relationships and the integrated
moment identity are checked. It writes no entries.
"""
import os,sys,json
from pathlib import Path
import numberdb.sage as numberdb
from sage.rings.rational_field import QQ
from sage.rings.real_mpfr import RealField
from sage.rings.real_arb import RealBallField
from sage.rings.real_mpfi import RealIntervalField
def scalar(row):
return str(row['number'] if isinstance(row,dict) else row)
def interval(text,F):
if '/' in text or ('.' not in text and 'e' not in text.lower()):
return F(QQ(text))
# Decimal spelling denotes +/- one unit in the last printed place.
if 'e' in text.lower():
mantissa,exponent=text.lower().split('e');exponent=int(exponent)
else:mantissa=text;exponent=0
places=len(mantissa.split('.')[1]) if '.' in mantissa else 0
unit=F(10)**(exponent-places)
return F(text)+F(-1,1)*unit
def contains(outer,inner):
return outer.lower() <= inner.lower() and outer.upper() >= inner.upper()
def overlaps(a,b):
return a.lower() <= b.upper() and b.lower() <= a.upper()
def main():
if os.environ.get('NUMBERDB_KEY_FROM_STDIN')=='1':
token=sys.stdin.read().strip()
if '=' in token and token.split('=',1)[0].replace('_','').isalnum():token=token.split('=',1)[1].strip().strip('\"\'')
os.environ['NUMBERDB_API_KEY']=token
root=Path(__file__).parent
if os.environ.get('READBACK_DOCUMENT'):
document=json.loads(Path(os.environ['READBACK_DOCUMENT']).read_text())
else:document=numberdb.table('T616')
rows=document['Numbers'];indices=['0','1/2','1','3/2','2','5/2','3','7/2','4','9/2']
assert list(rows)==indices
assert scalar(rows['0'])=='2/5'
evidence=json.loads((root/'numerical-evidence.json').read_text())['values']
companions={tid:numberdb.table(tid)['Numbers'] for tid in ['T613','T614','T615']}
F=RealIntervalField(850);B=RealBallField(800);out={}
for n in indices:
v=interval(scalar(rows[n]),F);e=evidence[n]['210']
x=F(e['radius']);q=F(e['mass']);J=F(e['density_moment']);H=F(e['enthalpy_moment'])
direct=2*J/(3*q*x*x);parts=F(2)/3-4*H/(q*x*x)
if n=='0':
assert contains(v,F(QQ(2)/5))
assert abs(direct-F(QQ(2)/5)).upper()<F('1e-180').lower()
assert abs(parts-F(QQ(2)/5)).upper()<F('1e-180').lower()
else:
assert contains(v,direct),(n,'direct moment outside stored interval')
assert contains(v,parts),(n,'parts identity outside stored interval')
if n=='1':
anchor=F(B(2)/3-4/B.pi()**2)
assert contains(v,anchor)
xr=interval(scalar(companions['T613'][n]),F)
mu=interval(scalar(companions['T614'][n]),F)
concentration=interval(scalar(companions['T615'][n]),F)
assert contains(xr,x) and contains(mu,q)
# Use overlap, since the companion values have independent rounding.
c= xr**3/(3*mu)
assert overlaps(c,concentration)
companion_inertia=2*J/(3*mu*xr*xr)
assert overlaps(v,companion_inertia)
assert v.lower()>0 and v.upper()<(F(2)/3).lower()
# A displaced 25-digit value must fail the 100-digit enclosure check.
assert not contains(v,direct*(1+F('1e-25')))
out[n]={'stored':scalar(rows[n]),'moment_identity':True,'companion_normalizations':True,'displaced_control_rejected':True}
print('DATA '+json.dumps({'table':'T616','skill_manifest':'agents/runs/20261030T025528Z-build-skills/manifest.json','checks':out}),flush=True)
if __name__=='__main__':main()