{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KAQPETWVACTMDY5J3FH5RZIGNY","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":"7a4e5b3940e544878e00e596d9640fa5ce6dd907f0bc7ed50fa5419d68bda87b","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-28T17:30:53Z","title_canon_sha256":"db468e4c6acb614c294fa2af0ea875db1f6d11e122dddc98785c3def1be5d777"},"schema_version":"1.0","source":{"id":"1004.5087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5087","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5087v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5087","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"KAQPETWVACTM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KAQPETWVACTMDY5J","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KAQPETWV","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:40ad9a3f533269ef2216f378594fef67c07e507682f2c691b98464dcc77c0b53","target":"graph","created_at":"2026-05-18T04:39:59Z","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":"We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts $\\tilde{p}$ and that of the ordinary bonds $p$. The system has a critical phase in which the percolating probability $P$ takes an intermediate value $0<P<1$. Using generating function approach, we calculate the fractal exponent $\\psi$ of the root clusters to show that $\\psi$ varies continuously with $\\tilde{p}$ in the critical phase. We confirm numerically that the distribution $n_s$ of cluster size $s$ in the critical phase obeys a power law $n_s \\propto s^{-\\tau}$, where $\\tau$ sati","authors_text":"Koji Nemoto, Masataka Sato, Takehisa Hasegawa","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-28T17:30:53Z","title":"Generating-function approach for bond percolations in hierarchical networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5087","kind":"arxiv","version":2},"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":"sha256:2400ff5113554c1d25393c462c2936fb4e6db10cc2aadc8cdaf5537783430545","target":"record","created_at":"2026-05-18T04:39:59Z","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":"7a4e5b3940e544878e00e596d9640fa5ce6dd907f0bc7ed50fa5419d68bda87b","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-28T17:30:53Z","title_canon_sha256":"db468e4c6acb614c294fa2af0ea875db1f6d11e122dddc98785c3def1be5d777"},"schema_version":"1.0","source":{"id":"1004.5087","kind":"arxiv","version":2}},"canonical_sha256":"5020f24ed500a6c1e3a9d94fd8e5066e34cb494df679750ceb8ca6f697c6223d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5020f24ed500a6c1e3a9d94fd8e5066e34cb494df679750ceb8ca6f697c6223d","first_computed_at":"2026-05-18T04:39:59.246258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.246258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HzFIgGO5aM6r/+hWkcy7u3FIccXn3nJ6jICZt8M0fBw+Af39Xc9U/cSTlaoWORAJUH+hajVw+q5Ef6Gyy2sJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.246771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2400ff5113554c1d25393c462c2936fb4e6db10cc2aadc8cdaf5537783430545","sha256:40ad9a3f533269ef2216f378594fef67c07e507682f2c691b98464dcc77c0b53"],"state_sha256":"d649db5d502c2a4f73ae4f1b0a8f0e11ddaa20bb415cc9830f4309f3043ca443"}