{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BNF4NVPBHLSQ3IWVSNY6EAITZN","short_pith_number":"pith:BNF4NVPB","canonical_record":{"source":{"id":"1209.1601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-07T18:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"eb584246d9e313239e5202808f3d42bcacf6b5668e5ce67d021fd7f2d493a460","abstract_canon_sha256":"e71e54c729f709976133a5b55cc0095de638d5dfa654dbbce68ff30f714ad5b3"},"schema_version":"1.0"},"canonical_sha256":"0b4bc6d5e13ae50da2d59371e20113cb796f5f772f18a1a7f481675786980efb","source":{"kind":"arxiv","id":"1209.1601","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1601","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1601v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1601","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"BNF4NVPBHLSQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BNF4NVPBHLSQ3IWV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BNF4NVPB","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BNF4NVPBHLSQ3IWVSNY6EAITZN","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-07T18:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"eb584246d9e313239e5202808f3d42bcacf6b5668e5ce67d021fd7f2d493a460","abstract_canon_sha256":"e71e54c729f709976133a5b55cc0095de638d5dfa654dbbce68ff30f714ad5b3"},"schema_version":"1.0"},"canonical_sha256":"0b4bc6d5e13ae50da2d59371e20113cb796f5f772f18a1a7f481675786980efb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.483101Z","signature_b64":"ok/gSdbJ6zvCAz/5tSCE/PyN//+pF6ppuh3Zf7fsjBExUvTTGVVfOmu6zXxSUPxQQjJDEJ1wjS4/xB32BBx5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b4bc6d5e13ae50da2d59371e20113cb796f5f772f18a1a7f481675786980efb","last_reissued_at":"2026-05-17T23:53:18.482381Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.482381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1601","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uSxoZ8H3/e7Z/tnNUgpMAs7gbMXYrsZd6ynHiv0M1M1OH50Hdf7q9bXEyWMkshm+IASVV65iQKT9pmIiUSbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:08:17.486252Z"},"content_sha256":"ef3bd3233e88a4738b3b0c96fb245247bf2423876169b9d4d29c3d33ca9dd8c6","schema_version":"1.0","event_id":"sha256:ef3bd3233e88a4738b3b0c96fb245247bf2423876169b9d4d29c3d33ca9dd8c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BNF4NVPBHLSQ3IWVSNY6EAITZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connectedness of the space of smooth actions of $\\Z^n$ on the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, H\\'el\\`ene Eynard","submitted_at":"2012-09-07T18:10:40Z","abstract_excerpt":"We prove that the spaces of $\\Cinf$ orientation-preserving actions of $\\Z^n$ on $[0,1]$ and nonfree actions of $\\Z^2$ on the circle are connected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1601","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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXpFwfMC22GKWuU0k6On3uJHxkGB3kALpdiJ2kHH9+jRKFjR9bWohMlnbB3ZSz7M5DjXJ+zoZZ15x6/RXeicCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:08:17.486613Z"},"content_sha256":"137ca5049ed11a2e4ab4000a7d51083d2a95e2802a86ae59b35b411cabe920b3","schema_version":"1.0","event_id":"sha256:137ca5049ed11a2e4ab4000a7d51083d2a95e2802a86ae59b35b411cabe920b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/bundle.json","state_url":"https://pith.science/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/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":"2026-05-28T05:08:17Z","links":{"resolver":"https://pith.science/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN","bundle":"https://pith.science/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/bundle.json","state":"https://pith.science/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNF4NVPBHLSQ3IWVSNY6EAITZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BNF4NVPBHLSQ3IWVSNY6EAITZN","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":"e71e54c729f709976133a5b55cc0095de638d5dfa654dbbce68ff30f714ad5b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-07T18:10:40Z","title_canon_sha256":"eb584246d9e313239e5202808f3d42bcacf6b5668e5ce67d021fd7f2d493a460"},"schema_version":"1.0","source":{"id":"1209.1601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1601","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1601v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1601","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"BNF4NVPBHLSQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BNF4NVPBHLSQ3IWV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BNF4NVPB","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:137ca5049ed11a2e4ab4000a7d51083d2a95e2802a86ae59b35b411cabe920b3","target":"graph","created_at":"2026-05-17T23:53:18Z","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 prove that the spaces of $\\Cinf$ orientation-preserving actions of $\\Z^n$ on $[0,1]$ and nonfree actions of $\\Z^2$ on the circle are connected.","authors_text":"Christian Bonatti, H\\'el\\`ene Eynard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-07T18:10:40Z","title":"Connectedness of the space of smooth actions of $\\Z^n$ on the interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1601","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:ef3bd3233e88a4738b3b0c96fb245247bf2423876169b9d4d29c3d33ca9dd8c6","target":"record","created_at":"2026-05-17T23:53:18Z","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":"e71e54c729f709976133a5b55cc0095de638d5dfa654dbbce68ff30f714ad5b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-07T18:10:40Z","title_canon_sha256":"eb584246d9e313239e5202808f3d42bcacf6b5668e5ce67d021fd7f2d493a460"},"schema_version":"1.0","source":{"id":"1209.1601","kind":"arxiv","version":1}},"canonical_sha256":"0b4bc6d5e13ae50da2d59371e20113cb796f5f772f18a1a7f481675786980efb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b4bc6d5e13ae50da2d59371e20113cb796f5f772f18a1a7f481675786980efb","first_computed_at":"2026-05-17T23:53:18.482381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.482381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ok/gSdbJ6zvCAz/5tSCE/PyN//+pF6ppuh3Zf7fsjBExUvTTGVVfOmu6zXxSUPxQQjJDEJ1wjS4/xB32BBx5BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.483101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef3bd3233e88a4738b3b0c96fb245247bf2423876169b9d4d29c3d33ca9dd8c6","sha256:137ca5049ed11a2e4ab4000a7d51083d2a95e2802a86ae59b35b411cabe920b3"],"state_sha256":"c7785fca1173171aa611ca9e323b4d37e7690e3fa9784ab1be0f33b4648039b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Op7ems763NN33yxMFPjyL1dOSVPzZRzIFmmmDuxiU4SkWqkCgEW+DZ6MgZhjnk23215qWZBhFx/SbNsKIEFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:08:17.488589Z","bundle_sha256":"e5907427a9702dfb6fadaefe76695fb80238727fb0c1259f0410975eef0c6810"}}