{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GO3RGMQLDNAOOOTJMQ5VSRURJT","short_pith_number":"pith:GO3RGMQL","canonical_record":{"source":{"id":"2602.05968","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-05T18:22:02Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d63c1f4439e6b4c3b5dda034cd53be9af688424fc52bac14304ea25eddae3cae","abstract_canon_sha256":"b49078234801b37ffd83ed33b0a0bf0d23a2dfbe0e4633d5e94d9895765ce902"},"schema_version":"1.0"},"canonical_sha256":"33b713320b1b40e73a69643b5946914cd86c598558049bfc4feb16fbf3530df2","source":{"kind":"arxiv","id":"2602.05968","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.05968","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"arxiv_version","alias_value":"2602.05968v4","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.05968","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_12","alias_value":"GO3RGMQLDNAO","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_16","alias_value":"GO3RGMQLDNAOOOTJ","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_8","alias_value":"GO3RGMQL","created_at":"2026-07-16T01:22:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GO3RGMQLDNAOOOTJMQ5VSRURJT","target":"record","payload":{"canonical_record":{"source":{"id":"2602.05968","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-05T18:22:02Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d63c1f4439e6b4c3b5dda034cd53be9af688424fc52bac14304ea25eddae3cae","abstract_canon_sha256":"b49078234801b37ffd83ed33b0a0bf0d23a2dfbe0e4633d5e94d9895765ce902"},"schema_version":"1.0"},"canonical_sha256":"33b713320b1b40e73a69643b5946914cd86c598558049bfc4feb16fbf3530df2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:34.339980Z","signature_b64":"TYbE8FUxJVJtj4A4SB9xfQ5KEiSzaJKgoEQrevyjgH6xNF7qOYRf9jJysx0GXWFEX400rjbYe1icRz6kX3f4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33b713320b1b40e73a69643b5946914cd86c598558049bfc4feb16fbf3530df2","last_reissued_at":"2026-07-16T01:22:34.339096Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:34.339096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.05968","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-16T01:22:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPOZwp4tv8tDf/c94rfApS5GKbS+4gFqiwmIO9u8V2Ye56Tiqr+FZJg6wB06ILsixMlFKZKJ1Qkz3oAjzMp5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:19:03.911431Z"},"content_sha256":"99a94b78802a62c9ef0d89ba06657ad48ee76a4f6b3a5c6213d501cf03f2f531","schema_version":"1.0","event_id":"sha256:99a94b78802a62c9ef0d89ba06657ad48ee76a4f6b3a5c6213d501cf03f2f531"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GO3RGMQLDNAOOOTJMQ5VSRURJT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of the $L^{p}$-Poincar\\'e inequality for the Lebesgue measure and Gaussian probability measure with explicit geometric dependence and applications to spectral gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Amir Zhangirbayev, Nurgissa Yessirkegenov","submitted_at":"2026-02-05T18:22:02Z","abstract_excerpt":"In this paper, we obtain stability results for the $L^{p}$-Poincar\\'e inequality for both Lebesgue measure and Gaussian probability measure (Theorem 3.3 and Theorem 3.13) that involve explicit dependence on the geometry of the domain. As a byproduct, the explicit constant allows us to recover important results of Yu, Zhong [YZ86] and Smits [Smi96] (Corollary 3.9), related to the fundamental gap conjecture of the Laplacian (resolved by Andrews and Clutterbuck [AC11]), thereby providing an alternative proof. Moreover, we extend this spectral gap result to the $p$-Laplacian (Corollary 3.6). Such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.05968","kind":"arxiv","version":4},"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/2602.05968/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-16T01:22:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFaGbKakhCdsdFocQyJChYrKoBLeDMwD3GRoPVC3WGt/F0KlhpJCOePPWXCx7wqt2VpHCm0iYAPo9dOj3ehuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:19:03.911958Z"},"content_sha256":"d4f173b2db5cd030f6dcd942e1df4955dbb10580c80739318af5d0a66a147f70","schema_version":"1.0","event_id":"sha256:d4f173b2db5cd030f6dcd942e1df4955dbb10580c80739318af5d0a66a147f70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/bundle.json","state