{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:25P4XPFUMX7VWGAZ6RDJIKBFF7","short_pith_number":"pith:25P4XPFU","canonical_record":{"source":{"id":"1401.2363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-10T15:07:11Z","cross_cats_sorted":[],"title_canon_sha256":"f9da201547081cdd5c6e49e0c2c16a9a873c0799138c38dbca5fcb3a3955c7c1","abstract_canon_sha256":"6567a2519d6b9c4cfbfc43ec7e7ff2e2b6e8b50384667e5cd936366866c36e62"},"schema_version":"1.0"},"canonical_sha256":"d75fcbbcb465ff5b1819f4469428252ff9321ebf7b335bcc19dfe777ae828083","source":{"kind":"arxiv","id":"1401.2363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2363","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2363v1","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2363","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"pith_short_12","alias_value":"25P4XPFUMX7V","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"25P4XPFUMX7VWGAZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"25P4XPFU","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:25P4XPFUMX7VWGAZ6RDJIKBFF7","target":"record","payload":{"canonical_record":{"source":{"id":"1401.2363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-10T15:07:11Z","cross_cats_sorted":[],"title_canon_sha256":"f9da201547081cdd5c6e49e0c2c16a9a873c0799138c38dbca5fcb3a3955c7c1","abstract_canon_sha256":"6567a2519d6b9c4cfbfc43ec7e7ff2e2b6e8b50384667e5cd936366866c36e62"},"schema_version":"1.0"},"canonical_sha256":"d75fcbbcb465ff5b1819f4469428252ff9321ebf7b335bcc19dfe777ae828083","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:26.760662Z","signature_b64":"lWw6NKehmCrZZDuGjU0W+DyQg+16JN8FBPzA2a782juQ9bs+2Yu1db4603iHvNlwcaRXqcUtxhaMiBFYFIs0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d75fcbbcb465ff5b1819f4469428252ff9321ebf7b335bcc19dfe777ae828083","last_reissued_at":"2026-05-18T01:45:26.760244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:26.760244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.2363","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":"2026-05-18T01:45:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQDGzCAY06keIMrwj/CAn6on9/2E6f1LLyLvpitf1vW0ddRlITxBUv388hZUPaXuhWSuCCZEI30B1ZrjuzbmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:38:59.424259Z"},"content_sha256":"d901ae71d702707c9deefb6f774e61601511508e9d0e80e25e2e5c6251d94d5f","schema_version":"1.0","event_id":"sha256:d901ae71d702707c9deefb6f774e61601511508e9d0e80e25e2e5c6251d94d5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:25P4XPFUMX7VWGAZ6RDJIKBFF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-n conditional facedness m_n of 3D Poisson-Voronoi cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"H.J. Hilhorst","submitted_at":"2014-01-10T15:07:11Z","abstract_excerpt":"We consider the three-dimensional Poisson-Voronoi tessellation and study the average facedness m_n of a cell known to neighbor an n-faced cell. Whereas Aboav's law states that m_n=A+B/n, theoretical arguments indicate an asymptotic expansion m_n = 8 + k_1 n^{-1/6} +.... Recent new Monte Carlo data due to Lazar et al., based on a very large data set, now clearly rule out Aboav's law. In this work we determine the numerical value of k_1 and compare the expansion to the Monte Carlo data. The calculation of k_1 involves an auxiliary planar cellular structure composed of circular arcs, that we will"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2363","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":"2026-05-18T01:45:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNoRI1xqKAtjmD9h1hoEs50IAuQLQSiYygws81b8SO5YsBskMN4E6eeCB5mn5RMMV7n/O/zchgXl+rYQTwpDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:38:59.424654Z"},"content_sha256":"74d251aa2accc1816efa1ff3083364f88d8e5d0d8de3db986fd50e60724df2de","schema_version":"1.0","event_id":"sha256:74d251aa2accc1816efa1ff3083364f88d8e5d0d8de3db986fd50e60724df2de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/bundle.json","state_url":"https://pith.science/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/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":"2026-06-23T01:38:59Z","links":{"resolver":"https://pith.science/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7","bundle":"https://pith.science/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/bundle.json","state":"https://pith.science/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25P4XPFUMX7VWGAZ6RDJIKBFF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:25P4XPFUMX7VWGAZ6RDJIKBFF7","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":"6567a2519d6b9c4cfbfc43ec7e7ff2e2b6e8b50384667e5cd936366866c36e62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-10T15:07:11Z","title_canon_sha256":"f9da201547081cdd5c6e49e0c2c16a9a873c0799138c38dbca5fcb3a3955c7c1"},"schema_version":"1.0","source":{"id":"1401.2363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2363","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2363v1","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2363","created_at":"2026-05-18T01:45:26Z"},{"alias_kind":"pith_short_12","alias_value":"25P4XPFUMX7V","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"25P4XPFUMX7VWGAZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"25P4XPFU","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:74d251aa2accc1816efa1ff3083364f88d8e5d0d8de3db986fd50e60724df2de","target":"graph","created_at":"2026-05-18T01:45:26Z","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":"We consider the three-dimensional Poisson-Voronoi tessellation and study the average facedness m_n of a cell known to neighbor an n-faced cell. Whereas Aboav's law states that m_n=A+B/n, theoretical arguments indicate an asymptotic expansion m_n = 8 + k_1 n^{-1/6} +.... Recent new Monte Carlo data due to Lazar et al., based on a very large data set, now clearly rule out Aboav's law. In this work we determine the numerical value of k_1 and compare the expansion to the Monte Carlo data. The calculation of k_1 involves an auxiliary planar cellular structure composed of circular arcs, that we will","authors_text":"H.J. Hilhorst","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-10T15:07:11Z","title":"Large-n conditional facedness m_n of 3D Poisson-Voronoi cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2363","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:d901ae71d702707c9deefb6f774e61601511508e9d0e80e25e2e5c6251d94d5f","target":"record","created_at":"2026-05-18T01:45:26Z","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":"6567a2519d6b9c4cfbfc43ec7e7ff2e2b6e8b50384667e5cd936366866c36e62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-10T15:07:11Z","title_canon_sha256":"f9da201547081cdd5c6e49e0c2c16a9a873c0799138c38dbca5fcb3a3955c7c1"},"schema_version":"1.0","source":{"id":"1401.2363","kind":"arxiv","version":1}},"canonical_sha256":"d75fcbbcb465ff5b1819f4469428252ff9321ebf7b335bcc19dfe777ae828083","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75fcbbcb465ff5b1819f4469428252ff9321ebf7b335bcc19dfe777ae828083","first_computed_at":"2026-05-18T01:45:26.760244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:26.760244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lWw6NKehmCrZZDuGjU0W+DyQg+16JN8FBPzA2a782juQ9bs+2Yu1db4603iHvNlwcaRXqcUtxhaMiBFYFIs0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:26.760662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d901ae71d702707c9deefb6f774e61601511508e9d0e80e25e2e5c6251d94d5f","sha256:74d251aa2accc1816efa1ff3083364f88d8e5d0d8de3db986fd50e60724df2de"],"state_sha256":"4c02861ed38e8a67fb8771366b850a9f7c21ae5ffb327a7407b5ff588f01990e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGSrmjxMpsidv0r8sELkjbXepiX66mE6Bas4MzkfD9oypg5RtWG++CLhtEQ5P1MEQauCUk4OTj5lvZyg2gl5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:38:59.426700Z","bundle_sha256":"d472e5a572691f30afbbc2c9eac3b0aa64cf49e22d4c071be3cd0e08957cdf3e"}}