{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:N7PBBZF64FLERTEUNDV44UZXYV","short_pith_number":"pith:N7PBBZF6","schema_version":"1.0","canonical_sha256":"6fde10e4bee15648cc9468ebce5337c57e27fe332ccc383d2f03ef81bd331c8d","source":{"kind":"arxiv","id":"2605.30817","version":1},"attestation_state":"computed","paper":{"title":"Boundedness of Dehn surgery slopes admitting hyperbolic $\\mathrm{PSL}(2,\\mathbb{R})$-representations for two-bridge knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ran Tao, Shunjiang Jiang","submitted_at":"2026-05-29T04:08:22Z","abstract_excerpt":"We study Dehn fillings on two-bridge knots via non-abelian representations into $\\mathrm{PSL}(2,\\mathbb{R})$ whose meridian image is hyperbolic. For each fixed nontrivial two-bridge knot, we prove that the set of surgery slopes admitting such representations is bounded. Equivalently, Dehn fillings along slopes with sufficiently large absolute value admit no non-abelian $\\mathrm{PSL}(2,\\mathbb{R})$ representations with hyperbolic meridian image. The proof combines the Riley polynomial with Khoi's surgery-slope formula. On each admissible real algebraic branch, we express the meridian and longit"},"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":"2605.30817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-29T04:08:22Z","cross_cats_sorted":[],"title_canon_sha256":"590e9f0a3fef876f4a84bc1115cfdf2d463febaba68ad56ddcce034308c25b7d","abstract_canon_sha256":"5b3217a708dd28e751e33123b6970d40b9b01dc398b92cdb1cfbc4900e78f297"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:18.576961Z","signature_b64":"SvF2RdDrGNaF81/a5Zl0SRMxSkAG729WN0k+JN1OnYkW9b6eVpxIrDAO05etjuIPLtAr4Wts78P0lxaXqJ7OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fde10e4bee15648cc9468ebce5337c57e27fe332ccc383d2f03ef81bd331c8d","last_reissued_at":"2026-06-01T01:03:18.575938Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:18.575938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundedness of Dehn surgery slopes admitting hyperbolic $\\mathrm{PSL}(2,\\mathbb{R})$-representations for two-bridge knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ran Tao, Shunjiang Jiang","submitted_at":"2026-05-29T04:08:22Z","abstract_excerpt":"We study Dehn fillings on two-bridge knots via non-abelian representations into $\\mathrm{PSL}(2,\\mathbb{R})$ whose meridian image is hyperbolic. For each fixed nontrivial two-bridge knot, we prove that the set of surgery slopes admitting such representations is bounded. Equivalently, Dehn fillings along slopes with sufficiently large absolute value admit no non-abelian $\\mathrm{PSL}(2,\\mathbb{R})$ representations with hyperbolic meridian image. The proof combines the Riley polynomial with Khoi's surgery-slope formula. On each admissible real algebraic branch, we express the meridian and longit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30817","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30817/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.30817","created_at":"2026-06-01T01:03:18.576096+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30817v1","created_at":"2026-06-01T01:03:18.576096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30817","created_at":"2026-06-01T01:03:18.576096+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7PBBZF64FLE","created_at":"2026-06-01T01:03:18.576096+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7PBBZF64FLERTEU","created_at":"2026-06-01T01:03:18.576096+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7PBBZF6","created_at":"2026-06-01T01:03:18.576096+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV","json":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV.json","graph_json":"https://pith.science/api/pith-number/N7PBBZF64FLERTEUNDV44UZXYV/graph.json","events_json":"https://pith.science/api/pith-number/N7PBBZF64FLERTEUNDV44UZXYV/events.json","paper":"https://pith.science/paper/N7PBBZF6"},"agent_actions":{"view_html":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV","download_json":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV.json","view_paper":"https://pith.science/paper/N7PBBZF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30817&json=true","fetch_graph":"https://pith.science/api/pith-number/N7PBBZF64FLERTEUNDV44UZXYV/graph.json","fetch_events":"https://pith.science/api/pith-number/N7PBBZF64FLERTEUNDV44UZXYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV/action/storage_attestation","attest_author":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV/action/author_attestation","sign_citation":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV/action/citation_signature","submit_replication":"https://pith.science/pith/N7PBBZF64FLERTEUNDV44UZXYV/action/replication_record"}},"created_at":"2026-06-01T01:03:18.576096+00:00","updated_at":"2026-06-01T01:03:18.576096+00:00"}