{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VR4F6ZBBPQ7H3BF5TF64GCMSVY","short_pith_number":"pith:VR4F6ZBB","schema_version":"1.0","canonical_sha256":"ac785f64217c3e7d84bd997dc30992ae2d3a6dddffc78ac73ca781f4b62692d8","source":{"kind":"arxiv","id":"1512.04624","version":2},"attestation_state":"computed","paper":{"title":"Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Kahng, H. J. Herrmann, J. S. Lee, Y. S. Cho","submitted_at":"2015-12-15T02:14:18Z","abstract_excerpt":"Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a phase transition barely studied before, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.04624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-15T02:14:18Z","cross_cats_sorted":[],"title_canon_sha256":"e893bf906008cc6acf1bdde2887fbb5683d6baa4eea9463061a418290f27a9aa","abstract_canon_sha256":"35eb8f54f0822a4aaed9e74bbc6a68d366b3589dbbfbe3a386cb2978ca50cefe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:32.355192Z","signature_b64":"vsI5yvoe6RUK3OAw9b8mX/mj62v+WIxrw2rM+5BVo3Gx5X/dYRL1jb5Akd+8yC03e8e2OPqTPkmUOZCt00RyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac785f64217c3e7d84bd997dc30992ae2d3a6dddffc78ac73ca781f4b62692d8","last_reissued_at":"2026-05-18T01:22:32.354732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:32.354732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Kahng, H. J. Herrmann, J. S. Lee, Y. S. Cho","submitted_at":"2015-12-15T02:14:18Z","abstract_excerpt":"Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a phase transition barely studied before, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04624","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.04624","created_at":"2026-05-18T01:22:32.354801+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04624v2","created_at":"2026-05-18T01:22:32.354801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04624","created_at":"2026-05-18T01:22:32.354801+00:00"},{"alias_kind":"pith_short_12","alias_value":"VR4F6ZBBPQ7H","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VR4F6ZBBPQ7H3BF5","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VR4F6ZBB","created_at":"2026-05-18T12:29:47.479230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY","json":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY.json","graph_json":"https://pith.science/api/pith-number/VR4F6ZBBPQ7H3BF5TF64GCMSVY/graph.json","events_json":"https://pith.science/api/pith-number/VR4F6ZBBPQ7H3BF5TF64GCMSVY/events.json","paper":"https://pith.science/paper/VR4F6ZBB"},"agent_actions":{"view_html":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY","download_json":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY.json","view_paper":"https://pith.science/paper/VR4F6ZBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04624&json=true","fetch_graph":"https://pith.science/api/pith-number/VR4F6ZBBPQ7H3BF5TF64GCMSVY/graph.json","fetch_events":"https://pith.science/api/pith-number/VR4F6ZBBPQ7H3BF5TF64GCMSVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY/action/storage_attestation","attest_author":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY/action/author_attestation","sign_citation":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY/action/citation_signature","submit_replication":"https://pith.science/pith/VR4F6ZBBPQ7H3BF5TF64GCMSVY/action/replication_record"}},"created_at":"2026-05-18T01:22:32.354801+00:00","updated_at":"2026-05-18T01:22:32.354801+00:00"}