{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6DEXTRMPQGIV74263HL55PHFW6","short_pith_number":"pith:6DEXTRMP","canonical_record":{"source":{"id":"2501.09629","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-01-16T16:18:53Z","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"title_canon_sha256":"807defcc7f0e96e093bfcb8c5e998e8742465a5aa9e16d417985627e543d816d","abstract_canon_sha256":"6e6cfe8606f582900c71f39590a9813eada7a44d663b58460879043157475c84"},"schema_version":"1.0"},"canonical_sha256":"f0c979c58f81915ff35ed9d7debce5b7aa99a89dace6d21042c0b1b1904828d7","source":{"kind":"arxiv","id":"2501.09629","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09629","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09629v1","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09629","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"6DEXTRMPQGIV","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_16","alias_value":"6DEXTRMPQGIV7426","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_8","alias_value":"6DEXTRMP","created_at":"2026-07-05T10:01:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6DEXTRMPQGIV74263HL55PHFW6","target":"record","payload":{"canonical_record":{"source":{"id":"2501.09629","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-01-16T16:18:53Z","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"title_canon_sha256":"807defcc7f0e96e093bfcb8c5e998e8742465a5aa9e16d417985627e543d816d","abstract_canon_sha256":"6e6cfe8606f582900c71f39590a9813eada7a44d663b58460879043157475c84"},"schema_version":"1.0"},"canonical_sha256":"f0c979c58f81915ff35ed9d7debce5b7aa99a89dace6d21042c0b1b1904828d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:49.966103Z","signature_b64":"PTeACdia6MLuWMnd/BlGREAcBKIaL7ou5IiwFPBwG+UHFuoW/w0J9rfUXgk1HtEtjM69tNWVDREQ3bNjaajUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0c979c58f81915ff35ed9d7debce5b7aa99a89dace6d21042c0b1b1904828d7","last_reissued_at":"2026-07-05T10:01:49.965499Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:49.965499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.09629","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4+/lq6THGQ6ch2h+Ty69RTAOYNkVUV8QeLhUGW+G/RexojDzc6WkcAnLbL5M2SYTXW5sF2MbxfMi4vGFlTzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-29T07:03:41.003342Z"},"content_sha256":"11ea790560c873ffe27eb50db4994fe64be0ac863fdc01586f26459748a5eb45","schema_version":"1.0","event_id":"sha256:11ea790560c873ffe27eb50db4994fe64be0ac863fdc01586f26459748a5eb45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6DEXTRMPQGIV74263HL55PHFW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Pablo I. Hurtado","submitted_at":"2025-01-16T16:18:53Z","abstract_excerpt":"Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation statistics of the current, a central observable out of equilibrium, using mostly macroscopic fluctuation theory (MFT) but also microscopic spectral methods. Special emphasis is put on describing the optimal path leading to a rare fluctuation, as well as on different dynamical symmetry breaking phenomena that appear at the fluctuating level. We start with an overview"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09629","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/2501.09629/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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csFEzJnz7iBZExIOGp9uh/N7fx86TcYdMUBAsBiUbYVi8E2pUUulRPYaxyW9ImFWjQR3V1uoN9oLo71letUTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-29T07:03:41.003729Z"},"content_sha256":"56869127b6f63f98c14e3993502c77ac72e9f497ad9ad7ecff57f6a3f976ffb7","schema_version":"1.0","event_id":"sha256:56869127b6f63f98c14e3993502c77ac72e9f497ad9ad7ecff57f6a3f976ffb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DEXTRMPQGIV74263HL55PHFW6/bundle.json","state_url":"https://pith.science/pith/6DEXTRMPQGIV74263HL55PHFW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DEXTRMPQGIV74263HL55PHFW6/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":"2026-07-29T07:03:41Z","links":{"resolver":"https://pith.science/pith/6DEXTRMPQGIV74263HL55PHFW6","bundle":"https://pith.science/pith/6DEXTRMPQGIV74263HL55PHFW6/bundle.json","state":"https://pith.science/pith/6DEXTRMPQGIV74263HL55PHFW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DEXTRMPQGIV74263HL55PHFW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6DEXTRMPQGIV74263HL55PHFW6","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":"6e6cfe8606f582900c71f39590a9813eada7a44d663b58460879043157475c84","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-01-16T16:18:53Z","title_canon_sha256":"807defcc7f0e96e093bfcb8c5e998e8742465a5aa9e16d417985627e543d816d"},"schema_version":"1.0","source":{"id":"2501.09629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09629","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09629v1","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09629","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"6DEXTRMPQGIV","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_16","alias_value":"6DEXTRMPQGIV7426","created_at":"2026-07-05T10:01:49Z"},{"alias_kind":"pith_short_8","alias_value":"6DEXTRMP","created_at":"2026-07-05T10:01:49Z"}],"graph_snapshots":[{"event_id":"sha256:56869127b6f63f98c14e3993502c77ac72e9f497ad9ad7ecff57f6a3f976ffb7","target":"graph","created_at":"2026-07-05T10:01:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.09629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation statistics of the current, a central observable out of equilibrium, using mostly macroscopic fluctuation theory (MFT) but also microscopic spectral methods. Special emphasis is put on describing the optimal path leading to a rare fluctuation, as well as on different dynamical symmetry breaking phenomena that appear at the fluctuating level. We start with an overview","authors_text":"Pablo I. Hurtado","cross_cats":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-01-16T16:18:53Z","title":"Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09629","kind":"arxiv","version":1},"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":"sha256:11ea790560c873ffe27eb50db4994fe64be0ac863fdc01586f26459748a5eb45","target":"record","created_at":"2026-07-05T10:01:49Z","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":"6e6cfe8606f582900c71f39590a9813eada7a44d663b58460879043157475c84","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","nlin.PS","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2025-01-16T16:18:53Z","title_canon_sha256":"807defcc7f0e96e093bfcb8c5e998e8742465a5aa9e16d417985627e543d816d"},"schema_version":"1.0","source":{"id":"2501.09629","kind":"arxiv","version":1}},"canonical_sha256":"f0c979c58f81915ff35ed9d7debce5b7aa99a89dace6d21042c0b1b1904828d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0c979c58f81915ff35ed9d7debce5b7aa99a89dace6d21042c0b1b1904828d7","first_computed_at":"2026-07-05T10:01:49.965499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:49.965499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PTeACdia6MLuWMnd/BlGREAcBKIaL7ou5IiwFPBwG+UHFuoW/w0J9rfUXgk1HtEtjM69tNWVDREQ3bNjaajUDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:49.966103Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.09629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11ea790560c873ffe27eb50db4994fe64be0ac863fdc01586f26459748a5eb45","sha256:56869127b6f63f98c14e3993502c77ac72e9f497ad9ad7ecff57f6a3f976ffb7"],"state_sha256":"a6d40262638f5084f129194352dacc10380c8c1fa53e195e56962cdf99b95da4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxGKAhe//HrpCeidVDRYr40n+j0XhWP1Wdf9wSoPcqD251YVqv1NIT+oVAZJ02lJX5HJOnacmS1Q9zI5pdt8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-29T07:03:41.006167Z","bundle_sha256":"246d09bc1323cc1df6143012c0d586f59b122d99024e58ba31fc4180d040387f"}}