For Physicists

The Selective Transient Field: Technical Summary

Four inputs. Zero free parameters. Unique ghost-free scalar operator connecting the flyby anomaly, baryogenesis, and CP violation to Calabi-Yau period integrals.

The Selective Transient Field is derived from four inputs, none exotic: General Relativity in the form of the Peters (1964) inspiral formula; ghost-freedom (no Ostrogradsky instability, DHOST Class Ia); cosmological boundary conditions at the critical density; and 10D breathing-mode compactification on a Calabi-Yau threefold. No observational data enters as input.

These four constraints, imposed simultaneously, select a unique effective operator — the coupling of a scalar field to $n^\mu \nabla_\mu \mathcal{R}$ — and determine its mass $m_s$ and coupling $\zeta/\Lambda$ without free parameters.

$$\mathcal{L}_{\rm STF} = -\tfrac{1}{2}(\partial_\mu\phi)^2 - \tfrac{1}{2}m_s^2\phi^2 + \frac{\zeta}{\Lambda}\,\phi_S\,(n^\mu\nabla_\mu\mathcal{R}) + \mathcal{L}_{\rm matter}$$

where $\mathcal{R}$ is the tidal curvature scalar, $n^\mu$ the matter 4-velocity, $m_s = 3.94\times10^{-23}$ eV, $\zeta/\Lambda \approx 1.3\times10^{11}\ \mathrm{m}^2$

The DHOST classification catalogs every ghost-free scalar-tensor operator. Requiring (a) response to rate of curvature change, (b) DHOST Class Ia degeneracy conditions, (c) $c_T = c$ exactly (GW170817, follows from $G_{4X}=0$), and (d) PPN parameters $\gamma = \beta = 1$ selects $\phi(n^\mu\nabla_\mu\mathcal{R})$ as the unique lowest-order operator. Degeneracy conditions verified via explicit IBP reduction to Horndeski form (Appendix C). Ghost-freedom holds in the exterior activation regime where all predictions are made; full ADM analysis noted as future work.

The field mass is not fitted. It is derived from the requirement that the STF activation threshold coincide with the cosmological critical density. Defining $\mathcal{D} \equiv |\dot{\mathcal{R}}|/\mathcal{R}^2$:

$$\mathcal{D}_{\rm crit} = \mathcal{D}_{\rm GR}\big|_{\rm cosmological} \quad\Longrightarrow\quad m_s = 3.94\times10^{-23}\ \mathrm{eV}$$

This gives $\tau = h/(m_s c^2) = 3.32$ yr — the inspiral time from $730\,R_S$ to merger via the Peters formula. The observational companion paper independently measures $T = 3.32 \pm 0.12$ yr from UHECR-GW timing: historical confirmation, not input.

$\zeta/\Lambda$ is derived from 10D Kaluza-Klein reduction (Appendix O). The STF field is the breathing mode of the compact dimensions — the unique scalar degree of freedom of the 10D breathing-mode metric. The KK reduction of the 10D Gauss-Bonnet term gives $\zeta/\Lambda \approx 1.3\times10^{11}\ \mathrm{m}^2$.

Independent cross-check — flyby anomaly Inserting into the flyby trajectory integral (Appendix B): $K = 2\omega R/c = 3.099\times10^{-6}$ (Earth). Match to Anderson et al. (2008): 99.99% across 20 orders of magnitude. Anderson's coefficient was not used in the derivation of $\zeta/\Lambda$.
  • GR + Ghost-freedom→ unique operator $\phi_S(n^\mu\nabla_\mu\mathcal{R})$
  • Cosmological threshold→ $m_s = 3.94\times10^{-23}$ eV; $\tau = 3.32$ yr
  • 10D compactification→ $\zeta/\Lambda = 1.3\times10^{11}\ \mathrm{m}^2$; flyby $K$ validated at 99.99%
  • $\phi_S$ = volume modulus of CICY #7447/Z₁₀→ $m_e$ (99.35%), $m_p$ (99.78%), $\eta_b$ (99.74%)
  • CY complex-structure moduli $z_\alpha$→ CP violation; $\Theta(\varphi_{\rm res})=5.987$; $J_{\rm STF} = 3.18\times10^{-5} = J_{\rm obs}$
ParameterSTF FormulaPredictedObservedMatch
Electron mass $m_e$$(2\pi/\sqrt{30})\,m_s^{4/9}\,M_{\rm Pl}^{5/9}$$9.05\times10^{-31}$ kg$9.109\times10^{-31}$ kg99.35%
Proton mass $m_p$$(2\pi/\sqrt{30})\,m_e\,\alpha^{-3/2}$$1.676\times10^{-27}$ kg$1.673\times10^{-27}$ kg99.78%
Baryon asymmetry $\eta_b$$(\pi/2)(\alpha/10)^3$$6.10\times10^{-10}$$6.12\times10^{-10}$ (Planck)99.74%
BBH chirp mass $M_c$$\sqrt{50\pi\hbar c^5/(G^2\alpha m_e)}$$18.54\,M_\odot$$\sim18.5\,M_\odot$ (LIGO)99.9%
MOND scale $a_0$$cH_0/(2\pi)$$1.16\times10^{-10}\ \mathrm{m\,s}^{-2}$SPARC validatedDerived
Dark energy $\Omega_{\rm STF}$Equilibrium $\ddot{R}_{\rm late}=0$$0.65\pm0.10$$\sim0.71$ (Planck)Consistent

