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Let $K$ be a pure $r$-dimensional complex on $n$ vertices, ${\\mathfrak q}_{r-1}(K)$ be the spectral radius of the $(r-1)$-up signless Laplacian of $K$, and ${\\operatorname{lk}}_K(\\sigma)$ be the link of a face $\\sigma$ in $K$. We prove that if the homology $\\widetilde H_t({\\operatorname{lk}}_K(\\sigma), {\\mathbb R})=0$ for every face $\\sigma\\in K$ with $|\\sigma|=r-t$, then \\[ {\\mathfrak q}_{r-1}(K)\\le tn-(t-1)(r+1).\\] Moreover, if $K$ is $r$-down path connec"},"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":"2606.22825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-22T04:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"bc4cdd23c5168cdb7ed7e0b60d84c180a873700416aadf20bbd866dc268433eb","abstract_canon_sha256":"2a69566c98f89903977c03d94a40e71f72bf128ac59d0a65550da340177dd34a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:14:00.463925Z","signature_b64":"7WVzuALhjeBT4am0CMC4wBmBlpJ4rkphqTF6bafu21ZxeanYe1ZqkyMnjpsFu2roWhOCDYm7FObdYEbr/+L7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed1a4dd1e1c7d9ae612473db1674ed8935260cef961c399e6e6e335069679a71","last_reissued_at":"2026-06-23T02:14:00.463478Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:14:00.463478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signless Laplacian Spectral Radius and Link Homology of Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huan-Zhi Zhang, Yi-Zheng Fan","submitted_at":"2026-06-22T04:08:21Z","abstract_excerpt":"In this paper, we study the signless Laplacian spectral radius of pure simplicial complexes under local homological restrictions on links. Let $K$ be a pure $r$-dimensional complex on $n$ vertices, ${\\mathfrak q}_{r-1}(K)$ be the spectral radius of the $(r-1)$-up signless Laplacian of $K$, and ${\\operatorname{lk}}_K(\\sigma)$ be the link of a face $\\sigma$ in $K$. We prove that if the homology $\\widetilde H_t({\\operatorname{lk}}_K(\\sigma), {\\mathbb R})=0$ for every face $\\sigma\\in K$ with $|\\sigma|=r-t$, then \\[ {\\mathfrak q}_{r-1}(K)\\le tn-(t-1)(r+1).\\] Moreover, if $K$ is $r$-down path connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22825","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/2606.22825/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":"2606.22825","created_at":"2026-06-23T02:14:00.463538+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22825v1","created_at":"2026-06-23T02:14:00.463538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22825","created_at":"2026-06-23T02:14:00.463538+00:00"},{"alias_kind":"pith_short_12","alias_value":"5UNE3UPBY7M2","created_at":"2026-06-23T02:14:00.463538+00:00"},{"alias_kind":"pith_short_16","alias_value":"5UNE3UPBY7M24YJE","created_at":"2026-06-23T02:14:00.463538+00:00"},{"alias_kind":"pith_short_8","alias_value":"5UNE3UPB","created_at":"2026-06-23T02:14:00.463538+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/5UNE3UPBY7M24YJEOPNRM5HNRE","json":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE.json","graph_json":"https://pith.science/api/pith-number/5UNE3UPBY7M24YJEOPNRM5HNRE/graph.json","events_json":"https://pith.science/api/pith-number/5UNE3UPBY7M24YJEOPNRM5HNRE/events.json","paper":"https://pith.science/paper/5UNE3UPB"},"agent_actions":{"view_html":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE","download_json":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE.json","view_paper":"https://pith.science/paper/5UNE3UPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22825&json=true","fetch_graph":"https://pith.science/api/pith-number/5UNE3UPBY7M24YJEOPNRM5HNRE/graph.json","fetch_events":"https://pith.science/api/pith-number/5UNE3UPBY7M24YJEOPNRM5HNRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE/action/storage_attestation","attest_author":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE/action/author_attestation","sign_citation":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE/action/citation_signature","submit_replication":"https://pith.science/pith/5UNE3UPBY7M24YJEOPNRM5HNRE/action/replication_record"}},"created_at":"2026-06-23T02:14:00.463538+00:00","updated_at":"2026-06-23T02:14:00.463538+00:00"}