{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NJQY2LKEFA6AWLB2MT6SHRDXPA","short_pith_number":"pith:NJQY2LKE","schema_version":"1.0","canonical_sha256":"6a618d2d44283c0b2c3a64fd23c4777830fca6b8e51ddf7b20fd7eaf7fed3614","source":{"kind":"arxiv","id":"2606.14148","version":2},"attestation_state":"computed","paper":{"title":"Virtual inheritance properties of graph products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Shengkui Ye, Xiaolei Wu, Xiaoming Huang","submitted_at":"2026-06-12T06:21:15Z","abstract_excerpt":"We prove that many virtual properties are closed under taking graph products, including: virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally poly-free. Our proof uses Januszkiewicz and \\'Swi\\k{a}tkowski's strong commensurability theorem for graph products, for which we provide an elementary proof."},"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":"2606.14148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-12T06:21:15Z","cross_cats_sorted":[],"title_canon_sha256":"734cf61d673b37be8964bf87811f294b3a3523784c11f2e741a10fc4cdf5fec4","abstract_canon_sha256":"d90712cb74cffbdcd5b277fb70a9b209b4cd1d81ea22e397de32f0a2c817a21e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:21.557779Z","signature_b64":"3ih0t1uv1xZV5ZyGoGIsP24kLMhqDsKIyl5PQu5ov4zfriN4vbCIvNc+n7ttn1rQNoaf4W+uaZ0NarRL79uZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a618d2d44283c0b2c3a64fd23c4777830fca6b8e51ddf7b20fd7eaf7fed3614","last_reissued_at":"2026-06-19T16:12:21.557423Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:21.557423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtual inheritance properties of graph products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Shengkui Ye, Xiaolei Wu, Xiaoming Huang","submitted_at":"2026-06-12T06:21:15Z","abstract_excerpt":"We prove that many virtual properties are closed under taking graph products, including: virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally poly-free. Our proof uses Januszkiewicz and \\'Swi\\k{a}tkowski's strong commensurability theorem for graph products, for which we provide an elementary proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.14148","kind":"arxiv","version":2},"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/2606.14148/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":"2606.14148","created_at":"2026-06-19T16:12:21.557485+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.14148v2","created_at":"2026-06-19T16:12:21.557485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.14148","created_at":"2026-06-19T16:12:21.557485+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJQY2LKEFA6A","created_at":"2026-06-19T16:12:21.557485+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJQY2LKEFA6AWLB2","created_at":"2026-06-19T16:12:21.557485+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJQY2LKE","created_at":"2026-06-19T16:12:21.557485+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/NJQY2LKEFA6AWLB2MT6SHRDXPA","json":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA.json","graph_json":"https://pith.science/api/pith-number/NJQY2LKEFA6AWLB2MT6SHRDXPA/graph.json","events_json":"https://pith.science/api/pith-number/NJQY2LKEFA6AWLB2MT6SHRDXPA/events.json","paper":"https://pith.science/paper/NJQY2LKE"},"agent_actions":{"view_html":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA","download_json":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA.json","view_paper":"https://pith.science/paper/NJQY2LKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.14148&json=true","fetch_graph":"https://pith.science/api/pith-number/NJQY2LKEFA6AWLB2MT6SHRDXPA/graph.json","fetch_events":"https://pith.science/api/pith-number/NJQY2LKEFA6AWLB2MT6SHRDXPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA/action/storage_attestation","attest_author":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA/action/author_attestation","sign_citation":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA/action/citation_signature","submit_replication":"https://pith.science/pith/NJQY2LKEFA6AWLB2MT6SHRDXPA/action/replication_record"}},"created_at":"2026-06-19T16:12:21.557485+00:00","updated_at":"2026-06-19T16:12:21.557485+00:00"}