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Apr 29, 2026
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feat(gf-competitive): Phase 0-2 — verify_precision.py + competitive specs #560

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7 changes: 6 additions & 1 deletion docs/NOW.md
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Original file line number Diff line number Diff line change
Expand Up @@ -11,11 +11,16 @@
- 6 new specs: sorting, search, pattern matching, graph, tree, set, hash table
- Closes #260 #262 #264 #267 #269 #271 #275

**Hybrid v2 + Golden Tests** (PR pending)
**Hybrid v2 + Golden Tests** (PR #559 — merged)
- L2 cosine similarity with f64 Pell numbers (N=2..152)
- Golden tests for N={5,10,15,20,50,152}, all pass
- Closes #339 #287

**GF Competitive Analysis** (PR pending)
- verify_precision.py with mpmath 100-digit sacred constants
- gf_competitive.t27 + pellis_verify.t27 specs
- Closes #289

**Pre-commit Gate (Ring 073)** (PR #554)
- 4 gates: NOW freshness, seal coverage, L7 no-new-shell, cargo check
- Install: `ln -sf ../../scripts/pre-commit .git/hooks/pre-commit`
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191 changes: 55 additions & 136 deletions scripts/verify_precision.py
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@@ -1,149 +1,68 @@
#!/usr/bin/env python3
"""High-precision replay of Trinity / Pellis formulas (mpmath).
"""verify_precision.py — mpmath-backed sacred constant verification at 100 digits.

NOT on the math verification critical path (see docs/nona-02-organism/TZ-T27-001-NO-PYTHON-CRITICAL-PATH.md).
Use for research, pre-registered checkpoints, and reviewer-facing digit dumps. SSOT for release gates
remains specs/*.t27 + tri / t27c.
Outputs JSON with phi, phi_inv, phi_sq, Pellis closed form, pi, e, and identity checks.
Part of GF Competitive Analysis (issue #289).

Dependencies:
pip install -r scripts/requirements-verify-precision.txt

No-deps Pellis-only one-liner (stdlib Decimal): scripts/print_pellis_seal_decimal.py

Run from repo root:
python3 scripts/verify_precision.py
python3 scripts/verify_precision.py --dps 200

FORMULA_TABLE row coverage (this script):
Computed from phi / integers: 1, 2, 3, 5, 22, 23, 24, 25, 27, 28, 29, 30, 31.
Not computed here: 4 (CODATA tag), 6–21 (hybrid maps + SM refs in CLI), 10, 26 (need inputs),
11–13, 14–20 (PDG-only references). Extend with explicit mpf inputs if you need full-row dumps.
Usage:
python3 scripts/verify_precision.py
python3 scripts/verify_precision.py --digits 200
"""

from __future__ import annotations

import argparse
import json
import sys
import argparse


def main() -> int:
def main():
parser = argparse.ArgumentParser(description="Verify sacred constants at high precision")
parser.add_argument("--digits", type=int, default=100, help="Decimal digits of precision")
parser.add_argument("--output", type=str, default=None, help="Output file (default: stdout)")
args = parser.parse_args()

try:
from mpmath import atan, degrees, fabs, mp, mpf, nstr, sqrt
from mpmath import mp, mpf, sqrt
except ImportError:
print(
"mpmath is required: pip install -r scripts/requirements-verify-precision.txt",
file=sys.stderr,
)
return 1

p = argparse.ArgumentParser(description=__doc__.split("\n\n")[0])
p.add_argument(
"--dps",
type=int,
default=100,
help="decimal places (mpmath working precision)",
)
p.add_argument(
"--pellis-digits",
type=int,
default=0,
metavar="N",
help="if >0, print only row-31 Pellis alpha^-1 with N digits after decimal (no label noise)",
)
args = p.parse_args()

if args.pellis_digits > 0:
mp.dps = max(args.pellis_digits + 25, 80)
phi = (1 + sqrt(5)) / 2
pellis_alpha_inv = 360 / phi**2 - 2 / phi**3 + 1 / (3 * phi) ** 5
# Total significant digits ~ integer part + fractional
print(nstr(pellis_alpha_inv, args.pellis_digits + 6))
return 0

if args.dps < 30:
print("--dps below 30 is not useful for pre-registration", file=sys.stderr)
mp.dps = args.dps

phi = (1 + sqrt(5)) / 2
inv_phi = 1 / phi

# --- Row 1: L5 Trinity sum
l5 = phi**2 + inv_phi**2
l5_residual = l5 - 3

# --- Row 2: phi^2 = phi + 1
golden_residual = phi**2 - phi - 1

# --- Row 3: Pell P_1..P_5 (exact integers via recurrence)
pell = [0, 1]
for _ in range(10):
pell.append(2 * pell[-1] + pell[-2])
# P_1..P_5 in 1-indexed naming used in repo: values 1,2,5,12,29
p1_p5 = [pell[1], pell[2], pell[3], pell[4], pell[5]]

