{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BRQ2BNEVOB26JD2UOMCR2RJ4IA","short_pith_number":"pith:BRQ2BNEV","canonical_record":{"source":{"id":"1803.09790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T18:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"b9313143cec5dbf0de176f27e186d690687d383d47f25e38d9d75446fb49914c","abstract_canon_sha256":"230120dc45c37f689e7a61ddbab58507db799133f10b3352681bf743b177d6cd"},"schema_version":"1.0"},"canonical_sha256":"0c61a0b4957075e48f5473051d453c401bfe68f9b476704574425280f51fcd6d","source":{"kind":"arxiv","id":"1803.09790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09790","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09790v1","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09790","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"BRQ2BNEVOB26","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BRQ2BNEVOB26JD2U","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BRQ2BNEV","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BRQ2BNEVOB26JD2UOMCR2RJ4IA","target":"record","payload":{"canonical_record":{"source":{"id":"1803.09790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T18:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"b9313143cec5dbf0de176f27e186d690687d383d47f25e38d9d75446fb49914c","abstract_canon_sha256":"230120dc45c37f689e7a61ddbab58507db799133f10b3352681bf743b177d6cd"},"schema_version":"1.0"},"canonical_sha256":"0c61a0b4957075e48f5473051d453c401bfe68f9b476704574425280f51fcd6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:10.482766Z","signature_b64":"/tCGdhL4laog7wVX6q7F0c6K6v/3pd7ucWdakGUFqMug7c4TorHRDncy51r19bg4Vd0d4rlOU4HI8ZV8i1a8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c61a0b4957075e48f5473051d453c401bfe68f9b476704574425280f51fcd6d","last_reissued_at":"2026-05-18T00:20:10.482037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:10.482037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.09790","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dI7u3i95zejN8IpBkjk7e2n9zjEH9DhlHd0wewo8Ly+WltY7xbgRzFrLUq1dXdSa1qyeubZue75n1N8I5SSLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:09:08.829496Z"},"content_sha256":"96297186fa27517a7157b9f5507ec53be12bba9dda4c57cc8aeb8c104aa0cd13","schema_version":"1.0","event_id":"sha256:96297186fa27517a7157b9f5507ec53be12bba9dda4c57cc8aeb8c104aa0cd13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BRQ2BNEVOB26JD2UOMCR2RJ4IA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the first Robin eigenvalue of a class of anisotropic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leonardo Trani, Nunzia Gavitone","submitted_at":"2018-03-26T18:53:20Z","abstract_excerpt":"The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\\beta$ which in general is not constant. In particular we obtain sharp lower bounds in terms of the measure of the domain and we prove a monotonicity property of the eigenvalue with respect the set inclusion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09790","kind":"arxiv","version":1},"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":"2026-05-18T00:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mmfz3xJknc+IJosJ1Zao+FbkGFZFlEJUs8DSjpIIfGn+xz98BLtulVdE8u3x4n62pRObKwr0nxMVSh4YLZ52Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:09:08.829839Z"},"content_sha256":"532300c7a0eebc2af51ae02b07f81b6726921faa193420e7365e0a56ce65802a","schema_version":"1.0","event_id":"sha256:532300c7a0eebc2af51ae02b07f81b6726921faa193420e7365e0a56ce65802a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/bundle.json","state_url":"https://pith.science/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/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":"2026-08-04T21:09:08Z","links":{"resolver":"https://pith.science/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA","bundle":"https://pith.science/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/bundle.json","state":"https://pith.science/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRQ2BNEVOB26JD2UOMCR2RJ4IA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BRQ2BNEVOB26JD2UOMCR2RJ4IA","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":"230120dc45c37f689e7a61ddbab58507db799133f10b3352681bf743b177d6cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T18:53:20Z","title_canon_sha256":"b9313143cec5dbf0de176f27e186d690687d383d47f25e38d9d75446fb49914c"},"schema_version":"1.0","source":{"id":"1803.09790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09790","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09790v1","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09790","created_at":"2026-05-18T00:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"BRQ2BNEVOB26","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BRQ2BNEVOB26JD2U","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BRQ2BNEV","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:532300c7a0eebc2af51ae02b07f81b6726921faa193420e7365e0a56ce65802a","target":"graph","created_at":"2026-05-18T00:20:10Z","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":"The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\\beta$ which in general is not constant. In particular we obtain sharp lower bounds in terms of the measure of the domain and we prove a monotonicity property of the eigenvalue with respect the set inclusion.","authors_text":"Leonardo Trani, Nunzia Gavitone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T18:53:20Z","title":"On the first Robin eigenvalue of a class of anisotropic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09790","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":"sha256:96297186fa27517a7157b9f5507ec53be12bba9dda4c57cc8aeb8c104aa0cd13","target":"record","created_at":"2026-05-18T00:20:10Z","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":"230120dc45c37f689e7a61ddbab58507db799133f10b3352681bf743b177d6cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-26T18:53:20Z","title_canon_sha256":"b9313143cec5dbf0de176f27e186d690687d383d47f25e38d9d75446fb49914c"},"schema_version":"1.0","source":{"id":"1803.09790","kind":"arxiv","version":1}},"canonical_sha256":"0c61a0b4957075e48f5473051d453c401bfe68f9b476704574425280f51fcd6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c61a0b4957075e48f5473051d453c401bfe68f9b476704574425280f51fcd6d","first_computed_at":"2026-05-18T00:20:10.482037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:10.482037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/tCGdhL4laog7wVX6q7F0c6K6v/3pd7ucWdakGUFqMug7c4TorHRDncy51r19bg4Vd0d4rlOU4HI8ZV8i1a8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:10.482766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96297186fa27517a7157b9f5507ec53be12bba9dda4c57cc8aeb8c104aa0cd13","sha256:532300c7a0eebc2af51ae02b07f81b6726921faa193420e7365e0a56ce65802a"],"state_sha256":"cf575aba14b6e0caddf61985967edf83d49aca0e29eaea8a592efbaccb62069f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVVZlGQqV1E7wo8mF4nq2epC8ZgiWNKDXUSNA1I1UMATeI24tq3ZbcLCMa31+Qs4WxyR6r4FKMWYwfpE9uCMAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:09:08.832045Z","bundle_sha256":"d7a382c1e0cc3b26f22edc45d590360e06d885d2275be4034e69a61ee8285e12"}}