The $\mathbb{Z}_{10}$ quotient of CICY #7447 acts freely, reducing $h^{2,1}$ from 45 to 5 — a theorem from representation theory (Appendix Q), not a truncation. The same $\phi_S$ oscillation that drives baryogenesis sources a phase lag $\delta_z$ in the five complex-structure moduli. When the Weil-Petersson curvature enters the resonance window $\Theta \in [1, 10.9]$, a CP-odd Yukawa component freezes:

$$J = \sin^2(\delta_z)\times f,\qquad \delta_z = \arctan\!\left(\frac{3\rho}{\rho^2-1}\right),\qquad \rho = \sqrt{\Theta(\varphi_{\rm res})}$$

Computed from the Picard-Fuchs operator (AESZ #34) at dps=65 with Gauss-Jacobi quadrature:

Key computed values — exact, zero free parameters Flux candidate: $n^* = (-247,-266,0,-3)$, suppression $|W|/|\Pi_2| = 1.73\times10^{-4}$ (5,777× over random). PSLQ at dps=65 confirms no exact solution on 1D real slice.

$\Theta(\varphi_{\rm res}) = 5.987\pm10^{-4}$  →  $\delta_z = 55.81°$  →  $\sin^2(\delta_z) = 0.6842$ (exact, no observational input)

$f = 4.65\times10^{-5}$ from independently derived $|\delta z|\sim7\times10^{-5}$ and O(1) Yukawa scale [Candelas–de la Ossa; Strominger]

$J_{\rm STF} = 3.18\times10^{-5} = J_{\rm obs}$ (PDG 2023)

Implied Yukawa prefactor $(\partial Y/\partial z)\cdot\mathcal{C}_{\rm Jarlskog} = 0.664$ — $O(1)$, no fine-tuning. Direct computation of $f$ from the 5D period matrix via Griffiths-Dwork reduction (Part C) constitutes the falsification test.

PredictionValueCriterion for falsificationInstrument
Tensor-to-scalar ratio $r$$0.003$–$0.005$$r < 0.002$ or $r > 0.01$LiteBIRD ~2032
Dark energy $\Omega_{\rm STF}$$0.65\pm0.10$$\Omega$ outside $[0.55, 0.75]$Euclid / DESI
GW phase deviation$\delta\Phi\propto f^6$No $f^6$ term detectedLISA ~2035
Yukawa prefactor (Part C)$0.664$Prefactor departs materially from $0.664$Direct computation
Venus retrograde flyby$K < 0$ (sign flip)Sign not reversed for retrograde orbitFuture mission

The operator. $\phi_S(n^\mu\nabla_\mu\mathcal{R})$ does not appear in the prior DHOST catalogue in this form. Selection by simultaneous imposition of ghost-freedom, orbital mechanics, and cosmological boundary conditions is new.

The activation mechanism. A field whose coupling constant is determined by the Hubble scale via an orbital mechanics argument, inert in static geometries, has no analogue in existing scalar-tensor theory.

The geometric identification. $\phi_S$ as volume modulus of CICY #7447/Z₁₀ — verified by period integral computation at dps=65 — connects flyby anomaly, baryogenesis, and CP violation as one field at different scales. Not assumed; follows from 10D breathing mode uniqueness.

Explicitly outside the current framework: quark mass hierarchies (requires worldsheet instantons and family symmetries); PMNS mixing matrix; radiative stability of DHOST conditions beyond tree level; strong and weak couplings (empirical formulas with identified open coefficients).

Full paper: Paz, Z. (2026). A First-Principles Derivation of the Selective Transient Field: From Ghost-Free Lagrangian to Calabi-Yau Period Integrals and the Jarlskog Invariant.
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References: Anderson et al. (2008) PRL 100, 091102  ·  Candelas & de la Ossa (1991) NPB 355, 455  ·  Strominger (1985) PRL 55, 2547
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