{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:4XKB5KOUFHONMDYHPNLB3M6JZ3","short_pith_number":"pith:4XKB5KOU","canonical_record":{"source":{"id":"2106.06511","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"nlin.AO","submitted_at":"2021-06-11T17:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"c5d0449d8a60ce977d297e16f49fffc770b31c08f69fb4406c4261919e3b5634","abstract_canon_sha256":"dc44b1cdf7ee2484f039649283082039ce042d7dedf71d7df5feabdb9f606761"},"schema_version":"1.0"},"canonical_sha256":"e5d41ea9d429dcd60f077b561db3c9cecb1d48bd16edbc98a1c97b433328369e","source":{"kind":"arxiv","id":"2106.06511","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06511","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06511v2","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06511","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_12","alias_value":"4XKB5KOUFHON","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_16","alias_value":"4XKB5KOUFHONMDYH","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_8","alias_value":"4XKB5KOU","created_at":"2026-07-05T06:34:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:4XKB5KOUFHONMDYHPNLB3M6JZ3","target":"record","payload":{"canonical_record":{"source":{"id":"2106.06511","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"nlin.AO","submitted_at":"2021-06-11T17:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"c5d0449d8a60ce977d297e16f49fffc770b31c08f69fb4406c4261919e3b5634","abstract_canon_sha256":"dc44b1cdf7ee2484f039649283082039ce042d7dedf71d7df5feabdb9f606761"},"schema_version":"1.0"},"canonical_sha256":"e5d41ea9d429dcd60f077b561db3c9cecb1d48bd16edbc98a1c97b433328369e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:34:16.083635Z","signature_b64":"b5Br/tsoLGjqBLZIEPt/MzOTm8odKY6k+9BZ+Ritddazf1OnPXAxZsvFhtxDMuYgZJwu8ma3lDNkZ8gineR0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5d41ea9d429dcd60f077b561db3c9cecb1d48bd16edbc98a1c97b433328369e","last_reissued_at":"2026-07-05T06:34:16.083250Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:34:16.083250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.06511","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":"2026-07-05T06:34:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53363MYlivTWN6LGYls7jFzgASogA11yELBk8bqCpAmsrccGNWyUcDQp4ncJWEZW4CXBym7IMAWM36eg/nVpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:03:16.974501Z"},"content_sha256":"1319f9a81d5a999ae492c41e5ed3f3736768fe28b6e7ca9d26ea2f3ddfc03880","schema_version":"1.0","event_id":"sha256:1319f9a81d5a999ae492c41e5ed3f3736768fe28b6e7ca9d26ea2f3ddfc03880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:4XKB5KOUFHONMDYHPNLB3M6JZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Anil K. Seth, Lionel Barnett","submitted_at":"2021-06-11T17:11:45Z","abstract_excerpt":"We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system \"in its own right\", with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06511","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.06511/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:34:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nBtdgajeE9yBDtQqYhh3vXRkbksl4bDSIsxF7wn4SnpEaUvUDuHDMywOjjNlhI5nf0xz7KDnIOkO8E+FcTT/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:03:16.975485Z"},"content_sha256":"8ab25850cf640de494dbe4058475051141e8a266c90cd72d77d5493aca3134a3","schema_version":"1.0","event_id":"sha256:8ab25850cf640de494dbe4058475051141e8a266c90cd72d77d5493aca3134a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/bundle.json","state_url":"https://pith.science/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/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":"2026-08-11T18:03:16Z","links":{"resolver":"https://pith.science/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3","bundle":"https://pith.science/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/bundle.json","state":"https://pith.science/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XKB5KOUFHONMDYHPNLB3M6JZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4XKB5KOUFHONMDYHPNLB3M6JZ3","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":"dc44b1cdf7ee2484f039649283082039ce042d7dedf71d7df5feabdb9f606761","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"nlin.AO","submitted_at":"2021-06-11T17:11:45Z","title_canon_sha256":"c5d0449d8a60ce977d297e16f49fffc770b31c08f69fb4406c4261919e3b5634"},"schema_version":"1.0","source":{"id":"2106.06511","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06511","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06511v2","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06511","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_12","alias_value":"4XKB5KOUFHON","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_16","alias_value":"4XKB5KOUFHONMDYH","created_at":"2026-07-05T06:34:16Z"},{"alias_kind":"pith_short_8","alias_value":"4XKB5KOU","created_at":"2026-07-05T06:34:16Z"}],"graph_snapshots":[{"event_id":"sha256:8ab25850cf640de494dbe4058475051141e8a266c90cd72d77d5493aca3134a3","target":"graph","created_at":"2026-07-05T06:34:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.06511/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system \"in its own right\", with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasi","authors_text":"Anil K. Seth, Lionel Barnett","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"nlin.AO","submitted_at":"2021-06-11T17:11:45Z","title":"Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06511","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":"sha256:1319f9a81d5a999ae492c41e5ed3f3736768fe28b6e7ca9d26ea2f3ddfc03880","target":"record","created_at":"2026-07-05T06:34:16Z","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":"dc44b1cdf7ee2484f039649283082039ce042d7dedf71d7df5feabdb9f606761","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"nlin.AO","submitted_at":"2021-06-11T17:11:45Z","title_canon_sha256":"c5d0449d8a60ce977d297e16f49fffc770b31c08f69fb4406c4261919e3b5634"},"schema_version":"1.0","source":{"id":"2106.06511","kind":"arxiv","version":2}},"canonical_sha256":"e5d41ea9d429dcd60f077b561db3c9cecb1d48bd16edbc98a1c97b433328369e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5d41ea9d429dcd60f077b561db3c9cecb1d48bd16edbc98a1c97b433328369e","first_computed_at":"2026-07-05T06:34:16.083250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:34:16.083250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b5Br/tsoLGjqBLZIEPt/MzOTm8odKY6k+9BZ+Ritddazf1OnPXAxZsvFhtxDMuYgZJwu8ma3lDNkZ8gineR0CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:34:16.083635Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.06511","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1319f9a81d5a999ae492c41e5ed3f3736768fe28b6e7ca9d26ea2f3ddfc03880","sha256:8ab25850cf640de494dbe4058475051141e8a266c90cd72d77d5493aca3134a3"],"state_sha256":"9f0a78d501f0093291195441af340247e51b9dd83cc932012c45fbf212995d48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvOrD7wMNp6auf59r2ThLntip3/bj+VuD6EnVx/XYcxLQeFjpHw7wuErFlWqzCmXIUZ5yKRI3OZN4s+BBamrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T18:03:16.983674Z","bundle_sha256":"9903b63fffe8061c9f571d96d9ae439f8e353c05d008fe1ed49f694304146f70"}}