{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:GEBM6FERM2YIDTI6QD26WEAIKM","short_pith_number":"pith:GEBM6FER","canonical_record":{"source":{"id":"math/0502236","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-02-11T10:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"5aa1be60829490d229a9a887cf08eba9cb210c0046a2d4b8bdc795d6e6aedd24","abstract_canon_sha256":"ebf4b43a40e36baadff42bfc156e395f7746e76cfc9a798a55ddaccd8f42559b"},"schema_version":"1.0"},"canonical_sha256":"3102cf149166b081cd1e80f5eb10085312d1901ab4b0dfd881bb3be36d018674","source":{"kind":"arxiv","id":"math/0502236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502236","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502236v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502236","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"GEBM6FERM2YI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GEBM6FERM2YIDTI6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GEBM6FER","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:GEBM6FERM2YIDTI6QD26WEAIKM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0502236","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-02-11T10:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"5aa1be60829490d229a9a887cf08eba9cb210c0046a2d4b8bdc795d6e6aedd24","abstract_canon_sha256":"ebf4b43a40e36baadff42bfc156e395f7746e76cfc9a798a55ddaccd8f42559b"},"schema_version":"1.0"},"canonical_sha256":"3102cf149166b081cd1e80f5eb10085312d1901ab4b0dfd881bb3be36d018674","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:21.695330Z","signature_b64":"skRlEgwkYgXVYuRitpYaKWkhg5wwMkyNhTcpHqHuTd3/ki7w0WZvwdRfghiHc5C2Di7YtSrol5YDeZdCYoWqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3102cf149166b081cd1e80f5eb10085312d1901ab4b0dfd881bb3be36d018674","last_reissued_at":"2026-05-18T03:41:21.694852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:21.694852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0502236","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEXA0QowkY0t5FjQAr+lTjGNi9NoW33p9OPEJ75+G5AbaDX96b2sRBw8eBuYR6nmB0+jbgYYdHA1n0T8AjB1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:05:47.731190Z"},"content_sha256":"84b5e2ed855250e295962d89f7f32ed467f8304d6274ee64d42d73369e267ea6","schema_version":"1.0","event_id":"sha256:84b5e2ed855250e295962d89f7f32ed467f8304d6274ee64d42d73369e267ea6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:GEBM6FERM2YIDTI6QD26WEAIKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable manifolds under very weak hyperbolicity conditions","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Holland, Stefano Luzzatto","submitted_at":"2005-02-11T10:38:48Z","abstract_excerpt":"We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502236","kind":"arxiv","version":1},"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":"2026-05-18T03:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7K+RRz6xirbkX37PRkW0kmfMjNfWIFQoZ1+MKc9+bB3TX6jZzxsgZWI8GYSEgyAQkgoGJ1Vy30tLCMgBk5dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:05:47.731535Z"},"content_sha256":"9abbbf68ad84021e3bf8d2b1e9debd1097bdeda22661be6f6cb4849de769c56f","schema_version":"1.0","event_id":"sha256:9abbbf68ad84021e3bf8d2b1e9debd1097bdeda22661be6f6cb4849de769c56f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEBM6FERM2YIDTI6QD26WEAIKM/bundle.json","state_url":"https://pith.science/pith/GEBM6FERM2YIDTI6QD26WEAIKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEBM6FERM2YIDTI6QD26WEAIKM/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":"2026-06-03T14:05:47Z","links":{"resolver":"https://pith.science/pith/GEBM6FERM2YIDTI6QD26WEAIKM","bundle":"https://pith.science/pith/GEBM6FERM2YIDTI6QD26WEAIKM/bundle.json","state":"https://pith.science/pith/GEBM6FERM2YIDTI6QD26WEAIKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEBM6FERM2YIDTI6QD26WEAIKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:GEBM6FERM2YIDTI6QD26WEAIKM","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":"ebf4b43a40e36baadff42bfc156e395f7746e76cfc9a798a55ddaccd8f42559b","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-02-11T10:38:48Z","title_canon_sha256":"5aa1be60829490d229a9a887cf08eba9cb210c0046a2d4b8bdc795d6e6aedd24"},"schema_version":"1.0","source":{"id":"math/0502236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502236","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502236v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502236","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"GEBM6FERM2YI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GEBM6FERM2YIDTI6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GEBM6FER","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9abbbf68ad84021e3bf8d2b1e9debd1097bdeda22661be6f6cb4849de769c56f","target":"graph","created_at":"2026-05-18T03:41:21Z","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 present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.","authors_text":"Mark Holland, Stefano Luzzatto","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-02-11T10:38:48Z","title":"Stable manifolds under very weak hyperbolicity conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502236","kind":"arxiv","version":1},"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":"sha256:84b5e2ed855250e295962d89f7f32ed467f8304d6274ee64d42d73369e267ea6","target":"record","created_at":"2026-05-18T03:41:21Z","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":"ebf4b43a40e36baadff42bfc156e395f7746e76cfc9a798a55ddaccd8f42559b","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-02-11T10:38:48Z","title_canon_sha256":"5aa1be60829490d229a9a887cf08eba9cb210c0046a2d4b8bdc795d6e6aedd24"},"schema_version":"1.0","source":{"id":"math/0502236","kind":"arxiv","version":1}},"canonical_sha256":"3102cf149166b081cd1e80f5eb10085312d1901ab4b0dfd881bb3be36d018674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3102cf149166b081cd1e80f5eb10085312d1901ab4b0dfd881bb3be36d018674","first_computed_at":"2026-05-18T03:41:21.694852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:21.694852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skRlEgwkYgXVYuRitpYaKWkhg5wwMkyNhTcpHqHuTd3/ki7w0WZvwdRfghiHc5C2Di7YtSrol5YDeZdCYoWqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:21.695330Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84b5e2ed855250e295962d89f7f32ed467f8304d6274ee64d42d73369e267ea6","sha256:9abbbf68ad84021e3bf8d2b1e9debd1097bdeda22661be6f6cb4849de769c56f"],"state_sha256":"ad4cee4e06ab30f3e79104121e044c0a2aa84d9a694392731b80ae9033506b5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkSbKcgVAVmM+4DHKKjmoXJe5Ai09LIAfRHCIoaonUTwqNq1TdJhioRAcgUPR0B0YLqjcuZzlqYdSr+rrfGGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:05:47.734182Z","bundle_sha256":"9f37f98fc8da490f8360e2ba1f0405292796c47776fb9bc581547874d0714b13"}}