{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D3HKDNOVUAD42PD2GX5U3Y43M4","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":"f7e981b5cf93683a0f4e956f7e261d75a1b7e76b94dd56122337ec534cb151b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-15T09:25:36Z","title_canon_sha256":"45cffa01d10f965076b99508f6cedef2b474ac37865f85bd582fb69cab36244c"},"schema_version":"1.0","source":{"id":"1509.04456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04456","created_at":"2026-05-18T01:28:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04456v2","created_at":"2026-05-18T01:28:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04456","created_at":"2026-05-18T01:28:02Z"},{"alias_kind":"pith_short_12","alias_value":"D3HKDNOVUAD4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D3HKDNOVUAD42PD2","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D3HKDNOV","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:92e4dcd94d22158f4e02eeecb9b7887d45b702dd0c980bbd41caf10159abcde0","target":"graph","created_at":"2026-05-18T01:28:02Z","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 obtain some optimal estimates for multilinear forms on $\\ell _{p}$ spaces.","authors_text":"Daniel Pellegrino, Tony Nogueira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-15T09:25:36Z","title":"A note on summability of multilinear forms on classical sequence spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04456","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":"sha256:97d90b6e8b6248ff78eb1e52aafbda88b25fc0393fba4aab2a46832e0b0832b7","target":"record","created_at":"2026-05-18T01:28:02Z","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":"f7e981b5cf93683a0f4e956f7e261d75a1b7e76b94dd56122337ec534cb151b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-15T09:25:36Z","title_canon_sha256":"45cffa01d10f965076b99508f6cedef2b474ac37865f85bd582fb69cab36244c"},"schema_version":"1.0","source":{"id":"1509.04456","kind":"arxiv","version":2}},"canonical_sha256":"1ecea1b5d5a007cd3c7a35fb4de39b6717292eef411ad6ec9c4227e2501ee0e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ecea1b5d5a007cd3c7a35fb4de39b6717292eef411ad6ec9c4227e2501ee0e2","first_computed_at":"2026-05-18T01:28:02.994630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:02.994630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HwOyrkmbiLnru7oz8z7X7kgtm+nCEsJO13H+S/5Ib/AVELvmPHDWZtV0fBMqLpMlJOwFRu1UcFLzr4AVmVBKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:02.995382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97d90b6e8b6248ff78eb1e52aafbda88b25fc0393fba4aab2a46832e0b0832b7","sha256:92e4dcd94d22158f4e02eeecb9b7887d45b702dd0c980bbd41caf10159abcde0"],"state_sha256":"d1b121bae149bbddc58a490788ebf1fc0fb3a94f07b1c021b1d03504ade0bad8"}