{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:TIRJNRO37FPB3O2OJHUZQ737MY","short_pith_number":"pith:TIRJNRO3","canonical_record":{"source":{"id":"math/0701342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-01-12T11:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"b497f3eda387a259f0d0f25a450a1fd9c0252fa91cdb69451e9014f1eabec2e3","abstract_canon_sha256":"a2f2d784c7b4615cef5d94c8d64a7120c2f3d127474c0173412d47e4d0f8d47e"},"schema_version":"1.0"},"canonical_sha256":"9a2296c5dbf95e1dbb4e49e9987f7f660888b258fdba4de5e2a875d348cb1a75","source":{"kind":"arxiv","id":"math/0701342","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701342","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701342v2","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701342","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"TIRJNRO37FPB","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TIRJNRO37FPB3O2O","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TIRJNRO3","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:TIRJNRO37FPB3O2OJHUZQ737MY","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-01-12T11:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"b497f3eda387a259f0d0f25a450a1fd9c0252fa91cdb69451e9014f1eabec2e3","abstract_canon_sha256":"a2f2d784c7b4615cef5d94c8d64a7120c2f3d127474c0173412d47e4d0f8d47e"},"schema_version":"1.0"},"canonical_sha256":"9a2296c5dbf95e1dbb4e49e9987f7f660888b258fdba4de5e2a875d348cb1a75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:02.315163Z","signature_b64":"7a+3E+UwGVfvAXMVQgvskxLTRXaRtwMzZBfIXKhDRPv7V6Sa+ndkMuLpanTj8acbKqV3mlIWu9HfsjhMtij0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a2296c5dbf95e1dbb4e49e9987f7f660888b258fdba4de5e2a875d348cb1a75","last_reissued_at":"2026-05-18T04:19:02.314735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:02.314735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701342","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":"2026-05-18T04:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGG5RUAIBKQKHWQihwfNJ+DPcjnT/htvSdZbcu4pbQ3Xq2RJQa4N9S6CKCAKQ4eKaEwnZLoXsyVHdV4qCQ+MAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:42:25.940824Z"},"content_sha256":"5dd25fe2e424dda56f055e0622785e47691ab3c282e03ce83f98d515c2a50a53","schema_version":"1.0","event_id":"sha256:5dd25fe2e424dda56f055e0622785e47691ab3c282e03ce83f98d515c2a50a53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:TIRJNRO37FPB3O2OJHUZQ737MY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence and divergence of Kleinian punctured torus groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kentaro Ito","submitted_at":"2007-01-12T11:54:27Z","abstract_excerpt":"In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary. Thus we obtain a complete description of the set of points at which the space of Kleinian punctured torus groups self-bumps. We also discuss geometric limits of sequences of Bers slices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701342","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":"2026-05-18T04:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkC+ofjbfjvERdZWcmLe8j6J/3uDdH9f/0AyO8N41HGNRo3pZxF/abFYXQBuuPrmD3GLijkUOqfEtqZWkFn1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:42:25.941369Z"},"content_sha256":"1d07f4afb6a228d84d0596b8d9fa12a170e12b276a57052dfb519ef83807dbe6","schema_version":"1.0","event_id":"sha256:1d07f4afb6a228d84d0596b8d9fa12a170e12b276a57052dfb519ef83807dbe6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIRJNRO37FPB3O2OJHUZQ737MY/bundle.json","state_url":"https://pith.science/pith/TIRJNRO37FPB3O2OJHUZQ737MY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIRJNRO37FPB3O2OJHUZQ737MY/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":"2026-06-26T00:42:25Z","links":{"resolver":"https://pith.science/pith/TIRJNRO37FPB3O2OJHUZQ737MY","bundle":"https://pith.science/pith/TIRJNRO37FPB3O2OJHUZQ737MY/bundle.json","state":"https://pith.science/pith/TIRJNRO37FPB3O2OJHUZQ737MY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIRJNRO37FPB3O2OJHUZQ737MY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TIRJNRO37FPB3O2OJHUZQ737MY","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":"a2f2d784c7b4615cef5d94c8d64a7120c2f3d127474c0173412d47e4d0f8d47e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-01-12T11:54:27Z","title_canon_sha256":"b497f3eda387a259f0d0f25a450a1fd9c0252fa91cdb69451e9014f1eabec2e3"},"schema_version":"1.0","source":{"id":"math/0701342","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701342","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701342v2","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701342","created_at":"2026-05-18T04:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"TIRJNRO37FPB","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TIRJNRO37FPB3O2O","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TIRJNRO3","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1d07f4afb6a228d84d0596b8d9fa12a170e12b276a57052dfb519ef83807dbe6","target":"graph","created_at":"2026-05-18T04:19:02Z","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 give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary. Thus we obtain a complete description of the set of points at which the space of Kleinian punctured torus groups self-bumps. We also discuss geometric limits of sequences of Bers slices.","authors_text":"Kentaro Ito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-01-12T11:54:27Z","title":"Convergence and divergence of Kleinian punctured torus groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701342","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":"sha256:5dd25fe2e424dda56f055e0622785e47691ab3c282e03ce83f98d515c2a50a53","target":"record","created_at":"2026-05-18T04:19:02Z","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":"a2f2d784c7b4615cef5d94c8d64a7120c2f3d127474c0173412d47e4d0f8d47e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-01-12T11:54:27Z","title_canon_sha256":"b497f3eda387a259f0d0f25a450a1fd9c0252fa91cdb69451e9014f1eabec2e3"},"schema_version":"1.0","source":{"id":"math/0701342","kind":"arxiv","version":2}},"canonical_sha256":"9a2296c5dbf95e1dbb4e49e9987f7f660888b258fdba4de5e2a875d348cb1a75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a2296c5dbf95e1dbb4e49e9987f7f660888b258fdba4de5e2a875d348cb1a75","first_computed_at":"2026-05-18T04:19:02.314735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:02.314735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7a+3E+UwGVfvAXMVQgvskxLTRXaRtwMzZBfIXKhDRPv7V6Sa+ndkMuLpanTj8acbKqV3mlIWu9HfsjhMtij0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:02.315163Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701342","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd25fe2e424dda56f055e0622785e47691ab3c282e03ce83f98d515c2a50a53","sha256:1d07f4afb6a228d84d0596b8d9fa12a170e12b276a57052dfb519ef83807dbe6"],"state_sha256":"1932dfdd4422bbaaea18d3644d8211e952739c1bf6af73cef5f85f1fc052ca58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOma0DzrEFt5YC+85PEt/WLe5uSZ1WFFond5Uwod3DqSuKnoSqbLzbeSExXPR+qPugrRW6IHZnlrF/HXH8mVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:42:25.944055Z","bundle_sha256":"fc392d85224f73cb0d50033e99dfd2ee435dcba9313bcd2623e3fa4fd9d0bca7"}}