{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WVZYEF47JQFSGC7IU35QYFZSJ2","short_pith_number":"pith:WVZYEF47","schema_version":"1.0","canonical_sha256":"b57382179f4c0b230be8a6fb0c17324e8e3b57469bd85e63c3ee7a34255f09f2","source":{"kind":"arxiv","id":"2605.30948","version":1},"attestation_state":"computed","paper":{"title":"Competing heterogeneities shape ordering via higher-order interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Deok-Sun Lee, Federico Battiston, Gangmin Son, K.-I. Goh","submitted_at":"2026-05-29T07:34:54Z","abstract_excerpt":"Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double tra"},"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":"2605.30948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-29T07:34:54Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"524e2ad07b10339632a67c619bcb8626c7235a7d1a212c12063db2ed29a5fb31","abstract_canon_sha256":"14c4bb6d082cb81167361c092d98d6f4a6840a79e377f491c32ddffb75c03097"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:27.162070Z","signature_b64":"A8lcka/WbCsSQPN/SFMGmwmzz5x4/K+IMQFtYyzJf4qX4DMoRBQYjNgr/TP1owDHjvr1/SYRpo0QqpinQzdMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b57382179f4c0b230be8a6fb0c17324e8e3b57469bd85e63c3ee7a34255f09f2","last_reissued_at":"2026-06-01T01:03:27.161525Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:27.161525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Competing heterogeneities shape ordering via higher-order interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Deok-Sun Lee, Federico Battiston, Gangmin Son, K.-I. Goh","submitted_at":"2026-05-29T07:34:54Z","abstract_excerpt":"Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30948","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/2605.30948/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":"2605.30948","created_at":"2026-06-01T01:03:27.161609+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30948v1","created_at":"2026-06-01T01:03:27.161609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30948","created_at":"2026-06-01T01:03:27.161609+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVZYEF47JQFS","created_at":"2026-06-01T01:03:27.161609+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVZYEF47JQFSGC7I","created_at":"2026-06-01T01:03:27.161609+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVZYEF47","created_at":"2026-06-01T01:03:27.161609+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/WVZYEF47JQFSGC7IU35QYFZSJ2","json":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2.json","graph_json":"https://pith.science/api/pith-number/WVZYEF47JQFSGC7IU35QYFZSJ2/graph.json","events_json":"https://pith.science/api/pith-number/WVZYEF47JQFSGC7IU35QYFZSJ2/events.json","paper":"https://pith.science/paper/WVZYEF47"},"agent_actions":{"view_html":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2","download_json":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2.json","view_paper":"https://pith.science/paper/WVZYEF47","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30948&json=true","fetch_graph":"https://pith.science/api/pith-number/WVZYEF47JQFSGC7IU35QYFZSJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/WVZYEF47JQFSGC7IU35QYFZSJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2/action/storage_attestation","attest_author":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2/action/author_attestation","sign_citation":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2/action/citation_signature","submit_replication":"https://pith.science/pith/WVZYEF47JQFSGC7IU35QYFZSJ2/action/replication_record"}},"created_at":"2026-06-01T01:03:27.161609+00:00","updated_at":"2026-06-01T01:03:27.161609+00:00"}