The Worlds Surveys Don’t See

1Motivation

Nearly 6,000 exoplanets are confirmed, and most were found the same way: a planet crossed the face of its star and dimmed it for a few hours. The transit method is spectacularly productive and spectacularly biased. It requires an orbital plane aligned with our line of sight — a coin-flip a planet at 1 AU around a Sun-like star wins less than half a percent of the time — and it favors big planets on short orbits around quiet, bright stars. The catalog we reason from is not the population that exists; it is the population that geometry and noise let through.

Astronomers correct for this with completeness models fitted to each survey. exoverse takes the complementary route: build the underlying population first. If you can generate stellar systems that are physically self-consistent and statistically faithful to known occurrence rates, you can push them through modeled instruments and watch the selection function act on individual worlds — not as an abstract correction factor, but as a named planet, with a mass and a sky position, that a given telescope does or does not see.

2Goals and approach

The project has three standing goals:

• Generate plausible planetary systems from physics upward — a Kroupa mass function for the stars, disk-structure distances normalized to the real local density, main-sequence scaling relations, occurrence-shaped periods and radii (including the Fulton radius valley), probabilistic mass–radius relations, orbital-stability screening, stellar noise, atmosphere assignment, and per-planet reflected-light albedos.
• Observe every world with modeled instruments spanning past, present, and future: Kepler (archival), TESS, JWST transit spectroscopy, ground-based 1-m surveys, the Roman Space Telescope’s bulge survey, and the Habitable Worlds Observatory’s coronagraphic imaging.
• Validate the generator against reality — running real cataloged planets through the same physical-validity rules, and comparing the synthetic detectable population against the real detected one with the selection forward-modeled.

Three design commitments shape everything. First, plausibility is first-class output: every approximation carries a severity-graded flag. Hard physics violations (denser than pure iron, above the deuterium-burning mass limit, dynamically unstable pairs) are rejected and resampled; questionable-but-possible regimes are kept and labeled, because “plausible but uncertain” is exactly where the interesting science lives. Second, every world is reproducible: a system regenerates bit-for-bit from its random seed, so light curves are never stored — they are re-derived on demand. Third, the database is the product: over a million systems, each individually inspectable through a CLI and a web interface, with full metadata down to limb-darkening coefficients, per-planet albedos, and cloud-suppression factors.

2.1  Two populations, calibrated to the real sky

How many systems should a 300 pc population contain? Anchoring the local density on the RECONS 10 pc census and Gaia’s Catalogue of Nearby Stars (0.065 main-sequence systems per pc³) and letting density fall off vertically with the thin disk’s ~300 pc scale height, the answer is ≈5.2 million — the earlier 100,000-system run sampled just 2% of them. Version 0.3 therefore (a) replaces the uniform-density distance draw with the disk-structure one, (b) grows the main population tenfold to 1,000,000 systems — a 19% random sample of reality, and a bit-exact prefix of a future full 5.2-million run, since seeds form a stream — and (c) reports in every stats output what fraction of reality a population represents.

The companion population goes further: within 30 pc the same density model expects 7,083 systems, so the neighborhood dataset is generated at exactly that count. It is a 1:1 analog of the real solar neighborhood — when the modeled Habitable Worlds Observatory images 19 exo-Earth candidates there, that number is an absolute yield estimate, no scaling required.

3The generative model

This section specifies the model at the level a collaborator would need to audit it: every distribution, threshold, and instrument assumption behind the numbers in §4–§5. The generator is ~2,900 lines of core Python (NumPy for the physics, SQLite for persistence), organized as a pipeline — star → planets → dynamical stability → geometry → stellar noise → atmospheres → observatories — in which each stage consumes draws from a single per-system random stream (§3.8). No parameter below was tuned to produce the findings; each traces either to the cited literature or to a named calibration choice, and the flag framework (§3.3) records where the model stands on thin ice. Generation runs at ~2,000 fully validated systems per second on a laptop, so the million-system population regenerates in about nine minutes.

3.1  Stars and the local density normalization

Host masses follow the Kroupa (2001) broken power-law initial mass function, dN/dM ∝ M^−1.3 below 0.5 M_☉ and M^−2.3 above it, sampled by analytic inverse-CDF over 0.08–2.2 M_☉. The truncation is a deliberate scope choice — transit surveys overwhelmingly target FGKM dwarfs, and more massive stars are rare, short-lived, and poor transit hosts — recorded as an INFO flag on every star. Luminosity and radius come from piecewise main-sequence scaling relations, L/L_☉ = 0.23 M^2.3 (M < 0.43), M^4.0 (0.43 ≤ M < 2.0), 1.4 M^3.5 above, and R/R_☉ = M^0.9 below 1 M_☉, M^0.6 above — each with lognormal scatter (10% in L, 5% in R) standing in for age and metallicity spread. Effective temperature follows from the Stefan–Boltzmann law; main-sequence lifetime is t_MS ≈ 10 (M/L) Gyr, with age drawn uniformly on [0.5, min(12, t_MS)] Gyr and stars in the last 10% of their lifetime flagged QUESTIONABLE (turnoff radius inflation is not modeled). Metallicity is the local thin-disk distribution, [Fe/H] ~ N(−0.1, 0.2) clipped to [−1.0, +0.5] (Hayden et al. 2015).

