{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MUDH2PPJB7VFLD4EXIUYQGKPLU","short_pith_number":"pith:MUDH2PPJ","schema_version":"1.0","canonical_sha256":"65067d3de90fea558f84ba2988194f5d233704543aa4c4f238dfb0e130907a2c","source":{"kind":"arxiv","id":"1604.08699","version":1},"attestation_state":"computed","paper":{"title":"Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. K. Hassan, M. M. Rahman","submitted_at":"2016-04-29T06:14:19Z","abstract_excerpt":"In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it exhibits threshold phenomena as we find sudden or abrupt jump in spanning probability across $p_c$ accompanied by the divergence of some other observable quantities which is reminiscent of continuous phase transition. Indeed, percolation is characterized by the critical behavior of percolation strength $P(p)\\sim (p_c-p)^\\beta$, mean cluster size $S\\sim (p_c-p)^{"},"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":"1604.08699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-04-29T06:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"b89e4ce531da9dd8ee896560a71bd72d9c28706c2a6a979c955daeb82d3a7cc2","abstract_canon_sha256":"0a3852d15b2fb630f96aed8209c85d0af9e08fc8341ebf3be804795d3e50ac62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:31.128272Z","signature_b64":"ZZDkFD9CX3eYuyZA6ld+CdKTY8bEDA9DPCsuHU+upboIkJPk2yj/7K62skPbRO4EcmJRDlVkze7J0aIHZl7DAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65067d3de90fea558f84ba2988194f5d233704543aa4c4f238dfb0e130907a2c","last_reissued_at":"2026-05-18T00:56:31.127521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:31.127521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. K. Hassan, M. M. Rahman","submitted_at":"2016-04-29T06:14:19Z","abstract_excerpt":"In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it exhibits threshold phenomena as we find sudden or abrupt jump in spanning probability across $p_c$ accompanied by the divergence of some other observable quantities which is reminiscent of continuous phase transition. Indeed, percolation is characterized by the critical behavior of percolation strength $P(p)\\sim (p_c-p)^\\beta$, mean cluster size $S\\sim (p_c-p)^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08699","kind":"arxiv","version":1},"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":"1604.08699","created_at":"2026-05-18T00:56:31.127634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08699v1","created_at":"2026-05-18T00:56:31.127634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08699","created_at":"2026-05-18T00:56:31.127634+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUDH2PPJB7VF","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUDH2PPJB7VFLD4E","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUDH2PPJ","created_at":"2026-05-18T12:30:32.724797+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/MUDH2PPJB7VFLD4EXIUYQGKPLU","json":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU.json","graph_json":"https://pith.science/api/pith-number/MUDH2PPJB7VFLD4EXIUYQGKPLU/graph.json","events_json":"https://pith.science/api/pith-number/MUDH2PPJB7VFLD4EXIUYQGKPLU/events.json","paper":"https://pith.science/paper/MUDH2PPJ"},"agent_actions":{"view_html":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU","download_json":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU.json","view_paper":"https://pith.science/paper/MUDH2PPJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08699&json=true","fetch_graph":"https://pith.science/api/pith-number/MUDH2PPJB7VFLD4EXIUYQGKPLU/graph.json","fetch_events":"https://pith.science/api/pith-number/MUDH2PPJB7VFLD4EXIUYQGKPLU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU/action/storage_attestation","attest_author":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU/action/author_attestation","sign_citation":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU/action/citation_signature","submit_replication":"https://pith.science/pith/MUDH2PPJB7VFLD4EXIUYQGKPLU/action/replication_record"}},"created_at":"2026-05-18T00:56:31.127634+00:00","updated_at":"2026-05-18T00:56:31.127634+00:00"}