{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N7YNCRU7K3H33CTHHKJEEX5APC","short_pith_number":"pith:N7YNCRU7","canonical_record":{"source":{"id":"1407.7771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T16:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"db02c7196ec975eee41088aa18803e00fcd64655ed7d4a67379c0d8bfaeb0c4d","abstract_canon_sha256":"0baeb2a0722c8405d572049ee46192584fed4eb127067df70f68e364f928202a"},"schema_version":"1.0"},"canonical_sha256":"6ff0d1469f56cfbd8a673a92425fa078bd966288938a2422ac77ef45452439da","source":{"kind":"arxiv","id":"1407.7771","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7771","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7771v2","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7771","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"N7YNCRU7K3H3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7YNCRU7K3H33CTH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7YNCRU7","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N7YNCRU7K3H33CTHHKJEEX5APC","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T16:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"db02c7196ec975eee41088aa18803e00fcd64655ed7d4a67379c0d8bfaeb0c4d","abstract_canon_sha256":"0baeb2a0722c8405d572049ee46192584fed4eb127067df70f68e364f928202a"},"schema_version":"1.0"},"canonical_sha256":"6ff0d1469f56cfbd8a673a92425fa078bd966288938a2422ac77ef45452439da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:01.291701Z","signature_b64":"H1+JTu1MgoFBnFuEL++YUSYav6mh32ALy3/8oTZAb5NSVCM61EVRMnSNJQF35VQIbPbTDU4HKC0JginQ9L/0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff0d1469f56cfbd8a673a92425fa078bd966288938a2422ac77ef45452439da","last_reissued_at":"2026-05-18T01:17:01.290988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:01.290988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7771","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":"2026-05-18T01:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVFsdMN34dlwmLWsbnvOe8gAY6m7Fq/ytT99+TBudcZ2TmwEWfMqrvaAR7uxu72j8r5XgpOPS9vibTEt5NmMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:43:05.430744Z"},"content_sha256":"ae2278a08710a18ea6ab623a0d0aa94aa8e388f76c8a575adda129d275d8966f","schema_version":"1.0","event_id":"sha256:ae2278a08710a18ea6ab623a0d0aa94aa8e388f76c8a575adda129d275d8966f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N7YNCRU7K3H33CTHHKJEEX5APC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bootstrap for local rigidity of Anosov automorphisms on the 3-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrey Gogolev","submitted_at":"2014-07-29T16:51:28Z","abstract_excerpt":"We establish a strong form of local rigidity for hyperbolic automorphisms of the 3-torus with real spectrum. Namely, let $L\\colon\\mathbb T^3\\to\\mathbb T^3$ be a hyperbolic automorphism of the 3-torus with real spectrum and let $f$ be a $C^1$ small perturbation of $L$. Then $f$ is smoothly ($C^\\infty$) conjugate to $L$ if and only if obstructions to $C^1$ conjugacy given by the eigenvalues at periodic points of $f$ vanish. By combining our result and a local rigidity result of Kalinin and Sadovskaya for conformal automorphisms this completes the local rigidity program for hyperbolic automorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7771","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":"2026-05-18T01:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MywsbChitFR8xlH2AxtAN6mZ7QOjcNkXF41z8uVib3xmwxHLdrKrRlf1uwHtcZ72mQrCtp1sVWBAyWUk2BSgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:43:05.431094Z"},"content_sha256":"0e17638c32925d84ca34a8e91041951ff5927b94575d29a829beb2794a098837","schema_version":"1.0","event_id":"sha256:0e17638c32925d84ca34a8e91041951ff5927b94575d29a829beb2794a098837"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7YNCRU7K3H33CTHHKJEEX5APC/bundle.json","state_url":"https://pith.science/pith/N7YNCRU7K3H33CTHHKJEEX5APC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7YNCRU7K3H33CTHHKJEEX5APC/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":"2026-06-01T02:43:05Z","links":{"resolver":"https://pith.science/pith/N7YNCRU7K3H33CTHHKJEEX5APC","bundle":"https://pith.science/pith/N7YNCRU7K3H33CTHHKJEEX5APC/bundle.json","state":"https://pith.science/pith/N7YNCRU7K3H33CTHHKJEEX5APC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7YNCRU7K3H33CTHHKJEEX5APC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N7YNCRU7K3H33CTHHKJEEX5APC","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":"0baeb2a0722c8405d572049ee46192584fed4eb127067df70f68e364f928202a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T16:51:28Z","title_canon_sha256":"db02c7196ec975eee41088aa18803e00fcd64655ed7d4a67379c0d8bfaeb0c4d"},"schema_version":"1.0","source":{"id":"1407.7771","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7771","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7771v2","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7771","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"N7YNCRU7K3H3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7YNCRU7K3H33CTH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7YNCRU7","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:0e17638c32925d84ca34a8e91041951ff5927b94575d29a829beb2794a098837","target":"graph","created_at":"2026-05-18T01:17:01Z","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":"We establish a strong form of local rigidity for hyperbolic automorphisms of the 3-torus with real spectrum. Namely, let $L\\colon\\mathbb T^3\\to\\mathbb T^3$ be a hyperbolic automorphism of the 3-torus with real spectrum and let $f$ be a $C^1$ small perturbation of $L$. Then $f$ is smoothly ($C^\\infty$) conjugate to $L$ if and only if obstructions to $C^1$ conjugacy given by the eigenvalues at periodic points of $f$ vanish. By combining our result and a local rigidity result of Kalinin and Sadovskaya for conformal automorphisms this completes the local rigidity program for hyperbolic automorphis","authors_text":"Andrey Gogolev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T16:51:28Z","title":"Bootstrap for local rigidity of Anosov automorphisms on the 3-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7771","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:ae2278a08710a18ea6ab623a0d0aa94aa8e388f76c8a575adda129d275d8966f","target":"record","created_at":"2026-05-18T01:17:01Z","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":"0baeb2a0722c8405d572049ee46192584fed4eb127067df70f68e364f928202a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-29T16:51:28Z","title_canon_sha256":"db02c7196ec975eee41088aa18803e00fcd64655ed7d4a67379c0d8bfaeb0c4d"},"schema_version":"1.0","source":{"id":"1407.7771","kind":"arxiv","version":2}},"canonical_sha256":"6ff0d1469f56cfbd8a673a92425fa078bd966288938a2422ac77ef45452439da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff0d1469f56cfbd8a673a92425fa078bd966288938a2422ac77ef45452439da","first_computed_at":"2026-05-18T01:17:01.290988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:01.290988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H1+JTu1MgoFBnFuEL++YUSYav6mh32ALy3/8oTZAb5NSVCM61EVRMnSNJQF35VQIbPbTDU4HKC0JginQ9L/0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:01.291701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7771","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae2278a08710a18ea6ab623a0d0aa94aa8e388f76c8a575adda129d275d8966f","sha256:0e17638c32925d84ca34a8e91041951ff5927b94575d29a829beb2794a098837"],"state_sha256":"c60409c055464ea59aa6060b922ef0b406a8337d996796b29c7cdd72af185d84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZzPKKY4j8Ut6wdBuf0SErgGctcEhP73wXmMXmqgjWY2wN2vVo5raQ3jzr8LSXnfE8P2FZi8DHTbH510n9mJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:43:05.433098Z","bundle_sha256":"361b6ceb444ab36299a0a14cd47929b8a1d82ec78ce4f052920a9b4d0e60a6c2"}}