Observables are derived, not drawn: bolometric magnitude from L; V-band bolometric corrections from the Flower (1996) polynomials with the Torres (2010) coefficient corrections (Sun: BC_V ≈ −0.07, test-enforced); TESS-band and J magnitudes via V−I_c and V−J colors interpolated on the Pecaut & Mamajek (2013) dwarf sequence (±0.1 mag class accuracy, INFO-flagged); and quadratic limb-darkening coefficients (u₁, u₂) as a coarse fit in T_eff to the Claret & Bloemen (2011) Kepler-band tabulations.

Distances are where the synthetic universe is pinned to the real one. Systems are placed with uniform density in the Galactic plane and an exponential vertical falloff exp(−|z|/h) with scale height h = 300 pc, observer at the midplane. Averaging that profile over spheres gives a closed-form cumulative count,

The absolute normalization n₀ = 0.065 main-sequence systems per pc³ is anchored on the RECONS 10 pc census (Henry et al. 2018) and the Gaia Catalogue of Nearby Stars (Gaia Collaboration 2021), and is uncertain at the ±20% level. It implies ≈5.20 million systems within 300 pc and 7,083 within 30 pc — the numbers that make the two populations of §2.1 a 19% sample and a 1:1 analog of reality, respectively. Each star consumes exactly one uniform draw for distance, inverted through this CDF by bisection; capping the volume at a different d_max therefore reshapes only the distance (and apparent magnitudes), never the rest of the random stream.

3.2  Planetary systems: occurrence, masses, orbits

Each star targets a truncated-Poisson number of planets (mean 2.2, maximum 7; cf. Zhu et al. 2018), with candidate periods drawn by accept–reject so that occurrence rises as dN/dlnP ∝ P^1.5 inside 10 days and is flat per log-interval from 10 to 640 days (Petigura et al. 2013); candidates closer than a period ratio of 1.2 to an existing planet are rediscarded before any physics is drawn.

Small-planet radii are a bimodal lognormal mixture — 45% super-Earths centered at 1.3 R_⊕ (σ_ln = 0.20) and 55% sub-Neptunes at 2.4 R_⊕ (σ_ln = 0.25) — producing the photoevaporation valley near 1.9 R_⊕ (Fulton et al. 2017), with the whole branch sliding as (P/10 d)^−0.05 so the valley moves to smaller radii at longer periods, in the spirit of the measured slope (Van Eylen et al. 2018). A planet is instead drawn on the giant branch with probability p = 0.10 · 10^1.2[Fe/H] · min(M_★/M_☉, 1.5), clipped to [0.005, 0.30] — the Fischer & Valenti (2005) metallicity correlation with a stellar-mass factor. Giant radii sit on a lognormal plateau near 1 R_Jup (σ_ln = 0.12) with an empirical irradiation-inflation factor of up to ~1.6 switched on above T_eq = 1000 K.

Masses follow probabilistic mass–radius relations in the spirit of Chen & Kipping (2017) and Wolfgang et al. (2016): rocky (R < 1.6 R_⊕) M = R^3.7 with 25% lognormal scatter; volatile-rich (1.6–8 R_⊕) M = 2.7 R^1.3 with 35–40% scatter; giants get masses drawn nearly independently of radius (the degenerate-EOS plateau), lognormal around 0.9 M_Jup and clipped at 15 M_Jup so the deuterium-burning rule of §3.3 can act. Eccentricities distinguish architecture: single planets draw from the Kipping (2013) Beta(0.867, 3.03) distribution, while members of multis draw from a dynamically cold Rayleigh(0.05), matching the observed single–multi eccentricity dichotomy (Xie et al. 2016). Each system takes one isotropic plane orientation (uniform in cos i), and each planet a Rayleigh(1.5°) mutual inclination about it with random sign (Fabrycky et al. 2014). Inclinations are deliberately not reflected into [0°, 90°]: values beyond 90° are geometrically equivalent mirror transits, and clipping them would pile impact parameters up at b = 0.

Equilibrium temperature assumes albedo 0.3 with full heat redistribution; insolation is L/a² in Earth units. Habitable-zone membership uses the conservative (runaway-greenhouse to maximum-greenhouse) limits in a simplified Kopparapu et al. (2013) form — effective fluxes 1.11 and 0.36 with mild T_eff corrections — which places the Sun’s conservative zone at 0.95–1.67 AU (test-enforced to contain Earth).

