{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ASRIE3SKFNVXFUUCWHTOQKLP77","short_pith_number":"pith:ASRIE3SK","canonical_record":{"source":{"id":"1505.07656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-28T11:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"c6e064e4e57db1154d4a015a3f6c99616ffcade9ec387f9a67b34f71b65cbc72","abstract_canon_sha256":"4757db10a27ef5ace70d875f98fd0c1e36a40749c41a7fbc2322eaad033df647"},"schema_version":"1.0"},"canonical_sha256":"04a2826e4a2b6b72d282b1e6e8296ffff89248612f3c230f49c5f1ad4304eecd","source":{"kind":"arxiv","id":"1505.07656","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07656","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07656v2","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07656","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"ASRIE3SKFNVX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASRIE3SKFNVXFUUC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASRIE3SK","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ASRIE3SKFNVXFUUCWHTOQKLP77","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-28T11:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"c6e064e4e57db1154d4a015a3f6c99616ffcade9ec387f9a67b34f71b65cbc72","abstract_canon_sha256":"4757db10a27ef5ace70d875f98fd0c1e36a40749c41a7fbc2322eaad033df647"},"schema_version":"1.0"},"canonical_sha256":"04a2826e4a2b6b72d282b1e6e8296ffff89248612f3c230f49c5f1ad4304eecd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:41.079106Z","signature_b64":"LFTUwEKcNCsDWwlC0AslzQnujaphsfTbGJXMx2wAyQkzjh/626G8JUiykXKvGqFdLvZTVyOspPZMa0uqMOACCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04a2826e4a2b6b72d282b1e6e8296ffff89248612f3c230f49c5f1ad4304eecd","last_reissued_at":"2026-05-18T01:06:41.078484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:41.078484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07656","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":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ox2vknQMwB4v/x9AnJOkTfqDUH3Y8v70JXdMt8cmD7qv7BKOR6M+lW58aLirEaaUvg+0NJCu2Y/a2xo+/RmyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:13:52.951369Z"},"content_sha256":"1d5997711e2413842d07f6116d1883316e2377db2be3aa886cc4fe9a197ef557","schema_version":"1.0","event_id":"sha256:1d5997711e2413842d07f6116d1883316e2377db2be3aa886cc4fe9a197ef557"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ASRIE3SKFNVXFUUCWHTOQKLP77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"{\\sigma}-Porosity of the set of strict contractions in a space of non-expansive mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christian Bargetz, Michael Dymond","submitted_at":"2015-05-28T11:48:36Z","abstract_excerpt":"We consider the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of strict contractions is a {\\sigma}-porous subset."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07656","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":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9o/naEu5itBtwmsESKBVYHAcpNm9t794tSaJAWBeFhqz5IJvD8OH/HWX4BSQsck0GaEhq0+L8dVzxD6SzIXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:13:52.951770Z"},"content_sha256":"aeb3f4ac4bcd60cf3ba8f74efea062aaeccc7ac8abc5a1304b254234435893e1","schema_version":"1.0","event_id":"sha256:aeb3f4ac4bcd60cf3ba8f74efea062aaeccc7ac8abc5a1304b254234435893e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/bundle.json","state_url":"https://pith.science/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/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":"2026-05-31T18:13:52Z","links":{"resolver":"https://pith.science/pith/ASRIE3SKFNVXFUUCWHTOQKLP77","bundle":"https://pith.science/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/bundle.json","state":"https://pith.science/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASRIE3SKFNVXFUUCWHTOQKLP77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ASRIE3SKFNVXFUUCWHTOQKLP77","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":"4757db10a27ef5ace70d875f98fd0c1e36a40749c41a7fbc2322eaad033df647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-28T11:48:36Z","title_canon_sha256":"c6e064e4e57db1154d4a015a3f6c99616ffcade9ec387f9a67b34f71b65cbc72"},"schema_version":"1.0","source":{"id":"1505.07656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07656","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07656v2","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07656","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"ASRIE3SKFNVX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASRIE3SKFNVXFUUC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASRIE3SK","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:aeb3f4ac4bcd60cf3ba8f74efea062aaeccc7ac8abc5a1304b254234435893e1","target":"graph","created_at":"2026-05-18T01:06:41Z","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 the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of strict contractions is a {\\sigma}-porous subset.","authors_text":"Christian Bargetz, Michael Dymond","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-28T11:48:36Z","title":"{\\sigma}-Porosity of the set of strict contractions in a space of non-expansive mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07656","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":"sha256:1d5997711e2413842d07f6116d1883316e2377db2be3aa886cc4fe9a197ef557","target":"record","created_at":"2026-05-18T01:06:41Z","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":"4757db10a27ef5ace70d875f98fd0c1e36a40749c41a7fbc2322eaad033df647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-28T11:48:36Z","title_canon_sha256":"c6e064e4e57db1154d4a015a3f6c99616ffcade9ec387f9a67b34f71b65cbc72"},"schema_version":"1.0","source":{"id":"1505.07656","kind":"arxiv","version":2}},"canonical_sha256":"04a2826e4a2b6b72d282b1e6e8296ffff89248612f3c230f49c5f1ad4304eecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04a2826e4a2b6b72d282b1e6e8296ffff89248612f3c230f49c5f1ad4304eecd","first_computed_at":"2026-05-18T01:06:41.078484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:41.078484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFTUwEKcNCsDWwlC0AslzQnujaphsfTbGJXMx2wAyQkzjh/626G8JUiykXKvGqFdLvZTVyOspPZMa0uqMOACCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:41.079106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d5997711e2413842d07f6116d1883316e2377db2be3aa886cc4fe9a197ef557","sha256:aeb3f4ac4bcd60cf3ba8f74efea062aaeccc7ac8abc5a1304b254234435893e1"],"state_sha256":"391118bfd32ca37dea4480e9117d7cc3fab63b304cbff92feb9aeb6b6d30f9df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rPv8YRWv0ZOzOKOzOFLewbEZflxl7JhUpth4lZO3wS+hi35qlJ8J5sjL3bozvtE4dRlQmDRUglVAzkh1L6+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:13:52.954061Z","bundle_sha256":"d708a999534541fc7183c067a5216683acafaeca1705ded28334182b33f8a954"}}