{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NDQ7Y27WOKNWSLZE7KXCVUZ4NO","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":"10ba896a429aac2d339356d2b3dc1952da650984480ae6a463b035c922df79b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-27T04:25:18Z","title_canon_sha256":"9c872871e746504d514dddc79a85e3b03252e3581ac6767a1b933609b791ecfb"},"schema_version":"1.0","source":{"id":"1712.09488","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09488","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09488v2","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09488","created_at":"2026-05-18T00:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"NDQ7Y27WOKNW","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NDQ7Y27WOKNWSLZE","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NDQ7Y27W","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:ece8c126a640aaef68a0fab9a30f5c4c36af90ba01fe9043a6880a7ac433ad4d","target":"graph","created_at":"2026-05-18T00:25:50Z","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"},"paper":{"abstract_excerpt":"Let $G=(V,E)$ be a connected infinite and locally finite weighted graph, $\\Delta_p$ be the $p$-th discrete graph Laplacian. In this paper, we consider the $p$-th Yamabe type equation $$-\\Delta_pu+h|u|^{p-2}u=gu^{\\alpha-1}$$ on $G$, where $h$ and $g$ are known, $2<\\alpha\\leq p$. The prototype of this equation comes from the smooth Yamabe equation on an open manifold. We prove that the above equation has at least one positive solution on $G$.","authors_text":"Aijin Lin, Xiaoxiao Zhang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-27T04:25:18Z","title":"Positive Solutions of p-th Yamabe Type Equations on Infinite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09488","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":"sha256:5403292cae28d48922e8aaa95631ff37b34adc5a297a57186ff6725fb2045fde","target":"record","created_at":"2026-05-18T00:25:50Z","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":"10ba896a429aac2d339356d2b3dc1952da650984480ae6a463b035c922df79b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-27T04:25:18Z","title_canon_sha256":"9c872871e746504d514dddc79a85e3b03252e3581ac6767a1b933609b791ecfb"},"schema_version":"1.0","source":{"id":"1712.09488","kind":"arxiv","version":2}},"canonical_sha256":"68e1fc6bf6729b692f24faae2ad33c6bb50674687871f9d3a2286c9a64d25fdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68e1fc6bf6729b692f24faae2ad33c6bb50674687871f9d3a2286c9a64d25fdf","first_computed_at":"2026-05-18T00:25:50.764191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:50.764191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rnye4LKjHSjYu+cIgO97rbsipcnFiht2aBBu7iAzcDctC+XrnFt6GyokwggPy01pfxTNNXdzShTvPqHqy5cmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:50.764869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09488","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5403292cae28d48922e8aaa95631ff37b34adc5a297a57186ff6725fb2045fde","sha256:ece8c126a640aaef68a0fab9a30f5c4c36af90ba01fe9043a6880a7ac433ad4d"],"state_sha256":"e8f7d353b4f126f620b68af4f0c426769c8eac675c7e16327919f447e0ee221f"}