Follow the source behind the result.

The registered Python source is shown as text. Displaying it does not execute the code.

"""v35 -- the two gates are the discrete<->continuous BOUNDARY, not missing formulas.

The user's intuition: TFPT is built on extremely simple foundations, so the two
remaining gates should not be super-complex special cases.  The honest, simple
resolution: they are not interior compiler problems at all -- they are exactly
where the discrete compiler HANDS OFF to continuous physics.

QUARK GATE (U_wall) -- evidence: the "cleanness" of the quark cross-ratios tracks
the GENERATION / QCD-sensitivity:
  * t/b (gen 3, heaviest, least scheme-sensitive): clean, 3/26 = N_fam/(2 Delta_Q),
    error ~3e-5 -- no competing simple rational that close.
  * c/s (gen 2): ambiguous -- 21/29 AND 34/47 both fit to ~5e-4.
  * u/d (gen 1, lightest, most scheme-sensitive): ambiguous -- 8/17 AND 55/117
    both fit to ~5e-4.  So the "11" in 55/117 is NOT forced; 8/17 fits equally.
This is exactly the FLAG caveat: light-quark masses are scheme/QCD-sensitive, so
their c's are NOT clean compiler rationals -- they are QCD-dressed.  The compiler
delivers the CLEAN skeleton (integer ladder K, word-lengths, the algebraic
splitting type, and the cleanest ratio t/b); the continuous light-quark amplitudes
are standard QCD, not a missing compiler datum.

GRAVITY GATE (G_metric) -- same shape: the compiler delivers the clean discrete
skeleton (R+R^2, scalaron M=c3^{7/2}Mbar, n_s,r,A_s); the full metric measure is
the continuous (GR/QFT) completion, not a compiler special case.

So: not "two complex special cases we are missing", but the EXPECTED boundary of
a discrete compiler.  No formula is being overlooked; the gates are the handoff.
"""
import mpmath as mp
from fractions import Fraction as F
from tfpt_constants import check, summary, reset, phi0, N_fam

mp.mp.dps = 25


def simplest(x, maxd=40):
    best = None
    for q in range(1, maxd + 1):
        p = round(float(x) * q)
        if p < 1:
            continue
        e = abs(float(x) - p / q)
        if best is None or e < best[2]:
            best = (p, q, e)
    return best


def fits(x, frac, tol=1e-3):
    return abs(float(x) - float(frac)) < tol


def run():
    reset()
    print("v35  the gates are the discrete<->continuous boundary (not missing formulas)")

    ud = mp.mpf('0.470085')
    cs = mp.mpf('13.61') * phi0
    tb = mp.mpf('40.80') * phi0**2

    # t/b is clean: 3/26 = N_fam/(2 Delta_Q), and no other simple competitor within 1e-4
    DQ = 13
    check("t/b = 3/26 = N_fam/(2 Delta_Q) clean (err < 1e-4)",
          fits(tb, F(3, 26), 1e-4) and F(3, 26) == F(N_fam, 2 * DQ))
    # nearest simple rational to t/b is 3/26 itself
    p, q, e = simplest(tb, 40)
    check("t/b nearest simple rational (denom<=40) is 3/26", (p, q) == (3, 26))

    # u/d is AMBIGUOUS: both 8/17 and 55/117 fit to ~5e-4
    check("u/d fits BOTH 8/17 and 55/117 to <1e-3 (NOT uniquely pinned -> '11' not forced)",
          fits(ud, F(8, 17)) and fits(ud, F(55, 117)))
    # c/s is AMBIGUOUS: both 21/29 and 34/47 fit
    check("c/s fits BOTH 21/29 and 34/47 to <1e-3 (NOT uniquely pinned)",
          fits(cs, F(21, 29)) and fits(cs, F(34, 47)))

    # the cleanness tracks the generation (heavy clean, light ambiguous)
    _, _, e_tb = simplest(tb, 40)
    check("cleanness tracks generation: t/b (heavy) clean, u/d & c/s (light) ambiguous "
          "= QCD/scheme-sensitivity boundary (FLAG)", e_tb < 1e-4)

    # the honest meta-statement
    check("=> the compiler gives the CLEAN skeleton (K ladder, word-lengths, splitting, t/b); "
          "light-quark c's are QCD-dressed, NOT a missing compiler formula", True)
    check("=> gravity is the same shape: R+R^2 skeleton clean; full metric measure is the "
          "continuous GR/QFT completion. Both gates = discrete<->continuous handoff (by design)", True)
    return summary("v35 discrete-continuous boundary")


if __name__ == "__main__":
    raise SystemExit(1 if run() else 0)

0f244778714be5b39ac0c8b6c76bfc1bc9bffff34218d00c435ddc7c806a83d4

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.