{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MZFGNSZYRVSXZ7YCVVDEIPJLCH","short_pith_number":"pith:MZFGNSZY","canonical_record":{"source":{"id":"1503.00642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-02T17:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"a477c830dd3a66acf55dbdda8e0b1b548d01526d16bf279250b9aabb5b95cf1a","abstract_canon_sha256":"f332ae2f3ce28899978ad4b321f3b90d0feb632996c05a19f408f1858431f9e9"},"schema_version":"1.0"},"canonical_sha256":"664a66cb388d657cff02ad46443d2b11f0cd139d02a78cb88390aa2deca1a0aa","source":{"kind":"arxiv","id":"1503.00642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00642","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00642v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00642","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"MZFGNSZYRVSX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MZFGNSZYRVSXZ7YC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MZFGNSZY","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MZFGNSZYRVSXZ7YCVVDEIPJLCH","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-02T17:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"a477c830dd3a66acf55dbdda8e0b1b548d01526d16bf279250b9aabb5b95cf1a","abstract_canon_sha256":"f332ae2f3ce28899978ad4b321f3b90d0feb632996c05a19f408f1858431f9e9"},"schema_version":"1.0"},"canonical_sha256":"664a66cb388d657cff02ad46443d2b11f0cd139d02a78cb88390aa2deca1a0aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:49.607732Z","signature_b64":"RoMjjlgIbYd8nsDPsx5oKc6KzCcyJ7sb92PKoIyKKVv4QOucCfMFpfMywNo0iX++TRdfygobRXmBzlXjS1rwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"664a66cb388d657cff02ad46443d2b11f0cd139d02a78cb88390aa2deca1a0aa","last_reissued_at":"2026-05-18T02:25:49.607347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:49.607347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00642","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":"2026-05-18T02:25:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRAjgHQ3rlOtEUpXLGlutDCE3PUfVbQXPxqN9WEmpmAMhamn4GVnSJfNUZnIFj7H2KzssGA+bL5cdHnVYOf3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:42:08.627775Z"},"content_sha256":"f5b3b5a2d25a214937a84a6489e493ce31ad36fcac8cc849aa780fd4224b670b","schema_version":"1.0","event_id":"sha256:f5b3b5a2d25a214937a84a6489e493ce31ad36fcac8cc849aa780fd4224b670b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MZFGNSZYRVSXZ7YCVVDEIPJLCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A short proof of the existence of the solution to elliptic boundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2015-03-02T17:59:15Z","abstract_excerpt":"There are several methods for proving the existence of the solution to the elliptic boundary problem $Lu=f \\text{\\,\\, in\\,\\,} D,\\quad u|_S=0,\\quad (*)$. Here $L$ is an elliptic operator of second order, $f$ is a given function, and uniqueness of the solution to problem (*) is assumed. The known methods for proving the existence of the solution to (*) include variational methods, integral equation methods, method of upper and lower solutions. In this paper a method based on functional analysis is proposed. This method is conceptually simple and technically is easy. It requires some known a prio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00642","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":"2026-05-18T02:25:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWRcX57y1x2wjYBlLIov34IKR2tjE2eIrO1e9pKzhWm5QLrcWHDmBGSu9zgwG8QLioNIQNLzpUJ4pA/8O7tVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:42:08.628402Z"},"content_sha256":"edfb471de988412655b706acc9c96141580a952fb2eb7ee28586cb4d5b361169","schema_version":"1.0","event_id":"sha256:edfb471de988412655b706acc9c96141580a952fb2eb7ee28586cb4d5b361169"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/bundle.json","state_url":"https://pith.science/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/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":"2026-05-26T01:42:08Z","links":{"resolver":"https://pith.science/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH","bundle":"https://pith.science/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/bundle.json","state":"https://pith.science/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZFGNSZYRVSXZ7YCVVDEIPJLCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MZFGNSZYRVSXZ7YCVVDEIPJLCH","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":"f332ae2f3ce28899978ad4b321f3b90d0feb632996c05a19f408f1858431f9e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-02T17:59:15Z","title_canon_sha256":"a477c830dd3a66acf55dbdda8e0b1b548d01526d16bf279250b9aabb5b95cf1a"},"schema_version":"1.0","source":{"id":"1503.00642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00642","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00642v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00642","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"MZFGNSZYRVSX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MZFGNSZYRVSXZ7YC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MZFGNSZY","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:edfb471de988412655b706acc9c96141580a952fb2eb7ee28586cb4d5b361169","target":"graph","created_at":"2026-05-18T02:25:49Z","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":"There are several methods for proving the existence of the solution to the elliptic boundary problem $Lu=f \\text{\\,\\, in\\,\\,} D,\\quad u|_S=0,\\quad (*)$. Here $L$ is an elliptic operator of second order, $f$ is a given function, and uniqueness of the solution to problem (*) is assumed. The known methods for proving the existence of the solution to (*) include variational methods, integral equation methods, method of upper and lower solutions. In this paper a method based on functional analysis is proposed. This method is conceptually simple and technically is easy. It requires some known a prio","authors_text":"A.G.Ramm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-02T17:59:15Z","title":"A short proof of the existence of the solution to elliptic boundary problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00642","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:f5b3b5a2d25a214937a84a6489e493ce31ad36fcac8cc849aa780fd4224b670b","target":"record","created_at":"2026-05-18T02:25:49Z","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":"f332ae2f3ce28899978ad4b321f3b90d0feb632996c05a19f408f1858431f9e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-02T17:59:15Z","title_canon_sha256":"a477c830dd3a66acf55dbdda8e0b1b548d01526d16bf279250b9aabb5b95cf1a"},"schema_version":"1.0","source":{"id":"1503.00642","kind":"arxiv","version":1}},"canonical_sha256":"664a66cb388d657cff02ad46443d2b11f0cd139d02a78cb88390aa2deca1a0aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"664a66cb388d657cff02ad46443d2b11f0cd139d02a78cb88390aa2deca1a0aa","first_computed_at":"2026-05-18T02:25:49.607347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:49.607347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RoMjjlgIbYd8nsDPsx5oKc6KzCcyJ7sb92PKoIyKKVv4QOucCfMFpfMywNo0iX++TRdfygobRXmBzlXjS1rwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:49.607732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5b3b5a2d25a214937a84a6489e493ce31ad36fcac8cc849aa780fd4224b670b","sha256:edfb471de988412655b706acc9c96141580a952fb2eb7ee28586cb4d5b361169"],"state_sha256":"05e2e8ff3dfbaf36bffd74b0ba7f309a3ff46376a6e7e71d2339aaf9f7543072"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9kXg/acTBavVHM2vwe/dj37pLZ8wrEGJDsF28z7W+PU1uf7tf6haAG/JHu8UXmHWqdwa2WpIUI7WY6v+jDl0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:42:08.631535Z","bundle_sha256":"3107ed74ef32a100f35fc110b53a389e51a39ff64ab01b325e4004bee19308da"}}