{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KI4UQ7Z2SSNR7KAO6IUNRIK4OS","short_pith_number":"pith:KI4UQ7Z2","canonical_record":{"source":{"id":"1309.3792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-15T20:06:56Z","cross_cats_sorted":["cs.IT","math.IT","nlin.CD","nlin.CG"],"title_canon_sha256":"460af8ad311a0f4cf764987d2f491cf743344a601444da4bcba76ab226c45b40","abstract_canon_sha256":"f20dc90f59f53daf08970db1214a05d99f620819bf9928678bde543c3ccd3170"},"schema_version":"1.0"},"canonical_sha256":"5239487f3a949b1fa80ef228d8a15c74834e9debd26867228dd6d6c4d7e629df","source":{"kind":"arxiv","id":"1309.3792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3792","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3792v1","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3792","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"KI4UQ7Z2SSNR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KI4UQ7Z2SSNR7KAO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KI4UQ7Z2","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KI4UQ7Z2SSNR7KAO6IUNRIK4OS","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-15T20:06:56Z","cross_cats_sorted":["cs.IT","math.IT","nlin.CD","nlin.CG"],"title_canon_sha256":"460af8ad311a0f4cf764987d2f491cf743344a601444da4bcba76ab226c45b40","abstract_canon_sha256":"f20dc90f59f53daf08970db1214a05d99f620819bf9928678bde543c3ccd3170"},"schema_version":"1.0"},"canonical_sha256":"5239487f3a949b1fa80ef228d8a15c74834e9debd26867228dd6d6c4d7e629df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:20.529240Z","signature_b64":"udMa/1YdOyjowZ29yMTPxfiskuctUGNBhdAa4DzUb4+jVCawGc2m0vWf+N1r8EwopV6tWzu8cGHIEumnO5qVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5239487f3a949b1fa80ef228d8a15c74834e9debd26867228dd6d6c4d7e629df","last_reissued_at":"2026-05-18T03:13:20.528693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:20.528693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3792","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":"2026-05-18T03:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQ42fQ3MxdAOnu6RGuDl3yrG7QY/nwpcbPc09jLoyp602ltXQj89y1aEqIAaLVzrgtj2iAA0IPSZuWTw0gXABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:15:32.615514Z"},"content_sha256":"95358a020ff0a6536d8745ee0bdc28a5084bcec4eb71d89de44ee930ab09e78f","schema_version":"1.0","event_id":"sha256:95358a020ff0a6536d8745ee0bdc28a5084bcec4eb71d89de44ee930ab09e78f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KI4UQ7Z2SSNR7KAO6IUNRIK4OS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Complexity: The Spectral Decomposition of Intrinsic Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","nlin.CD","nlin.CG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Christopher J. Ellison, James P. Crutchfield, Paul M. Riechers","submitted_at":"2013-09-15T20:06:56Z","abstract_excerpt":"We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's epsilon-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3792","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":"2026-05-18T03:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmMGSUwG/UYhtwM5y2zrUY1ALUvutf4UkFTFGOFHyvs2xdWHX/643gYCT4dNmXSkJ4cDyipgKc/x5HnBRPR9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:15:32.616247Z"},"content_sha256":"764df4c37e9b4e0d6436e9ddf870001e128caa87365787bb8164c5a742e9a739","schema_version":"1.0","event_id":"sha256:764df4c37e9b4e0d6436e9ddf870001e128caa87365787bb8164c5a742e9a739"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/bundle.json","state_url":"https://pith.science/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/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":"2026-06-08T05:15:32Z","links":{"resolver":"https://pith.science/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS","bundle":"https://pith.science/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/bundle.json","state":"https://pith.science/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KI4UQ7Z2SSNR7KAO6IUNRIK4OS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KI4UQ7Z2SSNR7KAO6IUNRIK4OS","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":"f20dc90f59f53daf08970db1214a05d99f620819bf9928678bde543c3ccd3170","cross_cats_sorted":["cs.IT","math.IT","nlin.CD","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-15T20:06:56Z","title_canon_sha256":"460af8ad311a0f4cf764987d2f491cf743344a601444da4bcba76ab226c45b40"},"schema_version":"1.0","source":{"id":"1309.3792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3792","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3792v1","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3792","created_at":"2026-05-18T03:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"KI4UQ7Z2SSNR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KI4UQ7Z2SSNR7KAO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KI4UQ7Z2","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:764df4c37e9b4e0d6436e9ddf870001e128caa87365787bb8164c5a742e9a739","target":"graph","created_at":"2026-05-18T03:13:20Z","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 give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's epsilon-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organizatio","authors_text":"Christopher J. Ellison, James P. Crutchfield, Paul M. Riechers","cross_cats":["cs.IT","math.IT","nlin.CD","nlin.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-15T20:06:56Z","title":"Exact Complexity: The Spectral Decomposition of Intrinsic Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3792","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":"sha256:95358a020ff0a6536d8745ee0bdc28a5084bcec4eb71d89de44ee930ab09e78f","target":"record","created_at":"2026-05-18T03:13:20Z","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":"f20dc90f59f53daf08970db1214a05d99f620819bf9928678bde543c3ccd3170","cross_cats_sorted":["cs.IT","math.IT","nlin.CD","nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-15T20:06:56Z","title_canon_sha256":"460af8ad311a0f4cf764987d2f491cf743344a601444da4bcba76ab226c45b40"},"schema_version":"1.0","source":{"id":"1309.3792","kind":"arxiv","version":1}},"canonical_sha256":"5239487f3a949b1fa80ef228d8a15c74834e9debd26867228dd6d6c4d7e629df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5239487f3a949b1fa80ef228d8a15c74834e9debd26867228dd6d6c4d7e629df","first_computed_at":"2026-05-18T03:13:20.528693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:20.528693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"udMa/1YdOyjowZ29yMTPxfiskuctUGNBhdAa4DzUb4+jVCawGc2m0vWf+N1r8EwopV6tWzu8cGHIEumnO5qVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:20.529240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95358a020ff0a6536d8745ee0bdc28a5084bcec4eb71d89de44ee930ab09e78f","sha256:764df4c37e9b4e0d6436e9ddf870001e128caa87365787bb8164c5a742e9a739"],"state_sha256":"239e664863d9dcc1982d628540f225a45bc41f4a5e6ff7f2b2baddc6fa1788c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvUqmEQhxa26QhNUud4VvNo3SIPaovRmTqiPFZBdv0n7z2ONqEQDK08rIir56f7bYBzjkOhXW5p9hnzPDOKtCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:15:32.619922Z","bundle_sha256":"a74f513d27bfb8c816e809c4966d9e2bbab31cf3f34fd2bea86e06dc90c85c82"}}