{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DGEZEJHT6YZ5XZ3L67T5TVK7MK","short_pith_number":"pith:DGEZEJHT","canonical_record":{"source":{"id":"1612.02181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-07T10:11:24Z","cross_cats_sorted":[],"title_canon_sha256":"7919a02584678fcb19aaf4a794f405a2f216a18a6533d718b59fb413ad7b3bc7","abstract_canon_sha256":"575fb1b1a251ab1ccab17398709640f4b9abcc9d14ff26c0da90ae82875fc15a"},"schema_version":"1.0"},"canonical_sha256":"19899224f3f633dbe76bf7e7d9d55f629abfb30e42916e134a7aa09dea955727","source":{"kind":"arxiv","id":"1612.02181","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02181","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02181v2","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02181","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"pith_short_12","alias_value":"DGEZEJHT6YZ5","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DGEZEJHT6YZ5XZ3L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DGEZEJHT","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DGEZEJHT6YZ5XZ3L67T5TVK7MK","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-07T10:11:24Z","cross_cats_sorted":[],"title_canon_sha256":"7919a02584678fcb19aaf4a794f405a2f216a18a6533d718b59fb413ad7b3bc7","abstract_canon_sha256":"575fb1b1a251ab1ccab17398709640f4b9abcc9d14ff26c0da90ae82875fc15a"},"schema_version":"1.0"},"canonical_sha256":"19899224f3f633dbe76bf7e7d9d55f629abfb30e42916e134a7aa09dea955727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:44.404177Z","signature_b64":"nyVdDEhHHOZWlIYSApK7O7Eh/MAgBCFUB/c1Qvs0/ArM35VYncgfeO/65uNjVPbGyLyTFHfziBtR8vQuGVo0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19899224f3f633dbe76bf7e7d9d55f629abfb30e42916e134a7aa09dea955727","last_reissued_at":"2026-05-18T00:45:44.403584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:44.403584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02181","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":"2026-05-18T00:45:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FA/tn4ltLojItB7BB+zZIgPX2M52xBkpIZhDgORxktk4VRMaegXLN7+/NWhO0dexA+5p5L1QI+j5VEfl4aWwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:18:14.157505Z"},"content_sha256":"ab5d3c21c3a4f2b6720e07098d2b767e46e6b99640021e6a119261e8e95cdf8f","schema_version":"1.0","event_id":"sha256:ab5d3c21c3a4f2b6720e07098d2b767e46e6b99640021e6a119261e8e95cdf8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DGEZEJHT6YZ5XZ3L67T5TVK7MK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Maxim Dolgushev, Oliver Muelken, Sarah Heinzelmann","submitted_at":"2016-12-07T10:11:24Z","abstract_excerpt":"We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation's transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochast"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02181","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":""},"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":"2026-05-18T00:45:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjcdOnQ1CN/eFEBik/s/402uwKF/t4qC07vn2tdb5kqCTn4QP9FJU9lAm1dEINEZifC8wig7OqoKDojuw+vSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:18:14.157852Z"},"content_sha256":"50f2b603267c43ff09d0ef1a003e6a1ffbd8cbb5c760ef4926d1081e0863f1df","schema_version":"1.0","event_id":"sha256:50f2b603267c43ff09d0ef1a003e6a1ffbd8cbb5c760ef4926d1081e0863f1df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/bundle.json","state_url":"https://pith.science/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/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":"2026-06-23T18:18:14Z","links":{"resolver":"https://pith.science/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK","bundle":"https://pith.science/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/bundle.json","state":"https://pith.science/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGEZEJHT6YZ5XZ3L67T5TVK7MK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DGEZEJHT6YZ5XZ3L67T5TVK7MK","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":"575fb1b1a251ab1ccab17398709640f4b9abcc9d14ff26c0da90ae82875fc15a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-07T10:11:24Z","title_canon_sha256":"7919a02584678fcb19aaf4a794f405a2f216a18a6533d718b59fb413ad7b3bc7"},"schema_version":"1.0","source":{"id":"1612.02181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02181","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02181v2","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02181","created_at":"2026-05-18T00:45:44Z"},{"alias_kind":"pith_short_12","alias_value":"DGEZEJHT6YZ5","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DGEZEJHT6YZ5XZ3L","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DGEZEJHT","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:50f2b603267c43ff09d0ef1a003e6a1ffbd8cbb5c760ef4926d1081e0863f1df","target":"graph","created_at":"2026-05-18T00:45:44Z","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":"We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation's transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochast","authors_text":"Maxim Dolgushev, Oliver Muelken, Sarah Heinzelmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-07T10:11:24Z","title":"Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02181","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:ab5d3c21c3a4f2b6720e07098d2b767e46e6b99640021e6a119261e8e95cdf8f","target":"record","created_at":"2026-05-18T00:45:44Z","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":"575fb1b1a251ab1ccab17398709640f4b9abcc9d14ff26c0da90ae82875fc15a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-07T10:11:24Z","title_canon_sha256":"7919a02584678fcb19aaf4a794f405a2f216a18a6533d718b59fb413ad7b3bc7"},"schema_version":"1.0","source":{"id":"1612.02181","kind":"arxiv","version":2}},"canonical_sha256":"19899224f3f633dbe76bf7e7d9d55f629abfb30e42916e134a7aa09dea955727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19899224f3f633dbe76bf7e7d9d55f629abfb30e42916e134a7aa09dea955727","first_computed_at":"2026-05-18T00:45:44.403584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:44.403584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nyVdDEhHHOZWlIYSApK7O7Eh/MAgBCFUB/c1Qvs0/ArM35VYncgfeO/65uNjVPbGyLyTFHfziBtR8vQuGVo0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:44.404177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab5d3c21c3a4f2b6720e07098d2b767e46e6b99640021e6a119261e8e95cdf8f","sha256:50f2b603267c43ff09d0ef1a003e6a1ffbd8cbb5c760ef4926d1081e0863f1df"],"state_sha256":"24b884ffd6e6d0d664d0c55c871017a60097a7c32969d8053a66b4cddde1a81a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQIag4wWmGXtLu2alUq20k7MNt8m069RJPESHxdxzczzMMVNHW9u3aL9A2S4Hw5w/ifx86JOaPm6YHZ/GCitAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:18:14.159790Z","bundle_sha256":"12e49e456c886b066965da76c00424a1d59151a564045808d8fe48f5bceb923f"}}