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We show the timescale in which the half of Twotinos becomes unstable, t_{half}, obey the formula, t_{half} = 4 \\times 106(Mtot0.1M\\oplus)-1(mp7.6 \\times 1023g)-1(hi2i1/20.002)(years), if we assume the primordial planetesimals disk have the power low surface mass density, \\Sigma = \\Sigma_0 \\times r-2/3. Where Mtot, mp, hi2i1/2 are the total mass of large bodies of Twotinos, the maximum mass of planetesimals, and"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.3309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2011-05-17T08:53:29Z","cross_cats_sorted":[],"title_canon_sha256":"c7f3eee2f46f0975aaebfc5ae9fd6d7ff30a875b28389c898892a5462338c581","abstract_canon_sha256":"59fe85b406d4ad939d35792f7ea9b82524056cd65c76d5d3c5b13dfb16ed127d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:57.355199Z","signature_b64":"7gYwHD2lo3+HwVly/G85STceLL6s1uH0OWPW31k3IEt+zAc7MW8p+MMutR+bQzjihvYQa8TeJc+VIBLRXPFuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c987ca1ecd859be6c3a9d5c670f3d3160fa7d0645795eb7305ede80ed5c29b2","last_reissued_at":"2026-05-18T02:01:57.354535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:57.354535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The self gravity effect on the orbital stability of Twotinos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Yusuke Tsukamoto","submitted_at":"2011-05-17T08:53:29Z","abstract_excerpt":"We investigate how the self gravity changes the orbital stability of Twotinos using N-body simulations in which the gravitational interaction between planetesimals are fully calculated. 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