{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TFBJR35VU7EH57PALKAA4WWKL5","short_pith_number":"pith:TFBJR35V","canonical_record":{"source":{"id":"1709.10218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-29T02:36:22Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"113bcf84afb5ac56f18f71ac7635bdba36aca2fa9b8d856611bf1d6bfa949ed9","abstract_canon_sha256":"5c219ad8f65a7262f94f870e221a18ed3ca5a1a6aeb14fd9ad97a7f6b0d1d786"},"schema_version":"1.0"},"canonical_sha256":"994298efb5a7c87efde05a800e5aca5f724dc43ed7049c1740fbaffe4f079e2d","source":{"kind":"arxiv","id":"1709.10218","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10218","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10218v2","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10218","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"TFBJR35VU7EH","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TFBJR35VU7EH57PA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TFBJR35V","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TFBJR35VU7EH57PALKAA4WWKL5","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-29T02:36:22Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"113bcf84afb5ac56f18f71ac7635bdba36aca2fa9b8d856611bf1d6bfa949ed9","abstract_canon_sha256":"5c219ad8f65a7262f94f870e221a18ed3ca5a1a6aeb14fd9ad97a7f6b0d1d786"},"schema_version":"1.0"},"canonical_sha256":"994298efb5a7c87efde05a800e5aca5f724dc43ed7049c1740fbaffe4f079e2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:29.706143Z","signature_b64":"XLBo0bdZaCx0UN+VfwHNxuOtIOJuLY+QRNXrxMuM82Gjk+4O6Ox66JRDl/r38EwcdTEgsKPv3v+S3I6PA0vECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"994298efb5a7c87efde05a800e5aca5f724dc43ed7049c1740fbaffe4f079e2d","last_reissued_at":"2026-05-18T00:33:29.705614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:29.705614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10218","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":"2026-05-18T00:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQ2m4xoOp90MBV0Ol9NUYAAvBFVplf/Kj3zNnPqktqA8vmz+7r+jE/Xi7NmdSrlwM2sQ1xHfCVL+ey41D6qBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:14:13.727729Z"},"content_sha256":"12397ed77943dc9b465bfda936299f18bcf09d1b0c8e4047302f2705bb212ec2","schema_version":"1.0","event_id":"sha256:12397ed77943dc9b465bfda936299f18bcf09d1b0c8e4047302f2705bb212ec2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TFBJR35VU7EH57PALKAA4WWKL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divergence, Undistortion and H\\\"older Continuous Cocycle Superrigidity for Full Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Nhan-Phu Chung, Yongle Jiang","submitted_at":"2017-09-29T02:36:22Z","abstract_excerpt":"In this article, we will prove a full topological version of Popa's measurable cocycle superrigidity theorem for full shifts. More precisely, we prove that every H\\\"older continuous cocycle for the full shifts of every finitely generated group $G$ that has one end, undistorted elements and sub-exponential divergence function is cohomologous to a group homomorphism via a H\\\"older continuous transfer map if the target group is complete and admits a compatible bi-invariant metric. Using the ideas of Behrstock, Dru\\c {t}u, Mosher, Mozes and Sapir, we show that the class of our acting groups is lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10218","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":"2026-05-18T00:33:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsKhy5fJFq5niOkhmLrc98t5gjz7WfYw/jbv3mQzUh52fVptD4VQyZ1u5e1AuS6YEk/4ejdpf1F1NEocTGI9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:14:13.728077Z"},"content_sha256":"b64ddc8a63db487f87bd401236a7932e7b414008b82b4a691bd8dd65545af1b3","schema_version":"1.0","event_id":"sha256:b64ddc8a63db487f87bd401236a7932e7b414008b82b4a691bd8dd65545af1b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFBJR35VU7EH57PALKAA4WWKL5/bundle.json","state_url":"https://pith.science/pith/TFBJR35VU7EH