{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A6C4WIP27U4WUHKI65TV3UQQSH","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":"dca3e01e28ccc492e8b637c2aead7c018256ac9018388bbdab3c3b212ca84704","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-01-27T20:24:07Z","title_canon_sha256":"5b1e6f7d8bd115832ee444e34cc4dd4187ea23baa05e21eb0e849813b81ffc97"},"schema_version":"1.0","source":{"id":"1101.5383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5383","created_at":"2026-05-18T02:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5383v1","created_at":"2026-05-18T02:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5383","created_at":"2026-05-18T02:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"A6C4WIP27U4W","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A6C4WIP27U4WUHKI","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A6C4WIP2","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:e6af05580540d2062b861f256bae7447df2a690f7326df170cef0f6c838aeffd","target":"graph","created_at":"2026-05-18T02:22:42Z","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":"The Gauss's law, in an abstract sense, is a theorem that relates quantities on the boundary (flux) to the interior (charge) of a surface. An identity for soap froths were proved with the same boundary-interior relation. In this article, we try to construct a definition of flux for other graphs, such that a similar boundary-interior relation can be satisfied.","authors_text":"Ching King Chan, Kwok Yip Szeto","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-01-27T20:24:07Z","title":"Connecting boundary and interior - \"Gauss's law\" for graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5383","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":"sha256:868e429bad9cb991c323fddedd6c9f3be830f02fd13304d78cddff592e443a89","target":"record","created_at":"2026-05-18T02:22:42Z","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":"dca3e01e28ccc492e8b637c2aead7c018256ac9018388bbdab3c3b212ca84704","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-01-27T20:24:07Z","title_canon_sha256":"5b1e6f7d8bd115832ee444e34cc4dd4187ea23baa05e21eb0e849813b81ffc97"},"schema_version":"1.0","source":{"id":"1101.5383","kind":"arxiv","version":1}},"canonical_sha256":"0785cb21fafd396a1d48f7675dd21091ec79aaa2b9754621c8b25273840efaae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0785cb21fafd396a1d48f7675dd21091ec79aaa2b9754621c8b25273840efaae","first_computed_at":"2026-05-18T02:22:42.392925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:42.392925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aWffq5e/FPnVEi6UgZnzW7W9KVamp6bHncl/XZ7oOK1M29e/yJqUEScvMX6wZZUmoJ8PIVzX/014rhyQUMqcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:42.393578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:868e429bad9cb991c323fddedd6c9f3be830f02fd13304d78cddff592e443a89","sha256:e6af05580540d2062b861f256bae7447df2a690f7326df170cef0f6c838aeffd"],"state_sha256":"f715e30484f48ad3bbfd8d7db18d3fae22363b78d332811d4532d353ce0fb1e8"}