{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KLYL6QYP5QKXIFUYQDXTYP4QHE","short_pith_number":"pith:KLYL6QYP","canonical_record":{"source":{"id":"1906.09848","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-24T10:54:29Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"9d33311f7a7a28237bd0b42db02c0810660d969ca6b0690379bf571b49524dc6","abstract_canon_sha256":"cff22bb45e09ce104426100dd152f472147ede18b6049cf522b46502d6d79a58"},"schema_version":"1.0"},"canonical_sha256":"52f0bf430fec1574169880ef3c3f90391a2f14eb5ea2b94c3e0a4f7d1f256056","source":{"kind":"arxiv","id":"1906.09848","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09848","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09848v3","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09848","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"KLYL6QYP5QKX","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_16","alias_value":"KLYL6QYP5QKXIFUY","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_8","alias_value":"KLYL6QYP","created_at":"2026-07-05T03:31:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KLYL6QYP5QKXIFUYQDXTYP4QHE","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09848","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-24T10:54:29Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"9d33311f7a7a28237bd0b42db02c0810660d969ca6b0690379bf571b49524dc6","abstract_canon_sha256":"cff22bb45e09ce104426100dd152f472147ede18b6049cf522b46502d6d79a58"},"schema_version":"1.0"},"canonical_sha256":"52f0bf430fec1574169880ef3c3f90391a2f14eb5ea2b94c3e0a4f7d1f256056","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:20.330346Z","signature_b64":"ajFePVTFTMm06QQSTRQSuIfeve/w6TkM9KMjay0Cuyngyroc6iAeyuYEX/Cf4ny4ZNqV7EFfD05wHhid2qJjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52f0bf430fec1574169880ef3c3f90391a2f14eb5ea2b94c3e0a4f7d1f256056","last_reissued_at":"2026-07-05T03:31:20.329839Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:20.329839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09848","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":"2026-07-05T03:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k9KIdWHLWcjN/KJokj3HFB/wYivWEIG8p27wtm9HujoWfZ3e5GRbDEhpx0ryQCUiD/X0Js/gxFtoE3uX/GDVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:24:31.939126Z"},"content_sha256":"4fb07d9e1389fcc5dee303ccaeec33cef88927c3dda6b785b24fa2223e14ee7b","schema_version":"1.0","event_id":"sha256:4fb07d9e1389fcc5dee303ccaeec33cef88927c3dda6b785b24fa2223e14ee7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KLYL6QYP5QKXIFUYQDXTYP4QHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local laws and rigidity for Coulomb gases at any temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Scott Armstrong, Sylvia Serfaty","submitted_at":"2019-06-24T10:54:29Z","abstract_excerpt":"We study Coulomb gases in any dimension $d \\geq 2$ and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes generalizing the Ginibre point process for arbitrary temperature and dimension. The local laws come together with a quantitative expansion of the free energy with a new explicit error rate in the case of a uniform background density. These estimates have explicit temperature dependence, allowing to treat regimes of very large or very small temperature, and exh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09848","kind":"arxiv","version":3},"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/1906.09848/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":"2026-07-05T03:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RPRvO5f/OBKXNe3WLfFrAybn7CkUmJsaz+TvbbuJB4rTCHObzslRtw29gFRDphF78Oyf+P9/H8jXznMBuwVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:24:31.939655Z"},"content_sha256":"19b821dd4a8f49910414528ebab840e1c5d7a8420b9e91bd0dcb077fcf5a8308","schema_version":"1.0","event_id":"sha256:19b821dd4a8f49910414528ebab840e1c5d7a8420b9e91bd0dcb077fcf5a8308"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/bundle.json","state_url":"https://pith.science/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/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":"2026-08-08T06:24:31Z","links":{"resolver":"https://pith.science/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE","bundle":"https://pith.science/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/bundle.json","state":"https://pith.science/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLYL6QYP5QKXIFUYQDXTYP4QHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KLYL6QYP5QKXIFUYQDXTYP4QHE","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":"cff22bb45e09ce104426100dd152f472147ede18b6049cf522b46502d6d79a58","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-24T10:54:29Z","title_canon_sha256":"9d33311f7a7a28237bd0b42db02c0810660d969ca6b0690379bf571b49524dc6"},"schema_version":"1.0","source":{"id":"1906.09848","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09848","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09848v3","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09848","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"KLYL6QYP5QKX","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_16","alias_value":"KLYL6QYP5QKXIFUY","created_at":"2026-07-05T03:31:20Z"},{"alias_kind":"pith_short_8","alias_value":"KLYL6QYP","created_at":"2026-07-05T03:31:20Z"}],"graph_snapshots":[{"event_id":"sha256:19b821dd4a8f49910414528ebab840e1c5d7a8420b9e91bd0dcb077fcf5a8308","target":"graph","created_at":"2026-07-05T03:31:20Z","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/1906.09848/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study Coulomb gases in any dimension $d \\geq 2$ and in a broad temperature regime. We prove local laws on the energy, separation and number of points down to the microscopic scale. These yield the existence of limiting point processes generalizing the Ginibre point process for arbitrary temperature and dimension. The local laws come together with a quantitative expansion of the free energy with a new explicit error rate in the case of a uniform background density. These estimates have explicit temperature dependence, allowing to treat regimes of very large or very small temperature, and exh","authors_text":"Scott Armstrong, Sylvia Serfaty","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-24T10:54:29Z","title":"Local laws and rigidity for Coulomb gases at any temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09848","kind":"arxiv","version":3},"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":"sha256:4fb07d9e1389fcc5dee303ccaeec33cef88927c3dda6b785b24fa2223e14ee7b","target":"record","created_at":"2026-07-05T03:31:20Z","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":"cff22bb45e09ce104426100dd152f472147ede18b6049cf522b46502d6d79a58","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-06-24T10:54:29Z","title_canon_sha256":"9d33311f7a7a28237bd0b42db02c0810660d969ca6b0690379bf571b49524dc6"},"schema_version":"1.0","source":{"id":"1906.09848","kind":"arxiv","version":3}},"canonical_sha256":"52f0bf430fec1574169880ef3c3f90391a2f14eb5ea2b94c3e0a4f7d1f256056","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52f0bf430fec1574169880ef3c3f90391a2f14eb5ea2b94c3e0a4f7d1f256056","first_computed_at":"2026-07-05T03:31:20.329839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:20.329839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ajFePVTFTMm06QQSTRQSuIfeve/w6TkM9KMjay0Cuyngyroc6iAeyuYEX/Cf4ny4ZNqV7EFfD05wHhid2qJjAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:20.330346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09848","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fb07d9e1389fcc5dee303ccaeec33cef88927c3dda6b785b24fa2223e14ee7b","sha256:19b821dd4a8f49910414528ebab840e1c5d7a8420b9e91bd0dcb077fcf5a8308"],"state_sha256":"6c6b633d150cd70ba20d2a66b93e2d94a9e9e0aff45e69aecf3aa1f7d4b54d83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hX+6uV2hu52AnuA6LJ2u4ngmLWZPLom9XhhQ3WjNqxAytoV+FxW645M0EGhu6yfB20cYHj4OSjxOzEE1L34iBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T06:24:31.943710Z","bundle_sha256":"64b8b5db8fb2316825773ef59992a8d99ca7c4f24858ff9d3fd1038f09607ca3"}}