{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4D6KTYKJF3J2EN7AQ7CAST2Q2L","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":"a735e54d32b8705d3a06b4c67ace8e6dc94ce2e55e263f0564aa092ee089516b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-06-15T02:32:41Z","title_canon_sha256":"73b02b97f8db8351063712b73f8e48515cd826a87cf2badaa053146def160463"},"schema_version":"1.0","source":{"id":"1706.04725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04725","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04725v1","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04725","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"4D6KTYKJF3J2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4D6KTYKJF3J2EN7A","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4D6KTYKJ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:365ab6e086c3befd03f9ba25711d89f1962d73a08928570b2486f1a8981bc7f4","target":"graph","created_at":"2026-05-18T00:23:35Z","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 study critical bond percolation on a seven-dimensional (7D) hypercubic lattice with periodic boundary conditions and on the complete graph (CG) of finite volume $V$. We numerically confirm that for both cases, the critical number density $n(s,V)$ of clusters of size $s$ obeys a scaling form $n(s,V) \\sim s^{-\\tau} \\tilde{n} (s/V^{d^*_{\\rm f}})$ with identical volume fractal dimension $d^*_{\\rm f}=2/3$ and exponent $\\tau = 1+1/d^*_{\\rm f}=5/2$. We then classify occupied bonds into {\\em bridge} bonds, which includes {\\em branch} and {\\em junction} bonds, and {\\em non-bridge} bonds; a bridge bo","authors_text":"Junfeng Wang, Pengcheng Hou, Robert M. Ziff, Wei Huang, Youjin Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-06-15T02:32:41Z","title":"Critical percolation clusters in seven dimensions and on a complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04725","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:bec1011f94e529ee256f38e9c065d7f7b09b7a34c85629c0c0200c04130e9cc8","target":"record","created_at":"2026-05-18T00:23:35Z","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":"a735e54d32b8705d3a06b4c67ace8e6dc94ce2e55e263f0564aa092ee089516b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-06-15T02:32:41Z","title_canon_sha256":"73b02b97f8db8351063712b73f8e48515cd826a87cf2badaa053146def160463"},"schema_version":"1.0","source":{"id":"1706.04725","kind":"arxiv","version":1}},"canonical_sha256":"e0fca9e1492ed3a237e087c4094f50d2d796cd63f31a5ca9562aec7acdd95bb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0fca9e1492ed3a237e087c4094f50d2d796cd63f31a5ca9562aec7acdd95bb8","first_computed_at":"2026-05-18T00:23:35.615004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:35.615004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RBGaxskgTxy2NmwGOLZPfazotpi7nwm2+nuBoEX3HzjG4Eooy/zt9wnKj22NNO/hyBp7Orz/Q/WPufWclmH8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:35.615590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bec1011f94e529ee256f38e9c065d7f7b09b7a34c85629c0c0200c04130e9cc8","sha256:365ab6e086c3befd03f9ba25711d89f1962d73a08928570b2486f1a8981bc7f4"],"state_sha256":"ed55ff6d46194cb8c7e1924c7f9afa4a5f6b95a4ba3e90d3ec6000b1f3833183"}