WAKE: a visitation-statistics atlas of the solar neighbourhood — arrival statistics, an exclusion map, and a flyby network on Gaia DR3 kinematics

Abstract (English) Should we have been visited? We present the first calculation of visitation statistics for the solar system on the observed stellar kinematics of the solar neighbourhood: arrival statistics of close stellar passages on Gaia DR3 (56,286 stars with 6D phase-space data within 100 pc), combined with settlement dynamics in the probe-based, entry-driven convention of Carroll-Nellenback et al. Our contributions are three layers on one catalogue. (1) Arrival statistics: a completeness-corrected, exposure-normalized encounter rate with explicitly declared accounting conventions. Reconstructing the accounting of the two published rate camps on our own data, we find their factor-of-two split is dominated by the population that the completeness correction targets, not by data quality; we also identify a third systematic mode (faint-end Gaia RVS radial-velocity artifacts) that evades both value- and error-based quarantines and can inflate encounter rates severalfold, and we introduce a tangential-velocity consistency test to flag it. Our clean rate is λ(1 pc)=4.5 (+4.0/−2.7) Myr⁻¹ for the FGK+early-M population. (2) An exclusion map: conditional statements of the form ``if the settled fraction exceeds f*, the solar system should have been visited within the past 10 Myr (silence rejected at 95%)''; at the standard probe range of 3.07 pc we obtain f*=5.0×10⁻³. A three-valued theorem layer imports the survival theory proved in a companion mathematics paper (DOI 10.5281/zenodo.21955413), separating where survival is theorem-guaranteed, where the theorem is silent, and recording that no extinction theorem exists for the full model anywhere. (3) A flyby network: on the time-varying graph of close passages, a propellant-minimal visiting route exists at all times in the window, with a single-transfer departure budget of Δ v≈5.8 km/s — a statistical property of the network, not of any particular star. All statements are conditional probability statements over a declared population; undecidable regions are reported as undecidable. This is surveying, not proof. Bundle. This record carries the bilingual paper (wake_en.pdf authoritative; wake_ja.pdf translation), the released data set (arrival_catalog_v1.json, exclusion_map_v1.json, flyby_network_v1.json with a SHA-256 MANIFEST.json), and the complete repository archive wake-atlas-v1.tar.gz (code, phase documents, ruling records — the reference target of Appendices B and C). Code files are additionally licensed under MIT (LICENSE in the archive); the record as a whole is CC BY 4.0. Interactive simulator: https://yukie-lab.github.io/wake-atlas/ — reads exactly the released JSONs; its verification harness (16 checks incl. SHA-256) is displayed before any visualization. AI disclosure: all computations and drafts were executed by an AI system (Claude Code, model Claude Fable 5) under the direction and arbitration of the human author (paper Appendix B); the internal verification protocol is not a substitute for human peer review. 要旨(日本語) 太陽系は訪問済みのはずか。本論文は、太陽近傍の実測恒星運動学の 上で太陽系の来訪統計を初めて計算する: Gaia DR3(100 pc 以内の 6 次元位相空間 データを持つ 56,286 星)の接近統計に、Carroll-Nellenback らの探査機型・進入駆動 規約の入植動力学を重ねる。寄与は一つのカタログの上の三層である。 (1)到来統計: 会計規約を明示宣言した完備性補正・露出正規化の接近率。 公刊2陣営の会計規約を自データ上で再構成した結果、約2倍の分裂の主因は完備性補正が 対象とする母集団の違いであり、データ品質ではない。さらに値検疫・誤差検疫の双方を すり抜ける第三の系統モード(Gaia RVS 暗端の視線速度アーティファクト。接近率を 数倍膨張させうる)を同定し、接線速度整合検査を判別器として導入した。クリーン率は FGK+早中期M母集団で λ(1 pc)=4.5 (+4.0/−2.7) Myr⁻¹。 (2)排除地図:「入植割合が f* を超えるなら、太陽系は過去 10 Myr に 訪問済みのはず(沈黙は 95% で棄却)」という条件付き言明。標準探査機航続距離 3.07 pc で f*=5.0×10⁻³。三値の定理レイヤは、姉妹数学論文 (DOI 10.5281/zenodo.21955413)で証明された生存理論を輸入し、生存が定理保証される 領域・定理が沈黙する領域を分離し、完全モデルの絶滅定理は全域で存在しないことを 記録する。(3)フライバイ網: 接近通過の時変グラフ上に、推進剤最小の来訪 経路が窓内の全時刻で存在し、単一乗換の離脱予算は Δ v≈5.8 km/s。 これは特定の星ではなく網の統計的性質である。すべての言明は宣言された母集団上の条件付き 確率文であり、判定不能領域は判定不能として報告する。これは測量であって証明ではない。 同梱物: 日英二版 PDF(英語版が正文)・公開データ3 JSON+SHA-256 マニフェスト・リポジトリ全量 wake-atlas-v1.tar.gz(付録B/C の参照先)。コードは MIT 併用宣言、レコード全体は CC BY 4.0。シミュレータ: https://yukie-lab.github.io/wake-atlas/