{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SITQBIBDFGKOEYDMVFABATH4ZR","short_pith_number":"pith:SITQBIBD","canonical_record":{"source":{"id":"2603.01278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-03-01T21:31:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0fc39303bc78b900729d2ec80210f5d19052bf98b8f04d4d3fd6697d56ae4465","abstract_canon_sha256":"fb35f431741fb86a7174caad71c85be80afe78c4f1ea0e09852d922d5b24c308"},"schema_version":"1.0"},"canonical_sha256":"922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf","source":{"kind":"arxiv","id":"2603.01278","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.01278","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.01278v3","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.01278","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"SITQBIBDFGKO","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_16","alias_value":"SITQBIBDFGKOEYDM","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_8","alias_value":"SITQBIBD","created_at":"2026-05-25T02:01:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SITQBIBDFGKOEYDMVFABATH4ZR","target":"record","payload":{"canonical_record":{"source":{"id":"2603.01278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-03-01T21:31:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0fc39303bc78b900729d2ec80210f5d19052bf98b8f04d4d3fd6697d56ae4465","abstract_canon_sha256":"fb35f431741fb86a7174caad71c85be80afe78c4f1ea0e09852d922d5b24c308"},"schema_version":"1.0"},"canonical_sha256":"922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:16.304030Z","signature_b64":"K0MO/5epjCBkuiAIRN22T9hwhKIw4CP0fvvfpOpzCouzapldrdj+71oH8hVdGjaRKSQbSTtdhtcrlUsattLRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf","last_reissued_at":"2026-05-25T02:01:16.303146Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:16.303146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.01278","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":"2026-05-25T02:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ax4+U+osbD1hxZ47v9AVaCsFhBy9owWNOgp3H42JTLf2wLPPFIyaUKlXLTo6plQORliPPyjZEXRJC0s2phNQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:26:47.494152Z"},"content_sha256":"432b6cf6b1aaaccd3ff27c64445bbe826f24271c7d4aa8aa0b604c2f39014a8b","schema_version":"1.0","event_id":"sha256:432b6cf6b1aaaccd3ff27c64445bbe826f24271c7d4aa8aa0b604c2f39014a8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SITQBIBDFGKOEYDMVFABATH4ZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density.","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hiroki Suyari","submitted_at":"2026-03-01T21:31:32Z","abstract_excerpt":"Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by introducing the Linearization Principle directly at the dynamical stage. By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the $q$-de"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the q-deformed geometry... exhibits a fundamental duality between the dynamic index q and the thermodynamic index 2-q.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Linearization Principle itself, introduced directly at the dynamical stage as the central geometric rule that forces the drift to stay linear while allowing nonlinear diffusion.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A geometric Linearization Principle derives nonlinear Fokker-Planck equations that preserve linear drift and Einstein relation while producing q-Gaussian equilibria minimizing a 2-q entropy functional.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"52556522ddc80f1154e2735a84f7c1743e5cd49bb18ec26d9bc438c12a975859"},"source":{"id":"2603.01278","kind":"arxiv","version":3},"verdict":{"id":"8bdd8f03-b74e-4a57-ab02-03a89099cdd6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T17:42:35.692756Z","strongest_claim":"By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the q-deformed geometry... exhibits a fundamental duality between the dynamic index q and the thermodynamic index 2-q.","one_line_summary":"A geometric Linearization Principle derives nonlinear Fokker-Planck equations that preserve linear drift and Einstein relation while producing q-Gaussian equilibria minimizing a 2-q entropy functional.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Linearization Principle itself, introduced directly at the dynamical stage as the central geometric rule that forces the drift to stay linear while allowing nonlinear diffusion.","pith_extraction_headline":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.01278/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":3,"snapshot_sha256":"f683d09d715f4652a096f2eef3f7319d174752d7d644fade326100f4406dc84d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"8bdd8f03-b74e-4a57-ab02-03a89099cdd6"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4+wsTZAucp6+unqtrh5A9ZGLvoYUmGU7H3DWeEvj4kGn42z1FnRHPS82px+dKUXoRBGrNrNdsaBy1+0lkTgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:26:47.495115Z"},"content_sha256":"5a8bd2d90a312e56f086d43e4c04cc1c1b8d935dda88a479c6657df91d01b802","schema_version":"1.0","event_id":"sha256:5a8bd2d90a312e56f086d43e4c04cc1c1b8d935dda88a479c6657df91d01b802"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR/bundle.json","state_url":"https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