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As links and Dehn surgeries vary vastly in the universe, a question arises: how can we describe their properties in vague?\n  We introduce a counting model on links and Dehn surgeries, and prove that under this model, (1) a randon link is hyperbolic; (2) a random 3-manifold is hyperbolic."},"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":"2607.11057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-13T03:36:10Z","cross_cats_sorted":[],"title_canon_sha256":"18e3948b4bac74ee55e68d016df69a829cda51286a3a902942e25bd85a72eaa4","abstract_canon_sha256":"431760f46a945c4e758faf30f9b83859cbb69a36a824bdf253818d4b0706c5ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:22:14.066166Z","signature_b64":"rfsY/eDktew8yxexpthhtYfXegd88LsJrvct23KIHogTV39QnCfs25r1hOd97i0xl6EYXLM2wUFVCd9culysBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99e68fcd8c340459fc299f5925d13512cff9442595fa5d065820ae5d494c9410","last_reissued_at":"2026-07-14T01:22:14.065283Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:22:14.065283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Genericity of hyperbolic 3-manifolds via Dehn surgery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Renxing Wan, Yanqing Zou","submitted_at":"2026-07-13T03:36:10Z","abstract_excerpt":"A significant result by Lickorish and Wallace shows that every closed, orientable 3-manifold can be obtained from a Dehn surgery on one link in 3-sphere. 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