3.3  Hard validity rules and the plausibility ladder

Plausibility is enforced by rejection sampling against typed, severity-graded rules. INVALID means the draw violates physics or a robust empirical limit: the generator resamples, and no INVALID object ever reaches the database (asserted by the test suite). QUESTIONABLE means allowed-but-weakly-modeled: the object is kept and the doubt is stored as a queryable flag with a literature citation. INFO records honest scope simplifications. The hard rules:

The Hill separation uses Δ = (a_out − a_in)/R_H with R_H = [(m_in+m_out)/3M_★]^1/3 (a_in+a_out)/2. Pairs with Δ ∈ [2√3, 9) survive but are flagged QUESTIONABLE, since Gyr survival of packed multis typically requires Δ ≳ 9–12 (Pu & Wu 2015). Other QUESTIONABLE regimes — kept because “plausible but uncertain” is product, not error — include super-puff densities (0.03–0.1 g cm⁻³, cf. Kepler-51), inflated giants without strong irradiation, hot-Neptune-desert occupants (P < 1 d, R > 2 R_⊕; Mazeh et al. 2016), giants around late M dwarfs (the GJ 3512 b regime), rocky planets above 10 M_⊕ (mega-Earths), ultra-hot atmospheres (T_eq > 2500 K), near-turnoff hosts, and metal-poor hosts. Every flag is a row in a queryable table keyed by a dotted rule id, so “show me all super-puffs” is a one-line SQL query.

3.4  Stellar photometric noise

Every star carries an astrophysical noise state, because detectability against a quiet photon budget is the wrong question for most real stars. Four components are modeled, each reduced to its effective white-noise contribution on a transit-depth measurement of duration T₁₄: granulation, anchored at the solar ~40 ppm per hour and scaled as (ν_max,☉/ν_max)^0.6 with ν_max ∝ g/√T_eff (Kallinger et al. 2014), averaging down slowly (∝ T₁₄^−0.35) because it is correlated; p-mode oscillations at 3 ppm (L/M)^0.9 (Kjeldsen & Bedding 1995), incoherent over hours and averaging as white noise; rotational spot variability, with rotation from gyrochronology (P_rot = 24.5 d · √(age/4.57 Gyr) · M^−0.6), an activity index declining as exp(−age/τ) where τ = 1, 2.5, and 5 Gyr for earlier-than-K, early-M, and fully convective stars respectively (M dwarfs stay active longer), and variability semi-amplitudes spanning the quiet-Sun ~300 ppm to the ~20,000 ppm of young active stars (McQuillan et al. 2014) — of which the residual trend over one transit window plus a 5% spot-crossing term contaminate the depth; and flares, an extra stochastic term for active stars below 0.5 M_☉.

Spots and flares are contrast effects and weaken toward the red: each observatory band applies a chromatic factor of 1.0 (blue optical / Kepler), 0.75 (TESS), or 0.40 (JWST/Roman near-IR), following Rackham et al. (2018). The total noise on any transit measurement is then σ_tot² = σ_instr²/T₁₄ + σ_★² — stellar noise enters every observatory’s budget in quadrature, and it is why bright-but-active hosts can be worse targets than fainter quiet ones. The coefficients are population-level Kepler calibrations: adequate for demographics, not for fitting any individual star (an explicit limitation, §6).

3.5  Atmospheres and per-planet albedos

Atmosphere class follows bulk properties plus an escape criterion. Giants and Neptunians keep primary H/He envelopes (μ = 2.3); sub-Neptunes split by bulk density into H/He-rich (ρ < 2 g cm⁻³, μ = 3.5) and steam worlds (μ = 18) — a genuinely degenerate call, flagged as such. Rocky planets face the cosmic shoreline (Zahnle & Catling 2017): an atmosphere survives when the received insolation stays below

Retained rocky atmospheres are secondary CO₂/N₂ (μ = 33); stripped ones are airless. Rocky planets around M dwarfs are flagged QUESTIONABLE either way — whether they hold atmospheres at all is exactly what JWST is currently testing on TRAPPIST-1. Transmission signals use the scale height H = kT_eq/(μm_Hg): one scale height subtends δ_1H = 2HR_p/R_★², a feature spans two scale heights, and a cloud/haze suppression factor drawn uniformly on [0.15, 1.0] is applied — clouds being the dominant, and genuinely unpredictable, uncertainty. TSM and ESM follow Kempton et al. (2018, eqs. 1 and 4) with the published per-radius-bin scale factors. JWST feature detectability converts each instrument’s white-light precision into an effective per-feature noise via a √5 penalty (features are fit across the full band, not read off one spectral bin; the value is calibrated so K2-18 b-class targets need ~2–3 transits, matching published results), adds a stellar-contamination floor proportional to the host’s variability amplitude (the transit-light-source effect of Rackham et al. 2018), and reports transits-to-5σ, with >25 scored impractical.

