{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MRYFFNNGE2XNUDALARQOE62ZGH","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":"c2d92dc519e085848fc7462bf03d8ac5cdd592be0efd76f79dc3a37433b9f6e5","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-08-18T15:02:40Z","title_canon_sha256":"7cb6f304aa9c6b833a1290ebc9109552bacdbafa93d58364d5f29ec6334dc28d"},"schema_version":"1.0","source":{"id":"1908.06456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06456","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06456v2","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06456","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"MRYFFNNGE2XN","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_16","alias_value":"MRYFFNNGE2XNUDAL","created_at":"2026-07-05T01:25:35Z"},{"alias_kind":"pith_short_8","alias_value":"MRYFFNNG","created_at":"2026-07-05T01:25:35Z"}],"graph_snapshots":[{"event_id":"sha256:37e3624903bf40be64df1b4a7c7baad0c16799e71631f3f42e535a5166a4d97e","target":"graph","created_at":"2026-07-05T01:25:35Z","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/1908.06456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.","authors_text":"Steffen Lauritzen","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-08-18T15:02:40Z","title":"Harmonic Analysis of Symmetric Random Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06456","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:d60d06e5033dc915f05638f0aba27cbe18deb9c51362b64aa6d1752c86208b8f","target":"record","created_at":"2026-07-05T01:25:35Z","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":"c2d92dc519e085848fc7462bf03d8ac5cdd592be0efd76f79dc3a37433b9f6e5","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-08-18T15:02:40Z","title_canon_sha256":"7cb6f304aa9c6b833a1290ebc9109552bacdbafa93d58364d5f29ec6334dc28d"},"schema_version":"1.0","source":{"id":"1908.06456","kind":"arxiv","version":2}},"canonical_sha256":"647052b5a626aeda0c0b0460e27b5931c813fc81be1dad1205574cc3f67ce0df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"647052b5a626aeda0c0b0460e27b5931c813fc81be1dad1205574cc3f67ce0df","first_computed_at":"2026-07-05T01:25:35.048608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:35.048608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CC2Xu56hggaqyU8weJXnt4Uzom8VkTXrLA6k7EDQutyAfNp/2x7OerO5ciB6Xk1AUsKtajcfol6Ft4XTYNLhAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:35.049008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d60d06e5033dc915f05638f0aba27cbe18deb9c51362b64aa6d1752c86208b8f","sha256:37e3624903bf40be64df1b4a7c7baad0c16799e71631f3f42e535a5166a4d97e"],"state_sha256":"67aff2fd9c33fdcc56e388244b2d2672ab5970f71d173254e00082809600505a"}