{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IHD2YCX2U7STXIMUN7KJ4AHEDC","short_pith_number":"pith:IHD2YCX2","canonical_record":{"source":{"id":"1409.2748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T14:22:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"2884ce0a2c7d979754fcf483cfca7e71c9a6a3c9e515b0b2f07e0567af9e771b","abstract_canon_sha256":"86b4d70b8d6ebac896b74d956aa556808e255313595e2ad2d7f366a399f5611f"},"schema_version":"1.0"},"canonical_sha256":"41c7ac0afaa7e53ba1946fd49e00e418884bbba32eca75a7cfc2ac8ff35dd6af","source":{"kind":"arxiv","id":"1409.2748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2748","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2748v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2748","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"IHD2YCX2U7ST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IHD2YCX2U7STXIMU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IHD2YCX2","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IHD2YCX2U7STXIMUN7KJ4AHEDC","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T14:22:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"2884ce0a2c7d979754fcf483cfca7e71c9a6a3c9e515b0b2f07e0567af9e771b","abstract_canon_sha256":"86b4d70b8d6ebac896b74d956aa556808e255313595e2ad2d7f366a399f5611f"},"schema_version":"1.0"},"canonical_sha256":"41c7ac0afaa7e53ba1946fd49e00e418884bbba32eca75a7cfc2ac8ff35dd6af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:09.857399Z","signature_b64":"ruoqpqwX3uHQCMDiGt1OAw7jlTUljxAy23ONR1F+EEjXn8x5pEZ4IJjXAQ8jN+t9Um4qsVKOghFKK2L2vOsBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41c7ac0afaa7e53ba1946fd49e00e418884bbba32eca75a7cfc2ac8ff35dd6af","last_reissued_at":"2026-05-18T02:43:09.856939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:09.856939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2748","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":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfRJfw1WKw927lopuuLQais3OfHbCLnnGYJwKWiYx4owT0RO8hoIP+TIwo6eOUpELbLXmNDvT/P9C4daoeLgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:50.185644Z"},"content_sha256":"a4193f5e9abad7657dc5a855e1bf651112f44ab1544c0d7c7833d341821fe09f","schema_version":"1.0","event_id":"sha256:a4193f5e9abad7657dc5a855e1bf651112f44ab1544c0d7c7833d341821fe09f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IHD2YCX2U7STXIMUN7KJ4AHEDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"A. Ferrero, E. Berchio, M. Vallarino","submitted_at":"2014-09-09T14:22:49Z","abstract_excerpt":"We consider least energy solutions to the nonlinear equation $-\\Delta_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\\ge 2$ which include the classical hyperbolic space $\\mathbb H^n$ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities $f(r,u)$, where $r$ denotes the geodesic distance from the pole of $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2748","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":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91N5qPxdMZuoB6N7BgoyEHkcUWgIs4UQOjZPuPvs8OV8rMUcENfUm5CFaUatfN7n9QfK7oVgRMF4gquNgd0eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:50.186292Z"},"content_sha256":"2111449b0f28d385cf6f9b7adff97b17acb05b339a8c0554a1581defa063c394","schema_version":"1.0","event_id":"sha256:2111449b0f28d385cf6f9b7adff97b17acb05b339a8c0554a1581defa063c394"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/bundle.json","state_url":"https://pith.science/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/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":"2026-05-26T12:40:50Z","links":{"resolver":"https://pith.science/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC","bundle":"https://pith.science/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/bundle.json","state":"https://pith.science/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHD2YCX2U7STXIMUN7KJ4AHEDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IHD2YCX2U7STXIMUN7KJ4AHEDC","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":"86b4d70b8d6ebac896b74d956aa556808e255313595e2ad2d7f366a399f5611f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T14:22:49Z","title_canon_sha256":"2884ce0a2c7d979754fcf483cfca7e71c9a6a3c9e515b0b2f07e0567af9e771b"},"schema_version":"1.0","source":{"id":"1409.2748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2748","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2748v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2748","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"IHD2YCX2U7ST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IHD2YCX2U7STXIMU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IHD2YCX2","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:2111449b0f28d385cf6f9b7adff97b17acb05b339a8c0554a1581defa063c394","target":"graph","created_at":"2026-05-18T02:43:09Z","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 least energy solutions to the nonlinear equation $-\\Delta_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\\ge 2$ which include the classical hyperbolic space $\\mathbb H^n$ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities $f(r,u)$, where $r$ denotes the geodesic distance from the pole of $M$.","authors_text":"A. Ferrero, E. Berchio, M. Vallarino","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T14:22:49Z","title":"Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2748","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:a4193f5e9abad7657dc5a855e1bf651112f44ab1544c0d7c7833d341821fe09f","target":"record","created_at":"2026-05-18T02:43:09Z","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":"86b4d70b8d6ebac896b74d956aa556808e255313595e2ad2d7f366a399f5611f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T14:22:49Z","title_canon_sha256":"2884ce0a2c7d979754fcf483cfca7e71c9a6a3c9e515b0b2f07e0567af9e771b"},"schema_version":"1.0","source":{"id":"1409.2748","kind":"arxiv","version":1}},"canonical_sha256":"41c7ac0afaa7e53ba1946fd49e00e418884bbba32eca75a7cfc2ac8ff35dd6af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41c7ac0afaa7e53ba1946fd49e00e418884bbba32eca75a7cfc2ac8ff35dd6af","first_computed_at":"2026-05-18T02:43:09.856939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.856939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ruoqpqwX3uHQCMDiGt1OAw7jlTUljxAy23ONR1F+EEjXn8x5pEZ4IJjXAQ8jN+t9Um4qsVKOghFKK2L2vOsBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.857399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4193f5e9abad7657dc5a855e1bf651112f44ab1544c0d7c7833d341821fe09f","sha256:2111449b0f28d385cf6f9b7adff97b17acb05b339a8c0554a1581defa063c394"],"state_sha256":"c780b4b73b80de5d01c10770a69ff4ec24ffedcefdefc5ee788f6a896f4ea788"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4TkcteqioyZQGZ4FPLqOGp/EHQmPe58S80cvZTn9+RJDTk9Jj1mwbuTMvvVX9rTaXy0+ZigPUAP0JsR5MZYRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:40:50.189727Z","bundle_sha256":"58a1e01dfa48b8d732af9ce9d42b3e30ea015285b9b1485590fea860648cb694"}}