For reflected-light imaging, every planet draws a V-band geometric albedo from class- and temperature-dependent distributions spanning the measured range — a factor of ~20, where the classic yield-study convention is a flat 0.2:

The draw consumes exactly two random deviates for every class (a branch selector and a scatter deviate), preserving the stream layout that determinism requires. Albedos are stored per planet and used directly by the HWO model of §3.7; §5.4 quantifies how much they matter.

3.6  Transit geometry and light curves

Geometry follows Winn (2010) throughout, including full eccentricity corrections: the impact parameter is b = (a/R_★) cos i · (1−e²)/(1+e sin ω), a planet transits when |b| < 1+k (with k = R_p/R_★), the a-priori transit probability carries the same eccentricity factor, and the T₁₄/T₂₃ durations use Winn’s eqs. 14–16. The light-curve model integrates the quadratic limb-darkening law I(μ) = 1 − u₁(1−μ) − u₂(1−μ)² over annuli spanning only the radial band [z−k, z+k] the planet actually covers, so fractional accuracy is independent of planet size — a fixed whole-disk grid, the obvious implementation, was measured to err by ~20% for Earth-size planets and rejected. Against the analytic uniform-source depth the integrator is exact to ~10⁻¹³ at mid-transit and better than 10⁻⁴ along the chord, and the limb-darkened depth is internally converged at the sub-ppm level — equivalent to the Mandel & Agol (2002) model, with no external dependencies.

3.7  Observatory models and detection rules

Every transiting planet is scored against six transit instruments, and every planet — transiting or not — against HWO imaging. Transit noise budgets combine the instrument precision scaled to the transit duration with the star’s astrophysical noise in the appropriate band (§3.4); folded surveys multiply the per-transit SNR by √N_transits over the mission baseline and duty cycle.

(⊕ denotes addition in quadrature.) The HWO model computes each planet’s reflected contrast at quadrature from its own stored albedo,

Two honesty clauses attach to the future instruments. Roman’s survey points at ~2 deg² of Galactic bulge while our systems are local, so every Roman row answers the counterfactual “if this system sat in a Roman field” — flagged in the observation note. And the HWO detection rule has no integration-time budget: a planet outside the working angles or below the floor is undetectable at any exposure, but a planet above both is scored detected regardless of how long that detection would take. That asymmetry is why §5.4 finds yields geometry-limited — and why those results speak to detectability, not survey scheduling. Both models are requirement-era and expected to drift; the project maintains dated, sourced assumption logs per instrument (docs/OBSERVATORIES.md).

3.8  Determinism, reproducibility, and tests

One system is one seed: all draws — star, planets, stability retries, inclinations, noise state, atmospheres, albedos — come in fixed order from a single numpy PCG64 stream, so a stored world regenerates bit-for-bit from its (seed, name) pair. Light curves are therefore never stored; the CLI and the web interface re-simulate them on demand and are guaranteed the identical world. Population seeds come from a SeedSequence stream, which makes any N-system population an exact prefix of every larger run: the million-system population is bit-for-bit the first million systems of the eventual full-reality run (N = 5,199,422). The distance cap consumes exactly one draw and the albedo exactly two per planet, preserving stream alignment across model variants.

The test suite pins the physics to known values rather than to itself: the Sun’s bolometric correction (−0.07), Earth’s transit depth and duration across the Sun (84 ppm, ~13 h) and its geometric transit probability (<1%), Jupiter’s ~1% depth, the conservative habitable zone containing Earth, Venus–Earth dynamical separation (Δ > 25 mutual Hill radii), GJ 1214 b-class TSM values, and an Earth twin’s HWO contrast at 10 pc. A pipeline test asserts the INVALID invariant end-to-end: no hard-rule violator is ever persisted.

4Validation against the real catalog

Before trusting conclusions from synthetic worlds, the generator is audited against 8,240 confirmed planets (snapshot of 2026-07-02; NASA Exoplanet Archive TAP when healthy, The Extrasolar Planets Encyclopaedia as automatic fallback, provenance recorded in the snapshot). The audit runs in both directions: real planets are pushed through exoverse’s physical-validity rules, and the synthetic detectable population is compared against real transit discoveries.

The rule audit asks a falsifiable question: would our INVALID rules reject real planets? A generator whose validity rules exclude confirmed worlds has wrong rules. Catalog data are noisy in specific, known ways, so the audit filters for evidential strength before charging a violation: mass rules consider only transiting planets whose masses are measured at >2σ (M sin i lower limits cannot prove a deuterium-limit violation, and the fallback catalog silently mixes upper limits into its mass column — the provenance filter catches both).

No real planet violates a rule for a reason the generator can’t account for — the two nonzero rows are known catalog artifacts, and their rates are stable from the 10,000-system era through 1,000,000. The deuterium-limit violators are the familiar transiting brown dwarfs (the CoRoT-3 b / KELT-1 b class) that catalogs file alongside planets and exoverse excludes by definition; the iron-limit violators are planets whose low-SNR masses scatter above the physical bound.

