{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2BPHMNGSIFYJJXEN6I7A7V2FZY","short_pith_number":"pith:2BPHMNGS","canonical_record":{"source":{"id":"2412.16054","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T16:53:54Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e4cd9c835e4a9ae9c899c337b975435cc76edca2bb3b5df0569ee646216ddbb0","abstract_canon_sha256":"293d8dd43b30537d29047dabff22cadbac6605cd01b56347f1a17fa3d8e7f068"},"schema_version":"1.0"},"canonical_sha256":"d05e7634d2417094dc8df23e0fd745ce306ee3f13c3a1b1bf63eab5f5d08cca8","source":{"kind":"arxiv","id":"2412.16054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16054","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16054v1","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16054","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"2BPHMNGSIFYJ","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_16","alias_value":"2BPHMNGSIFYJJXEN","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_8","alias_value":"2BPHMNGS","created_at":"2026-07-05T09:52:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2BPHMNGSIFYJJXEN6I7A7V2FZY","target":"record","payload":{"canonical_record":{"source":{"id":"2412.16054","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T16:53:54Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e4cd9c835e4a9ae9c899c337b975435cc76edca2bb3b5df0569ee646216ddbb0","abstract_canon_sha256":"293d8dd43b30537d29047dabff22cadbac6605cd01b56347f1a17fa3d8e7f068"},"schema_version":"1.0"},"canonical_sha256":"d05e7634d2417094dc8df23e0fd745ce306ee3f13c3a1b1bf63eab5f5d08cca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:33.830835Z","signature_b64":"8u5kQ+tS4zYGeQJ5CkR53fYtJdOcbtrPwbbFBd8jWecmCkN4XsGNRgre6UwgS9VO3WW0Sd8P1h+Y5q6auvbVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d05e7634d2417094dc8df23e0fd745ce306ee3f13c3a1b1bf63eab5f5d08cca8","last_reissued_at":"2026-07-05T09:52:33.830365Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:33.830365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.16054","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":"2026-07-05T09:52:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmfZl3EeXFFFvyOa1TfLmS0acGEU5QW3+uquzKsjY9jfCs1HupEM/O2QPfi7y2FDi4Ot2m7C9gsrMtU6frDmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:20:47.281612Z"},"content_sha256":"79baaa5ad4c27e9934e28275727353180d8ecc6ce2ad83ddd1b4aa25fdcfdee9","schema_version":"1.0","event_id":"sha256:79baaa5ad4c27e9934e28275727353180d8ecc6ce2ad83ddd1b4aa25fdcfdee9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2BPHMNGSIFYJJXEN6I7A7V2FZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Theorems for the Volume of Random Projections and Sections of $\\ell_p^N$-balls","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Joscha Prochno, Philipp Tuchel","submitted_at":"2024-12-20T16:53:54Z","abstract_excerpt":"Let $\\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\\ell_p$-norm. For each $N\\in\\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\\in\\mathbb{N}$ and consider the volume of $\\mathbb{B}_p^N$ projected onto $E_N$ or intersected with $E_N$. We also consider geometric quantities other than the volume such as the intrinsic volumes or the dual volumes. In this setting we prove central limit theorems, moderate deviation principles, and large deviation principles as $N\\to\\infty$. Our results provide a complete asymptotic picture. In particular, they gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16054","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/2412.16054/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":"2026-07-05T09:52:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54LC/QIZahvP6NXiJytt0Cj8QVMXQS6gJE1bYbIBMn31pZ1DcqsFjZUDFJqvQPUfQhc89sTh9rwaxMFNHvnTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:20:47.282101Z"},"content_sha256":"5af0e5aefe4c32e12c1a1cab95ba6634c622d0a31890cc915f1efc043ddb1a9b","schema_version":"1.0","event_id":"sha256:5af0e5aefe4c32e12c1a1cab95ba6634c622d0a31890cc915f1efc043ddb1a9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/bundle.json","state_url":"https://pith.science/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/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":"2026-08-12T06:20:47Z","links":{"resolver":"https://pith.science/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY","bundle":"https://pith.science/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/bundle.json","state":"https://pith.science/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BPHMNGSIFYJJXEN6I7A7V2FZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2BPHMNGSIFYJJXEN6I7A7V2FZY","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":"293d8dd43b30537d29047dabff22cadbac6605cd01b56347f1a17fa3d8e7f068","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T16:53:54Z","title_canon_sha256":"e4cd9c835e4a9ae9c899c337b975435cc76edca2bb3b5df0569ee646216ddbb0"},"schema_version":"1.0","source":{"id":"2412.16054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16054","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16054v1","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16054","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"2BPHMNGSIFYJ","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_16","alias_value":"2BPHMNGSIFYJJXEN","created_at":"2026-07-05T09:52:33Z"},{"alias_kind":"pith_short_8","alias_value":"2BPHMNGS","created_at":"2026-07-05T09:52:33Z"}],"graph_snapshots":[{"event_id":"sha256:5af0e5aefe4c32e12c1a1cab95ba6634c622d0a31890cc915f1efc043ddb1a9b","target":"graph","created_at":"2026-07-05T09:52:33Z","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/2412.16054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\\ell_p$-norm. For each $N\\in\\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\\in\\mathbb{N}$ and consider the volume of $\\mathbb{B}_p^N$ projected onto $E_N$ or intersected with $E_N$. We also consider geometric quantities other than the volume such as the intrinsic volumes or the dual volumes. In this setting we prove central limit theorems, moderate deviation principles, and large deviation principles as $N\\to\\infty$. Our results provide a complete asymptotic picture. In particular, they gener","authors_text":"Christoph Thaele, Joscha Prochno, Philipp Tuchel","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T16:53:54Z","title":"Limit Theorems for the Volume of Random Projections and Sections of $\\ell_p^N$-balls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16054","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":"sha256:79baaa5ad4c27e9934e28275727353180d8ecc6ce2ad83ddd1b4aa25fdcfdee9","target":"record","created_at":"2026-07-05T09:52:33Z","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":"293d8dd43b30537d29047dabff22cadbac6605cd01b56347f1a17fa3d8e7f068","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T16:53:54Z","title_canon_sha256":"e4cd9c835e4a9ae9c899c337b975435cc76edca2bb3b5df0569ee646216ddbb0"},"schema_version":"1.0","source":{"id":"2412.16054","kind":"arxiv","version":1}},"canonical_sha256":"d05e7634d2417094dc8df23e0fd745ce306ee3f13c3a1b1bf63eab5f5d08cca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d05e7634d2417094dc8df23e0fd745ce306ee3f13c3a1b1bf63eab5f5d08cca8","first_computed_at":"2026-07-05T09:52:33.830365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:33.830365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8u5kQ+tS4zYGeQJ5CkR53fYtJdOcbtrPwbbFBd8jWecmCkN4XsGNRgre6UwgS9VO3WW0Sd8P1h+Y5q6auvbVBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:33.830835Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79baaa5ad4c27e9934e28275727353180d8ecc6ce2ad83ddd1b4aa25fdcfdee9","sha256:5af0e5aefe4c32e12c1a1cab95ba6634c622d0a31890cc915f1efc043ddb1a9b"],"state_sha256":"07abcb25be7faa302d898697d5f36db2cd3e32a9afbb62565c9b98ab962ee6e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nBeG9+uQZdc8swtIw64KAedr5OO7RHnhfw3dukVnen+NDYcj8QJ9QvMCDCsLWzZENgkHlasB1ZW33+8ZbfcYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T06:20:47.285684Z","bundle_sha256":"430344ab23da747c064d797afb2d5bf3fca2cbcaf62803b9bef31127ee11e999"}}