{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M6GTY25A2IGU2QACKTEIFJ2NA3","short_pith_number":"pith:M6GTY25A","canonical_record":{"source":{"id":"1211.1063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-05T22:37:24Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"625f1b0b879925cc9184f5f468ce341d9b082d02f55cf2c8aca2680e869656ac","abstract_canon_sha256":"2b86ec128c6f635c413ef809cbfcbcbd2720c01c7081045f391b2c2ffddacbfa"},"schema_version":"1.0"},"canonical_sha256":"678d3c6ba0d20d4d400254c882a74d06fa24e2c79c9db4ffe5af1f119d04643b","source":{"kind":"arxiv","id":"1211.1063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1063","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1063v1","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1063","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"M6GTY25A2IGU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M6GTY25A2IGU2QAC","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M6GTY25A","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M6GTY25A2IGU2QACKTEIFJ2NA3","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-05T22:37:24Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"625f1b0b879925cc9184f5f468ce341d9b082d02f55cf2c8aca2680e869656ac","abstract_canon_sha256":"2b86ec128c6f635c413ef809cbfcbcbd2720c01c7081045f391b2c2ffddacbfa"},"schema_version":"1.0"},"canonical_sha256":"678d3c6ba0d20d4d400254c882a74d06fa24e2c79c9db4ffe5af1f119d04643b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:25.414972Z","signature_b64":"2dt99klx50C0fNLOxMxQGT70b9FDx1VJyZcpzRT23Vq9hJ3pEGaIpCLmvpEeL12HulqlGcJrBkIHJG9PuQMCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"678d3c6ba0d20d4d400254c882a74d06fa24e2c79c9db4ffe5af1f119d04643b","last_reissued_at":"2026-05-18T01:53:25.414278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:25.414278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1063","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":"2026-05-18T01:53:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HzK+X2CgR6vDoTOy7fJI8/RxPl4OTXpf7bQ1W3zcHawmaNyDFHZSlO1xeiqqiEMKupYP2DoGs5dJJbb7pF2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:19:05.433145Z"},"content_sha256":"58de9f757d05f0d0f42f41058f01ecd7442873f5e5a2f509626bdcb20acdb103","schema_version":"1.0","event_id":"sha256:58de9f757d05f0d0f42f41058f01ecd7442873f5e5a2f509626bdcb20acdb103"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M6GTY25A2IGU2QACKTEIFJ2NA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A dynamical model for hierarchy and modular organization: The trajectories en route to the attractor at the transition to chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Alberto Robledo","submitted_at":"2012-11-05T22:37:24Z","abstract_excerpt":"We show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut emergent property. This well-known nonlinear model system combines a simple and precise definition, an intricate nested hierarchical dynamical structure, and emergence of a power-law dynamical property absent in the exponential-law that governs the dynamics within the modules. This classic nonlinear system is put forward as a working example for complex collect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1063","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":"2026-05-18T01:53:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5dpIJkgjRSsoF7Jowx2hukFS6wHtf040i2dFD9RfBC25LKZ51ChawvlUFw7pg9XN1m6CjRwKJ1M5TLnXoyTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:19:05.433517Z"},"content_sha256":"d015b3b4b8c851b095c2cce1bd01c3f1940d610992b5c447bc9141786340d3a1","schema_version":"1.0","event_id":"sha256:d015b3b4b8c851b095c2cce1bd01c3f1940d610992b5c447bc9141786340d3a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/bundle.json","state_url":"https://pith.science/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/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":"2026-06-20T08:19:05Z","links":{"resolver":"https://pith.science/pith/M6GTY25A2IGU2QACKTEIFJ2NA3","bundle":"https://pith.science/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/bundle.json","state":"https://pith.science/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6GTY25A2IGU2QACKTEIFJ2NA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M6GTY25A2IGU2QACKTEIFJ2NA3","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":"2b86ec128c6f635c413ef809cbfcbcbd2720c01c7081045f391b2c2ffddacbfa","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-05T22:37:24Z","title_canon_sha256":"625f1b0b879925cc9184f5f468ce341d9b082d02f55cf2c8aca2680e869656ac"},"schema_version":"1.0","source":{"id":"1211.1063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1063","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1063v1","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1063","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"M6GTY25A2IGU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M6GTY25A2IGU2QAC","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M6GTY25A","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:d015b3b4b8c851b095c2cce1bd01c3f1940d610992b5c447bc9141786340d3a1","target":"graph","created_at":"2026-05-18T01:53:25Z","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 show that the full features of the dynamics towards the Feigenbaum attractor, present in all low-dimensional maps with a unimodal leading component, form a hierarchical construction with modular organization that leads to a clear-cut emergent property. This well-known nonlinear model system combines a simple and precise definition, an intricate nested hierarchical dynamical structure, and emergence of a power-law dynamical property absent in the exponential-law that governs the dynamics within the modules. This classic nonlinear system is put forward as a working example for complex collect","authors_text":"Alberto Robledo","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-05T22:37:24Z","title":"A dynamical model for hierarchy and modular organization: The trajectories en route to the attractor at the transition to chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1063","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":"sha256:58de9f757d05f0d0f42f41058f01ecd7442873f5e5a2f509626bdcb20acdb103","target":"record","created_at":"2026-05-18T01:53:25Z","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":"2b86ec128c6f635c413ef809cbfcbcbd2720c01c7081045f391b2c2ffddacbfa","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-11-05T22:37:24Z","title_canon_sha256":"625f1b0b879925cc9184f5f468ce341d9b082d02f55cf2c8aca2680e869656ac"},"schema_version":"1.0","source":{"id":"1211.1063","kind":"arxiv","version":1}},"canonical_sha256":"678d3c6ba0d20d4d400254c882a74d06fa24e2c79c9db4ffe5af1f119d04643b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"678d3c6ba0d20d4d400254c882a74d06fa24e2c79c9db4ffe5af1f119d04643b","first_computed_at":"2026-05-18T01:53:25.414278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:25.414278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2dt99klx50C0fNLOxMxQGT70b9FDx1VJyZcpzRT23Vq9hJ3pEGaIpCLmvpEeL12HulqlGcJrBkIHJG9PuQMCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:25.414972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58de9f757d05f0d0f42f41058f01ecd7442873f5e5a2f509626bdcb20acdb103","sha256:d015b3b4b8c851b095c2cce1bd01c3f1940d610992b5c447bc9141786340d3a1"],"state_sha256":"1f6cbac9f2bfc836a10addc3c1aeb366f3663d197e220ae51b709611ed7968d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7cMJMGal0gQbpbgLrmQRGldz+lLI7oZkl+QCpzet1rRtHCQY+EzJqvGEHfBBsofUaJB+2JxHFbk/FvyM/A0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:19:05.435541Z","bundle_sha256":"767db0cef2235ce0a3898e112ec25adf815e86fbda3916ccba2648c169d0aba6"}}