{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4NTHQYVV2BXBSEONCQCRXFPPQE","short_pith_number":"pith:4NTHQYVV","schema_version":"1.0","canonical_sha256":"e3667862b5d06e1911cd14051b95ef8133710e907574056d1a29bfc9b974e6a5","source":{"kind":"arxiv","id":"1106.4212","version":2},"attestation_state":"computed","paper":{"title":"Markov processes follow from the principle of Maximum Caliber","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hao Ge, Ken Dill, Kingshuk Ghosh, Steve Presse","submitted_at":"2011-06-21T14:24:36Z","abstract_excerpt":"Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible dynamical trajectories in a time-homogeneous process, then the only type of process that maximizes the path entropy, for any given singlet statistics, is a sequence of identical, independently distributed (i.i.d.) random variables, which is the simplest Markov process. If the data is in the form of sequentially pairwise statistics, then maximizing the caliber di"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.4212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-21T14:24:36Z","cross_cats_sorted":["physics.bio-ph","physics.chem-ph"],"title_canon_sha256":"40432a9f85010124673b0c3a67f8fb4ba9c7a75afa0bd91e376624ad43539c4a","abstract_canon_sha256":"4bea4edcd12f16e66d6048ff9fcd9bc9e809b81b534eb8c7471696cf0a65f1ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:32.384796Z","signature_b64":"+d7NGiaHlgDXZujUMvOc6fiowItUrPsGpItC1onZv3BnrP0+jWWC6uP9woF1qT7BJJAqKAtXf0swjWpRJkIOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3667862b5d06e1911cd14051b95ef8133710e907574056d1a29bfc9b974e6a5","last_reissued_at":"2026-05-18T02:01:32.384368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:32.384368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Markov processes follow from the principle of Maximum Caliber","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hao Ge, Ken Dill, Kingshuk Ghosh, Steve Presse","submitted_at":"2011-06-21T14:24:36Z","abstract_excerpt":"Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible dynamical trajectories in a time-homogeneous process, then the only type of process that maximizes the path entropy, for any given singlet statistics, is a sequence of identical, independently distributed (i.i.d.) random variables, which is the simplest Markov process. If the data is in the form of sequentially pairwise statistics, then maximizing the caliber di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4212","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.4212","created_at":"2026-05-18T02:01:32.384431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.4212v2","created_at":"2026-05-18T02:01:32.384431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4212","created_at":"2026-05-18T02:01:32.384431+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NTHQYVV2BXB","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NTHQYVV2BXBSEON","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NTHQYVV","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE","json":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE.json","graph_json":"https://pith.science/api/pith-number/4NTHQYVV2BXBSEONCQCRXFPPQE/graph.json","events_json":"https://pith.science/api/pith-number/4NTHQYVV2BXBSEONCQCRXFPPQE/events.json","paper":"https://pith.science/paper/4NTHQYVV"},"agent_actions":{"view_html":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE","download_json":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE.json","view_paper":"https://pith.science/paper/4NTHQYVV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.4212&json=true","fetch_graph":"https://pith.science/api/pith-number/4NTHQYVV2BXBSEONCQCRXFPPQE/graph.json","fetch_events":"https://pith.science/api/pith-number/4NTHQYVV2BXBSEONCQCRXFPPQE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE/action/storage_attestation","attest_author":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE/action/author_attestation","sign_citation":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE/action/citation_signature","submit_replication":"https://pith.science/pith/4NTHQYVV2BXBSEONCQCRXFPPQE/action/replication_record"}},"created_at":"2026-05-18T02:01:32.384431+00:00","updated_at":"2026-05-18T02:01:32.384431+00:00"}