{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CFFSYDVZS5L65TUUANVRNX24D6","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":"3707095fde8ee0ca54c6ac0b5976525a667aff554f69f5c91426206ab8a37341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-13T22:09:42Z","title_canon_sha256":"f320c9736c322b770ceedcf36885312960af53d66b03746886cf474578beffc0"},"schema_version":"1.0","source":{"id":"1203.2967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2967","created_at":"2026-05-18T04:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2967v1","created_at":"2026-05-18T04:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2967","created_at":"2026-05-18T04:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"CFFSYDVZS5L6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CFFSYDVZS5L65TUU","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CFFSYDVZ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:b68dc8b2b2985e6ab1acdc69226e07e6e37d442bacb7d9d3416548e17fde5cc8","target":"graph","created_at":"2026-05-18T04:00:13Z","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":"Given a multi-index sequence $\\mu_{\\mathbf{k}}$, $\\mathbf{k} = (k_1,..., k_n) \\in \\mathbb{N}_0^n$, necessary and sufficient conditions are given for the existence of a regular Borel polymeasure $\\gamma$ on the unit interval $I= [0,1]$ such that $\\mu_{\\mathbf{k}} = \\int_{I^n} t_1^{k_1}\\otimes ... \\otimes t_n^{k_n} \\gamma$. This problem will be called the weak multilinear Hausdorff problem of moments for $\\mu_{\\mathbf{k}}$. Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear","authors_text":"A. Ibort, J. G. Llavona, P. Linares","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-13T22:09:42Z","title":"On the multilinear Hausdorff problem of moments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2967","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":"sha256:96569bbe5fbef5b6449b984af6ac468c08bbecc304f37a082681379835bc7283","target":"record","created_at":"2026-05-18T04:00:13Z","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":"3707095fde8ee0ca54c6ac0b5976525a667aff554f69f5c91426206ab8a37341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-13T22:09:42Z","title_canon_sha256":"f320c9736c322b770ceedcf36885312960af53d66b03746886cf474578beffc0"},"schema_version":"1.0","source":{"id":"1203.2967","kind":"arxiv","version":1}},"canonical_sha256":"114b2c0eb99757eece94036b16df5c1fb2e876d13b3c6e95d0e644ca10aba524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"114b2c0eb99757eece94036b16df5c1fb2e876d13b3c6e95d0e644ca10aba524","first_computed_at":"2026-05-18T04:00:13.033682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:13.033682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bfuUjSr5k+nw/LmyFIXEICpzZfksycKoHK5nikHbK7+yipxiIGfUHdxw6xqHC8Cu+yszr1trpzh9xpYk8jpuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:13.034508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96569bbe5fbef5b6449b984af6ac468c08bbecc304f37a082681379835bc7283","sha256:b68dc8b2b2985e6ab1acdc69226e07e6e37d442bacb7d9d3416548e17fde5cc8"],"state_sha256":"7ee67e17124fff962fb6885894cf6094891f3ec75aceaa4c24d477e861d2b5cd"}