{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EMAVKGBAITWBGZ6MJS2P6TPHSH","short_pith_number":"pith:EMAVKGBA","canonical_record":{"source":{"id":"1805.12193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-30T19:35:29Z","cross_cats_sorted":[],"title_canon_sha256":"5ea7af17b96e61922e4c5c247516692798ea3bc8ec6e86612f4483c7991ff0a4","abstract_canon_sha256":"76afd1c6fec88e812dc1636ddd6cb106b9dd5930d5e998b7a774cb6d4d1c0a60"},"schema_version":"1.0"},"canonical_sha256":"230155182044ec1367cc4cb4ff4de791c5e54a8e74bca6fb8aadb7589a68083e","source":{"kind":"arxiv","id":"1805.12193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12193","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12193v1","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12193","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"pith_short_12","alias_value":"EMAVKGBAITWB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EMAVKGBAITWBGZ6M","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EMAVKGBA","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EMAVKGBAITWBGZ6MJS2P6TPHSH","target":"record","payload":{"canonical_record":{"source":{"id":"1805.12193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-30T19:35:29Z","cross_cats_sorted":[],"title_canon_sha256":"5ea7af17b96e61922e4c5c247516692798ea3bc8ec6e86612f4483c7991ff0a4","abstract_canon_sha256":"76afd1c6fec88e812dc1636ddd6cb106b9dd5930d5e998b7a774cb6d4d1c0a60"},"schema_version":"1.0"},"canonical_sha256":"230155182044ec1367cc4cb4ff4de791c5e54a8e74bca6fb8aadb7589a68083e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:31.197141Z","signature_b64":"v3EX95u/KwQq6XsmZE/n/gnVvCMNVNCoXu/EdazDqjcsZYYEZXA3443XpeEfmsxbIWcADa2DXW+bKrbaWpZ8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230155182044ec1367cc4cb4ff4de791c5e54a8e74bca6fb8aadb7589a68083e","last_reissued_at":"2026-05-18T00:14:31.196415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:31.196415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.12193","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":"2026-05-18T00:14:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LF1ZLspUMBxtsHBw8GH1TpKQIev/cPGbItLBQs18MIJlGs7iiTeP4xW6myr30DvNn08wbGDr5Qzvgp0GgbGFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:34:10.908036Z"},"content_sha256":"6d8998027943a14f7e8877acd3ec00ee33d52349c537fc003646e1e8057da026","schema_version":"1.0","event_id":"sha256:6d8998027943a14f7e8877acd3ec00ee33d52349c537fc003646e1e8057da026"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EMAVKGBAITWBGZ6MJS2P6TPHSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal element theorems revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas H Hamel, Constantin Zalinescu","submitted_at":"2018-05-30T19:35:29Z","abstract_excerpt":"Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are discussed and clarified, i.e., assumptions to the metric structure of the underlying space and boundedness assumptions. New results involving set-valued maps and the increasingly popular set relations are obtained along the way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12193","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":"2026-05-18T00:14:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7hr8dc07JqioGjoIMWl8FgRFnzJXqzeE2vb30+hXidobIMkdvLrxQwuCCH114r3G3nyGKaT3marWj7Bb+RsQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:34:10.908766Z"},"content_sha256":"4e2663422100a1059f0b09350c76f8bc8feee2f20e32198d1a46834e1fea46fa","schema_version":"1.0","event_id":"sha256:4e2663422100a1059f0b09350c76f8bc8feee2f20e32198d1a46834e1fea46fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/bundle.json","state_url":"https://pith.science/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/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":"2026-06-10T04:34:10Z","links":{"resolver":"https://pith.science/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH","bundle":"https://pith.science/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/bundle.json","state":"https://pith.science/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMAVKGBAITWBGZ6MJS2P6TPHSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EMAVKGBAITWBGZ6MJS2P6TPHSH","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":"76afd1c6fec88e812dc1636ddd6cb106b9dd5930d5e998b7a774cb6d4d1c0a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-30T19:35:29Z","title_canon_sha256":"5ea7af17b96e61922e4c5c247516692798ea3bc8ec6e86612f4483c7991ff0a4"},"schema_version":"1.0","source":{"id":"1805.12193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12193","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12193v1","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12193","created_at":"2026-05-18T00:14:31Z"},{"alias_kind":"pith_short_12","alias_value":"EMAVKGBAITWB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EMAVKGBAITWBGZ6M","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EMAVKGBA","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:4e2663422100a1059f0b09350c76f8bc8feee2f20e32198d1a46834e1fea46fa","target":"graph","created_at":"2026-05-18T00:14:31Z","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":"Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are discussed and clarified, i.e., assumptions to the metric structure of the underlying space and boundedness assumptions. New results involving set-valued maps and the increasingly popular set relations are obtained along the way.","authors_text":"Andreas H Hamel, Constantin Zalinescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-30T19:35:29Z","title":"Minimal element theorems revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12193","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":"sha256:6d8998027943a14f7e8877acd3ec00ee33d52349c537fc003646e1e8057da026","target":"record","created_at":"2026-05-18T00:14:31Z","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":"76afd1c6fec88e812dc1636ddd6cb106b9dd5930d5e998b7a774cb6d4d1c0a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-30T19:35:29Z","title_canon_sha256":"5ea7af17b96e61922e4c5c247516692798ea3bc8ec6e86612f4483c7991ff0a4"},"schema_version":"1.0","source":{"id":"1805.12193","kind":"arxiv","version":1}},"canonical_sha256":"230155182044ec1367cc4cb4ff4de791c5e54a8e74bca6fb8aadb7589a68083e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"230155182044ec1367cc4cb4ff4de791c5e54a8e74bca6fb8aadb7589a68083e","first_computed_at":"2026-05-18T00:14:31.196415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:31.196415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v3EX95u/KwQq6XsmZE/n/gnVvCMNVNCoXu/EdazDqjcsZYYEZXA3443XpeEfmsxbIWcADa2DXW+bKrbaWpZ8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:31.197141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.12193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d8998027943a14f7e8877acd3ec00ee33d52349c537fc003646e1e8057da026","sha256:4e2663422100a1059f0b09350c76f8bc8feee2f20e32198d1a46834e1fea46fa"],"state_sha256":"1fbc88f889ad7db26d15383025b6cda0c5c4693924e05d8d00785b0a87c9ee14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxa0somxYB1pDgFWcmht5TzeG+XErj1R4o/H/vBeFlLURBr+ajfiy0+UeqBiEN+ma4I/lOC8Br+01nn9OdbgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T04:34:10.912773Z","bundle_sha256":"ebf7c28995d3ae3107bcef61a526c615bd25bf71f2536a88d0f2b8b1bd584f18"}}