{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HY6GRPFFHZ2E5YB3YRKGHK3OS2","short_pith_number":"pith:HY6GRPFF","canonical_record":{"source":{"id":"1601.01015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-05T23:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"a1ce3f656dfab751ec429b44fb6112651a31ec8ba2a8537ab8f405fd829f6a57","abstract_canon_sha256":"10f150b7896758e49350216bc1003ecde8c57803c627621e8ce609bbdcf97a4a"},"schema_version":"1.0"},"canonical_sha256":"3e3c68bca53e744ee03bc45463ab6e96a6a786b94c190e6191c31741b4fdf1f9","source":{"kind":"arxiv","id":"1601.01015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01015","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01015v2","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01015","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"HY6GRPFFHZ2E","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HY6GRPFFHZ2E5YB3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HY6GRPFF","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HY6GRPFFHZ2E5YB3YRKGHK3OS2","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-05T23:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"a1ce3f656dfab751ec429b44fb6112651a31ec8ba2a8537ab8f405fd829f6a57","abstract_canon_sha256":"10f150b7896758e49350216bc1003ecde8c57803c627621e8ce609bbdcf97a4a"},"schema_version":"1.0"},"canonical_sha256":"3e3c68bca53e744ee03bc45463ab6e96a6a786b94c190e6191c31741b4fdf1f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:21.145590Z","signature_b64":"BG3MLhFp96zz/yjQA6q/MAJ72JP0Z6YuXj94yI7GQ5QkTfaPeWtwHmITBes3T5eZEbM30Msg6A+H4NQlodRKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3c68bca53e744ee03bc45463ab6e96a6a786b94c190e6191c31741b4fdf1f9","last_reissued_at":"2026-05-18T00:56:21.144770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:21.144770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01015","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"llPn4OEHa5GDMgTuLzzEqWuE9WjaHxoQ9ZCyyPhRrzIlDiYA2ewU+FRUyxijRyPUGFoT2NryCbkEm9MqKPyeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:10:26.671119Z"},"content_sha256":"eac9890c437ceacb8f7cb4a88fd44eeefaeb09243fe6ba3dcfb23f34b56bd1f3","schema_version":"1.0","event_id":"sha256:eac9890c437ceacb8f7cb4a88fd44eeefaeb09243fe6ba3dcfb23f34b56bd1f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HY6GRPFFHZ2E5YB3YRKGHK3OS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hidden Symmetries and Commensurability of 2-Bridge Link Complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christian Millichap, William Worden","submitted_at":"2016-01-05T23:10:39Z","abstract_excerpt":"In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of $3$-manifolds with non-trivial JSJ-decomposition and rank two fundamental groups. We also show that the only commensurable hyperbolic $2$-bridge link complements are the figure-eight knot complement and the $6_{2}^{2}$ link complement. Our work requires a carefu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01015","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORJ5rc0/t93tycRLjIYq15iMrt3qs5ozOLDXEwAzxt7GW6ylGa2pKPwN75M1xL7Z3F5IFrndIGe4sN5xvTA4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:10:26.671481Z"},"content_sha256":"7a0723680ee0eb23b2ed361fa1d1a089882c7241433aabe72fc58bc8ad5d65ac","schema_version":"1.0","event_id":"sha256:7a0723680ee0eb23b2ed361fa1d1a089882c7241433aabe72fc58bc8ad5d65ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/bundle.json","state_url":"https://pith.science/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-21T23:10:26Z","links":{"resolver":"https://pith.science/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2","bundle":"https://pith.science/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/bundle.json","state":"https://pith.science/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY6GRPFFHZ2E5YB3YRKGHK3OS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HY6GRPFFHZ2E5YB3YRKGHK3OS2","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":"10f150b7896758e49350216bc1003ecde8c57803c627621e8ce609bbdcf97a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-05T23:10:39Z","title_canon_sha256":"a1ce3f656dfab751ec429b44fb6112651a31ec8ba2a8537ab8f405fd829f6a57"},"schema_version":"1.0","source":{"id":"1601.01015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01015","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01015v2","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01015","created_at":"2026-05-18T00:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"HY6GRPFFHZ2E","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HY6GRPFFHZ2E5YB3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HY6GRPFF","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:7a0723680ee0eb23b2ed361fa1d1a089882c7241433aabe72fc58bc8ad5d65ac","target":"graph","created_at":"2026-05-18T00:56:21Z","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"},"paper":{"abstract_excerpt":"In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of $3$-manifolds with non-trivial JSJ-decomposition and rank two fundamental groups. We also show that the only commensurable hyperbolic $2$-bridge link complements are the figure-eight knot complement and the $6_{2}^{2}$ link complement. Our work requires a carefu","authors_text":"Christian Millichap, William Worden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-05T23:10:39Z","title":"Hidden Symmetries and Commensurability of 2-Bridge Link Complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01015","kind":"arxiv","version":2},"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:eac9890c437ceacb8f7cb4a88fd44eeefaeb09243fe6ba3dcfb23f34b56bd1f3","target":"record","created_at":"2026-05-18T00:56:21Z","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":"10f150b7896758e49350216bc1003ecde8c57803c627621e8ce609bbdcf97a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-01-05T23:10:39Z","title_canon_sha256":"a1ce3f656dfab751ec429b44fb6112651a31ec8ba2a8537ab8f405fd829f6a57"},"schema_version":"1.0","source":{"id":"1601.01015","kind":"arxiv","version":2}},"canonical_sha256":"3e3c68bca53e744ee03bc45463ab6e96a6a786b94c190e6191c31741b4fdf1f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3c68bca53e744ee03bc45463ab6e96a6a786b94c190e6191c31741b4fdf1f9","first_computed_at":"2026-05-18T00:56:21.144770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:21.144770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BG3MLhFp96zz/yjQA6q/MAJ72JP0Z6YuXj94yI7GQ5QkTfaPeWtwHmITBes3T5eZEbM30Msg6A+H4NQlodRKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:21.145590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eac9890c437ceacb8f7cb4a88fd44eeefaeb09243fe6ba3dcfb23f34b56bd1f3","sha256:7a0723680ee0eb23b2ed361fa1d1a089882c7241433aabe72fc58bc8ad5d65ac"],"state_sha256":"aec37bad936a8a5612f495846582db8ec66ce74c4c4fd5776558850079302db7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhmLKLsVVsdv2WaGCo6H2DzcikfVliPp446Whh0Sm8oTaU4MJfa9ywx5qKpu0gpXkFHBz3z1XWMBFMmkezxrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:10:26.674430Z","bundle_sha256":"554f3ebb4476f250d164eaaf10a327059c5e045e2fcc69af5ef9b51fe28ca059"}}