{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4FXN5KZQQQW7LEIFAXMKRFUVX","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":"e95a54455bf9836496c488fbb45599c6e181be396fd60434f039aa7be834b3cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2018-06-03T08:03:28Z","title_canon_sha256":"b68b496fe20342cfa8fb06bd6f2a90786487cdadf0cdad79eb0e6b5282778a6d"},"schema_version":"1.0","source":{"id":"1806.00748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00748","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00748v1","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00748","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"G4FXN5KZQQQW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4FXN5KZQQQW7LEI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4FXN5KZ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:81251a62eb67c66163e5ff40863e97faf7c0b5d6e38a827d8d602a14cb1a1d51","target":"graph","created_at":"2026-05-17T23:50:13Z","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":"Many physical processes result in very uneven, apparently random, distributions of matter, characterized by fluctuations of the local density over orders of magnitude. The density of matter in the sparsest regions can have a power-law distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.","authors_text":"Alain Pumir, Greg Huber, Marc Pradas, Michael Wilkinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2018-06-03T08:03:28Z","title":"Lacunarity Exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00748","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:f7ced300c782529b959329ace60f6468f7f651de52b553a0f862734a27614328","target":"record","created_at":"2026-05-17T23:50:13Z","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":"e95a54455bf9836496c488fbb45599c6e181be396fd60434f039aa7be834b3cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2018-06-03T08:03:28Z","title_canon_sha256":"b68b496fe20342cfa8fb06bd6f2a90786487cdadf0cdad79eb0e6b5282778a6d"},"schema_version":"1.0","source":{"id":"1806.00748","kind":"arxiv","version":1}},"canonical_sha256":"370b76f55984216fac88282ec544b4adeb7c686e7c2387a42c751b297a12f1a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370b76f55984216fac88282ec544b4adeb7c686e7c2387a42c751b297a12f1a3","first_computed_at":"2026-05-17T23:50:13.523427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:13.523427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/Hz1OsdpQuD9Cpa488JrbCtkBYaFKx4r6HaukLyA61Ut4vpGSf0bN0BYQLnakmCcX4xpIfEOCLDOFPx4dIPDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:13.524159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ced300c782529b959329ace60f6468f7f651de52b553a0f862734a27614328","sha256:81251a62eb67c66163e5ff40863e97faf7c0b5d6e38a827d8d602a14cb1a1d51"],"state_sha256":"001532a45cb319d1b6086e9e09658dc354f8db0e3ec439fdf4902c19c18334e7"}