{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JPTDDBACVRE4ZXCUK7NYR6GWOM","short_pith_number":"pith:JPTDDBAC","canonical_record":{"source":{"id":"2605.23371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T08:35:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5e3ae0abcee8f79c530ea5044f3148dcb2b9cd2b06f1c6c39475c5b256107454","abstract_canon_sha256":"05f791a331a7ffc0444e9343dabcc33cf792f76ff26fc17f714bc421357d99b8"},"schema_version":"1.0"},"canonical_sha256":"4be6318402ac49ccdc5457db88f8d67335508fc650ca51322094e355770be4e5","source":{"kind":"arxiv","id":"2605.23371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23371","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23371v1","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23371","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"JPTDDBACVRE4","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_16","alias_value":"JPTDDBACVRE4ZXCU","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_8","alias_value":"JPTDDBAC","created_at":"2026-05-25T02:01:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JPTDDBACVRE4ZXCUK7NYR6GWOM","target":"record","payload":{"canonical_record":{"source":{"id":"2605.23371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T08:35:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5e3ae0abcee8f79c530ea5044f3148dcb2b9cd2b06f1c6c39475c5b256107454","abstract_canon_sha256":"05f791a331a7ffc0444e9343dabcc33cf792f76ff26fc17f714bc421357d99b8"},"schema_version":"1.0"},"canonical_sha256":"4be6318402ac49ccdc5457db88f8d67335508fc650ca51322094e355770be4e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:51.287173Z","signature_b64":"8yH5W5UmRMk1Yic9hbIulJahgUZR15WhZHpHTy/QbSzCG/JunsRc+hgx+QRxWiCzJPvy3QykEqcMMIzqwIHEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4be6318402ac49ccdc5457db88f8d67335508fc650ca51322094e355770be4e5","last_reissued_at":"2026-05-25T02:01:51.286441Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:51.286441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.23371","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":"2026-05-25T02:01:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reEku8Koefw8vyNwz1qqXPCnpPEmfxZy9DoFUKihQG89XdSPvcjoEQCOvhTwhMYUGCCSZd1T8rWgwq73i3MTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:02:14.584837Z"},"content_sha256":"2f0df85d77bfa641878fbfea0c02f5a180215d2c1ea211c5d6b84efd42d485ae","schema_version":"1.0","event_id":"sha256:2f0df85d77bfa641878fbfea0c02f5a180215d2c1ea211c5d6b84efd42d485ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JPTDDBACVRE4ZXCUK7NYR6GWOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorems for high dimensional lattice polytopes: cosmological polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Benedikt Redno\\ss, Christoph Th\\\"ale, Martina Juhnke, Torben Donzelmann","submitted_at":"2026-05-22T08:35:56Z","abstract_excerpt":"We study cosmological polytopes induced by Erd\\H{o}s--R\\'enyi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the structure of the underlying random graph. Focusing on the number of polytope edges and on the number of edges in unimodular triangulations, we derive asymptotic formulas for expectations and variances and prove quantitative central limit theorems in the relevant parameter regime. The analysis relies on explicit graph-theoretic descriptions of the correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23371","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/2605.23371/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":"2026-05-25T02:01:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLlsj38F4ZhOjoeuHss1OiOoLfhpMcoH87oPNiYEbJACmPLk4MziVtjBWorAzDDPHrnB2mNYbLXb2cFRWbElAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:02:14.585588Z"},"content_sha256":"34dc11777b992e7130bfaaa36fdf5133b2863ba38fb4016dc84949da86c89d1f","schema_version":"1.0","event_id":"sha256:34dc11777b992e7130bfaaa36fdf5133b2863ba38fb4016dc84949da86c89d1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/bundle.json","state_url":"https://pith.science/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/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":"2026-05-26T06:02:14Z","links":{"resolver":"https://pith.science/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM","bundle":"https://pith.science/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/bundle.json","state":"https://pith.science/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPTDDBACVRE4ZXCUK7NYR6GWOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JPTDDBACVRE4ZXCUK7NYR6GWOM","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":"05f791a331a7ffc0444e9343dabcc33cf792f76ff26fc17f714bc421357d99b8","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T08:35:56Z","title_canon_sha256":"5e3ae0abcee8f79c530ea5044f3148dcb2b9cd2b06f1c6c39475c5b256107454"},"schema_version":"1.0","source":{"id":"2605.23371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23371","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23371v1","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23371","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"JPTDDBACVRE4","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_16","alias_value":"JPTDDBACVRE4ZXCU","created_at":"2026-05-25T02:01:51Z"},{"alias_kind":"pith_short_8","alias_value":"JPTDDBAC","created_at":"2026-05-25T02:01:51Z"}],"graph_snapshots":[{"event_id":"sha256:34dc11777b992e7130bfaaa36fdf5133b2863ba38fb4016dc84949da86c89d1f","target":"graph","created_at":"2026-05-25T02:01:51Z","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/2605.23371/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study cosmological polytopes induced by Erd\\H{o}s--R\\'enyi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the structure of the underlying random graph. Focusing on the number of polytope edges and on the number of edges in unimodular triangulations, we derive asymptotic formulas for expectations and variances and prove quantitative central limit theorems in the relevant parameter regime. The analysis relies on explicit graph-theoretic descriptions of the correspond","authors_text":"Benedikt Redno\\ss, Christoph Th\\\"ale, Martina Juhnke, Torben Donzelmann","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T08:35:56Z","title":"Central limit theorems for high dimensional lattice polytopes: cosmological polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23371","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":"sha256:2f0df85d77bfa641878fbfea0c02f5a180215d2c1ea211c5d6b84efd42d485ae","target":"record","created_at":"2026-05-25T02:01:51Z","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":"05f791a331a7ffc0444e9343dabcc33cf792f76ff26fc17f714bc421357d99b8","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T08:35:56Z","title_canon_sha256":"5e3ae0abcee8f79c530ea5044f3148dcb2b9cd2b06f1c6c39475c5b256107454"},"schema_version":"1.0","source":{"id":"2605.23371","kind":"arxiv","version":1}},"canonical_sha256":"4be6318402ac49ccdc5457db88f8d67335508fc650ca51322094e355770be4e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be6318402ac49ccdc5457db88f8d67335508fc650ca51322094e355770be4e5","first_computed_at":"2026-05-25T02:01:51.286441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:51.286441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8yH5W5UmRMk1Yic9hbIulJahgUZR15WhZHpHTy/QbSzCG/JunsRc+hgx+QRxWiCzJPvy3QykEqcMMIzqwIHEAA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:51.287173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f0df85d77bfa641878fbfea0c02f5a180215d2c1ea211c5d6b84efd42d485ae","sha256:34dc11777b992e7130bfaaa36fdf5133b2863ba38fb4016dc84949da86c89d1f"],"state_sha256":"4f0a3514a990fff7eb99c0249d037ab00550e4427a77027c727373df453b0793"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z53RXThf+sWP1JPRhldquwUrhNHdzFRI6YmvI+vP3IbQuMawIwFDTDwvKifQO0SAzWvG5nlntQN0wja9jx/FDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:02:14.589245Z","bundle_sha256":"75e17146675c582e7a55592d425417e5205842735dc5e0e0031d28c462433aa5"}}