{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AQVCHQTWCD6U3HKK7KHCPLMPKN","short_pith_number":"pith:AQVCHQTW","canonical_record":{"source":{"id":"2507.18601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-24T17:33:08Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"title_canon_sha256":"35d660c90a8868087b1260c51b6e7213906ad0170d1ddcfc2588d46e84b23aee","abstract_canon_sha256":"6ebaf4805472f51ff495c31dfbcd89e005cc619af819f583b7667b010186d840"},"schema_version":"1.0"},"canonical_sha256":"042a23c27610fd4d9d4afa8e27ad8f537a7fbc806a15e244635cc60ba4916841","source":{"kind":"arxiv","id":"2507.18601","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.18601","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.18601v2","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.18601","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"AQVCHQTWCD6U","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_16","alias_value":"AQVCHQTWCD6U3HKK","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_8","alias_value":"AQVCHQTW","created_at":"2026-07-05T12:09:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AQVCHQTWCD6U3HKK7KHCPLMPKN","target":"record","payload":{"canonical_record":{"source":{"id":"2507.18601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-24T17:33:08Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"title_canon_sha256":"35d660c90a8868087b1260c51b6e7213906ad0170d1ddcfc2588d46e84b23aee","abstract_canon_sha256":"6ebaf4805472f51ff495c31dfbcd89e005cc619af819f583b7667b010186d840"},"schema_version":"1.0"},"canonical_sha256":"042a23c27610fd4d9d4afa8e27ad8f537a7fbc806a15e244635cc60ba4916841","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:09:21.887112Z","signature_b64":"/M8Zi89j9EieUgdeUVkszKZsq7VixC/Rh4jUDp9o8HmJklQohwLFOd8M6yMpwy72D5oeoesCwgIaABR6g3RkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"042a23c27610fd4d9d4afa8e27ad8f537a7fbc806a15e244635cc60ba4916841","last_reissued_at":"2026-07-05T12:09:21.886686Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:09:21.886686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.18601","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":"2026-07-05T12:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVw4uWVESKSEpxYP5uzpWPA3EMhzKjZ8xrKBPKdIbR4+MC2rOldhBFosWjw5RItcTOV5M/gsqnOzsWDbbBvMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:45:39.137255Z"},"content_sha256":"717709745e48d746a2fedcf2647727b5967471a8f099e5e3e6fa3f42df26caa6","schema_version":"1.0","event_id":"sha256:717709745e48d746a2fedcf2647727b5967471a8f099e5e3e6fa3f42df26caa6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AQVCHQTWCD6U3HKK7KHCPLMPKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global fluctuations for standard Young tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Gabriel Raposo","submitted_at":"2025-07-24T17:33:08Z","abstract_excerpt":"We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.18601","kind":"arxiv","version":2},"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/2507.18601/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":"2026-07-05T12:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00ZcJJxXIF4WjkIDT+CInvaR/2CMxW5jsEZpYpf9uufRItidhTN/lK4DwhFZWtk7mLyI2+dxZk9j0RbAZTI1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:45:39.137758Z"},"content_sha256":"5520cbc87e1b013bddb87616ec35c8cf9002b3e8045c45193388e0c3864b8554","schema_version":"1.0","event_id":"sha256:5520cbc87e1b013bddb87616ec35c8cf9002b3e8045c45193388e0c3864b8554"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/bundle.json","state_url":"https://pith.science/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/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":"2026-08-21T13:45:39Z","links":{"resolver":"https://pith.science/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN","bundle":"https://pith.science/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/bundle.json","state":"https://pith.science/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQVCHQTWCD6U3HKK7KHCPLMPKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AQVCHQTWCD6U3HKK7KHCPLMPKN","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":"6ebaf4805472f51ff495c31dfbcd89e005cc619af819f583b7667b010186d840","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-24T17:33:08Z","title_canon_sha256":"35d660c90a8868087b1260c51b6e7213906ad0170d1ddcfc2588d46e84b23aee"},"schema_version":"1.0","source":{"id":"2507.18601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.18601","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.18601v2","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.18601","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"AQVCHQTWCD6U","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_16","alias_value":"AQVCHQTWCD6U3HKK","created_at":"2026-07-05T12:09:21Z"},{"alias_kind":"pith_short_8","alias_value":"AQVCHQTW","created_at":"2026-07-05T12:09:21Z"}],"graph_snapshots":[{"event_id":"sha256:5520cbc87e1b013bddb87616ec35c8cf9002b3e8045c45193388e0c3864b8554","target":"graph","created_at":"2026-07-05T12:09:21Z","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/2507.18601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distr","authors_text":"Gabriel Raposo","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-24T17:33:08Z","title":"Global fluctuations for standard Young tableaux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.18601","kind":"arxiv","version":2},"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":"sha256:717709745e48d746a2fedcf2647727b5967471a8f099e5e3e6fa3f42df26caa6","target":"record","created_at":"2026-07-05T12:09:21Z","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":"6ebaf4805472f51ff495c31dfbcd89e005cc619af819f583b7667b010186d840","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-24T17:33:08Z","title_canon_sha256":"35d660c90a8868087b1260c51b6e7213906ad0170d1ddcfc2588d46e84b23aee"},"schema_version":"1.0","source":{"id":"2507.18601","kind":"arxiv","version":2}},"canonical_sha256":"042a23c27610fd4d9d4afa8e27ad8f537a7fbc806a15e244635cc60ba4916841","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"042a23c27610fd4d9d4afa8e27ad8f537a7fbc806a15e244635cc60ba4916841","first_computed_at":"2026-07-05T12:09:21.886686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:21.886686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/M8Zi89j9EieUgdeUVkszKZsq7VixC/Rh4jUDp9o8HmJklQohwLFOd8M6yMpwy72D5oeoesCwgIaABR6g3RkBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:21.887112Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.18601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:717709745e48d746a2fedcf2647727b5967471a8f099e5e3e6fa3f42df26caa6","sha256:5520cbc87e1b013bddb87616ec35c8cf9002b3e8045c45193388e0c3864b8554"],"state_sha256":"56d749d04a442ad463aaa6a9304eb749733fc3e1c678de758b906a2dadf4e547"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqWABsCkhBgKdNSFI3Nz8PHkFjBgtEzvqUcePwz9YDMVSV18+1ArkaqdRSx/lTGgy1o4V5AJt24luv5tzkwsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T13:45:39.141426Z","bundle_sha256":"a0d55816557bb7978fdbfbabb3be9979fd821ac9496cfa97bb07a4001518c2e0"}}