The population comparison is deliberately selection-matched: raw synthetic worlds must never be compared against a raw catalog, because the catalog is the output of survey filters the raw population has not passed. Instead, synthetic planets are filtered to those detectable by the modeled Kepler — the deepest long-baseline instrument modeled, hence the best analog of the real transit census — and compared against real transit-discovered planets:

One statistical note at this scale: with 25,000 detections, KS p-values collapse to zero for even trivial differences, so the D statistic — not p — is the meaningful health metric. The regression watchlist is specific: a period-D drift means the occurrence shaping broke; a synthetic radius median drifting off ~0.31 dex means the radius valley or mass–radius relations broke. A third validation axis — system-level architecture, where disagreement is the point — is deferred to §5.5, where the synthetic population serves as an explicit null model.

5Findings

5.1  Scale makes rare regimes measurable

At a million systems, regimes that were statistical noise at 10,000 are now populations in their own right: 6,787 ultra-short-period planets, 390 mega-Earths, 188 ultra-hot worlds, and 37 super-puffs exist in queryable numbers, each with named, inspectable members. Detection counts continue to scale linearly with population size, and the Kepler-detectable radius median sits at 0.31 dex on a 25,121-planet detected sample. (The v0.3 physics changes — disk-structure distances and per-planet albedos — regenerated every world; within v0.3, the million systems are a bit-exact prefix of any future, larger run.)

5.2  Transit surveys are blind to 99% of habitable-zone rocky worlds

Figure 2 states the project’s central result at population scale. The transit method’s geometric filter removes 99.0% of habitable-zone rocky planets before noise or cadence even enter the picture, and instrument thresholds remove a further sliver. Statements like “transit probability is low” are textbook; what a synthetic population adds is the ability to hold the missing 170,000 worlds in a database — each with a name, a host star, an atmosphere class, and the specific reason it was missed. And because the population is now normalized to the real stellar density, the statement extends to the sky itself: within 300 pc of the Sun, the model implies roughly 900,000 habitable-zone rocky planets exist, of which transit geometry offers up fewer than 9,000.

5.3  An exo-Earth budget for the Habitable Worlds Observatory

HWO — NASA’s planned flagship for the 2040s — will not use transits at all. It will directly image reflected starlight, and its Astro2020 charge is to characterize at least 25 potentially habitable exo-Earths (National Academies 2021). exoverse models it with a coronagraphic contrast floor of 3×10⁻¹¹ that degrades photon-limited for hosts fainter than V≈7, working angles of 60–500 mas, and reflected-light contrast computed from each planet’s own geometric albedo. Where v0.2 assigned one fixed albedo per atmosphere class, v0.3 draws A_g per planet from temperature-dependent distributions spanning the measured range: clear alkali-absorbing hot Jupiters are nearly black (the Kepler/CHEOPS population sits at 0.03–0.11, TrES-2b below 0.04), cold ammonia-cloud giants reflect ~0.5, secondary atmospheres center on Earth’s re-measured 0.24 with a 22% Venus-like branch near 0.65, and cold airless worlds get an icy-bright branch (Europa-class). The classic yield-study convention is a flat 0.2 for everything; the real range spans a factor of ~20.

In the 7,083-system population — a 1:1 analog of the real solar neighborhood — HWO images 209 planets. Crucially, 19 of them are exo-Earth candidates — habitable-zone planets of 0.8–1.4 Earth radii. Because the population is no longer an arbitrary sample size, that count needs no scaling: it is the model’s yield estimate, and it lands just below the mission’s ≥25 goal from independent physics, with no tuning toward that number. The shortfall itself is informative, as §5.4 shows: the yield is sitting on the steep part of the inner-working-angle curve.

The loss accounting explains why M dwarfs — the most common stars — contribute nothing: their habitable zones are angularly too small to resolve and their photospheres too faint to post-process against, a conclusion that emerges here from the noise model rather than from an imposed target list. The per-planet albedo leaves its own fingerprint: only 3 of 400 airless worlds are ever imaged, while cloudy steam and secondary-atmosphere worlds dominate the detections (183 of 209) — and Venus-branch cloud decks are over-represented among the imaged secondaries (27%, against 22% in the population), the reflected-light analog of a selection effect.

5.4  The exo-Earth yield is an inner-working-angle problem

Because every planet’s contrast and separation are stored, HWO’s three design levers — inner working angle, post-processed contrast floor, and host-brightness envelope — can be swept over the same 1:1 neighborhood. The result is one-sided: over the plausible trade space, the yield responds only to the working angle. Deepening the contrast floor threefold (3×10⁻¹¹ → 1×10⁻¹¹) adds zero candidates; relaxing the host limit from V < 11 to 12.5 adds zero (the fainter hosts’ habitable zones are unresolvable anyway — those two loss modes are the same stars); and the detected planets clear the floor by a median factor of 12. But every milliarcsecond of working angle opens new K-dwarf habitable zones: 60 → 45 mas takes the yield from 19 to 48, and 30 mas reaches 99.

