{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:6K5UNXSDVTNN6XS36ZGZ4UMUW5","short_pith_number":"pith:6K5UNXSD","canonical_record":{"source":{"id":"math/0506044","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2005-06-02T15:36:05Z","cross_cats_sorted":[],"title_canon_sha256":"90a055fa2e16ab74e92cbe3f1e3205925fc24f605abbe3aa0740d11be848d908","abstract_canon_sha256":"4b143a245aedf5a5edb334e290ad5e41c1d60411590778557fb294b51b08fa26"},"schema_version":"1.0"},"canonical_sha256":"f2bb46de43acdadf5e5bf64d9e5194b742373a11d11432e326e2cb8a23010c80","source":{"kind":"arxiv","id":"math/0506044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506044","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506044v1","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506044","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"6K5UNXSDVTNN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6K5UNXSDVTNN6XS3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6K5UNXSD","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:6K5UNXSDVTNN6XS36ZGZ4UMUW5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0506044","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2005-06-02T15:36:05Z","cross_cats_sorted":[],"title_canon_sha256":"90a055fa2e16ab74e92cbe3f1e3205925fc24f605abbe3aa0740d11be848d908","abstract_canon_sha256":"4b143a245aedf5a5edb334e290ad5e41c1d60411590778557fb294b51b08fa26"},"schema_version":"1.0"},"canonical_sha256":"f2bb46de43acdadf5e5bf64d9e5194b742373a11d11432e326e2cb8a23010c80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:18.647159Z","signature_b64":"hPQFcx43hwPpyv/EiG96EzCw4IgyOcjoIu5le7wxgP+Sn7LYLXi+y9YwO7Ut5hKATiwBgQEWvBpbgdU6AJhAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2bb46de43acdadf5e5bf64d9e5194b742373a11d11432e326e2cb8a23010c80","last_reissued_at":"2026-05-18T01:25:18.646524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:18.646524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0506044","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":"2026-05-18T01:25:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vbm4xam3g4GMX9g9aGMjkIGj6v6vDKbEk26Gft30CrZ6iVZpvMfIHU5UFJxVx6pjujZ3iMZDFAE4DlPtoantDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:58:03.391472Z"},"content_sha256":"25c506782d10ac8d48b18bbfc2f9a2544cc88e7fec263d8bdea4dbc8821deae2","schema_version":"1.0","event_id":"sha256:25c506782d10ac8d48b18bbfc2f9a2544cc88e7fec263d8bdea4dbc8821deae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:6K5UNXSDVTNN6XS36ZGZ4UMUW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free-differentiability conditions on the free-energy function implying large deviations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Henri Comman","submitted_at":"2005-06-02T15:36:05Z","abstract_excerpt":"Let $(\\mu_{\\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\\alpha})$ be a net in $]0,+\\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\\lambda)$ exists for all $\\lambda$ in a nonempty open interval $G$, we give conditions on the left or right derivatives of $L_{\\mid G}$, implying vague (and thus narrow when $0\\in G$) large deviations. The rate function (which can be nonconvex) is obtained as an abstract Legendre-Fenchel transform. This allows us to strengthen the G\\\"{a}rtner-Ellis theorem by removing the usual differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506044","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":""},"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":"2026-05-18T01:25:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42HvIuKqfI68attgbmEogv4azd4rGEQqq03d5vGnRZAti9LegEooQVnuZfbasYGGkLguFm0VadVVyfo/PB3tBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:58:03.391817Z"},"content_sha256":"07a92ed99b94de2f470ea44627b91f82d72747ee6cb8b254254b8c7b7c437ebf","schema_version":"1.0","event_id":"sha256:07a92ed99b94de2f470ea44627b91f82d72747ee6cb8b254254b8c7b7c437ebf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/bundle.json","state_url":"https://pith.science/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/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":"2026-06-22T20:58:03Z","links":{"resolver":"https://pith.science/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5","bundle":"https://pith.science/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/bundle.json","state":"https://pith.science/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6K5UNXSDVTNN6XS36ZGZ4UMUW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:6K5UNXSDVTNN6XS36ZGZ4UMUW5","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":"4b143a245aedf5a5edb334e290ad5e41c1d60411590778557fb294b51b08fa26","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-06-02T15:36:05Z","title_canon_sha256":"90a055fa2e16ab74e92cbe3f1e3205925fc24f605abbe3aa0740d11be848d908"},"schema_version":"1.0","source":{"id":"math/0506044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506044","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506044v1","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506044","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"6K5UNXSDVTNN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6K5UNXSDVTNN6XS3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6K5UNXSD","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:07a92ed99b94de2f470ea44627b91f82d72747ee6cb8b254254b8c7b7c437ebf","target":"graph","created_at":"2026-05-18T01:25:18Z","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"},"paper":{"abstract_excerpt":"Let $(\\mu_{\\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\\alpha})$ be a net in $]0,+\\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\\lambda)$ exists for all $\\lambda$ in a nonempty open interval $G$, we give conditions on the left or right derivatives of $L_{\\mid G}$, implying vague (and thus narrow when $0\\in G$) large deviations. The rate function (which can be nonconvex) is obtained as an abstract Legendre-Fenchel transform. This allows us to strengthen the G\\\"{a}rtner-Ellis theorem by removing the usual differentia","authors_text":"Henri Comman","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2005-06-02T15:36:05Z","title":"Free-differentiability conditions on the free-energy function implying large deviations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506044","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":"sha256:25c506782d10ac8d48b18bbfc2f9a2544cc88e7fec263d8bdea4dbc8821deae2","target":"record","created_at":"2026-05-18T01:25:18Z","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":"4b143a245aedf5a5edb334e290ad5e41c1d60411590778557fb294b51b08fa26","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-06-02T15:36:05Z","title_canon_sha256":"90a055fa2e16ab74e92cbe3f1e3205925fc24f605abbe3aa0740d11be848d908"},"schema_version":"1.0","source":{"id":"math/0506044","kind":"arxiv","version":1}},"canonical_sha256":"f2bb46de43acdadf5e5bf64d9e5194b742373a11d11432e326e2cb8a23010c80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2bb46de43acdadf5e5bf64d9e5194b742373a11d11432e326e2cb8a23010c80","first_computed_at":"2026-05-18T01:25:18.646524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:18.646524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hPQFcx43hwPpyv/EiG96EzCw4IgyOcjoIu5le7wxgP+Sn7LYLXi+y9YwO7Ut5hKATiwBgQEWvBpbgdU6AJhAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:18.647159Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25c506782d10ac8d48b18bbfc2f9a2544cc88e7fec263d8bdea4dbc8821deae2","sha256:07a92ed99b94de2f470ea44627b91f82d72747ee6cb8b254254b8c7b7c437ebf"],"state_sha256":"da927b5364f255b8b314bb0b7332de208179036638bf1c49019ddd58431faf8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Y7JGLjCV8VppktxXW7jRKw9P+MKnpY2htV1XvqZv+LAtzbBhTC1uTK8EDVoRkiFL45X2FDajgd9RQlyy1oSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:58:03.393807Z","bundle_sha256":"e8fe9b6c78ddbc00f85977708011df26493f2c8bcc823b22897f6aabe7f56ee8"}}