{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:MTDSMGIAUEYU6I6CQBRIBWNUTJ","short_pith_number":"pith:MTDSMGIA","schema_version":"1.0","canonical_sha256":"64c7261900a1314f23c2806280d9b49a42ad7b3a7b860c28d781b5c53bfa1937","source":{"kind":"arxiv","id":"2204.11900","version":1},"attestation_state":"computed","paper":{"title":"Towards a Geometry and Analysis for Bayesian Mechanics","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS","math.MP","nlin.AO","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Dalton A R Sakthivadivel","submitted_at":"2022-04-25T18:04:50Z","abstract_excerpt":"In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference against these constraints, and that in a non-isolated system, such constraints imply external environmental variables embedding the system. Using aspects of classical dynamical systems theory in statistical mechanics, we show that this inference is equivalent to a gradient ascent on the Shannon entropy functional, recovering an approximate Bayesian inference"},"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":"2204.11900","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-04-25T18:04:50Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS","math.MP","nlin.AO","physics.bio-ph"],"title_canon_sha256":"41775473718d6acc499fef8a84963c428191a1f4095306299ae575c8c8928ea4","abstract_canon_sha256":"dc4da394ffe01feb242864e86a7a94044398d9ae285476ee61d90cfa0e24dfcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:17:42.097896Z","signature_b64":"9m6rMP4Q6GaOXsg8uzKh3vf0TAbY5iCDLBWW6tslCvJQ0VNGTQBgaPWvljO9PJNLByZoxDSUGEGjsZAw+mIVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64c7261900a1314f23c2806280d9b49a42ad7b3a7b860c28d781b5c53bfa1937","last_reissued_at":"2026-07-05T04:17:42.097320Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:17:42.097320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a Geometry and Analysis for Bayesian Mechanics","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS","math.MP","nlin.AO","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"Dalton A R Sakthivadivel","submitted_at":"2022-04-25T18:04:50Z","abstract_excerpt":"In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference against these constraints, and that in a non-isolated system, such constraints imply external environmental variables embedding the system. Using aspects of classical dynamical systems theory in statistical mechanics, we show that this inference is equivalent to a gradient ascent on the Shannon entropy functional, recovering an approximate Bayesian inference"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.11900","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.11900/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2204.11900","created_at":"2026-07-05T04:17:42.097404+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.11900v1","created_at":"2026-07-05T04:17:42.097404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.11900","created_at":"2026-07-05T04:17:42.097404+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTDSMGIAUEYU","created_at":"2026-07-05T04:17:42.097404+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTDSMGIAUEYU6I6C","created_at":"2026-07-05T04:17:42.097404+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTDSMGIA","created_at":"2026-07-05T04:17:42.097404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21585","citing_title":"A Transport-Based Geometry of Belief-Cost","ref_index":61,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04200","citing_title":"Neural Manifolds as Crystallized Embeddings: A Synthesis of the Free Energy Principle, Generalized Synchronization, and Hebbian Plasticity","ref_index":50,"is_internal_anchor":false},{"citing_arxiv_id":"2606.21585","citing_title":"A Transport-Based Geometry of Belief-Cost","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12536","citing_title":"Information as Maximum-Caliber Deviation: A bridge between Integrated Information Theory and the Free Energy Principle","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04200","citing_title":"Neural Manifolds as Crystallized Embeddings: A Synthesis of the Free Energy Principle, Generalized Synchronization, and Hebbian Plasticity","ref_index":43,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ","json":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ.json","graph_json":"https://pith.science/api/pith-number/MTDSMGIAUEYU6I6CQBRIBWNUTJ/graph.json","events_json":"https://pith.science/api/pith-number/MTDSMGIAUEYU6I6CQBRIBWNUTJ/events.json","paper":"https://pith.science/paper/MTDSMGIA"},"agent_actions":{"view_html":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ","download_json":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ.json","view_paper":"https://pith.science/paper/MTDSMGIA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.11900&json=true","fetch_graph":"https://pith.science/api/pith-number/MTDSMGIAUEYU6I6CQBRIBWNUTJ/graph.json","fetch_events":"https://pith.science/api/pith-number/MTDSMGIAUEYU6I6CQBRIBWNUTJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ/action/storage_attestation","attest_author":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ/action/author_attestation","sign_citation":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ/action/citation_signature","submit_replication":"https://pith.science/pith/MTDSMGIAUEYU6I6CQBRIBWNUTJ/action/replication_record"}},"created_at":"2026-07-05T04:17:42.097404+00:00","updated_at":"2026-07-05T04:17:42.097404+00:00"}