{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NTEBJOVP3OOVZ2FL4VBIXCJLF3","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":"b5bcf67e5b3aadc3d0dbfc3fc429a75b1a66d28c157503cc062e9827a71bcd50","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-06T08:28:02Z","title_canon_sha256":"5fed19ee7e64c593d3f72a570e323f639ed1dcd8224796e72a0cd98c84d43281"},"schema_version":"1.0","source":{"id":"1004.0795","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0795","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0795v1","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0795","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"pith_short_12","alias_value":"NTEBJOVP3OOV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NTEBJOVP3OOVZ2FL","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NTEBJOVP","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:638743f04d1c2ef1425a188ee29798c47390dab1e4a25849254bfc84538dddfc","target":"graph","created_at":"2026-05-18T04:23:54Z","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 critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s \\propto s^{-\\tau}$ in the whole range of open bond probability $p$. The exponent $\\tau$ and the fractal exponent $\\psi$ are also derived as a function of $p$ and the degree exponent $\\gamma$, and are found to satisfy the scaling relation $\\tau=1+\\psi^{-1}$. Numerical results with several network sizes are quite well fitted by a finite size scaling for a wid","authors_text":"Koji Nemoto, 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":"2010-04-06T08:28:02Z","title":"Critical Phase of Bond Percolations on Growing Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0795","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:ad50507a6b8c9c52f833f029dfb1f64a3ff28de268da425133c8ddf9742be5fb","target":"record","created_at":"2026-05-18T04:23:54Z","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":"b5bcf67e5b3aadc3d0dbfc3fc429a75b1a66d28c157503cc062e9827a71bcd50","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-06T08:28:02Z","title_canon_sha256":"5fed19ee7e64c593d3f72a570e323f639ed1dcd8224796e72a0cd98c84d43281"},"schema_version":"1.0","source":{"id":"1004.0795","kind":"arxiv","version":1}},"canonical_sha256":"6cc814baafdb9d5ce8abe5428b892b2eea6500fcb3d61d578f59c3f7574d9c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cc814baafdb9d5ce8abe5428b892b2eea6500fcb3d61d578f59c3f7574d9c2b","first_computed_at":"2026-05-18T04:23:54.505608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:54.505608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sEAc/xhOG6QsQLyNRYA+RcMfJkENqQO0Nph4uoMMsQ23klxFmyoXSXzaOGSn0MODtgtGgjZBG0H3qYmlJ+f0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:54.506044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0795","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad50507a6b8c9c52f833f029dfb1f64a3ff28de268da425133c8ddf9742be5fb","sha256:638743f04d1c2ef1425a188ee29798c47390dab1e4a25849254bfc84538dddfc"],"state_sha256":"c124bdf8ca640f093db4d12f980b3f2b569853c143444ec8f22f2e1d23b19a65"}