String theory and the spectral-fractal framework grow from the same root: physical reality is encoded in a spectrum of vibrational modes, and particles are stable resonances. This paper maps the two paths that diverge from this common origin, point by point, across 14 physical domains. The bifurcation occurs at a single question: vibrations of what, in what? String theory answers: vibrations of extended 1D objects in 10/11-dimensional spacetime, with extra dimensions compactified on Calabi-Yau manifolds. The spectral-fractal framework answers: vibrations of a temporal flow rate field τ (x) in 4D spacetime, organized by a fractal tower with scaling √2. The first path achieves quantum gravitational consistency at the cost of extra dimensions, supersymmetry, and a landscape of ~10⁵⁰⁰ vacua with no unique predictions. The second achieves gravitational emergence, UV regularization, and mass hierarchy resolution at the cost of not yet having a quantum gravity completion at Planck scale. A structural dictionary compares how each framework addresses gravity (graviton vs exact GR on the stabilized branch, with τ-gradient as heuristic on the non-constant branch), UV regularization (string length vs convergent tower Σ2⁻ⁿ), mass hierarchy (compactification vs 113 √2-levels), confinement (AdS/CFT vs τ-gradient flux tubes), dark energy (landscape vs frozen texture modes with wDE ≈ −1), inflation (moduli inflaton vs τ-gradient dynamics), dark matter (unspecified vs Chronostasis profile tested on 50 SPARC galaxies), entanglement (ER=EPR vs NSTB), cosmogenesis (ekpyrotic vs fractal rebound), biology (no coverage vs ATP synthase, LHCII, β-sheets), and number theory (limited Langlands vs Weil formula as trace formula specialization). Each entry references a dedicated companion paper with full derivations and DOI. Convergence points — where both frameworks arrive at the same result via different mechanisms — include glueball mass ratios (~√2, matching lattice QCD data from 1999), emergent gravity (both reduce to Einstein gravity in the appropriate limit), UV finiteness (different geometric mechanisms, same result), and trace formulas bridging arithmetic and physics. These convergences suggest both paths capture genuine structure. Divergence points include the graviton (string requires it; the spectral-fractal framework has none by design), extra dimensions (required for anomaly cancellation in string; the constraint does not apply without strings), supersymmetry (required for string stability; unnecessary with fractal convergence), and predictive uniqueness (landscape vs one Lagrangian with five free parameters and a structural closure hypothesis selecting √2). Open issues are documented for both frameworks. The testability asymmetry is the most consequential difference: the spectral-fractal framework has 6 predictions testable within 5–15 years (CMB log-periodic modulation, glueball √2 ratio, Mercury precession correction, dark energy equation of state — quintessence-like, in tension with DESI phantom-like best fit, cristae morphometry, protein PDB analysis), while string theory's predictions (KK towers, superpartners, cosmic strings) have been searched for and not found. The √2 constant is selected by theoretical constraints (noncollision, binary compatibility, Newtonian recovery, convergence, stability) — not by data fitting. An honest null result is documented: √2 is not empirically preferred in SPARC rotation curve free-ratio fits. This paper is cartography, not polemic: two paths from the same trailhead, mapped side by side. The data will arbitrate.
Thierry Marechal (Fri,) studied this question.