{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FJUKVISLEWDMTXMZCYR2BH2ZNK","short_pith_number":"pith:FJUKVISL","canonical_record":{"source":{"id":"1512.01859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-06T23:30:32Z","cross_cats_sorted":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"title_canon_sha256":"9fbe2081959969c88eda239e18edc2b888f5c560228cbbf80e4588a965ec1cbb","abstract_canon_sha256":"a548a8a2155f5aea4bbae7a122f05b4e64f03a1ac6e9090a4af49c8137174d72"},"schema_version":"1.0"},"canonical_sha256":"2a68aaa24b2586c9dd991623a09f596a830b32aea392ba88a337bf3ee0c04d5b","source":{"kind":"arxiv","id":"1512.01859","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01859","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01859v1","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01859","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"FJUKVISLEWDM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FJUKVISLEWDMTXMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FJUKVISL","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FJUKVISLEWDMTXMZCYR2BH2ZNK","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-06T23:30:32Z","cross_cats_sorted":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"title_canon_sha256":"9fbe2081959969c88eda239e18edc2b888f5c560228cbbf80e4588a965ec1cbb","abstract_canon_sha256":"a548a8a2155f5aea4bbae7a122f05b4e64f03a1ac6e9090a4af49c8137174d72"},"schema_version":"1.0"},"canonical_sha256":"2a68aaa24b2586c9dd991623a09f596a830b32aea392ba88a337bf3ee0c04d5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:44.976099Z","signature_b64":"djBTAmHXiRfdWsAFBVo3khecu2PfCpYhd8vHgA7SPERqrqsF/RQe5e3S/9zlA/lpPi4vA34KooEY/N2onqiZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a68aaa24b2586c9dd991623a09f596a830b32aea392ba88a337bf3ee0c04d5b","last_reissued_at":"2026-05-18T01:16:44.975383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:44.975383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01859","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":"2026-05-18T01:16:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VIhZE6mVXZzTYmNwQWbtXwsJjK7URfrnP6hll8GfuxPPU6S4s8j1E58996ry9Ws0mNDgufPqMMOCJj2HpEqUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:04:25.919921Z"},"content_sha256":"ab1ef737a4891c95f6ce4d0b062d6d83402195cf075c1d328868b6b41ec40056","schema_version":"1.0","event_id":"sha256:ab1ef737a4891c95f6ce4d0b062d6d83402195cf075c1d328868b6b41ec40056"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FJUKVISLEWDMTXMZCYR2BH2ZNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Signatures of Structural Organization: The case of long memory in renewal processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"primary_cat":"cond-mat.stat-mech","authors_text":"James P. Crutchfield, Sarah E. Marzen","submitted_at":"2015-12-06T23:30:32Z","abstract_excerpt":"Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations. The most common signatures employed rely on second-order temporal statistics and lead, for example, to identifying long memory in processes with power-law autocorrelation function and Hurst exponent greater than $1/2$. However, most stochastic processes hide their memory in higher-order temporal correlations. Information measures---specifically, divergences i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01859","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":"2026-05-18T01:16:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqtBeN3bsP+rUAhOgpJf8kqOL4FnJE+kZCrAMAZiYeJSfXV88pFXGe+d0yambSxZiebUzHdSd0ZsqMLEM02MAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:04:25.920638Z"},"content_sha256":"a39d99cac117b9602801ff8692d947b8cc12bb0372fad6782491b1e9b239ad44","schema_version":"1.0","event_id":"sha256:a39d99cac117b9602801ff8692d947b8cc12bb0372fad6782491b1e9b239ad44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/bundle.json","state_url":"https://pith.science/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/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":"2026-06-08T15:04:25Z","links":{"resolver":"https://pith.science/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK","bundle":"https://pith.science/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/bundle.json","state":"https://pith.science/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJUKVISLEWDMTXMZCYR2BH2ZNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FJUKVISLEWDMTXMZCYR2BH2ZNK","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":"a548a8a2155f5aea4bbae7a122f05b4e64f03a1ac6e9090a4af49c8137174d72","cross_cats_sorted":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-06T23:30:32Z","title_canon_sha256":"9fbe2081959969c88eda239e18edc2b888f5c560228cbbf80e4588a965ec1cbb"},"schema_version":"1.0","source":{"id":"1512.01859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01859","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01859v1","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01859","created_at":"2026-05-18T01:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"FJUKVISLEWDM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FJUKVISLEWDMTXMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FJUKVISL","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:a39d99cac117b9602801ff8692d947b8cc12bb0372fad6782491b1e9b239ad44","target":"graph","created_at":"2026-05-18T01:16:44Z","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":"Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations. The most common signatures employed rely on second-order temporal statistics and lead, for example, to identifying long memory in processes with power-law autocorrelation function and Hurst exponent greater than $1/2$. However, most stochastic processes hide their memory in higher-order temporal correlations. Information measures---specifically, divergences i","authors_text":"James P. Crutchfield, Sarah E. Marzen","cross_cats":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-06T23:30:32Z","title":"Statistical Signatures of Structural Organization: The case of long memory in renewal processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01859","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:ab1ef737a4891c95f6ce4d0b062d6d83402195cf075c1d328868b6b41ec40056","target":"record","created_at":"2026-05-18T01:16:44Z","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":"a548a8a2155f5aea4bbae7a122f05b4e64f03a1ac6e9090a4af49c8137174d72","cross_cats_sorted":["cs.IT","math.DS","math.IT","math.ST","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-06T23:30:32Z","title_canon_sha256":"9fbe2081959969c88eda239e18edc2b888f5c560228cbbf80e4588a965ec1cbb"},"schema_version":"1.0","source":{"id":"1512.01859","kind":"arxiv","version":1}},"canonical_sha256":"2a68aaa24b2586c9dd991623a09f596a830b32aea392ba88a337bf3ee0c04d5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a68aaa24b2586c9dd991623a09f596a830b32aea392ba88a337bf3ee0c04d5b","first_computed_at":"2026-05-18T01:16:44.975383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:44.975383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djBTAmHXiRfdWsAFBVo3khecu2PfCpYhd8vHgA7SPERqrqsF/RQe5e3S/9zlA/lpPi4vA34KooEY/N2onqiZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:44.976099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab1ef737a4891c95f6ce4d0b062d6d83402195cf075c1d328868b6b41ec40056","sha256:a39d99cac117b9602801ff8692d947b8cc12bb0372fad6782491b1e9b239ad44"],"state_sha256":"aeb55993b60e4c20ee663014aac3749721e7ec5a1eccb93672f0ccb8c61956e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUrHIr3ixOozg8AwR0gJUb2likI9ngk2pd7lZ7A2TF1wa/CIUVD8r7+U4VBNCaWPyqZmWPd9WqSvLKyl2COVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:04:25.924978Z","bundle_sha256":"b3ce8be009766488decc3f167ac3ccef72257a90c384ecaf0a9d3a4d0b3995dd"}}