_url":"https://pith.science/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T18:19:03Z","links":{"resolver":"https://pith.science/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT","bundle":"https://pith.science/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/bundle.json","state":"https://pith.science/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GO3RGMQLDNAOOOTJMQ5VSRURJT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GO3RGMQLDNAOOOTJMQ5VSRURJT","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":"b49078234801b37ffd83ed33b0a0bf0d23a2dfbe0e4633d5e94d9895765ce902","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-05T18:22:02Z","title_canon_sha256":"d63c1f4439e6b4c3b5dda034cd53be9af688424fc52bac14304ea25eddae3cae"},"schema_version":"1.0","source":{"id":"2602.05968","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.05968","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"arxiv_version","alias_value":"2602.05968v4","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.05968","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_12","alias_value":"GO3RGMQLDNAO","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_16","alias_value":"GO3RGMQLDNAOOOTJ","created_at":"2026-07-16T01:22:34Z"},{"alias_kind":"pith_short_8","alias_value":"GO3RGMQL","created_at":"2026-07-16T01:22:34Z"}],"graph_snapshots":[{"event_id":"sha256:d4f173b2db5cd030f6dcd942e1df4955dbb10580c80739318af5d0a66a147f70","target":"graph","created_at":"2026-07-16T01:22:34Z","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/2602.05968/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we obtain stability results for the $L^{p}$-Poincar\\'e inequality for both Lebesgue measure and Gaussian probability measure (Theorem 3.3 and Theorem 3.13) that involve explicit dependence on the geometry of the domain. As a byproduct, the explicit constant allows us to recover important results of Yu, Zhong [YZ86] and Smits [Smi96] (Corollary 3.9), related to the fundamental gap conjecture of the Laplacian (resolved by Andrews and Clutterbuck [AC11]), thereby providing an alternative proof. Moreover, we extend this spectral gap result to the $p$-Laplacian (Corollary 3.6). Such ","authors_text":"Amir Zhangirbayev, Nurgissa Yessirkegenov","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-05T18:22:02Z","title":"Stability of the $L^{p}$-Poincar\\'e inequality for the Lebesgue measure and Gaussian probability measure with explicit geometric dependence and applications to spectral gaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.05968","kind":"arxiv","version":4},"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":"sha256:99a94b78802a62c9ef0d89ba06657ad48ee76a4f6b3a5c6213d501cf03f2f531","target":"record","created_at":"2026-07-16T01:22:34Z","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":"b49078234801b37ffd83ed33b0a0bf0d23a2dfbe0e4633d5e94d9895765ce902","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-05T18:22:02Z","title_canon_sha256":"d63c1f4439e6b4c3b5dda034cd53be9af688424fc52bac14304ea25eddae3cae"},"schema_version":"1.0","source":{"id":"2602.05968","kind":"arxiv","version":4}},"canonical_sha256":"33b713320b1b40e73a69643b5946914cd86c598558049bfc4feb16fbf3530df2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33b713320b1b40e73a69643b5946914cd86c598558049bfc4feb16fbf3530df2","first_computed_at":"2026-07-16T01:22:34.339096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:22:34.339096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TYbE8FUxJVJtj4A4SB9xfQ5KEiSzaJKgoEQrevyjgH6xNF7qOYRf9jJysx0GXWFEX400rjbYe1icRz6kX3f4CQ==","signature_status":"signed_v1","signed_at":"2026-07-16T01:22:34.339980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.05968","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a94b78802a62c9ef0d89ba06657ad48ee76a4f6b3a5c6213d501cf03f2f531","sha256:d4f173b2db5cd030f6dcd942e1df4955dbb10580c80739318af5d0a66a147f70"],"state_sha256":"46727b0d7b173b0e908cda1b6f722ed88226da877edaa1c3ff4a26f2bae0559c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3FaepknS7+GtGZBrbeMAKO6KgwSZiBXM3NXnUbFRSZ4d8Dw2zpcAOmMxPk8M3n6mlqqLeZgtAtkdHOuRadyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:19:03.917645Z","bundle_sha256":"df0e9e5bac2c7fd979748bd99e6f8a447b5654b4e080a7e8cc69dcc987e29a9a"}}