Could Nature Fake It?

The whole argument rests on one question: can nature — specifically, a captured primordial black hole (PBH) — produce a planet-mass black hole on a circular habitable-zone orbit that carries a moon? We answer with an expected count of natural impostors, N_nat, in a searched stellar population, summed over every capture/exchange channel we could construct.

Code

from lastmoon.naturalness import (
    GALAXY_STRESS_TEST,
    SOLAR_NEIGHBORHOOD,
    NaturalnessInputs,
    estimate_naturalness,
)

inputs = NaturalnessInputs()
for ctx in (SOLAR_NEIGHBORHOOD, GALAXY_STRESS_TEST):
    res = estimate_naturalness(inputs, ctx)
    print(f"{res.context_label}:")
    print(f"  N_nat nominal {res.n_nat_nominal:.2e}, generous {res.n_nat_high:.2e}")
    print(f"  margin to N_nat = 1 (generous): {res.margin_to_unity:.1e}x")
    for name, count in sorted(res.per_channel_nominal.items(), key=lambda kv: -kv[1]):
        print(f"    {name}: {count:.2e}")

solar_neighborhood_10pc:
  N_nat nominal 4.03e-12, generous 9.73e-09
  margin to N_nat = 1 (generous): 1.0e+08x
    C4_in_situ_capture: 4.03e-12
    C3_planet_moon_exchange: 2.85e-16
    C5_moon_acquisition: 6.55e-17
    C1_to_C3_two_step: 7.12e-20
    C1_free_capture: 0.00e+00
    C2_exchange_no_moon: 0.00e+00
galaxy_stress_test:
  N_nat nominal 1.19e-03, generous 2.87e+00
  margin to N_nat = 1 (generous): 3.5e-01x
    C4_in_situ_capture: 1.19e-03
    C3_planet_moon_exchange: 8.40e-08
    C5_moon_acquisition: 1.93e-08
    C1_to_C3_two_step: 2.10e-11
    C1_free_capture: 0.00e+00
    C2_exchange_no_moon: 0.00e+00

Even at the most generous-to-nature end of every input, the expected impostor count is computed live above — these numbers regenerate from the package on every site build, so they always match the code.

Code

import matplotlib.pyplot as plt

from lastmoon.naturalness.figure import plot_naturalness_keystone

fig = plot_naturalness_keystone()
plt.close(fig)
fig

The keystone figure: expected natural impostors vs the PBH dark-matter fraction.

Caveat: order-of-magnitude analytic estimate; ranged literature anchors; expected impostor count, not a posterior.

What this means for the paper

N_nat is reported, never asserted: the code computes an expected count with explicit, swept, literature-anchored inputs, and the count is far below one for the searched 339 systems within 10 pc (Reylé et al. 2021), but a deliberate galaxy-wide stress test reaches ~2.87 at the generous corner — crossing unity — reported honestly rather than tuned away. A detection where N_nat ≪ 1 makes the natural hypothesis unlikely; inferring deliberate engineering additionally requires a prior on planetary conversion — which the paper flags as the weakest, unquantified anchor (population-level discriminator, not individual certification).

Idealizations

Order-of-magnitude analytic channel sum with ranged inputs — not a few-body simulation. The searched population is the 339 systems within 10 pc; the Galaxy number is an explicit stress-test extrapolation.

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