{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HDH7BUX3UTV3HENJFKJQVY3SRT","short_pith_number":"pith:HDH7BUX3","canonical_record":{"source":{"id":"1102.0539","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-02T19:58:17Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b6b50521f1adcc9f67a389288b26d0bc7d0c3f3b896ba904780cc0bdce858275","abstract_canon_sha256":"711d14032bfac81d5b427ba5353966705112e228a5063cac0e407d08670d2aef"},"schema_version":"1.0"},"canonical_sha256":"38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888","source":{"kind":"arxiv","id":"1102.0539","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0539","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0539v8","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0539","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"HDH7BUX3UTV3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HDH7BUX3UTV3HENJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HDH7BUX3","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HDH7BUX3UTV3HENJFKJQVY3SRT","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0539","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-02T19:58:17Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b6b50521f1adcc9f67a389288b26d0bc7d0c3f3b896ba904780cc0bdce858275","abstract_canon_sha256":"711d14032bfac81d5b427ba5353966705112e228a5063cac0e407d08670d2aef"},"schema_version":"1.0"},"canonical_sha256":"38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:10.510101Z","signature_b64":"77FgY8fk/V3TulLd+YO25EOBe0NurHx+EDghKvsy9N7Y1ZxoeUd3aS9xmtpfmKONb8rL+o74CIWMKbmlExzeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888","last_reissued_at":"2026-05-18T03:03:10.509606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:10.509606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0539","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEupOzPs+iSCpzQpG2Ba40aQwKOQaMkHMmM8lbpJuAzXXRHw+MMQ7sdTfqs2X2FMl9YI1Ckd1N8qPxUxcxKuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:36:59.354308Z"},"content_sha256":"a52a5beb908f5f74b718bad710b636f8dd74b423a263bc93af0b03519eb1a11b","schema_version":"1.0","event_id":"sha256:a52a5beb908f5f74b718bad710b636f8dd74b423a263bc93af0b03519eb1a11b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HDH7BUX3UTV3HENJFKJQVY3SRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Daniele Valtorta","submitted_at":"2011-02-02T19:58:17Z","abstract_excerpt":"We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (in this case we assume Neumann b.c. on the p-laplacian). The proof is based on a gradient comparison theorem. We will also charachterize the equality case in the estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0539","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cwu4g5j1HYqX9X+Br0kGGT918P7OtsK9Fw4hkzf6HIz39NxBp3etB0Rt8zV1vs3Zp3N7t/HFBozcEuRTU3lCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:36:59.354671Z"},"content_sha256":"6fbe70a280e2aca030bead6015816026f630d886fe3e27e8d4677219694eda84","schema_version":"1.0","event_id":"sha256:6fbe70a280e2aca030bead6015816026f630d886fe3e27e8d4677219694eda84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/bundle.json","state_url":"https://pith.science/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/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":"2026-05-28T03:36:59Z","links":{"resolver":"https://pith.science/pith/HDH7BUX3UTV3HENJFKJQVY3SRT","bundle":"https://pith.science/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/bundle.json","state":"https://pith.science/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDH7BUX3UTV3HENJFKJQVY3SRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HDH7BUX3UTV3HENJFKJQVY3SRT","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":"711d14032bfac81d5b427ba5353966705112e228a5063cac0e407d08670d2aef","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-02T19:58:17Z","title_canon_sha256":"b6b50521f1adcc9f67a389288b26d0bc7d0c3f3b896ba904780cc0bdce858275"},"schema_version":"1.0","source":{"id":"1102.0539","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0539","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0539v8","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0539","created_at":"2026-05-18T03:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"HDH7BUX3UTV3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HDH7BUX3UTV3HENJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HDH7BUX3","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:6fbe70a280e2aca030bead6015816026f630d886fe3e27e8d4677219694eda84","target":"graph","created_at":"2026-05-18T03:03:10Z","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":"We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (in this case we assume Neumann b.c. on the p-laplacian). The proof is based on a gradient comparison theorem. We will also charachterize the equality case in the estimate.","authors_text":"Daniele Valtorta","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-02T19:58:17Z","title":"Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0539","kind":"arxiv","version":8},"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:a52a5beb908f5f74b718bad710b636f8dd74b423a263bc93af0b03519eb1a11b","target":"record","created_at":"2026-05-18T03:03:10Z","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":"711d14032bfac81d5b427ba5353966705112e228a5063cac0e407d08670d2aef","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-02T19:58:17Z","title_canon_sha256":"b6b50521f1adcc9f67a389288b26d0bc7d0c3f3b896ba904780cc0bdce858275"},"schema_version":"1.0","source":{"id":"1102.0539","kind":"arxiv","version":8}},"canonical_sha256":"38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888","first_computed_at":"2026-05-18T03:03:10.509606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:10.509606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"77FgY8fk/V3TulLd+YO25EOBe0NurHx+EDghKvsy9N7Y1ZxoeUd3aS9xmtpfmKONb8rL+o74CIWMKbmlExzeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:10.510101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0539","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a52a5beb908f5f74b718bad710b636f8dd74b423a263bc93af0b03519eb1a11b","sha256:6fbe70a280e2aca030bead6015816026f630d886fe3e27e8d4677219694eda84"],"state_sha256":"5b68ddc4b55f1d6a0fdd6000d1190b0962813015d6407660a3d835bd5c6e9b56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqRWJGwCRAlZQdtUbkKMcnMq/P0yxJElw6ePd8lpJNjS1B1dG2IyMooW1soDh9Wngb5y603gydjvF9+S8Yl9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:36:59.356609Z","bundle_sha256":"4d10354a3e865ad5e32ce910f61899980b3fac1b2f7013a982afb43d455d6a58"}}