The same sweep quantifies the albedo question this version set out to test: replacing every drawn albedo with the conventional flat A_g = 0.2 changes the exo-Earth count by zero at every working angle, and the total imaged count by 1% (207 vs 209). Within this model’s envelope, reflected-light detectability is geometry-limited for any A_g ≳ 0.15 — albedo uncertainty instead moves each target’s contrast margin, i.e. how characterizable it is once found. The widened albedo range matters most at the bright end (Venus-branch worlds at 3–4× the contrast of an Earth twin) and for the darkest hot giants, which drop out entirely.

5.5  What the real sky has that the null universe lacks

exoverse deliberately omits formation and migration physics: radii are drawn independently within a system, spacings are shaped only by stability, and nothing depletes the hot-Neptune desert. That makes the synthetic detected population a null model — identical selection, no formation memory — so differences from the real detected population isolate astrophysics that selection cannot explain. Four architecture metrics, computed on 25,121 synthetic Kepler detections against 4,800 real transit discoveries:

Two of these are known results reproduced against a cleaner null — that is the tool working as intended. The third is the outside-the-box dividend: because the null has no formation correlations, it shows the “Kepler dichotomy” and “peas-in-a-pod” are not independent observations — a population with correlated sizes and no extra inclination component would already shift the singles ratio in the observed direction. Disentangling the two requires exactly the kind of joint forward model this population provides.

That disentangling has since been carried out: a DR25-conditioned decomposition study — the same generator run through the real Kepler target list over a grid of size-correlation (σ_R) and inclination-dispersion (σ_i) architectures — shows the two effects decouple cleanly under DR25 conditioning. The dominant population is consistent with coplanarity (σ_i ≤ 0.44° at 95%), sibling radii are strongly correlated (ρ ≈ 0.29), and a small dynamically hot fraction (f_hot ≈ 0.1) remains statistically required. Full methods and results are in paper/dichotomy_section.md.

6Limitations and model scope

Every simplification below is deliberate, documented at the object level by an INFO or QUESTIONABLE flag where applicable, and listed here so a reader can judge which conclusions it could touch.

• Single main-sequence stars only. No binaries (~45% of FGK stars have companions), no evolved hosts. Population counts are counts of single-MS-primary systems; the density normalization is defined consistently (systems, not stars).
• Occurrence distributions are literature-shaped parametric forms, not fits to the Kepler/TESS posterior samples. The known consequence visible in §4: the intrinsic small-planet radius distribution is bimodal but its valley is smeared rather than a resolved dip — the top candidate physics fix. Giant occurrence is metallicity- and mass-scaled but not period-structured (no three-day pileup).
• No formation or migration physics, by design. Radii are independent within a system, spacing is shaped only by stability, and the hot-Neptune desert is flagged, not depleted. This is what makes the §5.5 null model clean — but it means intra-system correlations must not be read off the synthetic population, only measured against it.
• Dynamics is Hill-spacing screening, not N-body integration. No mean-motion resonances, no transit-timing variations; ≥5-planet systems carry a standing QUESTIONABLE flag for exactly this reason.
• Stellar noise coefficients are population-level Kepler calibrations — order-of-magnitude per star, sound in aggregate. Instrument systematics are white-noise floors; red noise and window functions are not modeled, which flatters ground-based and single-sector recoveries slightly.
• Atmosphere classes are probabilistic assignments over genuinely degenerate bulk compositions (each carries its flag), and spectroscopy scoring is a calibrated scale-height heuristic, not radiative transfer. Steam-world albedos are unmeasured guesses spanning a plausible range.
• The density normalization is ±20% (RECONS vs GCNS anchoring), the thin disk is a single exponential (no thick-disk component, ~10% locally; the Sun’s ~20 pc midplane offset is ignored), and distances are floored at 5 pc. Absolute counts — including the 19-exo-Earth yield — inherit that envelope.
• Roman and HWO are requirement-era models and will drift. Roman rows are bulge counterfactuals for local systems; the HWO detection rule has no integration-time budget, no exozodiacal-dust term, and no multi-visit scheduling — its yields are detectability ceilings, not survey simulations. Assumptions and their research dates are logged per instrument in docs/OBSERVATORIES.md.

7Future directions

The findings above are demonstrations of an instrument — a population you can point at questions. Below are the directions where that instrument appears most valuable to the wider community, based on a survey of current literature.

7.1  Yield forecasting for missions now launching

ESA’s PLATO launches in late 2026, and yield studies built on population synthesis are already shaping its strategy — recent work forward-models ~13,000 expected detections across the Galactic thin disk, thick disk, and halo (Boettner et al. 2024). Roman’s bulge survey is predicted to find 60,000–200,000 transiting planets via pixel-level simulation (Wilson et al. 2023). exoverse’s contribution to this class of work is speed and inspectability: at ~2,000 fully-validated systems per second, survey trade studies (cadence, baseline, magnitude limits) can be re-run interactively, with every gained or lost detection traceable to a specific named world.

