{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:N7PBBZF64FLERTEUNDV44UZXYV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5b3217a708dd28e751e33123b6970d40b9b01dc398b92cdb1cfbc4900e78f297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-29T04:08:22Z","title_canon_sha256":"590e9f0a3fef876f4a84bc1115cfdf2d463febaba68ad56ddcce034308c25b7d"},"schema_version":"1.0","source":{"id":"2605.30817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30817","created_at":"2026-06-01T01:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30817v1","created_at":"2026-06-01T01:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30817","created_at":"2026-06-01T01:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"N7PBBZF64FLE","created_at":"2026-06-01T01:03:18Z"},{"alias_kind":"pith_short_16","alias_value":"N7PBBZF64FLERTEU","created_at":"2026-06-01T01:03:18Z"},{"alias_kind":"pith_short_8","alias_value":"N7PBBZF6","created_at":"2026-06-01T01:03:18Z"}],"graph_snapshots":[{"event_id":"sha256:3afa6e308148ec27a79e27584f53968359f6fd0d85b2d89ef4c759b921afae14","target":"graph","created_at":"2026-06-01T01:03:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.30817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Ran Tao, Shunjiang Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-29T04:08:22Z","title":"Boundedness of Dehn surgery slopes admitting hyperbolic $\\mathrm{PSL}(2,\\mathbb{R})$-representations for two-bridge knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30817","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d247484fe676f3fdfe89b1449afb8603949d9bf9a750fe80ee097b486390df8","target":"record","created_at":"2026-06-01T01:03:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5b3217a708dd28e751e33123b6970d40b9b01dc398b92cdb1cfbc4900e78f297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-29T04:08:22Z","title_canon_sha256":"590e9f0a3fef876f4a84bc1115cfdf2d463febaba68ad56ddcce034308c25b7d"},"schema_version":"1.0","source":{"id":"2605.30817","kind":"arxiv","version":1}},"canonical_sha256":"6fde10e4bee15648cc9468ebce5337c57e27fe332ccc383d2f03ef81bd331c8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fde10e4bee15648cc9468ebce5337c57e27fe332ccc383d2f03ef81bd331c8d","first_computed_at":"2026-06-01T01:03:18.575938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:18.575938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvF2RdDrGNaF81/a5Zl0SRMxSkAG729WN0k+JN1OnYkW9b6eVpxIrDAO05etjuIPLtAr4Wts78P0lxaXqJ7OCQ==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:18.576961Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d247484fe676f3fdfe89b1449afb8603949d9bf9a750fe80ee097b486390df8","sha256:3afa6e308148ec27a79e27584f53968359f6fd0d85b2d89ef4c759b921afae14"],"state_sha256":"78f8036bc0b3602d95d06ec9de65a8df796cd646ab8d114435a53aedeb2e17f9"}