{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SCGSMAG2JZKTY4KHZLNYTDXIKF","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":"d3fbcd973d6b5ac0769abb31f936501c1b679b30dd9c32ac1703034595ea66db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-05-07T21:19:59Z","title_canon_sha256":"ded9a7bd1fcf81b3a5378871c965a8814ab1c642d753dfacc1689d66fe6480e3"},"schema_version":"1.0","source":{"id":"2305.04378","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.04378","created_at":"2026-07-05T06:30:45Z"},{"alias_kind":"arxiv_version","alias_value":"2305.04378v2","created_at":"2026-07-05T06:30:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.04378","created_at":"2026-07-05T06:30:45Z"},{"alias_kind":"pith_short_12","alias_value":"SCGSMAG2JZKT","created_at":"2026-07-05T06:30:45Z"},{"alias_kind":"pith_short_16","alias_value":"SCGSMAG2JZKTY4KH","created_at":"2026-07-05T06:30:45Z"},{"alias_kind":"pith_short_8","alias_value":"SCGSMAG2","created_at":"2026-07-05T06:30:45Z"}],"graph_snapshots":[{"event_id":"sha256:50554d6e246f2a3f57d3385262bf5611b6e3284f7b983dbd77f9e78d41c1e57e","target":"graph","created_at":"2026-07-05T06:30:45Z","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/2305.04378/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a class of cellular automata growth models on the two-dimensional integer lattice with finite cross neighborhoods. These dynamics are determined by a Young diagram $\\mathcal Z$ and the radius $\\rho$ of the neighborhood, which we assume to be sufficiently large. A point becomes occupied if the pair of counts of currently occupied points on the horizontal and vertical parts of the neighborhood lies outside $\\mathcal Z$. Starting with a small density $p$ of occupied points, we focus on the first time $T$ at which the origin is occupied. We show that $T$ scales as a power of $1/p$, an","authors_text":"Daniel Blanquicett, David Sivakoff, Janko Gravner, Luke Wilson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-05-07T21:19:59Z","title":"Two-dimensional supercritical growth dynamics with one-dimensional nucleation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.04378","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":"sha256:77776f6eb8135bd7c514965194e0d461eacfa3f11b06849988a42ec409f509c7","target":"record","created_at":"2026-07-05T06:30:45Z","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":"d3fbcd973d6b5ac0769abb31f936501c1b679b30dd9c32ac1703034595ea66db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-05-07T21:19:59Z","title_canon_sha256":"ded9a7bd1fcf81b3a5378871c965a8814ab1c642d753dfacc1689d66fe6480e3"},"schema_version":"1.0","source":{"id":"2305.04378","kind":"arxiv","version":2}},"canonical_sha256":"908d2600da4e553c7147cadb898ee85146c854d77030a15576ad483a833e8221","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"908d2600da4e553c7147cadb898ee85146c854d77030a15576ad483a833e8221","first_computed_at":"2026-07-05T06:30:45.568851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:45.568851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xHWzgsOss1FP6iYSGKCcuK/dF/MPyFIcysJnCGZ2HkLWEou12Zs6xyxjzL7W4Rw1T+ETnbQwUkrSOp73trZxBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:45.569458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.04378","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77776f6eb8135bd7c514965194e0d461eacfa3f11b06849988a42ec409f509c7","sha256:50554d6e246f2a3f57d3385262bf5611b6e3284f7b983dbd77f9e78d41c1e57e"],"state_sha256":"59be644c049d349828cb7711e8084cead260c1ce6b1a4b581f9e81107b142ec6"}