{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FRFBLHQLMGK5BRSWLIB36LZ6IG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"96766a194bfb9d7beab440ccb34c9a5bf42fc061981f4486224870c47591a9c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-09-29T06:53:18Z","title_canon_sha256":"40a4e86acaf46c81e3f69ae08468bab5654ca1e7497a2ba0dc3e88fc79b21eff"},"schema_version":"1.0","source":{"id":"2509.24354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.24354","created_at":"2026-06-02T02:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2509.24354v2","created_at":"2026-06-02T02:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.24354","created_at":"2026-06-02T02:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"FRFBLHQLMGK5","created_at":"2026-06-02T02:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"FRFBLHQLMGK5BRSW","created_at":"2026-06-02T02:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"FRFBLHQL","created_at":"2026-06-02T02:04:09Z"}],"graph_snapshots":[{"event_id":"sha256:cc4595dcabec2141bbdd65d584104f954310b18a1707cb5584ab05f0ddf93108","target":"graph","created_at":"2026-06-02T02:04:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.24354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An $r$-pattern $P$ is an ordered pair $P=([l],E)$, where $l$ is a positive integer and $E$ is a set of $r$-multisets with elements from $[l]$. An $r$-graph $H$ is said to be $P$-colorable if there is a homomorphism $\\phi$: $V(H)\\rightarrow [l]$ such that $\\{\\phi(v_{1}),\\ldots,\\phi(v_{r})\\}\\in E$ for every edge $\\{v_{1},\\ldots,v_{r}\\}\\in E(H)$. Let $\\mathrm{Col}(P)$ denote the family of all $P$-colorable $r$-graphs. This paper studies spectral extremal problems for $\\alpha$-spectral radius of hypergraphs via analytic techniques.\n  We first prove that for any $r$-pattern $P$, the hypergraph atta","authors_text":"Honghai Li, Jian Zheng, Li Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-09-29T06:53:18Z","title":"Spectral Tur\\'an-type problems for the $\\alpha$-spectral radius of hypergraphs with degree stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.24354","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cfaecaf7e614190f4993742e32f1f5e023d401a446ba24bad1c0f58b86f964ef","target":"record","created_at":"2026-06-02T02:04:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"96766a194bfb9d7beab440ccb34c9a5bf42fc061981f4486224870c47591a9c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-09-29T06:53:18Z","title_canon_sha256":"40a4e86acaf46c81e3f69ae08468bab5654ca1e7497a2ba0dc3e88fc79b21eff"},"schema_version":"1.0","source":{"id":"2509.24354","kind":"arxiv","version":2}},"canonical_sha256":"2c4a159e0b6195d0c6565a03bf2f3e418354fef07b5d1c3df6ab6d03eb0b6405","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c4a159e0b6195d0c6565a03bf2f3e418354fef07b5d1c3df6ab6d03eb0b6405","first_computed_at":"2026-06-02T02:04:09.255296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:09.255296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkrP3xFQYX+ZfHrzw3Ll7zEiB4VZTNUCoGxWuhbZ4gjZDZ8wXszcSeYk+4j2bNfOJXf6RA3NlG+UNUZ38zWQAg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:09.255857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.24354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfaecaf7e614190f4993742e32f1f5e023d401a446ba24bad1c0f58b86f964ef","sha256:cc4595dcabec2141bbdd65d584104f954310b18a1707cb5584ab05f0ddf93108"],"state_sha256":"e9db87b6d31aea30ce288f371fe0f5709b3038ee7922df9d2acd8368d9874249"}