{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QYZTJYROWSPWEBNWJZX4RTFAER","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":"7487a9e869f98ec7f252982c91d37e120e5f5d60cc184015ccbee2e2b12d2402","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T11:10:33Z","title_canon_sha256":"fee936f015da87ec29716aab1b0924ecb95bc61220836e081f48f22c23ad1d9f"},"schema_version":"1.0","source":{"id":"1609.08859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08859","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08859v1","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08859","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"QYZTJYROWSPW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QYZTJYROWSPWEBNW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QYZTJYRO","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:13d7641103d1e13a1ffe98c128138e10cb5b9164dc256ff3404111303e1de4fb","target":"graph","created_at":"2026-05-18T00:54:59Z","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 study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted assemblies of tree-like combinatorial structures. As an application, we establish smooth growth along lattices for small block-stable classes of graphs. Random graphs with n vertices from such classes are shown to form a giant connected component. The small fragments may converge toward different Poisson Boltzmann limit graphs, depending along which lattice w","authors_text":"Benedikt Stufler","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T11:10:33Z","title":"Gibbs partitions: the convergent case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08859","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":"sha256:88860a61f0c7d1aaf8e25535d0ef6e271fdbff932f8b57033452483358c8675d","target":"record","created_at":"2026-05-18T00:54:59Z","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":"7487a9e869f98ec7f252982c91d37e120e5f5d60cc184015ccbee2e2b12d2402","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T11:10:33Z","title_canon_sha256":"fee936f015da87ec29716aab1b0924ecb95bc61220836e081f48f22c23ad1d9f"},"schema_version":"1.0","source":{"id":"1609.08859","kind":"arxiv","version":1}},"canonical_sha256":"863334e22eb49f6205b64e6fc8cca0245110b40f719b881a12328d32d2b5cc90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"863334e22eb49f6205b64e6fc8cca0245110b40f719b881a12328d32d2b5cc90","first_computed_at":"2026-05-18T00:54:59.905709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:59.905709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hZQiBqB7m6a5cv5P2J8pra3X2jvvGj8j8xbRZlpOkGKS44l5EZMge7dDJd9KXEVsDC6ep4F4sKqWZJXvq9h0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:59.906232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88860a61f0c7d1aaf8e25535d0ef6e271fdbff932f8b57033452483358c8675d","sha256:13d7641103d1e13a1ffe98c128138e10cb5b9164dc256ff3404111303e1de4fb"],"state_sha256":"f1a6db5c61aa6782cf06ba5e545eb0775a9fb896b7fac8bca014a7f5f9188839"}