{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IOJY4PHQ56CKLWILDXGUC2SSXO","short_pith_number":"pith:IOJY4PHQ","canonical_record":{"source":{"id":"2604.14346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-15T18:59:53Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"fe5dffff0807c616588eea29d55d64b6f71bb4ac6d79a7fa73dce4abc52aba10","abstract_canon_sha256":"5c8d1f24b8b35afc022ff7425ea85efb850b05f7212f5689650a3051a8f8352b"},"schema_version":"1.0"},"canonical_sha256":"43938e3cf0ef84a5d90b1dcd416a52bb9e80ba4de34536671191faee9cc327d2","source":{"kind":"arxiv","id":"2604.14346","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.14346","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"2604.14346v2","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.14346","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"IOJY4PHQ56CK","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_16","alias_value":"IOJY4PHQ56CKLWIL","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_8","alias_value":"IOJY4PHQ","created_at":"2026-05-20T01:05:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IOJY4PHQ56CKLWILDXGUC2SSXO","target":"record","payload":{"canonical_record":{"source":{"id":"2604.14346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-15T18:59:53Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"fe5dffff0807c616588eea29d55d64b6f71bb4ac6d79a7fa73dce4abc52aba10","abstract_canon_sha256":"5c8d1f24b8b35afc022ff7425ea85efb850b05f7212f5689650a3051a8f8352b"},"schema_version":"1.0"},"canonical_sha256":"43938e3cf0ef84a5d90b1dcd416a52bb9e80ba4de34536671191faee9cc327d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:13.370898Z","signature_b64":"KZW30SEfsuNCkG+DW1IVJiFaCI484C2FW0tv89wMLQ+BwI2HJVg8hf9X5TuI5rP94M5K5br6QZglg3uNLR76Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43938e3cf0ef84a5d90b1dcd416a52bb9e80ba4de34536671191faee9cc327d2","last_reissued_at":"2026-05-20T01:05:13.370286Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:13.370286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.14346","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":"2026-05-20T01:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p3rNm8OLMcHMHcnxkHd0N0pkmvWdJELA0JbUPyWbCFYsogwsmvxuuRpnDQMn9+WiNh5Tf1S5U1GBT3tBuXGJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:20:28.174873Z"},"content_sha256":"963ce67405eba0d70b4ec5b15ec555b7643caeb0983f4b37751984182c64b24d","schema_version":"1.0","event_id":"sha256:963ce67405eba0d70b4ec5b15ec555b7643caeb0983f4b37751984182c64b24d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IOJY4PHQ56CKLWILDXGUC2SSXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fluctuations for the Toda lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling.","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Amol Aggarwal, Matthew Nicoletti","submitted_at":"2026-04-15T18:59:53Z","abstract_excerpt":"In this paper we consider the Toda lattice $(\\mathbf{p}(t);\\mathbf{q}(t))$ at thermal equilibrium, meaning that its variables $(p_j)$ and $(e^{q_j-q_{j+1}})$ are independent Gaussian and Gamma random variables, respectively. We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce, (i) the scaling limit for the trajectory of a single particle $q_0$ is a Brownian motion; (ii) space-time two-point correlation functions for the model decay inversely with time, with explicit scaling distributions pr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce (i) the scaling limit for the trajectory of a single particle q_0 is a Brownian motion; (ii) space-time two-point correlation functions decay inversely with time with explicit scaling distributions predicted by Spohn.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The starting assumption that the Toda lattice variables (p_j) and (e^{q_j - q_{j+1}}) are independent Gaussian and Gamma random variables respectively, together with the modeling of the system as a dense collection of quasi-particles whose scattering produces the dressed Lévy-Chentsov field.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6cea5f54e9e7bacefe0e51856ae9208a82f64ea6ebba9375bccaf23ddd1f2623"},"source":{"id":"2604.14346","kind":"arxiv","version":2},"verdict":{"id":"60dee785-9690-40ce-b5c3-fbbe44db9fa2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T11:53:32.636180Z","strongest_claim":"We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce (i) the scaling limit for the trajectory of a single particle q_0 is a Brownian motion; (ii) space-time two-point correlation functions decay inversely with time with explicit scaling distributions predicted by Spohn.","one_line_summary":"Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The starting assumption that the Toda lattice variables (p_j) and (e^{q_j - q_{j+1}}) are independent Gaussian and Gamma random variables respectively, together with the modeling of the system as a dense collection of quasi-particles whose scattering produces the dressed Lévy-Chentsov field.","pith_extraction_headline":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.14346/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"},"verdict_id":"60dee785-9690-40ce-b5c3-fbbe44db9fa2"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T01:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZNRUc8fpLmyJtxVcs2zBUchqB2+i9VTHPvGm+S1NMVMliTSd/ZXXv6/E1s3JFMI7o9VvNc+BRtQpb/ZTn+A+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:20:28.175375Z"},"content_sha256":"41bf68dab7bb510e1d536b24d3ae02972ae6dbeb236cf2411492e2b7e92d2e9e","schema_version":"1.0","event_id":"sha256:41bf68dab7bb510e1d536b24d3ae02972ae6dbeb236cf2411492e2b7e92d2e9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/bundle.json","state_url":"https://pith.science/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/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":"2026-06-03T02:20:28Z","links":{"resolver":"https://pith.science/pith/IOJY4PHQ56CKLWILDXGUC2SSXO","bundle":"https://pith.science/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/bundle.json","state":"https://pith.science/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOJY4PHQ56CKLWILDXGUC2SSXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IOJY4PHQ56CKLWILDXGUC2SSXO","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":"5c8d1f24b8b35afc022ff7425ea85efb850b05f7212f5689650a3051a8f8352b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-15T18:59:53Z","title_canon_sha256":"fe5dffff0807c616588eea29d55d64b6f71bb4ac6d79a7fa73dce4abc52aba10"},"schema_version":"1.0","source":{"id":"2604.14346","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.14346","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"2604.14346v2","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.14346","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"IOJY4PHQ56CK","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_16","alias_value":"IOJY4PHQ56CKLWIL","created_at":"2026-05-20T01:05:13Z"},{"alias_kind":"pith_short_8","alias_value":"IOJY4PHQ","created_at":"2026-05-20T01:05:13Z"}],"graph_snapshots":[{"event_id":"sha256:41bf68dab7bb510e1d536b24d3ae02972ae6dbeb236cf2411492e2b7e92d2e9e","target":"graph","created_at":"2026-05-20T01:05:13Z","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":"We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce (i) the scaling limit for the trajectory of a single particle q_0 is a Brownian motion; (ii) space-time two-point correlation functions decay inversely with time with explicit scaling distributions predicted by Spohn."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The starting assumption that the Toda lattice variables (p_j) and (e^{q_j - q_{j+1}}) are independent Gaussian and Gamma random variables respectively, together with the modeling of the system as a dense collection of quasi-particles whose scattering produces the dressed Lévy-Chentsov field."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling."}],"snapshot_sha256":"6cea5f54e9e7bacefe0e51856ae9208a82f64ea6ebba9375bccaf23ddd1f2623"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.14346/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider the Toda lattice $(\\mathbf{p}(t);\\mathbf{q}(t))$ at thermal equilibrium, meaning that its variables $(p_j)$ and $(e^{q_j-q_{j+1}})$ are independent Gaussian and Gamma random variables, respectively. We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce, (i) the scaling limit for the trajectory of a single particle $q_0$ is a Brownian motion; (ii) space-time two-point correlation functions for the model decay inversely with time, with explicit scaling distributions pr","authors_text":"Amol Aggarwal, Matthew Nicoletti","cross_cats":["math.DS"],"headline":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-15T18:59:53Z","title":"Fluctuations for the Toda lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.14346","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T11:53:32.636180Z","id":"60dee785-9690-40ce-b5c3-fbbe44db9fa2","model_set":{"reader":"grok-4.3"},"one_line_summary":"Currents in the thermal Toda lattice have space-time fluctuations converging to an explicit Gaussian process under diffusive scaling, implying Brownian motion for particle positions and inverse-time decaying correlations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Fluctuations of currents in the Toda lattice converge to an explicit Gaussian limit under diffusive scaling.","strongest_claim":"We show under diffusive scaling that the space-time fluctuations for the model's currents converge to an explicit Gaussian limit. As consequences, we deduce (i) the scaling limit for the trajectory of a single particle q_0 is a Brownian motion; (ii) space-time two-point correlation functions decay inversely with time with explicit scaling distributions predicted by Spohn.","weakest_assumption":"The starting assumption that the Toda lattice variables (p_j) and (e^{q_j - q_{j+1}}) are independent Gaussian and Gamma random variables respectively, together with the modeling of the system as a dense collection of quasi-particles whose scattering produces the dressed Lévy-Chentsov field."}},"verdict_id":"60dee785-9690-40ce-b5c3-fbbe44db9fa2"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:963ce67405eba0d70b4ec5b15ec555b7643caeb0983f4b37751984182c64b24d","target":"record","created_at":"2026-05-20T01:05:13Z","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":"5c8d1f24b8b35afc022ff7425ea85efb850b05f7212f5689650a3051a8f8352b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-15T18:59:53Z","title_canon_sha256":"fe5dffff0807c616588eea29d55d64b6f71bb4ac6d79a7fa73dce4abc52aba10"},"schema_version":"1.0","source":{"id":"2604.14346","kind":"arxiv","version":2}},"canonical_sha256":"43938e3cf0ef84a5d90b1dcd416a52bb9e80ba4de34536671191faee9cc327d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43938e3cf0ef84a5d90b1dcd416a52bb9e80ba4de34536671191faee9cc327d2","first_computed_at":"2026-05-20T01:05:13.370286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:13.370286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZW30SEfsuNCkG+DW1IVJiFaCI484C2FW0tv89wMLQ+BwI2HJVg8hf9X5TuI5rP94M5K5br6QZglg3uNLR76Ag==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:13.370898Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.14346","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:963ce67405eba0d70b4ec5b15ec555b7643caeb0983f4b37751984182c64b24d","sha256:41bf68dab7bb510e1d536b24d3ae02972ae6dbeb236cf2411492e2b7e92d2e9e"],"state_sha256":"6eb02ed373d60a5d0a2ca5cb198192ef01fd39933979932936d678ac0dbdae32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVlF6wszXFfSll2bZiGGWoh2F65mvPNCiIPrcHG9qYqbhFou+sbvU9x0RPDNI/r40EL5vtlrG4Rv8PkfQbeMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:20:28.177698Z","bundle_sha256":"c5009caa874d76df343311496b09cb7e9da5cc831f19d6fb379a49b4afa29cf1"}}