7.2  HWO target selection and design trades

The HWO community is actively assembling prioritized target lists — the 2025 Target Stars and Systems catalog (Tuchow et al. 2025), the ExEP Mission Star List (NASA ExEP 2023), and new stellar-activity catalogs aimed squarely at reducing yield uncertainty. Published yield analyses identify the occurrence rate of Earth-like planets (η_⊕) and exozodiacal dust as the dominant unknowns, and ask which design changes would protect the 25-exo-Earth goal (Dietrich et al. 2026). A synthetic neighborhood population complements this directly — and §5.4 now delivers the first such trade quantitatively: over this model’s envelope the exo-Earth yield responds only to inner working angle, crossing the 25-planet goal between 60 and 45 mas. The natural next refinements are an integration-time budget (where albedo and contrast margin buy survey efficiency rather than detectability), exozodi levels, and multi-visit scheduling — each one grafts onto the same stored per-planet contrasts and separations.

7.3  Demographic inference and η_⊕

Occurrence-rate studies must invert the selection function to recover the true population from the observed one. A generative population where the truth is known by construction is the natural test harness for those inversion methods: inject a synthetic universe, apply a modeled survey, hand the “detections” to an occurrence-rate pipeline, and check whether it recovers the input. This closed-loop validation is difficult with real data — the answer is unknown — and is a standing gap the community fills with per-survey injection–recovery exercises that don’t transfer between instruments. The absolute density normalization added in v0.3 strengthens this use: occurrence rates inferred from the modeled surveys can now be compared against the generator’s truth in physical units (planets per star, planets per pc³), not just in shape. The architecture null model of §5.5 extends the same idea to system-level statistics — any inference method that claims to measure mutual inclinations or intra-system correlations can be handed the null universe first, where the right answer is “none.”

7.4  Training corpora for machine-learning detection

Deep-learning vetting models now routinely triage transit candidates at ~97% precision, and several groups report that models trained on combined real and synthetic light curves outperform those trained on real data alone (Lo & Lo 2025; Cuéllar et al. 2022). exoverse generates limb-darkened light curves with realistic stellar noise (granulation, spots, flares) and perfect ground-truth labels — including the hard negatives that matter: grazing transits, active hosts, and depths straddling detection thresholds. A pipeline exporting labeled light-curve corpora would be a small extension with a direct user base.

7.5  An open, explorable universe

Because every world is individually inspectable — with plausibility flags that say why a value is uncertain and citations for every approximation — the database doubles as a teaching instrument for selection effects, observational bias, and instrument design. Deploying the read-only web interface publicly, alongside downloadable populations, is the lowest-effort path to community use. On the modeling roadmap: N-body verification of tightly-packed systems, binary hosts, transit-timing variations, and radiative-transfer spectra to replace scale-height heuristics.

