{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UL52GY43FTEFJNLCHL55QKLFHW","short_pith_number":"pith:UL52GY43","schema_version":"1.0","canonical_sha256":"a2fba3639b2cc854b5623afbd829653dbe74a3c0f6cc9f7eb17c7a68fd129659","source":{"kind":"arxiv","id":"2605.25812","version":1},"attestation_state":"computed","paper":{"title":"Equivalent-neighbor $k$-core percolation in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ming Li, Qiyuan Shi, Youjin Deng","submitted_at":"2026-05-25T13:03:00Z","abstract_excerpt":"We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range $r$, we construct a comprehensive phase diagram in the $(k,r)$ plane. In contrast to $k$-core percolation in infinite dimensions, no hybrid transition is observed in two dimensions: the phase diagram contains only a continuous transition regime and a strictly first-order regime, separated by a tricritical or critical-end point $(k_s,r_s)$. For $k<k_s$ and $r"},"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":"2605.25812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-25T13:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"3b7d209eee84f4f2d308462ea20637fa17f0845ad0b33822b615c404eca9cec0","abstract_canon_sha256":"4e54a53309f99d0a6c62b767c275c8ea139fd5f1a4ed6e695e9a8dd17491523a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:12.894556Z","signature_b64":"Fz8nQZ7BQSQauvuhhL4Rd2DaoQXCBlyyJ5agxqPQsGiqqoAcPffTufZtcE6Nz0pmWgKO/mi6THYvOyXbfG82Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2fba3639b2cc854b5623afbd829653dbe74a3c0f6cc9f7eb17c7a68fd129659","last_reissued_at":"2026-05-26T02:05:12.893718Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:12.893718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalent-neighbor $k$-core percolation in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ming Li, Qiyuan Shi, Youjin Deng","submitted_at":"2026-05-25T13:03:00Z","abstract_excerpt":"We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range $r$, we construct a comprehensive phase diagram in the $(k,r)$ plane. In contrast to $k$-core percolation in infinite dimensions, no hybrid transition is observed in two dimensions: the phase diagram contains only a continuous transition regime and a strictly first-order regime, separated by a tricritical or critical-end point $(k_s,r_s)$. For $k<k_s$ and $r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25812","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25812/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.25812","created_at":"2026-05-26T02:05:12.893845+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25812v1","created_at":"2026-05-26T02:05:12.893845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25812","created_at":"2026-05-26T02:05:12.893845+00:00"},{"alias_kind":"pith_short_12","alias_value":"UL52GY43FTEF","created_at":"2026-05-26T02:05:12.893845+00:00"},{"alias_kind":"pith_short_16","alias_value":"UL52GY43FTEFJNLC","created_at":"2026-05-26T02:05:12.893845+00:00"},{"alias_kind":"pith_short_8","alias_value":"UL52GY43","created_at":"2026-05-26T02:05:12.893845+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/UL52GY43FTEFJNLCHL55QKLFHW","json":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW.json","graph_json":"https://pith.science/api/pith-number/UL52GY43FTEFJNLCHL55QKLFHW/graph.json","events_json":"https://pith.science/api/pith-number/UL52GY43FTEFJNLCHL55QKLFHW/events.json","paper":"https://pith.science/paper/UL52GY43"},"agent_actions":{"view_html":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW","download_json":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW.json","view_paper":"https://pith.science/paper/UL52GY43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25812&json=true","fetch_graph":"https://pith.science/api/pith-number/UL52GY43FTEFJNLCHL55QKLFHW/graph.json","fetch_events":"https://pith.science/api/pith-number/UL52GY43FTEFJNLCHL55QKLFHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW/action/storage_attestation","attest_author":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW/action/author_attestation","sign_citation":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW/action/citation_signature","submit_replication":"https://pith.science/pith/UL52GY43FTEFJNLCHL55QKLFHW/action/replication_record"}},"created_at":"2026-05-26T02:05:12.893845+00:00","updated_at":"2026-05-26T02:05:12.893845+00:00"}