{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:XYLGZV6YZPKHVTXIFXKP4WC4N3","short_pith_number":"pith:XYLGZV6Y","canonical_record":{"source":{"id":"cond-mat/0606211","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-06-08T12:55:22Z","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"title_canon_sha256":"44314821980f50cc96cfba4cf83855284235796a39e7513bec68671a4db38dcd","abstract_canon_sha256":"510690337154b01119a375a57dba3ea236861eed2a6ddfa8ca2641f579fb03d5"},"schema_version":"1.0"},"canonical_sha256":"be166cd7d8cbd47acee82dd4fe585c6eec0b8e434d4b91419d063085592eaf69","source":{"kind":"arxiv","id":"cond-mat/0606211","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0606211","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0606211v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0606211","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"XYLGZV6YZPKH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"XYLGZV6YZPKHVTXI","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"XYLGZV6Y","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:XYLGZV6YZPKHVTXIFXKP4WC4N3","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0606211","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-06-08T12:55:22Z","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"title_canon_sha256":"44314821980f50cc96cfba4cf83855284235796a39e7513bec68671a4db38dcd","abstract_canon_sha256":"510690337154b01119a375a57dba3ea236861eed2a6ddfa8ca2641f579fb03d5"},"schema_version":"1.0"},"canonical_sha256":"be166cd7d8cbd47acee82dd4fe585c6eec0b8e434d4b91419d063085592eaf69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:29.583828Z","signature_b64":"pkOm0Yj56iuJrtKlzMIQK0eEeJSIH7Fi5pzwKt4U0JkuboMvktppK96yi1B6/jrncFyQLF8V+HcjrQyk1OkQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be166cd7d8cbd47acee82dd4fe585c6eec0b8e434d4b91419d063085592eaf69","last_reissued_at":"2026-05-18T04:07:29.583338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:29.583338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0606211","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DMJzqlsDDNKFe2kM3d+bFEm4yYscZOJoSEij/OKZtyqnVvpvvqfmPb6dDjUo5QgreI7dzozastsCUpBnWyVvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:38:24.127500Z"},"content_sha256":"55aed9b3b4f2a921dab3563d6db9552293e540b9a34bf890f3779f878937b279","schema_version":"1.0","event_id":"sha256:55aed9b3b4f2a921dab3563d6db9552293e540b9a34bf890f3779f878937b279"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:XYLGZV6YZPKHVTXIFXKP4WC4N3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamic formalism for systems with Markov dynamics","license":"","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"C\\'ecile Appert-Rolland, Fr\\'ed\\'eric van Wijland, Vivien Lecomte","submitted_at":"2006-06-08T12:55:22Z","abstract_excerpt":"The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time.\n  We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0606211","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btle++gElAsiPiz9xgnk7JT+8oMSE/NjeO8D4fy3OmtoRPPLdyOh9tR7pAwavJHRSsp8eIBmDdmysIlCBhhPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:38:24.127902Z"},"content_sha256":"b736c230c49082add5d89f7102f8536756f05471c45fbc48bf8f4603a0c007f1","schema_version":"1.0","event_id":"sha256:b736c230c49082add5d89f7102f8536756f05471c45fbc48bf8f4603a0c007f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/bundle.json","state_url":"https://pith.science/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/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":"2026-05-27T02:38:24Z","links":{"resolver":"https://pith.science/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3","bundle":"https://pith.science/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/bundle.json","state":"https://pith.science/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XYLGZV6YZPKHVTXIFXKP4WC4N3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:XYLGZV6YZPKHVTXIFXKP4WC4N3","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":"510690337154b01119a375a57dba3ea236861eed2a6ddfa8ca2641f579fb03d5","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-06-08T12:55:22Z","title_canon_sha256":"44314821980f50cc96cfba4cf83855284235796a39e7513bec68671a4db38dcd"},"schema_version":"1.0","source":{"id":"cond-mat/0606211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0606211","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0606211v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0606211","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"XYLGZV6YZPKH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"XYLGZV6YZPKHVTXI","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"XYLGZV6Y","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:b736c230c49082add5d89f7102f8536756f05471c45fbc48bf8f4603a0c007f1","target":"graph","created_at":"2026-05-18T04:07:29Z","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":"The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time.\n  We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associ","authors_text":"C\\'ecile Appert-Rolland, Fr\\'ed\\'eric van Wijland, Vivien Lecomte","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-06-08T12:55:22Z","title":"Thermodynamic formalism for systems with Markov dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0606211","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":"sha256:55aed9b3b4f2a921dab3563d6db9552293e540b9a34bf890f3779f878937b279","target":"record","created_at":"2026-05-18T04:07:29Z","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":"510690337154b01119a375a57dba3ea236861eed2a6ddfa8ca2641f579fb03d5","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-06-08T12:55:22Z","title_canon_sha256":"44314821980f50cc96cfba4cf83855284235796a39e7513bec68671a4db38dcd"},"schema_version":"1.0","source":{"id":"cond-mat/0606211","kind":"arxiv","version":2}},"canonical_sha256":"be166cd7d8cbd47acee82dd4fe585c6eec0b8e434d4b91419d063085592eaf69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be166cd7d8cbd47acee82dd4fe585c6eec0b8e434d4b91419d063085592eaf69","first_computed_at":"2026-05-18T04:07:29.583338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.583338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pkOm0Yj56iuJrtKlzMIQK0eEeJSIH7Fi5pzwKt4U0JkuboMvktppK96yi1B6/jrncFyQLF8V+HcjrQyk1OkQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.583828Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0606211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55aed9b3b4f2a921dab3563d6db9552293e540b9a34bf890f3779f878937b279","sha256:b736c230c49082add5d89f7102f8536756f05471c45fbc48bf8f4603a0c007f1"],"state_sha256":"424a411100506aef2b4e30b056688c1a51a5d0a9379ab22fae730866f0391f99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKHGfpwIcBQLjBQPXOCpD0OLor26MxxjOB8mvPvBv/ffE1QSoU7Z/VOyUSOmrT21VL/U2h7hOdppPLpwL0DtAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:38:24.134197Z","bundle_sha256":"14d4014e073abe8cf752bb9e22099952c70977bb5f513a5d6b3e239dbea890ac"}}