{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5GP6LKUPBVFELQFM2QK3HUJ2TM","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":"a4fb0f9c613611b3214b938468284a73ecae9f103b3a8bcebc66bf6026439959","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T06:58:57Z","title_canon_sha256":"d7892fe7249cb683440660b3d3004d92a8a93ae1f49d698daea4078a98f8d74b"},"schema_version":"1.0","source":{"id":"1510.01453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01453","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01453v1","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01453","created_at":"2026-05-18T01:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"5GP6LKUPBVFE","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GP6LKUPBVFELQFM","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GP6LKUP","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:3c4420077ead8324da9c254fd35f3af7e5b3e2ffc8ae6cac6b2134b61d02a77d","target":"graph","created_at":"2026-05-18T01:30:56Z","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 countable graph $\\mathcal{G}$ and a finite graph $\\mathrm{H}$, we consider $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ the set of graph homomorphisms from $\\mathcal{G}$ to $\\mathrm{H}$ and we study Gibbs measures supported on $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ . We develop some sufficient and other necessary conditions on $\\mathrm{Hom}(\\mathcal{G},\\mathrm{H})$ for the existence of Gibbs specifications satisfying strong spatial mixing (with exponential decay rate). We relate this with previous work of Brightwell and Winkler, who showed that a graph $\\mathrm{H}$ has a combinatorial proper","authors_text":"Raimundo Brice\\~no, Ronnie Pavlov","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T06:58:57Z","title":"Strong spatial mixing in homomorphism spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01453","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":"sha256:7aba4e3eb2a6f2678c123d4edede359f442e81b32f0b27d7b6b3eb6e97c0bd6c","target":"record","created_at":"2026-05-18T01:30:56Z","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":"a4fb0f9c613611b3214b938468284a73ecae9f103b3a8bcebc66bf6026439959","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-06T06:58:57Z","title_canon_sha256":"d7892fe7249cb683440660b3d3004d92a8a93ae1f49d698daea4078a98f8d74b"},"schema_version":"1.0","source":{"id":"1510.01453","kind":"arxiv","version":1}},"canonical_sha256":"e99fe5aa8f0d4a45c0acd415b3d13a9b1a29df359155848fe8d399782c051df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e99fe5aa8f0d4a45c0acd415b3d13a9b1a29df359155848fe8d399782c051df5","first_computed_at":"2026-05-18T01:30:56.883178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:56.883178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Xn/uwv0AUdhiOFG3FfH2Ios4jZ5fdnTbJj1OhN3u0aLdZ2vwge227zIfwo+0mobTJIuzSZqj1d8eAnx8eBnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:56.883826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aba4e3eb2a6f2678c123d4edede359f442e81b32f0b27d7b6b3eb6e97c0bd6c","sha256:3c4420077ead8324da9c254fd35f3af7e5b3e2ffc8ae6cac6b2134b61d02a77d"],"state_sha256":"9ca83d596934774e3b549d47e182809c08bb1b89e368a49954af52c541feb83c"}