{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SW5MM6ZHU4R3QN6ZSKTEL36ZDP","short_pith_number":"pith:SW5MM6ZH","canonical_record":{"source":{"id":"1802.08625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T16:31:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"da291c46754279cc6913d7b95a63c2c31e020988416d6a72300df439020239d4","abstract_canon_sha256":"098f1ed455b205d146616a9eebb51a8201334c2dd754d212af0340bebf64ea93"},"schema_version":"1.0"},"canonical_sha256":"95bac67b27a723b837d992a645efd91be3f440454607b1afb9df356c1351a8f6","source":{"kind":"arxiv","id":"1802.08625","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08625","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08625v2","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08625","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"SW5MM6ZHU4R3","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SW5MM6ZHU4R3QN6Z","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SW5MM6ZH","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SW5MM6ZHU4R3QN6ZSKTEL36ZDP","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T16:31:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"da291c46754279cc6913d7b95a63c2c31e020988416d6a72300df439020239d4","abstract_canon_sha256":"098f1ed455b205d146616a9eebb51a8201334c2dd754d212af0340bebf64ea93"},"schema_version":"1.0"},"canonical_sha256":"95bac67b27a723b837d992a645efd91be3f440454607b1afb9df356c1351a8f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:45.536136Z","signature_b64":"njfwgKfeC5PA/qHHbUjIcOulTTBCp8NO/jlljcJQRWqLMFL3mBlkqXc834BIJ57l/8rWi1J8g+h1Whmj9IcRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95bac67b27a723b837d992a645efd91be3f440454607b1afb9df356c1351a8f6","last_reissued_at":"2026-05-18T00:21:45.535456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:45.535456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08625","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k5zgLTKqtzInPSDQuDwSi/DR+WHmM7dwVUFb8eu+DQcntkKsWlK/WGpQ1ZhgZKUpYYTiJkFK9Ryzy5FOvZ5BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:40:04.974560Z"},"content_sha256":"dda5e71759b17c9fd8a135f1eb880fbdd30984e20fbebd001ba2f7735b9832d0","schema_version":"1.0","event_id":"sha256:dda5e71759b17c9fd8a135f1eb880fbdd30984e20fbebd001ba2f7735b9832d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SW5MM6ZHU4R3QN6ZSKTEL36ZDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On polar actions invariant solutions of semilinear equations on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Edward Becerra, Juan Galvis, Nicolas Martinez Alba","submitted_at":"2018-02-23T16:31:00Z","abstract_excerpt":"In this paper we put together some tools from differential topology and analysis in order to study second order semi-linear partial differential equations on a Riemannian manifold $M$. We look for solutions that are constants along orbits of a given group action. Using some results obtained by Helgason in [J DIFFER GEOM,6(3), 411-419] we are able to write a (reduced) second order semi-linear problem on a submanifold $\\Sigma$. This submanifold is, in certain sense, transversal to the orbits of the group actions and its existence is assumed. We describe precise conditions on the Riemannian Manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08625","kind":"arxiv","version":2},"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":"2026-05-18T00:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7giDtPWZCPQFGtED5jzgCM4MitdCCss0zJ272AIXeRX39tfcJ7Rl91AWU+ofiCan8zMvXja/azDfcVGsWbpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:40:04.975333Z"},"content_sha256":"fe0361d1155489fd168aa7e0ce6c1dcb249697fccafb4d6a7870340e3849d748","schema_version":"1.0","event_id":"sha256:fe0361d1155489fd168aa7e0ce6c1dcb249697fccafb4d6a7870340e3849d748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/bundle.json","state_url":"https://pith.science/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/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":"2026-06-12T03:40:04Z","links":{"resolver":"https://pith.science/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP","bundle":"https://pith.science/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/bundle.json","state":"https://pith.science/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW5MM6ZHU4R3QN6ZSKTEL36ZDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SW5MM6ZHU4R3QN6ZSKTEL36ZDP","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":"098f1ed455b205d146616a9eebb51a8201334c2dd754d212af0340bebf64ea93","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T16:31:00Z","title_canon_sha256":"da291c46754279cc6913d7b95a63c2c31e020988416d6a72300df439020239d4"},"schema_version":"1.0","source":{"id":"1802.08625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08625","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08625v2","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08625","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"SW5MM6ZHU4R3","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SW5MM6ZHU4R3QN6Z","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SW5MM6ZH","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:fe0361d1155489fd168aa7e0ce6c1dcb249697fccafb4d6a7870340e3849d748","target":"graph","created_at":"2026-05-18T00:21:45Z","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":"In this paper we put together some tools from differential topology and analysis in order to study second order semi-linear partial differential equations on a Riemannian manifold $M$. We look for solutions that are constants along orbits of a given group action. Using some results obtained by Helgason in [J DIFFER GEOM,6(3), 411-419] we are able to write a (reduced) second order semi-linear problem on a submanifold $\\Sigma$. This submanifold is, in certain sense, transversal to the orbits of the group actions and its existence is assumed. We describe precise conditions on the Riemannian Manif","authors_text":"Edward Becerra, Juan Galvis, Nicolas Martinez Alba","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T16:31:00Z","title":"On polar actions invariant solutions of semilinear equations on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08625","kind":"arxiv","version":2},"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:dda5e71759b17c9fd8a135f1eb880fbdd30984e20fbebd001ba2f7735b9832d0","target":"record","created_at":"2026-05-18T00:21:45Z","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":"098f1ed455b205d146616a9eebb51a8201334c2dd754d212af0340bebf64ea93","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T16:31:00Z","title_canon_sha256":"da291c46754279cc6913d7b95a63c2c31e020988416d6a72300df439020239d4"},"schema_version":"1.0","source":{"id":"1802.08625","kind":"arxiv","version":2}},"canonical_sha256":"95bac67b27a723b837d992a645efd91be3f440454607b1afb9df356c1351a8f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95bac67b27a723b837d992a645efd91be3f440454607b1afb9df356c1351a8f6","first_computed_at":"2026-05-18T00:21:45.535456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:45.535456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njfwgKfeC5PA/qHHbUjIcOulTTBCp8NO/jlljcJQRWqLMFL3mBlkqXc834BIJ57l/8rWi1J8g+h1Whmj9IcRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:45.536136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dda5e71759b17c9fd8a135f1eb880fbdd30984e20fbebd001ba2f7735b9832d0","sha256:fe0361d1155489fd168aa7e0ce6c1dcb249697fccafb4d6a7870340e3849d748"],"state_sha256":"239b7818b0555ba27e88b8722f9605fe27472c722e236468d80dd17fa32d5758"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXflCFqBqmH2uZG6BK3lJJ3fdmUW8F/4EIUeubNhTOP2JAhXX0Kn3svjZaP6uM0JxTgcK6bjr2fK9PzME7dmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:40:04.979624Z","bundle_sha256":"835685b8286dc57c947a12018c89d8f2f40cc83510ff18a5a6d01e4b755f791a"}}