{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6CWJV4AKSTYXYCYJ2JJOFBSQUF","short_pith_number":"pith:6CWJV4AK","canonical_record":{"source":{"id":"1607.08357","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-28T08:44:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d34f13720ba0aa7df315a7f3a54b8334d3d7b32d4599b7b1997a394a0b7c196","abstract_canon_sha256":"4a98a03f3d9a40cf8a9c870c8ba49ceb3a4430e7e6c7b9d1716adde8b98dc6b4"},"schema_version":"1.0"},"canonical_sha256":"f0ac9af00a94f17c0b09d252e28650a171671fda99533c6ec6fe6edb27dcb50c","source":{"kind":"arxiv","id":"1607.08357","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08357","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08357v4","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08357","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"6CWJV4AKSTYX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6CWJV4AKSTYXYCYJ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6CWJV4AK","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6CWJV4AKSTYXYCYJ2JJOFBSQUF","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08357","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-28T08:44:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d34f13720ba0aa7df315a7f3a54b8334d3d7b32d4599b7b1997a394a0b7c196","abstract_canon_sha256":"4a98a03f3d9a40cf8a9c870c8ba49ceb3a4430e7e6c7b9d1716adde8b98dc6b4"},"schema_version":"1.0"},"canonical_sha256":"f0ac9af00a94f17c0b09d252e28650a171671fda99533c6ec6fe6edb27dcb50c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.262160Z","signature_b64":"ZYsUWItbN/ddw+TuuA1MBT/yH/W5yufYb2mAWRt6R3DN1DVl6cKobqTT0Z1RS74Z/arZM7Bpljcww5kSO15gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0ac9af00a94f17c0b09d252e28650a171671fda99533c6ec6fe6edb27dcb50c","last_reissued_at":"2026-05-18T00:20:59.258896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.258896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08357","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i1QR2Z7R4DX8NMzYO1EAlEV0M5N/9pPmEFVklVIt6/jmC3ZFBp+QqYkHH1iVoL0VTsORMFi1a2EV3X+2XCtICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:44:12.044656Z"},"content_sha256":"a25ea04246bea2125e400cc64952fad5bfb572f31c160b5c932460d8be34b703","schema_version":"1.0","event_id":"sha256:a25ea04246bea2125e400cc64952fad5bfb572f31c160b5c932460d8be34b703"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6CWJV4AKSTYXYCYJ2JJOFBSQUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing Properties for Hom-Shifts and the Distance between Walks on Associated Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Brian Marcus, Nishant Chandgotia","submitted_at":"2016-07-28T08:44:29Z","abstract_excerpt":"Let $\\mathcal H$ be a finite connected undirected graph and $\\mathcal H_{walk}$ be the graph of bi-infinite walks on $\\mathcal H$; two such walks $\\{x_i\\}_{i\\in \\mathbb Z}$ and $\\{y_i\\}_{i \\in \\mathbb Z}$ are said to be adjacent if $x_i$ is adjacent to $y_i$ for all $i \\in \\mathbb Z$. We consider the question: Given a graph $\\mathcal H$ when is the diameter (with respect to the graph metric) of $\\mathcal H_{walk}$ finite? Such questions arise while studying mixing properties of hom-shifts (shift spaces which arise as the space of graph homomorphisms from the Cayley graph of $\\mathbb Z^d$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08357","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pnT43F6RPIqV72EdZq635r8n4K0VSVHuVO1J4yzvRiIlLkdPEGrzY3Ie8AutZ1NfA/K9k0LkZkMbuw9wa3tdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:44:12.045011Z"},"content_sha256":"f3db6ad15fc5824ca425c8353a252cc43e3c3530138efbe026d4d08ca6b9f5af","schema_version":"1.0","event_id":"sha256:f3db6ad15fc5824ca425c8353a252cc43e3c3530138efbe026d4d08ca6b9f5af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/bundle.json","state_url":"https://pith.science/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T18:44:12Z","links":{"resolver":"https://pith.science/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF","bundle":"https://pith.science/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/bundle.json","state":"https://pith.science/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CWJV4AKSTYXYCYJ2JJOFBSQUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6CWJV4AKSTYXYCYJ2JJOFBSQUF","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":"4a98a03f3d9a40cf8a9c870c8ba49ceb3a4430e7e6c7b9d1716adde8b98dc6b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-28T08:44:29Z","title_canon_sha256":"9d34f13720ba0aa7df315a7f3a54b8334d3d7b32d4599b7b1997a394a0b7c196"},"schema_version":"1.0","source":{"id":"1607.08357","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08357","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08357v4","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08357","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"6CWJV4AKSTYX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6CWJV4AKSTYXYCYJ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6CWJV4AK","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:f3db6ad15fc5824ca425c8353a252cc43e3c3530138efbe026d4d08ca6b9f5af","target":"graph","created_at":"2026-05-18T00:20:59Z","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":"Let $\\mathcal H$ be a finite connected undirected graph and $\\mathcal H_{walk}$ be the graph of bi-infinite walks on $\\mathcal H$; two such walks $\\{x_i\\}_{i\\in \\mathbb Z}$ and $\\{y_i\\}_{i \\in \\mathbb Z}$ are said to be adjacent if $x_i$ is adjacent to $y_i$ for all $i \\in \\mathbb Z$. We consider the question: Given a graph $\\mathcal H$ when is the diameter (with respect to the graph metric) of $\\mathcal H_{walk}$ finite? Such questions arise while studying mixing properties of hom-shifts (shift spaces which arise as the space of graph homomorphisms from the Cayley graph of $\\mathbb Z^d$ with ","authors_text":"Brian Marcus, Nishant Chandgotia","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-28T08:44:29Z","title":"Mixing Properties for Hom-Shifts and the Distance between Walks on Associated Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08357","kind":"arxiv","version":4},"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:a25ea04246bea2125e400cc64952fad5bfb572f31c160b5c932460d8be34b703","target":"record","created_at":"2026-05-18T00:20:59Z","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":"4a98a03f3d9a40cf8a9c870c8ba49ceb3a4430e7e6c7b9d1716adde8b98dc6b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-28T08:44:29Z","title_canon_sha256":"9d34f13720ba0aa7df315a7f3a54b8334d3d7b32d4599b7b1997a394a0b7c196"},"schema_version":"1.0","source":{"id":"1607.08357","kind":"arxiv","version":4}},"canonical_sha256":"f0ac9af00a94f17c0b09d252e28650a171671fda99533c6ec6fe6edb27dcb50c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0ac9af00a94f17c0b09d252e28650a171671fda99533c6ec6fe6edb27dcb50c","first_computed_at":"2026-05-18T00:20:59.258896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.258896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZYsUWItbN/ddw+TuuA1MBT/yH/W5yufYb2mAWRt6R3DN1DVl6cKobqTT0Z1RS74Z/arZM7Bpljcww5kSO15gAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.262160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08357","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a25ea04246bea2125e400cc64952fad5bfb572f31c160b5c932460d8be34b703","sha256:f3db6ad15fc5824ca425c8353a252cc43e3c3530138efbe026d4d08ca6b9f5af"],"state_sha256":"c7261535e7ba4d9fce46acf42120a10968557cc2848475248e040b2f4d7571a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkX1dFm91OMfuyG2EETRSlgj5TMIpjUrnLFx19xlnIGgNXfcnhkKaIGR/Qd5ASRmawF3FqLOyIeazoVNtCb+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:44:12.047126Z","bundle_sha256":"b6403c6919074d8b48122a14dae797b72100e3390ca2a46dedcc734f322b6b84"}}