{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P2JB7LT5UC2BDH66B6AHRP5NY7","short_pith_number":"pith:P2JB7LT5","canonical_record":{"source":{"id":"1512.07749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-24T08:24:29Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"0d102e0d929ee66f7be0e4051cb4b594b333a31db2ef3e7d06f84871012c5421","abstract_canon_sha256":"677035d8d8565fe407aeb3adc6a9dabaf0566ed9e0bab299c08fea6607cfd204"},"schema_version":"1.0"},"canonical_sha256":"7e921fae7da0b4119fde0f8078bfadc7c203f7904503ab7460f853b966aa3fac","source":{"kind":"arxiv","id":"1512.07749","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07749","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07749v1","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07749","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"P2JB7LT5UC2B","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P2JB7LT5UC2BDH66","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P2JB7LT5","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P2JB7LT5UC2BDH66B6AHRP5NY7","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-24T08:24:29Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"0d102e0d929ee66f7be0e4051cb4b594b333a31db2ef3e7d06f84871012c5421","abstract_canon_sha256":"677035d8d8565fe407aeb3adc6a9dabaf0566ed9e0bab299c08fea6607cfd204"},"schema_version":"1.0"},"canonical_sha256":"7e921fae7da0b4119fde0f8078bfadc7c203f7904503ab7460f853b966aa3fac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:00.430940Z","signature_b64":"rfREyfxSMGo4OWQ78/ddmBJBCaI/bMaTdRSnUmfYmV007Tk2XhHJqPq3cjfEPG+VGz6MiqrKGAonHImT09miAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e921fae7da0b4119fde0f8078bfadc7c203f7904503ab7460f853b966aa3fac","last_reissued_at":"2026-05-18T01:01:00.430265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:00.430265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07749","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":"2026-05-18T01:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNB2TUK0J2giml2nlFL79UAJkrCZe6WSv74vuni4mpZMy0oH0CP0l4JjDFAehQcPPOEzGOGVDJvNsHVHgBYSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:10:34.452972Z"},"content_sha256":"51784cd6fceb066417a565d6b18734f1257804e3a46453ecd66b8d208891d4cc","schema_version":"1.0","event_id":"sha256:51784cd6fceb066417a565d6b18734f1257804e3a46453ecd66b8d208891d4cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P2JB7LT5UC2BDH66B6AHRP5NY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A rigidity problem on the round sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo, Luigi Vezzoni","submitted_at":"2015-12-24T08:24:29Z","abstract_excerpt":"We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07749","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":"2026-05-18T01:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUEq5+kbFUwiFxbq6Vcar3Zds5KfRB7wCjz+nHCeWtdW8rX5i2uqG1IcTlsjQomAf/puoYz4H94q4h9ZwvbFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:10:34.453664Z"},"content_sha256":"c3fea40d30f56bcb6ba9efdf25a5a7f6c612aa580d037958ced70115b39012bd","schema_version":"1.0","event_id":"sha256:c3fea40d30f56bcb6ba9efdf25a5a7f6c612aa580d037958ced70115b39012bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/bundle.json","state_url":"https://pith.science/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/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":"2026-06-09T09:10:34Z","links":{"resolver":"https://pith.science/pith/P2JB7LT5UC2BDH66B6AHRP5NY7","bundle":"https://pith.science/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/bundle.json","state":"https://pith.science/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2JB7LT5UC2BDH66B6AHRP5NY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P2JB7LT5UC2BDH66B6AHRP5NY7","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":"677035d8d8565fe407aeb3adc6a9dabaf0566ed9e0bab299c08fea6607cfd204","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-24T08:24:29Z","title_canon_sha256":"0d102e0d929ee66f7be0e4051cb4b594b333a31db2ef3e7d06f84871012c5421"},"schema_version":"1.0","source":{"id":"1512.07749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07749","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07749v1","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07749","created_at":"2026-05-18T01:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"P2JB7LT5UC2B","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P2JB7LT5UC2BDH66","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P2JB7LT5","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c3fea40d30f56bcb6ba9efdf25a5a7f6c612aa580d037958ced70115b39012bd","target":"graph","created_at":"2026-05-18T01:01:00Z","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 consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.","authors_text":"Giulio Ciraolo, Luigi Vezzoni","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-24T08:24:29Z","title":"A rigidity problem on the round sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07749","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":"sha256:51784cd6fceb066417a565d6b18734f1257804e3a46453ecd66b8d208891d4cc","target":"record","created_at":"2026-05-18T01:01:00Z","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":"677035d8d8565fe407aeb3adc6a9dabaf0566ed9e0bab299c08fea6607cfd204","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-24T08:24:29Z","title_canon_sha256":"0d102e0d929ee66f7be0e4051cb4b594b333a31db2ef3e7d06f84871012c5421"},"schema_version":"1.0","source":{"id":"1512.07749","kind":"arxiv","version":1}},"canonical_sha256":"7e921fae7da0b4119fde0f8078bfadc7c203f7904503ab7460f853b966aa3fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e921fae7da0b4119fde0f8078bfadc7c203f7904503ab7460f853b966aa3fac","first_computed_at":"2026-05-18T01:01:00.430265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:00.430265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfREyfxSMGo4OWQ78/ddmBJBCaI/bMaTdRSnUmfYmV007Tk2XhHJqPq3cjfEPG+VGz6MiqrKGAonHImT09miAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:00.430940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51784cd6fceb066417a565d6b18734f1257804e3a46453ecd66b8d208891d4cc","sha256:c3fea40d30f56bcb6ba9efdf25a5a7f6c612aa580d037958ced70115b39012bd"],"state_sha256":"07e24896e6765520660177888d5054b2e14ef3e474b62bcf65a3c607c27bb953"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3Y3tQtdeLFsFkxCcn/6fAavR8wq3ouwOLKf65NXxyL5YXrh9VTbdm6UZc8P0L27ssVBoHeZNqoY62+9mIWHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:10:34.457734Z","bundle_sha256":"27cf9c1b2b69c819e67df4c99bb2b41cb6f79029a215e37d1fac764a8859f078"}}