{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N4ZVK2OHPP2ZAKFEP27I6BCO43","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":"c3f6cdbfe1117a9e89064c8ef1a111fa1b805ad61d4bb617cdac82bd08a7bf4c","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T11:18:32Z","title_canon_sha256":"219b5cd34a9f6e3dd1b32a9adae675a2c335ce87e7351a10daff89894d5cb9a1"},"schema_version":"1.0","source":{"id":"1504.01263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01263","created_at":"2026-05-18T01:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01263v2","created_at":"2026-05-18T01:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01263","created_at":"2026-05-18T01:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"N4ZVK2OHPP2Z","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N4ZVK2OHPP2ZAKFE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N4ZVK2OH","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:f77c76f6cb75604b7cedc469e12fc567079095c72872016485747fb015f2bed4","target":"graph","created_at":"2026-05-18T01:20:20Z","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":"A Banach space valued graphon is a function $W:(\\Omega, \\mathcal{A},\\pi)^2\\to\\mathcal{Z}$ from a probability space to a Banach space with a separable predual, measurable in a suitable sense, and lying in appropriate $L^p$-spaces. As such we may consider $W(x,y)$ as a two-variable random element of the Banach space. A two-dimensional analogue of moments can be defined with the help of graphs and weak-* evaluations, and a natural question that then arises is whether these generalized moments determine the function $W$ uniquely -- up to measure preserving transformations. The main motivation come","authors_text":"D\\'avid Kunszenti-Kov\\'acs","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T11:18:32Z","title":"Uniqueness of Banach space valued graphons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01263","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:b8d9870e41808a13adee7e719b6a83c27e1546fc39de38018b7dcb89e45cf175","target":"record","created_at":"2026-05-18T01:20:20Z","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":"c3f6cdbfe1117a9e89064c8ef1a111fa1b805ad61d4bb617cdac82bd08a7bf4c","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T11:18:32Z","title_canon_sha256":"219b5cd34a9f6e3dd1b32a9adae675a2c335ce87e7351a10daff89894d5cb9a1"},"schema_version":"1.0","source":{"id":"1504.01263","kind":"arxiv","version":2}},"canonical_sha256":"6f335569c77bf59028a47ebe8f044ee6ee662c2c3c7a621b6c1d77b5303d167c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f335569c77bf59028a47ebe8f044ee6ee662c2c3c7a621b6c1d77b5303d167c","first_computed_at":"2026-05-18T01:20:20.732396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:20.732396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ubg0jWUMRr7TbuWvBBdkbaX9K8FcbznGxCh6Vu0xvqSBc9Jmky8Ba5z/R/WZv3MOqVq8OXEo3KORvtlVTI/lBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:20.733111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8d9870e41808a13adee7e719b6a83c27e1546fc39de38018b7dcb89e45cf175","sha256:f77c76f6cb75604b7cedc469e12fc567079095c72872016485747fb015f2bed4"],"state_sha256":"ee9dcb1decc3b5dc551873a673cb878eb701eb605fc2d606601843c84de8a4ca"}