SITQBIBDFGKOEYDMVFABATH4ZR/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":"2026-06-10T03:26:47Z","links":{"resolver":"https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR","bundle":"https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR/bundle.json","state":"https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SITQBIBDFGKOEYDMVFABATH4ZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SITQBIBDFGKOEYDMVFABATH4ZR","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":"fb35f431741fb86a7174caad71c85be80afe78c4f1ea0e09852d922d5b24c308","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-03-01T21:31:32Z","title_canon_sha256":"0fc39303bc78b900729d2ec80210f5d19052bf98b8f04d4d3fd6697d56ae4465"},"schema_version":"1.0","source":{"id":"2603.01278","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.01278","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.01278v3","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.01278","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"SITQBIBDFGKO","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_16","alias_value":"SITQBIBDFGKOEYDM","created_at":"2026-05-25T02:01:16Z"},{"alias_kind":"pith_short_8","alias_value":"SITQBIBD","created_at":"2026-05-25T02:01:16Z"}],"graph_snapshots":[{"event_id":"sha256:5a8bd2d90a312e56f086d43e4c04cc1c1b8d935dda88a479c6657df91d01b802","target":"graph","created_at":"2026-05-25T02:01:16Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the q-deformed geometry... exhibits a fundamental duality between the dynamic index q and the thermodynamic index 2-q."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The Linearization Principle itself, introduced directly at the dynamical stage as the central geometric rule that forces the drift to stay linear while allowing nonlinear diffusion."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A geometric Linearization Principle derives nonlinear Fokker-Planck equations that preserve linear drift and Einstein relation while producing q-Gaussian equilibria minimizing a 2-q entropy functional."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density."}],"snapshot_sha256":"52556522ddc80f1154e2735a84f7c1743e5cd49bb18ec26d9bc438c12a975859"},"formal_canon":{"evidence_count":3,"snapshot_sha256":"f683d09d715f4652a096f2eef3f7319d174752d7d644fade326100f4406dc84d"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.01278/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by introducing the Linearization Principle directly at the dynamical stage. By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the $q$-de","authors_text":"Hiroki Suyari","cross_cats":["math-ph","math.MP"],"headline":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-03-01T21:31:32Z","title":"Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.01278","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-15T17:42:35.692756Z","id":"8bdd8f03-b74e-4a57-ab02-03a89099cdd6","model_set":{"reader":"grok-4.3"},"one_line_summary":"A geometric Linearization Principle derives nonlinear Fokker-Planck equations that preserve linear drift and Einstein relation while producing q-Gaussian equilibria minimizing a 2-q entropy functional.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density.","strongest_claim":"By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the q-deformed geometry... exhibits a fundamental duality between the dynamic index q and the thermodynamic index 2-q.","weakest_assumption":"The Linearization Principle itself, introduced directly at the dynamical stage as the central geometric rule that forces the drift to stay linear while allowing nonlinear diffusion."}},"verdict_id":"8bdd8f03-b74e-4a57-ab02-03a89099cdd6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:432b6cf6b1aaaccd3ff27c64445bbe826f24271c7d4aa8aa0b604c2f39014a8b","target":"record","created_at":"2026-05-25T02:01:16Z","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":"fb35f431741fb86a7174caad71c85be80afe78c4f1ea0e09852d922d5b24c308","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-03-01T21:31:32Z","title_canon_sha256":"0fc39303bc78b900729d2ec80210f5d19052bf98b8f04d4d3fd6697d56ae4465"},"schema_version":"1.0","source":{"id":"2603.01278","kind":"arxiv","version":3}},"canonical_sha256":"922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf","first_computed_at":"2026-05-25T02:01:16.303146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:16.303146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0MO/5epjCBkuiAIRN22T9hwhKIw4CP0fvvfpOpzCouzapldrdj+71oH8hVdGjaRKSQbSTtdhtcrlUsattLRAQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:16.304030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.01278","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:432b6cf6b1aaaccd3ff27c64445bbe826f24271c7d4aa8aa0b604c2f39014a8b","sha256:5a8bd2d90a312e56f086d43e4c04cc1c1b8d935dda88a479c6657df91d01b802"],"state_sha256":"b93d08eb115f1a831713504f74422138b384143561c8d71d18c1427d7f3714dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTSUcKXc03jb7l0aIxUgYp3mWwp3pZo4zL156QydVDR4mgZE7JQUgSNVtwhwlOC+IcTyzUtRC9IAvId5xmtFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:26:47.499952Z","bundle_sha256":"ed5b3ae8b2bb9f554f993db442f1ef9d942d7a8729ebba201e75224968014aaf"}}