{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GWXSGKVBBHL3777BIOUNWAMYYJ","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":"65867ce543158c1eee4cebed5a1baa5777cfb804d532c97c567a0365d6b1569f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T15:45:59Z","title_canon_sha256":"f2d6cda1cf91d302771539fcf8c1dca9799c253206aaf4af00bc8d95dc51ba01"},"schema_version":"1.0","source":{"id":"1601.08163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08163","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08163v1","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08163","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"GWXSGKVBBHL3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GWXSGKVBBHL3777B","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GWXSGKVB","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:fa22d208a4b80500cb51dd958c3548c981ca8884e9926cb60b0374491fbfbc0f","target":"graph","created_at":"2026-05-18T00:07:51Z","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 consider two nonindependent random fields $\\psi$ and $\\phi$ defined on a countable set $Z$. For instance, $Z={\\mathbb Z}^d$ or $Z={\\mathbb Z}^d\\times I$, where $I$ denotes a finite set of possible \"internal degrees of freedom\" such as spin. We prove that, if the cumulants of both $\\psi$ and $\\phi$ are $\\ell_1$-clustering up to order $2 n$, then all joint cumulants between $\\psi$ and $\\phi$ are $\\ell_2$-summable up to order $n$, in the precise sense described in the text. We also provide explicit estimates in terms of the related $\\ell_1$-clustering norms, and derive a weighted $\\ell_2$-summ","authors_text":"Alessia Nota, Jani Lukkarinen, Matteo Marcozzi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T15:45:59Z","title":"Summability of joint cumulants of nonindependent lattice fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08163","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":"sha256:4e6f28207f9e23c0fccdf8828b1c9b71cdf37f0e2f77b006041ce045c32a09eb","target":"record","created_at":"2026-05-18T00:07:51Z","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":"65867ce543158c1eee4cebed5a1baa5777cfb804d532c97c567a0365d6b1569f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T15:45:59Z","title_canon_sha256":"f2d6cda1cf91d302771539fcf8c1dca9799c253206aaf4af00bc8d95dc51ba01"},"schema_version":"1.0","source":{"id":"1601.08163","kind":"arxiv","version":1}},"canonical_sha256":"35af232aa109d7bfffe143a8db0198c256300dde372aa3ea8ed82d9c9a6daf5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35af232aa109d7bfffe143a8db0198c256300dde372aa3ea8ed82d9c9a6daf5d","first_computed_at":"2026-05-18T00:07:51.230489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:51.230489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jczRCAF8eZ9W+4XC0AGn4oxEy2637IhkucMZuSHYgtU5nDAdj1R61GyDSjdkjmk2keJdX16v5B/VPtSE5rh3BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:51.231048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e6f28207f9e23c0fccdf8828b1c9b71cdf37f0e2f77b006041ce045c32a09eb","sha256:fa22d208a4b80500cb51dd958c3548c981ca8884e9926cb60b0374491fbfbc0f"],"state_sha256":"df1efd7e1a19dce0ac67b9a5d979e1d200a4491e89bd5a44989e84b903941311"}