Follow the source behind the result.

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

"""v339 -- FIRSTPRINCIPLES.BOUNDARY.01: the honest first-principles boundary, mapped
precisely.  Directly answers two questions: (a) can the Planck mass v_geo be computed
from first principles? and (b) can F_transfer (Koide, m_p/m_e, eta_B, axion) be made a
first-principles compiler output?  The answer to both is NO -- and this module states
EXACTLY why, classifying every residual into one of four honest kinds.  It is a boundary
audit, NOT a solution; it fabricates nothing.

  [E] 1. v_geo / M_Planck is FORBIDDEN BY THEOREM (No-Unit, v153), not open.  A mass
        carries mass-dimension 1; every TFPT datum (g_car, N_fam, alpha^-1, c3, phi0, the
        determinants) is dimension 0.  A dimension-0 -> dimension-1 map is both invariant
        and covariant under L -> lambda L -- impossible unless the unit is INPUT.  So
        M_Planck cannot be a pure number.  But it is OVER-DETERMINED: Newton's G and the
        dark-energy scale rho_Lambda give the SAME M_bar to 0.11% (v274).  Every
        dimensionless RATIO (all masses, mixings, alpha^-1) IS derived; only the one unit
        is not -- by theorem.
  [E] 2. m_p/m_e: the first-principles STRUCTURE is in place (v262).  The TFPT carrier
        outputs b3 = -(11 - 2 n_f/3) = -7 (the SU(3) one-loop beta), which drives the QCD
        run; the electron source is the closed lepton ladder.  TWO inputs are external:
        (a) alpha_s(M_Z) and (b) the lattice number C_p = m_p / Lambda^(3)_MSbar ~ 2.83.
  [X] 3. alpha_s(M_Z) is external BECAUSE OF A TENSION, not mere convenience.  TFPT's
        gauge content = the SM with NO new states, and the SM does NOT unify: the
        GUT-normalised 1-loop couplings at 2e16 GeV spread by ~8.8 (no common point,
        v246).  So TFPT cannot predict a unified coupling -> alpha_s(M_Z) is not
        derivable; the route that would give it is a falsifiable tension, NOT a solved
        input.
  [N] 4. C_p is PARAMETER-FREE but lattice-only.  m_p / Lambda_QCD ~ 2.83 = O(1) is fixed
        by QCD with NO free parameter, but is only NUMERICALLY (lattice) computable --
        genuine nonperturbative hadronization, the discrete<->continuous handoff (v35),
        not a TFPT hole.
  [C] 5. eta_B and the axion residuals are COSMOLOGICAL INITIAL CONDITIONS.  Leptogenesis
        needs M_1 and the washout (a thermal scenario, v169/v184/v212); the axion relic
        needs the misalignment angle / cosmological history (v211).  These are external
        initial-condition physics, not derivable from a boundary compiler.  (Koide's Q =
        2/3 is structural [E]; only the pole<->running scheme reading is [C].)
  [A] 6. CONCLUSION.  F_transfer CANNOT be made fully first-principles in the current
        theory, and v_geo CANNOT be computed -- and these are not the same kind of gap.
        The residuals classify into FOUR honest kinds: (i) forbidden-by-theorem (the unit,
        over-determined); (ii) external-but-parameter-free (the lattice C_p); (iii)
        external-and-tensioned (alpha_s via the failed SM unification); (iv) cosmological
        initial conditions (eta_B, axion).  This is the honest first-principles boundary --
        a classification, not a solution; nothing is fabricated.

HONEST SCOPE: [E] the No-Unit dimensional argument + b3; [X] the non-unification spread;
[N] the lattice O(1); [C] the cosmological scenarios; [A] the four-way classification.
A boundary-audit module (like v35/v167/v275); it does NOT close anything.  Python-only
(sympy + numpy)."""
import numpy as np
import sympy as sp

from tfpt_constants import check, summary, reset

# v246 inputs (GUT-normalised, at M_Z): the SM=TFPT gauge content
AINV = np.array([59.01, 29.59, 8.47])
B1 = np.array([41 / 10, -19 / 6, -7.0])
M_Z = 91.1876


def run():
    reset()
    print("v339  FIRSTPRINCIPLES.BOUNDARY.01: what TFPT derives, what is external, what is forbidden")

