Paper Review — Claim-Level

Direct answer: No source in the supplied evidence reports survival fractions of Earth-analogue planets in binaries from an N-body grid, so the number cannot be stated from data — it must be produced by a new simulation. The literature provided only establishes the ingredients: (1) binaries are dynamically hostile zones whose stability depends on separation and mass ratio (the 1974 premise, now known to be an over-generalization since planets do form and survive in binaries); (2) post-formation N-body evolution over 100 Myr preserves most planets in isolated systems but reshapes eccentricities — the same machinery needed for the binary grid; (3) modern N-body/TTV pipelines (jnkepler, SPOCK, exoplanet in JAX) are the validated toolchain for such experiments Kumar 1974 binary-rarity argument 100 Myr N-body survival synthesis Modern N-body/SPOCK toolchain

Grid design (BGPT plan, explicitly simulated/inferred — not observed data)

• Grid axes: binary semi-major axis a_bin = 10–1000 AU (log-spaced, 12 points) × binary eccentricity e_bin = 0–0.9 (10 points); fixed solar-type primary (1 M☉), mass ratio q = 0.5 and 1.0 sub-grids.
• Planet: 1 M☉ analogue at 1 AU (S-type orbit), 5° mutual inclination; 10 random phase seeds per cell for statistics.
• Integrator: REBOUND WHFast/IAS15 or MERCURY, 10 Gyr (with 100 Myr quick-screen); ejection, stellar collision, or crossing of the Mardling–Aitford-style critical radius counted as death.
• Expected analytic first-cut (illustrative, computed from the empirical stability boundary, shown below as a simulated curve — NOT observational data): survival ≈ 1 for a_bin above a few × the critical periastron ratio (~3:1 outer-to-inner periastron), collapsing sharply as a_bin shrinks or e_bin grows.

Curve is a BGPT parametrized expectation around the empirical critical periastron boundary; it must be replaced by the actual N-body histogram output of the grid.

Confidence note: high confidence that the empirical answer is absent from supplied sources and that the toolchain above is the validated route; the plotted fractions are assumptions to be falsified by the run.