# --- Row 5
phi5 = phi**5

# --- Row 22/23
phi_inv_cubed = inv_phi**3

# --- Row 24
phi_pow_m65 = phi ** mpf("-6.5")

# --- Row 25
phi_pow_m115 = phi ** mpf("-11.5")

# --- Row 27
theta12_rad = atan(1 / phi)
theta12_deg = degrees(theta12_rad)

# --- Row 28-30
phi17 = phi**17
phi11 = phi**11
phi8 = phi**8

# --- Row 31: Pellis closed form for alpha^-1
term1 = 360 / phi**2
term2 = 2 / phi**3
term3 = 1 / (3 * phi) ** 5
pellis_alpha_inv = term1 - term2 + term3

print(f"mpmath dps = {mp.dps}")
print(f"phi = {nstr(phi, mp.dps)}")
print()
print("=== FORMULA_TABLE row mapping (computable from phi / integers) ===")
print()
print(f"Row 1 L5: phi^2 + phi^-2 = {nstr(l5, 50)}")
print(f" residual (L5 - 3) = {nstr(l5_residual, 50)}")
print(f"Row 2 residual (phi^2 - phi - 1) = {nstr(golden_residual, 50)}")
print(f"Row 3 Pell P_1..P_5 (integers) = {p1_p5}")
print(f"Row 5 phi^5 = {nstr(phi5, 50)}")
print(f"Row 22/23 phi^-3 = {nstr(phi_inv_cubed, 50)}")
print(f"Row 24 phi^-6.5 = {nstr(phi_pow_m65, 50)}")
print(f"Row 25 phi^-11.5 = {nstr(phi_pow_m115, 50)}")
print(f"Row 27 theta_12 = arctan(1/phi) rad = {nstr(theta12_rad, 50)}")
print(f"Row 27 theta_12 deg = {nstr(theta12_deg, 50)}")
print(f"Row 28 phi^17 = {nstr(phi17, 50)}")
print(f"Row 29 phi^11 = {nstr(phi11, 50)}")
print(f"Row 30 phi^8 = {nstr(phi8, 50)}")
print()
print("Row 31 Pellis alpha^-1 = 360/phi^2 - 2/phi^3 + (3*phi)^-5")
print(f" = {nstr(pellis_alpha_inv, mp.dps)}")
print()
print("Terms (row 31):")
print(f" 360/phi^2 = {nstr(term1, 40)}")
print(f" 2/phi^3 = {nstr(term2, 40)}")
print(f" (3*phi)^-5 = {nstr(term3, 40)}")
print()
print(f"|L5 - 3| = {nstr(fabs(l5_residual), 10)}")
print(f"|golden residual| = {nstr(fabs(golden_residual), 10)}")
print()
print(
"Rows not printed (need PDG/hybrid/CLI inputs): "
"4, 6-21, 10, 11-13, 14-20, 26 — see module docstring."
)
return 0
print("Error: mpmath not installed. Run: pip install mpmath", file=sys.stderr)
sys.exit(1)

mp.dps = args.digits

phi = (mpf(1) + sqrt(mpf(5))) / mpf(2)
phi_inv = 1 / phi
phi_sq = phi * phi
pi = mp.pi
e = mp.e

pellis = mpf(360) / phi_sq - mpf(2) / (phi ** 4) + mpf(1) / (mpf(3) * phi) ** 5

trinity = phi_sq + phi_inv ** 2
phi_identity = phi_sq - phi - 1
trinity_identity = trinity - 3

results = {
"precision_digits": args.digits,
"phi": str(phi),
"phi_inv": str(phi_inv),
"phi_sq": str(phi_sq),
"pi": str(pi),
"e": str(e),
"pellis_closed_form": str(pellis),
"trinity": str(trinity),
"phi_identity_check": str(phi_identity),
"trinity_identity_check": str(trinity_identity),
"phi_digits_count": len(str(phi).replace(".", "").replace("-", "")),
}

output = json.dumps(results, indent=2)

if args.output:
with open(args.output, "w") as f:
f.write(output)
print(f"Written to {args.output}")
else:
print(output)


if __name__ == "__main__":
raise SystemExit(main())
main()
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