8References

• Boettner, C., Viswanathan, A., & Dayal, P. 2024, Exoplanets across Galactic stellar populations with PLATO, A&A 692, A150.
• Chen, J., & Kipping, D. M. 2017, Probabilistic forecasting of the masses and radii of other worlds, ApJ 834, 17.
• Claret, A., & Bloemen, S. 2011, Gravity and limb-darkening coefficients for the Kepler, CoRoT, Spitzer, uvby, UBVRIJHK, and Sloan photometric systems, A&A 529, A75.
• Cuéllar, S., et al. 2022, Deep learning exoplanet detection by combining real and synthetic data, PLOS ONE 17, e0268199.
• Dietrich, J., Ruppert, K., Ware, A., & Young, P. A. 2026, Predictive rankings of the probability for temperate terrestrial worlds for the HWO ExEP Mission Star List, arXiv:2606.04105.
• Fabrycky, D. C., et al. 2014, Architecture of Kepler’s multi-transiting systems. II. New investigations with twice as many candidates, ApJ 790, 146.
• Fischer, D. A., & Valenti, J. 2005, The planet–metallicity correlation, ApJ 622, 1102.
• Flower, P. J. 1996, Transformations from theoretical Hertzsprung–Russell diagrams to color–magnitude diagrams, ApJ 469, 355.
• Fulton, B. J., et al. 2017, The California-Kepler Survey. III. A gap in the radius distribution of small planets, AJ 154, 109.
• Gaia Collaboration (Smart, R. L., et al.) 2021, Gaia Early Data Release 3: The Gaia Catalogue of Nearby Stars, A&A 649, A6.
• Gladman, B. 1993, Dynamics of systems of two close planets, Icarus 106, 247.
• Hayden, M. R., et al. 2015, Chemical cartography with APOGEE: metallicity distribution functions and the chemical structure of the Milky Way disk, ApJ 808, 132.
• Henry, T. J., et al. 2018, The Solar Neighborhood XLIV: RECONS discoveries within 10 parsecs, AJ 155, 265.
• Kallinger, T., et al. 2014, The connection between stellar granulation and oscillation as seen by the Kepler mission, A&A 570, A41.
• Kempton, E. M.-R., et al. 2018, A framework for prioritizing the TESS planetary candidates most amenable to atmospheric characterization, PASP 130, 114401.
• Kipping, D. M. 2013, Parametrizing the exoplanet eccentricity distribution with the Beta distribution, MNRAS 434, L51.
• Kjeldsen, H., & Bedding, T. R. 1995, Amplitudes of stellar oscillations: the implications for asteroseismology, A&A 293, 87.
• Kopparapu, R. K., et al. 2013, Habitable zones around main-sequence stars: new estimates, ApJ 765, 131.
• Kroupa, P. 2001, On the variation of the initial mass function, MNRAS 322, 231.
• Lo, E., & Lo, D. C. 2025, Exoplanet detection using machine learning models trained on synthetic light curves, arXiv:2507.19520.
• Mandel, K., & Agol, E. 2002, Analytic light curves for planetary transit searches, ApJ 580, L171.
• Mazeh, T., Holczer, T., & Faigler, S. 2016, Dearth of short-period Neptunian exoplanets: a desert in period–mass and period–radius planes, A&A 589, A75.
• McQuillan, A., Mazeh, T., & Aigrain, S. 2014, Rotation periods of 34,030 Kepler main-sequence stars, ApJS 211, 24.
• NASA Exoplanet Exploration Program 2023, ExEP Mission Star List for the Habitable Worlds Observatory.
• National Academies of Sciences, Engineering, and Medicine 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s (the Astro2020 decadal survey).
• Pecaut, M. J., & Mamajek, E. E. 2013, Intrinsic colors, temperatures, and bolometric corrections of pre-main-sequence stars, ApJS 208, 9.
• Petigura, E. A., Howard, A. W., & Marcy, G. W. 2013, Prevalence of Earth-size planets orbiting Sun-like stars, PNAS 110, 19273.
• Pu, B., & Wu, Y. 2015, Spacing of Kepler planets: sculpting by dynamical instability, ApJ 807, 44.
• Rackham, B. V., Apai, D., & Giampapa, M. S. 2018, The transit light source effect: false spectral features and incorrect densities for M-dwarf transiting planets, ApJ 853, 122.
• Stassun, K. G., et al. 2018, The TESS Input Catalog and Candidate Target List, AJ 156, 102.
• Sudarsky, D., Burrows, A., & Pinto, P. 2000, Albedo and reflection spectra of extrasolar giant planets, ApJ 538, 885.
• Torres, G. 2010, On the use of empirical bolometric corrections for stars, AJ 140, 1158.
• Tuchow, N. W., Harada, C. K., Mamajek, E. E., et al. 2025, HWO Target Stars and Systems: a prioritized community list of potential stellar targets for the Habitable Worlds Observatory’s exo-Earth survey, arXiv:2509.20544.
• Van Eylen, V., et al. 2018, An asteroseismic view of the radius valley: stripped cores, not born rocky, MNRAS 479, 4786.
• Weiss, L. M., et al. 2018, The California-Kepler Survey. V. Peas in a pod: planets in a Kepler multi-planet system are similar in size and regularly spaced, AJ 155, 48.
• Wilson, R. F., et al. 2023, Transiting exoplanet yields for the Roman Galactic Bulge Time Domain Survey predicted from pixel-level simulations, ApJS 269, 5.
• Winn, J. N. 2010, Transits and occultations, in Exoplanets, ed. S. Seager (Univ. Arizona Press).
• Wolfgang, A., Rogers, L. A., & Ford, E. B. 2016, Probabilistic mass–radius relationships for sub-Neptune-sized planets, ApJ 825, 19.
• Xie, J.-W., et al. 2016, Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis, PNAS 113, 11431.
• Zahnle, K. J., & Catling, D. C. 2017, The cosmic shoreline: the evidence that escape determines which planets have atmospheres, and what this may mean for Proxima Centauri b, ApJ 843, 122.
• Zeng, L., Sasselov, D. D., & Jacobsen, S. B. 2016, Mass–radius relation for rocky planets based on PREM, ApJ 819, 127.
• Zhu, W., Petrovich, C., Wu, Y., Dong, S., & Xie, J. 2018, About 30% of Sun-like stars have Kepler-like planetary systems: a study of their intrinsic architecture, ApJ 860, 101.

Full modeling assumptions, sources, and volatility notes for each observatory — including which numbers are requirement-era and expected to change — are maintained in the project’s docs/OBSERVATORIES.md. Populations regenerate deterministically: exoverse generate --n 1000000 --seed 42 reproduces every world in this paper bit-for-bit (and --n 7083 --seed 137 --dmax 30 the neighborhood).