{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:X46VIBD4D2I4RDKLIZLT33KYXA","short_pith_number":"pith:X46VIBD4","canonical_record":{"source":{"id":"0706.3425","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-06-23T01:56:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bd7bdb868f8f7757a76783c331ac6acb9a05264d0d4f2993db05949dc45a227b","abstract_canon_sha256":"c580a042c8838dcdbb4cda98d92b5e8de1a2e691896f38c48b544856c670bae3"},"schema_version":"1.0"},"canonical_sha256":"bf3d54047c1e91c88d4b46573ded58b815ceec9b53e98212eb0a3248cb5a8502","source":{"kind":"arxiv","id":"0706.3425","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3425","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3425v2","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3425","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"X46VIBD4D2I4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"X46VIBD4D2I4RDKL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"X46VIBD4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:X46VIBD4D2I4RDKLIZLT33KYXA","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3425","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-06-23T01:56:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bd7bdb868f8f7757a76783c331ac6acb9a05264d0d4f2993db05949dc45a227b","abstract_canon_sha256":"c580a042c8838dcdbb4cda98d92b5e8de1a2e691896f38c48b544856c670bae3"},"schema_version":"1.0"},"canonical_sha256":"bf3d54047c1e91c88d4b46573ded58b815ceec9b53e98212eb0a3248cb5a8502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:32.082466Z","signature_b64":"UGr8rtgLHgh3zSePnMBVgsgrI726U44ai/qkvkotJiq53erSv0YUswTfkE2j2LPEdCpYCd3vEWYtZCFo9PUzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf3d54047c1e91c88d4b46573ded58b815ceec9b53e98212eb0a3248cb5a8502","last_reissued_at":"2026-05-18T04:22:32.082049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:32.082049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3425","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":"2026-05-18T04:22:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALEYMI+rt+lm2Lw/10mLA8jK2esktJC1jgC4zhPeFjN6mHX5VQh3Oj5BH5RDwVRtBos//oxr9wuN8f1LC59MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:32:42.472892Z"},"content_sha256":"f182606e2ac9e34422fba1c5af5e5c2f886653808bd439e890c7f9982b3a3649","schema_version":"1.0","event_id":"sha256:f182606e2ac9e34422fba1c5af5e5c2f886653808bd439e890c7f9982b3a3649"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:X46VIBD4D2I4RDKLIZLT33KYXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted conjugacy classes in nilpotent groups","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Daciberg Gon\\c{c}alves, Peter Wong","submitted_at":"2007-06-23T01:56:53Z","abstract_excerpt":"A group is said to have the $R_\\infty$ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether $G$ has the $R_\\infty$ property when $G$ is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer $n\\ge 5$, there is a compact nilmanifold of dimension $n$ on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the $R_\\infty$ property. The $R_{\\infty}$ property for virtu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3425","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":"2026-05-18T04:22:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uf1LsnfR634dFCVcaOfUXPZX/MwC8L2dW+nvb1cO/lZrNKySG5CtlD7+I9D0mPQ8CP7vyYCjO3kPIvIAiE90Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:32:42.473231Z"},"content_sha256":"9795acffa645080423ecd7b9f158b33456712a4afc8f5c397f7ad48418fd0b61","schema_version":"1.0","event_id":"sha256:9795acffa645080423ecd7b9f158b33456712a4afc8f5c397f7ad48418fd0b61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X46VIBD4D2I4RDKLIZLT33KYXA/bundle.json","state_url":"https://pith.science/pith/X46VIBD4D2I4RDKLIZLT33KYXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X46VIBD4D2I4RDKLIZLT33KYXA/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":"2026-05-28T10:32:42Z","links":{"resolver":"https://pith.science/pith/X46VIBD4D2I4RDKLIZLT33KYXA","bundle":"https://pith.science/pith/X46VIBD4D2I4RDKLIZLT33KYXA/bundle.json","state":"https://pith.science/pith/X46VIBD4D2I4RDKLIZLT33KYXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X46VIBD4D2I4RDKLIZLT33KYXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:X46VIBD4D2I4RDKLIZLT33KYXA","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":"c580a042c8838dcdbb4cda98d92b5e8de1a2e691896f38c48b544856c670bae3","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-06-23T01:56:53Z","title_canon_sha256":"bd7bdb868f8f7757a76783c331ac6acb9a05264d0d4f2993db05949dc45a227b"},"schema_version":"1.0","source":{"id":"0706.3425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3425","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3425v2","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3425","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"X46VIBD4D2I4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"X46VIBD4D2I4RDKL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"X46VIBD4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9795acffa645080423ecd7b9f158b33456712a4afc8f5c397f7ad48418fd0b61","target":"graph","created_at":"2026-05-18T04:22:32Z","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":"A group is said to have the $R_\\infty$ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether $G$ has the $R_\\infty$ property when $G$ is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer $n\\ge 5$, there is a compact nilmanifold of dimension $n$ on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the $R_\\infty$ property. The $R_{\\infty}$ property for virtu","authors_text":"Daciberg Gon\\c{c}alves, Peter Wong","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2007-06-23T01:56:53Z","title":"Twisted conjugacy classes in nilpotent groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3425","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:f182606e2ac9e34422fba1c5af5e5c2f886653808bd439e890c7f9982b3a3649","target":"record","created_at":"2026-05-18T04:22:32Z","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":"c580a042c8838dcdbb4cda98d92b5e8de1a2e691896f38c48b544856c670bae3","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-06-23T01:56:53Z","title_canon_sha256":"bd7bdb868f8f7757a76783c331ac6acb9a05264d0d4f2993db05949dc45a227b"},"schema_version":"1.0","source":{"id":"0706.3425","kind":"arxiv","version":2}},"canonical_sha256":"bf3d54047c1e91c88d4b46573ded58b815ceec9b53e98212eb0a3248cb5a8502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf3d54047c1e91c88d4b46573ded58b815ceec9b53e98212eb0a3248cb5a8502","first_computed_at":"2026-05-18T04:22:32.082049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:32.082049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UGr8rtgLHgh3zSePnMBVgsgrI726U44ai/qkvkotJiq53erSv0YUswTfkE2j2LPEdCpYCd3vEWYtZCFo9PUzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:32.082466Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f182606e2ac9e34422fba1c5af5e5c2f886653808bd439e890c7f9982b3a3649","sha256:9795acffa645080423ecd7b9f158b33456712a4afc8f5c397f7ad48418fd0b61"],"state_sha256":"44c9a1164928cd14c572377e7409f345a9a4924b67835907055d67f97fdd4ffb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8QR8lSaaeKaDd1U1y3X+RdRyiCMmwYLMgQKgRSv5UGGEL8ia2CCkV/jh974hXoD2omnbpJQm1KevAJEXR/QDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:32:42.475244Z","bundle_sha256":"f75e3c1bec5d81fe7d3557a57c6a3044603820b78c980ecaa7a16934fc74f604"}}