{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:NHNZ7CYAMBVMJTW2EXHABMPRMJ","short_pith_number":"pith:NHNZ7CYA","schema_version":"1.0","canonical_sha256":"69db9f8b00606ac4ceda25ce00b1f16254f09fb7fee42a6d6ced3a05327630db","source":{"kind":"arxiv","id":"2301.03230","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Liwang Zhu, Wanyue Xu, Wei Li, Yucheng Wang, Zhongzhi Zhang, Zixuan Xie","submitted_at":"2023-01-09T09:52:45Z","abstract_excerpt":"Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a graph product, which is an extension of the pseudo-fractal scale-free web. We determine explicitly the independence number, the domination number, and the chromatic number. Moreover, we derive closed-form expressions for the number of acyclic orientations, the number of root-connected acyclic orientations, the number of spanning trees, as well as the number of"},"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":"2301.03230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-01-09T09:52:45Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8db47a11942667a88e5ec9e8a924dc2455021601ee5656a72c8e4f1e359c5102","abstract_canon_sha256":"b98265978e5ed387640f31558299603da5de63c020da4e68a1be3cb7aa2d3768"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:10:27.475185Z","signature_b64":"KGMMj3UzwzTxzRybQjI2RuvjGxLn/TZ9tfiA7e6+rfU/ByE3X3iKYm2vlKE+2nK8GetWKJSz7cZT0Oz+zQL1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69db9f8b00606ac4ceda25ce00b1f16254f09fb7fee42a6d6ced3a05327630db","last_reissued_at":"2026-07-05T06:10:27.474745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:10:27.474745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Liwang Zhu, Wanyue Xu, Wei Li, Yucheng Wang, Zhongzhi Zhang, Zixuan Xie","submitted_at":"2023-01-09T09:52:45Z","abstract_excerpt":"Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a graph product, which is an extension of the pseudo-fractal scale-free web. We determine explicitly the independence number, the domination number, and the chromatic number. Moreover, we derive closed-form expressions for the number of acyclic orientations, the number of root-connected acyclic orientations, the number of spanning trees, as well as the number of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.03230","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/2301.03230/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":"2301.03230","created_at":"2026-07-05T06:10:27.474802+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.03230v1","created_at":"2026-07-05T06:10:27.474802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.03230","created_at":"2026-07-05T06:10:27.474802+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHNZ7CYAMBVM","created_at":"2026-07-05T06:10:27.474802+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHNZ7CYAMBVMJTW2","created_at":"2026-07-05T06:10:27.474802+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHNZ7CYA","created_at":"2026-07-05T06:10:27.474802+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/NHNZ7CYAMBVMJTW2EXHABMPRMJ","json":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ.json","graph_json":"https://pith.science/api/pith-number/NHNZ7CYAMBVMJTW2EXHABMPRMJ/graph.json","events_json":"https://pith.science/api/pith-number/NHNZ7CYAMBVMJTW2EXHABMPRMJ/events.json","paper":"https://pith.science/paper/NHNZ7CYA"},"agent_actions":{"view_html":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ","download_json":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ.json","view_paper":"https://pith.science/paper/NHNZ7CYA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.03230&json=true","fetch_graph":"https://pith.science/api/pith-number/NHNZ7CYAMBVMJTW2EXHABMPRMJ/graph.json","fetch_events":"https://pith.science/api/pith-number/NHNZ7CYAMBVMJTW2EXHABMPRMJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ/action/storage_attestation","attest_author":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ/action/author_attestation","sign_citation":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ/action/citation_signature","submit_replication":"https://pith.science/pith/NHNZ7CYAMBVMJTW2EXHABMPRMJ/action/replication_record"}},"created_at":"2026-07-05T06:10:27.474802+00:00","updated_at":"2026-07-05T06:10:27.474802+00:00"}