{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OFDFYT6UJZHRDFS6JQ2CIRF7MK","short_pith_number":"pith:OFDFYT6U","canonical_record":{"source":{"id":"1111.2253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-09T16:11:52Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"b0bb4e2697da8ede1e23df52a67ac325a1684e551745feac5e67bb648b21b76c","abstract_canon_sha256":"f3b44f705cb515882b5d91fdefc6f3651994502f218ae244c2930464738c35e0"},"schema_version":"1.0"},"canonical_sha256":"71465c4fd44e4f11965e4c342444bf629f87059453f8bbedadd76571ce13eee6","source":{"kind":"arxiv","id":"1111.2253","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2253","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2253v3","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2253","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"OFDFYT6UJZHR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OFDFYT6UJZHRDFS6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OFDFYT6U","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OFDFYT6UJZHRDFS6JQ2CIRF7MK","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-09T16:11:52Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"b0bb4e2697da8ede1e23df52a67ac325a1684e551745feac5e67bb648b21b76c","abstract_canon_sha256":"f3b44f705cb515882b5d91fdefc6f3651994502f218ae244c2930464738c35e0"},"schema_version":"1.0"},"canonical_sha256":"71465c4fd44e4f11965e4c342444bf629f87059453f8bbedadd76571ce13eee6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:43.118014Z","signature_b64":"yxHIXf4lZXZJVWTdoRml0JJFe9WoKnAO8i4KcHV8vbPKAYIxRFzhvOiA71uSkqSryGYsIaEKp15fLEvNa+S/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71465c4fd44e4f11965e4c342444bf629f87059453f8bbedadd76571ce13eee6","last_reissued_at":"2026-05-18T01:59:43.117120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:43.117120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2253","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtbwDtBh2ruJFSZo7/mApOY3pAdijl0atrQDlckw4TF4ve8IB4vs3p7uwgz6vMZWBY2F3szge9h6arp9JlHEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:59:18.049053Z"},"content_sha256":"10aa2a24221be110f1889522bae854262c0cfcf8a8bbcd67fa6d289e8ca08bd6","schema_version":"1.0","event_id":"sha256:10aa2a24221be110f1889522bae854262c0cfcf8a8bbcd67fa6d289e8ca08bd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OFDFYT6UJZHRDFS6JQ2CIRF7MK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Maximal Entropy Random Walk to quantum thermodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Jarek Duda","submitted_at":"2011-11-09T16:11:52Z","abstract_excerpt":"Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a new philosophy of stochastic modeling was introduced, which by being mathematically similar to euclidean path integrals, finally fulfills these principles exactly. Their local behavior is usually similar, but may lead to completely different global properties. In contrast to Brownian motion leading to nearly uniform stationary density, this recent approach tur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2253","kind":"arxiv","version":3},"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":"2026-05-18T01:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sgZ8LN45uNv0qGv8U8yYQCF6ebPB9/fQWRxi+HBRmCbwM0QFpQdnDzN9xXvnyXKjf6rFsykSx9ORXQkLyIb+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:59:18.049822Z"},"content_sha256":"8c81e84ac6793678f13629a29ae5f00ba082cfac7f59ac398b16446a9a0d4787","schema_version":"1.0","event_id":"sha256:8c81e84ac6793678f13629a29ae5f00ba082cfac7f59ac398b16446a9a0d4787"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/bundle.json","state_url":"https://pith.science/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/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":"2026-06-10T08:59:18Z","links":{"resolver":"https://pith.science/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK","bundle":"https://pith.science/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/bundle.json","state":"https://pith.science/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFDFYT6UJZHRDFS6JQ2CIRF7MK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OFDFYT6UJZHRDFS6JQ2CIRF7MK","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":"f3b44f705cb515882b5d91fdefc6f3651994502f218ae244c2930464738c35e0","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-09T16:11:52Z","title_canon_sha256":"b0bb4e2697da8ede1e23df52a67ac325a1684e551745feac5e67bb648b21b76c"},"schema_version":"1.0","source":{"id":"1111.2253","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2253","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2253v3","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2253","created_at":"2026-05-18T01:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"OFDFYT6UJZHR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OFDFYT6UJZHRDFS6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OFDFYT6U","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:8c81e84ac6793678f13629a29ae5f00ba082cfac7f59ac398b16446a9a0d4787","target":"graph","created_at":"2026-05-18T01:59:43Z","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":"Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a new philosophy of stochastic modeling was introduced, which by being mathematically similar to euclidean path integrals, finally fulfills these principles exactly. Their local behavior is usually similar, but may lead to completely different global properties. In contrast to Brownian motion leading to nearly uniform stationary density, this recent approach tur","authors_text":"Jarek Duda","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-09T16:11:52Z","title":"From Maximal Entropy Random Walk to quantum thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2253","kind":"arxiv","version":3},"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":"sha256:10aa2a24221be110f1889522bae854262c0cfcf8a8bbcd67fa6d289e8ca08bd6","target":"record","created_at":"2026-05-18T01:59:43Z","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":"f3b44f705cb515882b5d91fdefc6f3651994502f218ae244c2930464738c35e0","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-09T16:11:52Z","title_canon_sha256":"b0bb4e2697da8ede1e23df52a67ac325a1684e551745feac5e67bb648b21b76c"},"schema_version":"1.0","source":{"id":"1111.2253","kind":"arxiv","version":3}},"canonical_sha256":"71465c4fd44e4f11965e4c342444bf629f87059453f8bbedadd76571ce13eee6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71465c4fd44e4f11965e4c342444bf629f87059453f8bbedadd76571ce13eee6","first_computed_at":"2026-05-18T01:59:43.117120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:43.117120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxHIXf4lZXZJVWTdoRml0JJFe9WoKnAO8i4KcHV8vbPKAYIxRFzhvOiA71uSkqSryGYsIaEKp15fLEvNa+S/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:43.118014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2253","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10aa2a24221be110f1889522bae854262c0cfcf8a8bbcd67fa6d289e8ca08bd6","sha256:8c81e84ac6793678f13629a29ae5f00ba082cfac7f59ac398b16446a9a0d4787"],"state_sha256":"0a9996af4dd4d2fe057462a3d54e3a7578f056c6c37f28869feedcc6b17eb401"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t98bGff0S4ulKEv6tJLX/9tFVlQ+8Zfg2AXijWmmjIxmJzyk0o7SeeN3N1TLez3vOj5jpVq2KfQaf8OWlK4ACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:59:18.054428Z","bundle_sha256":"734814e4ccbc0a147fad96d9cd51af717c1c28edb4d510ded6087d5b1e0f8807"}}