{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WXRKOXFBUSTVVCSSG6TW5CA4DR","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":"1e1163e7bc867cf1ba3e192611d1b0d688f687843a82dcacf6715f886ac242a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-08T11:59:33Z","title_canon_sha256":"5fce900f04e482024bc6886af2044b0dbbcdd55e979244c97ee9e6219fe87343"},"schema_version":"1.0","source":{"id":"2506.07100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07100","created_at":"2026-07-05T11:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07100v1","created_at":"2026-07-05T11:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07100","created_at":"2026-07-05T11:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"WXRKOXFBUSTV","created_at":"2026-07-05T11:18:01Z"},{"alias_kind":"pith_short_16","alias_value":"WXRKOXFBUSTVVCSS","created_at":"2026-07-05T11:18:01Z"},{"alias_kind":"pith_short_8","alias_value":"WXRKOXFB","created_at":"2026-07-05T11:18:01Z"}],"graph_snapshots":[{"event_id":"sha256:3a2fead152186055b9873683c66559d103336fe04ecc04844390b7dce6163744","target":"graph","created_at":"2026-07-05T11:18:01Z","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/2506.07100/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove a Talenti-type comparison theorem for the $p$-Laplacian with Dirichlet boundary conditions on open subsets of a $\\mathrm{RCD}(0,N)$ space with $N\\in (1,\\infty)$. We also obtain an almost rigidity result of the Talenti-type comparison theorem, whose proof relies on a compactness on varying spaces.","authors_text":"Wenjing Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-08T11:59:33Z","title":"Almost rigidity of the Talenti-type comparison theorem on $\\mathrm{RCD}(0,N)$ space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07100","kind":"arxiv","version":1},"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":"sha256:9c5462e8c7278cce3357b54a73dc167d933e25e6cf01204902e91e5f66b6b0ac","target":"record","created_at":"2026-07-05T11:18:01Z","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":"1e1163e7bc867cf1ba3e192611d1b0d688f687843a82dcacf6715f886ac242a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-08T11:59:33Z","title_canon_sha256":"5fce900f04e482024bc6886af2044b0dbbcdd55e979244c97ee9e6219fe87343"},"schema_version":"1.0","source":{"id":"2506.07100","kind":"arxiv","version":1}},"canonical_sha256":"b5e2a75ca1a4a75a8a5237a76e881c1c7fadfd78d5418a1b3193c896876aea06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5e2a75ca1a4a75a8a5237a76e881c1c7fadfd78d5418a1b3193c896876aea06","first_computed_at":"2026-07-05T11:18:01.243249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:01.243249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wx1qV02l+QzGsBUdsuvRmO0JVev0IPOmszfTyofgkbrCgSA+M0UKxlDXvo1jUv4Yp1DTOBkwBpQgY8jyZmycCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:01.243661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c5462e8c7278cce3357b54a73dc167d933e25e6cf01204902e91e5f66b6b0ac","sha256:3a2fead152186055b9873683c66559d103336fe04ecc04844390b7dce6163744"],"state_sha256":"68b488a5f0973f507bab2bf3bc56684fdb199b951378d769b680b3151b09299d"}