{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:MRYFFNNGE2XNUDALARQOE62ZGH","short_pith_number":"pith:MRYFFNNG","schema_version":"1.0","canonical_sha256":"647052b5a626aeda0c0b0460e27b5931c813fc81be1dad1205574cc3f67ce0df","source":{"kind":"arxiv","id":"1908.06456","version":2},"attestation_state":"computed","paper":{"title":"Harmonic Analysis of Symmetric Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Steffen Lauritzen","submitted_at":"2019-08-18T15:02:40Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.06456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-08-18T15:02:40Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"7cb6f304aa9c6b833a1290ebc9109552bacdbafa93d58364d5f29ec6334dc28d","abstract_canon_sha256":"c2d92dc519e085848fc7462bf03d8ac5cdd592be0efd76f79dc3a37433b9f6e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:35.049008Z","signature_b64":"CC2Xu56hggaqyU8weJXnt4Uzom8VkTXrLA6k7EDQutyAfNp/2x7OerO5ciB6Xk1AUsKtajcfol6Ft4XTYNLhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"647052b5a626aeda0c0b0460e27b5931c813fc81be1dad1205574cc3f67ce0df","last_reissued_at":"2026-07-05T01:25:35.048608Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:35.048608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Analysis of Symmetric Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Steffen Lauritzen","submitted_at":"2019-08-18T15:02:40Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06456","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06456/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.06456","created_at":"2026-07-05T01:25:35.048671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06456v2","created_at":"2026-07-05T01:25:35.048671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06456","created_at":"2026-07-05T01:25:35.048671+00:00"},{"alias_kind":"pith_short_12","alias_value":"MRYFFNNGE2XN","created_at":"2026-07-05T01:25:35.048671+00:00"},{"alias_kind":"pith_short_16","alias_value":"MRYFFNNGE2XNUDAL","created_at":"2026-07-05T01:25:35.048671+00:00"},{"alias_kind":"pith_short_8","alias_value":"MRYFFNNG","created_at":"2026-07-05T01:25:35.048671+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH","json":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH.json","graph_json":"https://pith.science/api/pith-number/MRYFFNNGE2XNUDALARQOE62ZGH/graph.json","events_json":"https://pith.science/api/pith-number/MRYFFNNGE2XNUDALARQOE62ZGH/events.json","paper":"https://pith.science/paper/MRYFFNNG"},"agent_actions":{"view_html":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH","download_json":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH.json","view_paper":"https://pith.science/paper/MRYFFNNG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06456&json=true","fetch_graph":"https://pith.science/api/pith-number/MRYFFNNGE2XNUDALARQOE62ZGH/graph.json","fetch_events":"https://pith.science/api/pith-number/MRYFFNNGE2XNUDALARQOE62ZGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH/action/storage_attestation","attest_author":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH/action/author_attestation","sign_citation":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH/action/citation_signature","submit_replication":"https://pith.science/pith/MRYFFNNGE2XNUDALARQOE62ZGH/action/replication_record"}},"created_at":"2026-07-05T01:25:35.048671+00:00","updated_at":"2026-07-05T01:25:35.048671+00:00"}