57PALKAA4WWKL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFBJR35VU7EH57PALKAA4WWKL5/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":"2026-06-03T08:14:13Z","links":{"resolver":"https://pith.science/pith/TFBJR35VU7EH57PALKAA4WWKL5","bundle":"https://pith.science/pith/TFBJR35VU7EH57PALKAA4WWKL5/bundle.json","state":"https://pith.science/pith/TFBJR35VU7EH57PALKAA4WWKL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFBJR35VU7EH57PALKAA4WWKL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TFBJR35VU7EH57PALKAA4WWKL5","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":"5c219ad8f65a7262f94f870e221a18ed3ca5a1a6aeb14fd9ad97a7f6b0d1d786","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-29T02:36:22Z","title_canon_sha256":"113bcf84afb5ac56f18f71ac7635bdba36aca2fa9b8d856611bf1d6bfa949ed9"},"schema_version":"1.0","source":{"id":"1709.10218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10218","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10218v2","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10218","created_at":"2026-05-18T00:33:29Z"},{"alias_kind":"pith_short_12","alias_value":"TFBJR35VU7EH","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TFBJR35VU7EH57PA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TFBJR35V","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:b64ddc8a63db487f87bd401236a7932e7b414008b82b4a691bd8dd65545af1b3","target":"graph","created_at":"2026-05-18T00:33:29Z","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 article, we will prove a full topological version of Popa's measurable cocycle superrigidity theorem for full shifts. More precisely, we prove that every H\\\"older continuous cocycle for the full shifts of every finitely generated group $G$ that has one end, undistorted elements and sub-exponential divergence function is cohomologous to a group homomorphism via a H\\\"older continuous transfer map if the target group is complete and admits a compatible bi-invariant metric. Using the ideas of Behrstock, Dru\\c {t}u, Mosher, Mozes and Sapir, we show that the class of our acting groups is lar","authors_text":"Nhan-Phu Chung, Yongle Jiang","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-29T02:36:22Z","title":"Divergence, Undistortion and H\\\"older Continuous Cocycle Superrigidity for Full Shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10218","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":"sha256:12397ed77943dc9b465bfda936299f18bcf09d1b0c8e4047302f2705bb212ec2","target":"record","created_at":"2026-05-18T00:33:29Z","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":"5c219ad8f65a7262f94f870e221a18ed3ca5a1a6aeb14fd9ad97a7f6b0d1d786","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-29T02:36:22Z","title_canon_sha256":"113bcf84afb5ac56f18f71ac7635bdba36aca2fa9b8d856611bf1d6bfa949ed9"},"schema_version":"1.0","source":{"id":"1709.10218","kind":"arxiv","version":2}},"canonical_sha256":"994298efb5a7c87efde05a800e5aca5f724dc43ed7049c1740fbaffe4f079e2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"994298efb5a7c87efde05a800e5aca5f724dc43ed7049c1740fbaffe4f079e2d","first_computed_at":"2026-05-18T00:33:29.705614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:29.705614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLBo0bdZaCx0UN+VfwHNxuOtIOJuLY+QRNXrxMuM82Gjk+4O6Ox66JRDl/r38EwcdTEgsKPv3v+S3I6PA0vECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:29.706143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12397ed77943dc9b465bfda936299f18bcf09d1b0c8e4047302f2705bb212ec2","sha256:b64ddc8a63db487f87bd401236a7932e7b414008b82b4a691bd8dd65545af1b3"],"state_sha256":"41166dadee278805b8c629082da2fcf0531b3e9de1b64ad067a44bb811b7df47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bgAza8y+VStid1L3xCHwjQDu4Gqfqzy3/O50s++htQDgZG0e9/NiMJV1we33JdK32M8R2WCmNoIqSLTk3W18BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:14:13.730114Z","bundle_sha256":"80f90633303c487cfec3c60ab9e50b63423cb6d9e7dac9f08a61b98a1da39a4b"}}