{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SI76KWKYRGXUXL7UXQF2BEP7LK","short_pith_number":"pith:SI76KWKY","canonical_record":{"source":{"id":"1305.2044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-09T09:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"b3edde9b8a84e80c02e0eadc3379a6b7d5e1b41b050ec40059e9f1b7697a2e26","abstract_canon_sha256":"082088e323dae5a5c63e89093c8675c614700e0592952f28aebede98ef78d477"},"schema_version":"1.0"},"canonical_sha256":"923fe5595889af4baff4bc0ba091ff5aa59d259c0baac70c965cc13e73dae4ca","source":{"kind":"arxiv","id":"1305.2044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2044","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2044v2","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2044","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"SI76KWKYRGXU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SI76KWKYRGXUXL7U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SI76KWKY","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SI76KWKYRGXUXL7UXQF2BEP7LK","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-09T09:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"b3edde9b8a84e80c02e0eadc3379a6b7d5e1b41b050ec40059e9f1b7697a2e26","abstract_canon_sha256":"082088e323dae5a5c63e89093c8675c614700e0592952f28aebede98ef78d477"},"schema_version":"1.0"},"canonical_sha256":"923fe5595889af4baff4bc0ba091ff5aa59d259c0baac70c965cc13e73dae4ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:47.023138Z","signature_b64":"p8dMS+yW8AifCTcBjpmOc8t/myxBQCa6Lo+7/HOwrPyDgr2KfYhpMSM97IQTbWW9C0OHgYfF9z0vpWRUlLXzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"923fe5595889af4baff4bc0ba091ff5aa59d259c0baac70c965cc13e73dae4ca","last_reissued_at":"2026-05-18T02:48:47.022435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:47.022435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2044","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":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iTEr64QM4Qe77QI4fpmTSPWh/qoq7pjxe4hYgMzW8Z3nfS2aAvqU8cYbY/67kwRpuIginqqreZ2JAyJyOMPeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:11:58.499916Z"},"content_sha256":"82269b55f7b3ee45e527224183642de5822e7baf78fbc3c1942fa94007bd3a1d","schema_version":"1.0","event_id":"sha256:82269b55f7b3ee45e527224183642de5822e7baf78fbc3c1942fa94007bd3a1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SI76KWKYRGXUXL7UXQF2BEP7LK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugacy in Houghton's Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Armando Martino, Jos\\'e Burillo, Yago Antol\\'in","submitted_at":"2013-05-09T09:50:05Z","abstract_excerpt":"Let $n\\in \\mathbb{N}$. Houghton's group $H_n$ is the group of permutations of $\\{1,\\dots, n\\}\\times \\mathbb{N}$, that eventually act as a translation in each copy of $\\mathbb{N}$. We prove the solvability of the conjugacy problem and conjugator search problem for $H_n$, $n\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2044","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":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNvZNIqF/jVBZNmKa5ApdNHjKTM3rLcxfLJyTIPuwrZB0CjvVCrUBm3whHhV9fELiE09S+v0K+jiYtRfxZIZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:11:58.500524Z"},"content_sha256":"86bc46fd8434b18bb02e3684926d7e6159e0d974c87c869ea609b42c0ba002d5","schema_version":"1.0","event_id":"sha256:86bc46fd8434b18bb02e3684926d7e6159e0d974c87c869ea609b42c0ba002d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/bundle.json","state_url":"https://pith.science/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/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":"2026-06-23T15:11:58Z","links":{"resolver":"https://pith.science/pith/SI76KWKYRGXUXL7UXQF2BEP7LK","bundle":"https://pith.science/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/bundle.json","state":"https://pith.science/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SI76KWKYRGXUXL7UXQF2BEP7LK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SI76KWKYRGXUXL7UXQF2BEP7LK","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":"082088e323dae5a5c63e89093c8675c614700e0592952f28aebede98ef78d477","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-09T09:50:05Z","title_canon_sha256":"b3edde9b8a84e80c02e0eadc3379a6b7d5e1b41b050ec40059e9f1b7697a2e26"},"schema_version":"1.0","source":{"id":"1305.2044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2044","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2044v2","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2044","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"SI76KWKYRGXU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SI76KWKYRGXUXL7U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SI76KWKY","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:86bc46fd8434b18bb02e3684926d7e6159e0d974c87c869ea609b42c0ba002d5","target":"graph","created_at":"2026-05-18T02:48:47Z","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":"Let $n\\in \\mathbb{N}$. Houghton's group $H_n$ is the group of permutations of $\\{1,\\dots, n\\}\\times \\mathbb{N}$, that eventually act as a translation in each copy of $\\mathbb{N}$. We prove the solvability of the conjugacy problem and conjugator search problem for $H_n$, $n\\geq 2$.","authors_text":"Armando Martino, Jos\\'e Burillo, Yago Antol\\'in","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-09T09:50:05Z","title":"Conjugacy in Houghton's Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2044","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":"sha256:82269b55f7b3ee45e527224183642de5822e7baf78fbc3c1942fa94007bd3a1d","target":"record","created_at":"2026-05-18T02:48:47Z","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":"082088e323dae5a5c63e89093c8675c614700e0592952f28aebede98ef78d477","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-09T09:50:05Z","title_canon_sha256":"b3edde9b8a84e80c02e0eadc3379a6b7d5e1b41b050ec40059e9f1b7697a2e26"},"schema_version":"1.0","source":{"id":"1305.2044","kind":"arxiv","version":2}},"canonical_sha256":"923fe5595889af4baff4bc0ba091ff5aa59d259c0baac70c965cc13e73dae4ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"923fe5595889af4baff4bc0ba091ff5aa59d259c0baac70c965cc13e73dae4ca","first_computed_at":"2026-05-18T02:48:47.022435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:47.022435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p8dMS+yW8AifCTcBjpmOc8t/myxBQCa6Lo+7/HOwrPyDgr2KfYhpMSM97IQTbWW9C0OHgYfF9z0vpWRUlLXzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:47.023138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82269b55f7b3ee45e527224183642de5822e7baf78fbc3c1942fa94007bd3a1d","sha256:86bc46fd8434b18bb02e3684926d7e6159e0d974c87c869ea609b42c0ba002d5"],"state_sha256":"aa936ef4a369f2ac47dcc90e070caa7bfd4382135cab0ceb14d16d6b48b147a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gs/FtzJBg1u/8RA676IUJYIBwwNtQf0VkCmqKra8x68gKybMCwNxO5fMOv+RMOdmBCYg2U7i0w7He/ABCs2eBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:11:58.503198Z","bundle_sha256":"6a60a2992004055d1ca45cdad6cc2a1dc094a00a394313d1a385b488c42a216b"}}