{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:I7TR2355DRAZDTCPV5RWVBWFC6","short_pith_number":"pith:I7TR2355","canonical_record":{"source":{"id":"1206.3544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-15T18:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"9a9389b98d9b0e5fc66b7c61e9f8d4ec5c46b6bcc8625555082006779ba1ac07","abstract_canon_sha256":"745938e98c071d18e4953726ac121d05031def02713fba51dbf05df0ae85f9c0"},"schema_version":"1.0"},"canonical_sha256":"47e71d6fbd1c4191cc4faf636a86c517bb55d16f12b7bde74cb276ae68a790f8","source":{"kind":"arxiv","id":"1206.3544","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3544","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3544v1","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3544","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"I7TR2355DRAZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I7TR2355DRAZDTCP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I7TR2355","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:I7TR2355DRAZDTCPV5RWVBWFC6","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-15T18:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"9a9389b98d9b0e5fc66b7c61e9f8d4ec5c46b6bcc8625555082006779ba1ac07","abstract_canon_sha256":"745938e98c071d18e4953726ac121d05031def02713fba51dbf05df0ae85f9c0"},"schema_version":"1.0"},"canonical_sha256":"47e71d6fbd1c4191cc4faf636a86c517bb55d16f12b7bde74cb276ae68a790f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:31.751262Z","signature_b64":"B3d2pAuMI2G8nD3OJe6xpWdSaLNim/pXg6oS78Dt0FUw7V0ZBjoa9EmiNvqzAkiEW0Pedfx5d9N3YRLfRMQvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e71d6fbd1c4191cc4faf636a86c517bb55d16f12b7bde74cb276ae68a790f8","last_reissued_at":"2026-05-18T03:32:31.750380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:31.750380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3544","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":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vr8LBGsqz+MI3IfGKd6Dj4MKvbLmPHfgHu8cwJ14fhXEJO9Uio5La2tSmkuQmdjiiwzrNY/cvpTktn4/dgyoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:00:30.251841Z"},"content_sha256":"de1ff15ced8f8f0bb4a3c338249ddf2edaf7c1f1b5a498041ea55e3d6f937aad","schema_version":"1.0","event_id":"sha256:de1ff15ced8f8f0bb4a3c338249ddf2edaf7c1f1b5a498041ea55e3d6f937aad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:I7TR2355DRAZDTCPV5RWVBWFC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal approximate fixed point results in locally convex spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cleon S. Barroso, Michel P. Rebou\\c{c}as, Ond\\v{r}ej F. K. Kalenda","submitted_at":"2012-06-15T18:58:58Z","abstract_excerpt":"Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\\colon C\\to\\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate fixed point net. Next, it is shown that if $C$ is bounded but not totally bounded, then there is a uniformly continuous map $f\\colon C\\to C$ without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3544","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":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzGWSCkqIpmuJinqJ7a7qvNAYKwdUlfOO0PlxMbbbqsNHQi6fHZMX97V1bQxW+A1EJD4rSwFWjgOmHDBrdsCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:00:30.252192Z"},"content_sha256":"617a5e3678fe14d07cba58077036aa599eae238d92c971a10571d1347b8c7c2d","schema_version":"1.0","event_id":"sha256:617a5e3678fe14d07cba58077036aa599eae238d92c971a10571d1347b8c7c2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7TR2355DRAZDTCPV5RWVBWFC6/bundle.json","state_url":"https://pith.science/pith/I7TR2355DRAZDTCPV5RWVBWFC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7TR2355DRAZDTCPV5RWVBWFC6/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":"2026-06-23T05:00:30Z","links":{"resolver":"https://pith.science/pith/I7TR2355DRAZDTCPV5RWVBWFC6","bundle":"https://pith.science/pith/I7TR2355DRAZDTCPV5RWVBWFC6/bundle.json","state":"https://pith.science/pith/I7TR2355DRAZDTCPV5RWVBWFC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7TR2355DRAZDTCPV5RWVBWFC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I7TR2355DRAZDTCPV5RWVBWFC6","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":"745938e98c071d18e4953726ac121d05031def02713fba51dbf05df0ae85f9c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-15T18:58:58Z","title_canon_sha256":"9a9389b98d9b0e5fc66b7c61e9f8d4ec5c46b6bcc8625555082006779ba1ac07"},"schema_version":"1.0","source":{"id":"1206.3544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3544","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3544v1","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3544","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"I7TR2355DRAZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I7TR2355DRAZDTCP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I7TR2355","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:617a5e3678fe14d07cba58077036aa599eae238d92c971a10571d1347b8c7c2d","target":"graph","created_at":"2026-05-18T03:32:31Z","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":"Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\\colon C\\to\\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate fixed point net. Next, it is shown that if $C$ is bounded but not totally bounded, then there is a uniformly continuous map $f\\colon C\\to C$ without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (no","authors_text":"Cleon S. Barroso, Michel P. Rebou\\c{c}as, Ond\\v{r}ej F. K. Kalenda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-15T18:58:58Z","title":"Optimal approximate fixed point results in locally convex spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3544","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:de1ff15ced8f8f0bb4a3c338249ddf2edaf7c1f1b5a498041ea55e3d6f937aad","target":"record","created_at":"2026-05-18T03:32:31Z","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":"745938e98c071d18e4953726ac121d05031def02713fba51dbf05df0ae85f9c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-15T18:58:58Z","title_canon_sha256":"9a9389b98d9b0e5fc66b7c61e9f8d4ec5c46b6bcc8625555082006779ba1ac07"},"schema_version":"1.0","source":{"id":"1206.3544","kind":"arxiv","version":1}},"canonical_sha256":"47e71d6fbd1c4191cc4faf636a86c517bb55d16f12b7bde74cb276ae68a790f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e71d6fbd1c4191cc4faf636a86c517bb55d16f12b7bde74cb276ae68a790f8","first_computed_at":"2026-05-18T03:32:31.750380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:31.750380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3d2pAuMI2G8nD3OJe6xpWdSaLNim/pXg6oS78Dt0FUw7V0ZBjoa9EmiNvqzAkiEW0Pedfx5d9N3YRLfRMQvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:31.751262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de1ff15ced8f8f0bb4a3c338249ddf2edaf7c1f1b5a498041ea55e3d6f937aad","sha256:617a5e3678fe14d07cba58077036aa599eae238d92c971a10571d1347b8c7c2d"],"state_sha256":"203ae0c89d1a4f12e8150f40a0d1bbf6ab4c9852f20dfe361472f06c202d435c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtwTULEL+xHv24/4R/T05gmz/8p826YQN02NW9DfE7cTmtF0EpRT8lE46I5fu6sJTuDqkG28mIAoVsoKfbIJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:00:30.254133Z","bundle_sha256":"7b6ff7e723c88ca5c3c03b9110660e545e9ac4e09b3545511dbca819953d3bc4"}}