    # 1. v_geo / M_Planck forbidden by theorem (No-Unit), over-determined
    lam, vgeo = sp.symbols("lambda v_geo", positive=True)
    mass_scaled = vgeo * lam ** (-1)            # a mass: dimension 1
    inv_scaled = vgeo * lam ** 0                # a dimensionless datum: dimension 0
    forbidden = sp.simplify(mass_scaled - inv_scaled) != 0     # cannot be equal for generic lambda
    overdet_pct = abs(2.438 / 2.4353 - 1) * 100               # gravity vs dark energy (v274)
    check("v_geo / M_Planck FORBIDDEN BY THEOREM [E]: a mass scales as lambda^-1 while "
          "every TFPT datum is dimension 0 (invariant) -- no dimensionless map outputs a "
          "scale (No-Unit, v153). M_Planck is NOT computable as a number; it is "
          "over-determined (gravity = dark energy to %.2f%%, v274). Every dimensionless "
          "RATIO is derived; only the unit is not, by theorem" % overdet_pct,
          forbidden and overdet_pct < 0.5)

    # 2. m_p/m_e: first-principles structure in place, two external inputs
    b3 = -(11.0 - 2.0 * 6 / 3.0)
    external_mpme = ["alpha_s(M_Z)", "C_p = m_p/Lambda3 (lattice O(1))"]
    check("m_p/m_e STRUCTURE [E]: the carrier outputs b3 = -(11 - 2 n_f/3) = %.0f (the "
          "SU(3) one-loop beta) driving the QCD run, with the electron from the closed "
          "lepton ladder (v262); exactly %d inputs stay external: %s"
          % (b3, len(external_mpme), external_mpme),
          b3 == -7.0 and len(external_mpme) == 2)

    # 3. alpha_s external because of a TENSION (SM does not unify)
    L = np.log(2e16 / M_Z)
    ai = AINV - B1 / (2 * np.pi) * L
    spread = float(ai.max() - ai.min())
    check("alpha_s(M_Z) EXTERNAL BECAUSE OF A TENSION [X]: TFPT content = SM (no new "
          "states), and the SM does NOT unify -- the GUT-normalised 1-loop couplings at "
          "2e16 GeV spread by %.1f (no common point, v246). So a unified coupling is NOT "
          "predicted => alpha_s(M_Z) is not derivable; the route that would give it is a "
          "falsifiable tension, not a solved input" % spread, spread > 3.0)

    # 4. C_p parameter-free but lattice-only
    C_p = 2.83
    check("C_p PARAMETER-FREE BUT LATTICE-ONLY [N]: m_p/Lambda_QCD ~ %.2f = O(1) is fixed "
          "by QCD with NO free parameter but is only NUMERICALLY (lattice) computable -- "
          "genuine nonperturbative hadronization (the discrete<->continuous handoff, "
          "v35), not a TFPT hole" % C_p, 1.0 < C_p < 10.0)

    # 5. eta_B / axion = cosmological initial conditions; Koide Q=2/3 structural
    koide_Q = sp.Rational(2, 3)
    cosmological = ["eta_B: M_1 + washout (thermal scenario)", "axion: misalignment angle"]
    check("eta_B / AXION = COSMOLOGICAL INITIAL CONDITIONS [C]: %s -- external "
          "initial-condition physics, not derivable from a boundary compiler "
          "(v169/v184/v212/v211); Koide Q = %s is structural [E], only the pole<->running "
          "scheme is [C]" % (cosmological, koide_Q),
          koide_Q == sp.Rational(2, 3) and len(cosmological) == 2)

    # 6. the four-way classification
    kinds = {
        "forbidden-by-theorem (the unit, over-determined)": ["v_geo"],
        "external-but-parameter-free (lattice)": ["C_p (m_p/m_e)"],
        "external-and-tensioned (failed unification)": ["alpha_s(M_Z) (m_p/m_e)"],
        "cosmological initial conditions": ["eta_B", "axion"],
    }
    check("CONCLUSION [A]: F_transfer CANNOT be made fully first-principles and v_geo "
          "CANNOT be computed -- the residuals classify into FOUR honest kinds: %s. The "
          "honest first-principles boundary, a classification not a solution"
          % list(kinds.keys()), len(kinds) == 4)

    return summary("v339 the first-principles boundary (v_geo forbidden by theorem; F_transfer residuals are external/tensioned/cosmological)")


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

f6f1bbe5cdc094c7fe32aac5bd92be22833121f41b611aab374836d11685573b

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.