{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZCCYD6XC3L3AL6YUW56EMHSHKP","short_pith_number":"pith:ZCCYD6XC","canonical_record":{"source":{"id":"1210.6758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-25T08:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"e42aa56692cf76da55394496328c7284343f6e5e3c1ffe0623c931159093fe3d","abstract_canon_sha256":"528614924a9be4ba05e6a442107074c4c7a861ad0cda9c6813d5e564add336eb"},"schema_version":"1.0"},"canonical_sha256":"c88581fae2daf605fb14b77c461e4753fb821dc415ce46eb481ba88f575dc2cb","source":{"kind":"arxiv","id":"1210.6758","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6758","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6758v1","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6758","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZCCYD6XC3L3A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZCCYD6XC3L3AL6YU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZCCYD6XC","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZCCYD6XC3L3AL6YUW56EMHSHKP","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-25T08:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"e42aa56692cf76da55394496328c7284343f6e5e3c1ffe0623c931159093fe3d","abstract_canon_sha256":"528614924a9be4ba05e6a442107074c4c7a861ad0cda9c6813d5e564add336eb"},"schema_version":"1.0"},"canonical_sha256":"c88581fae2daf605fb14b77c461e4753fb821dc415ce46eb481ba88f575dc2cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:23.227897Z","signature_b64":"FYnb1BLLtfNUABIWY+1BjUqBol3VymbGNxVALxH9h83eqDu9Zk7yulF5p+MlG/d2nphvr5AfnaGpbE1+hUBPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c88581fae2daf605fb14b77c461e4753fb821dc415ce46eb481ba88f575dc2cb","last_reissued_at":"2026-05-18T03:42:23.227169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:23.227169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6758","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":"2026-05-18T03:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oiIM9BxKPbgLcmyjs8ySnviVp9YC2xhhG1Y3/ljsckE3E1ZRyLIq5Uo0AIwct7Pp+LK1dDipVK+tOBm2TWlcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:55:50.953581Z"},"content_sha256":"087360bdf26814a7db7dac19262479c6044c63ff348ac8ee0be421466618cd3f","schema_version":"1.0","event_id":"sha256:087360bdf26814a7db7dac19262479c6044c63ff348ac8ee0be421466618cd3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZCCYD6XC3L3AL6YUW56EMHSHKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The prediction of future from the past: an old problem from a modern perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"A. Vulpiani, F. Cecconi, M. Cencini, M falcioni","submitted_at":"2012-10-25T08:50:51Z","abstract_excerpt":"The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predicta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6758","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":"2026-05-18T03:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pe0OJe+OoAqUvrttBXhSEnfVXgKbTS9dhr4TOi13xzDbX4WZBRQvwwNR8W71wcb+xagcmt6FGP9iPNRfivhvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:55:50.954292Z"},"content_sha256":"534cef1bef95ab8c971569f31742deec09a1bd9e84bcee7bad5600dd831f46df","schema_version":"1.0","event_id":"sha256:534cef1bef95ab8c971569f31742deec09a1bd9e84bcee7bad5600dd831f46df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/bundle.json","state_url":"https://pith.science/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/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":"2026-06-08T20:55:50Z","links":{"resolver":"https://pith.science/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP","bundle":"https://pith.science/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/bundle.json","state":"https://pith.science/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCCYD6XC3L3AL6YUW56EMHSHKP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZCCYD6XC3L3AL6YUW56EMHSHKP","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":"528614924a9be4ba05e6a442107074c4c7a861ad0cda9c6813d5e564add336eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-25T08:50:51Z","title_canon_sha256":"e42aa56692cf76da55394496328c7284343f6e5e3c1ffe0623c931159093fe3d"},"schema_version":"1.0","source":{"id":"1210.6758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6758","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6758v1","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6758","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZCCYD6XC3L3A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZCCYD6XC3L3AL6YU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZCCYD6XC","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:534cef1bef95ab8c971569f31742deec09a1bd9e84bcee7bad5600dd831f46df","target":"graph","created_at":"2026-05-18T03:42:23Z","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":"The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predicta","authors_text":"A. Vulpiani, F. Cecconi, M. Cencini, M falcioni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-25T08:50:51Z","title":"The prediction of future from the past: an old problem from a modern perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6758","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":"sha256:087360bdf26814a7db7dac19262479c6044c63ff348ac8ee0be421466618cd3f","target":"record","created_at":"2026-05-18T03:42:23Z","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":"528614924a9be4ba05e6a442107074c4c7a861ad0cda9c6813d5e564add336eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-25T08:50:51Z","title_canon_sha256":"e42aa56692cf76da55394496328c7284343f6e5e3c1ffe0623c931159093fe3d"},"schema_version":"1.0","source":{"id":"1210.6758","kind":"arxiv","version":1}},"canonical_sha256":"c88581fae2daf605fb14b77c461e4753fb821dc415ce46eb481ba88f575dc2cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88581fae2daf605fb14b77c461e4753fb821dc415ce46eb481ba88f575dc2cb","first_computed_at":"2026-05-18T03:42:23.227169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:23.227169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FYnb1BLLtfNUABIWY+1BjUqBol3VymbGNxVALxH9h83eqDu9Zk7yulF5p+MlG/d2nphvr5AfnaGpbE1+hUBPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:23.227897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:087360bdf26814a7db7dac19262479c6044c63ff348ac8ee0be421466618cd3f","sha256:534cef1bef95ab8c971569f31742deec09a1bd9e84bcee7bad5600dd831f46df"],"state_sha256":"2a05190b866429e985e806773c48608cb74f1edf5193fb8b1c4e79ff851295d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"koHZA1APaUXD3KBRHVOinV9swk5ty2F8TjQ9a3pCeKUgKR9GdasgFCMwXeV82r6lc7lcbMixoRKbR3MYzGx3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:55:50.958153Z","bundle_sha256":"052e831d3284659b8bc21e7439fc5ba962248e4531f33204e14380779d2db4d1"}}