{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:45QZ6OAZG4HY2OS7PNOPJO4KJG","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":"204e181ba876977b529305b9745f8083820e06b92d91167931e7362bfbae2dc2","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2005-04-02T23:25:19Z","title_canon_sha256":"6a3a1078fee44002ab501589e980c301b956e9e1d860788c7b55a095033a1bed"},"schema_version":"1.0","source":{"id":"math/0504039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504039","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504039v2","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504039","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"45QZ6OAZG4HY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"45QZ6OAZG4HY2OS7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"45QZ6OAZ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:fc12c9da1273c2e8fa310dc77972d14c7eb35670cece1569c903f5ff2e7f4697","target":"graph","created_at":"2026-05-18T04:40:54Z","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 propose the further study of the rate of growth of the number of contiguous buildings which may be made from n LEGO blocks of the same size and color. Specializing to blocks of dimension 2x4 we give upper and lower bounds, and speculate on the true value.","authors_text":"Bergfinnur Durhuus, Soren Eilers","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2005-04-02T23:25:19Z","title":"On the entropy of LEGO"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504039","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":"sha256:2d1cfc0db6469076764b649bdc1460979881b207f7f899c11a16bb0f511cd068","target":"record","created_at":"2026-05-18T04:40:54Z","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":"204e181ba876977b529305b9745f8083820e06b92d91167931e7362bfbae2dc2","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2005-04-02T23:25:19Z","title_canon_sha256":"6a3a1078fee44002ab501589e980c301b956e9e1d860788c7b55a095033a1bed"},"schema_version":"1.0","source":{"id":"math/0504039","kind":"arxiv","version":2}},"canonical_sha256":"e7619f3819370f8d3a5f7b5cf4bb8a499e92375d214aad835e2d3b29e715b71a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7619f3819370f8d3a5f7b5cf4bb8a499e92375d214aad835e2d3b29e715b71a","first_computed_at":"2026-05-18T04:40:54.991182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.991182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AcFRWuuwtZ1lt2BertrEisSkEgVjc2AXHjDvpqx9k5kSuZNmG2jcHu2TlBwCisxZdz48QD7+p52b3Hn6YhdoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.991665Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d1cfc0db6469076764b649bdc1460979881b207f7f899c11a16bb0f511cd068","sha256:fc12c9da1273c2e8fa310dc77972d14c7eb35670cece1569c903f5ff2e7f4697"],"state_sha256":"ad1df7d06921fa7b7d88aadd195683a4453138b19370e27bbdae0e57384c50c9"}