{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XF4EOMWYDMXKF6QEGPIJ7AC4N6","short_pith_number":"pith:XF4EOMWY","canonical_record":{"source":{"id":"1603.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-07T07:00:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"4660dc1b0edac33f8994dca0a985e920d10266e6953d991d89c151c87e71c9fd","abstract_canon_sha256":"c1a1f8b8847437d48cb8ddc410d939a892c1c31738e9697f0165670e6d4b99d7"},"schema_version":"1.0"},"canonical_sha256":"b9784732d81b2ea2fa0433d09f805c6fb04ba4c49885dd3e8e3b8be909c11670","source":{"kind":"arxiv","id":"1603.01836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01836","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01836v1","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01836","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"XF4EOMWYDMXK","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XF4EOMWYDMXKF6QE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XF4EOMWY","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XF4EOMWYDMXKF6QEGPIJ7AC4N6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-07T07:00:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"4660dc1b0edac33f8994dca0a985e920d10266e6953d991d89c151c87e71c9fd","abstract_canon_sha256":"c1a1f8b8847437d48cb8ddc410d939a892c1c31738e9697f0165670e6d4b99d7"},"schema_version":"1.0"},"canonical_sha256":"b9784732d81b2ea2fa0433d09f805c6fb04ba4c49885dd3e8e3b8be909c11670","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:19.404828Z","signature_b64":"HXTC0CrpKNUuRySOzcZAcVq0M1lgrz3gCUHJjVIeVe4QHGNe3CqPKG7GYK7EpfZz14PLira0+9/4L09R0PkyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9784732d81b2ea2fa0433d09f805c6fb04ba4c49885dd3e8e3b8be909c11670","last_reissued_at":"2026-05-18T00:11:19.404296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:19.404296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01836","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":"2026-05-18T00:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5yV6Y3OF+BP3PvDNvdfheZHjZYtSqFnw/mC8Kv5qFYyXXof0rlIKTi3RmejR0aWD2GHQWMYCSkbhkjt0+oXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:13:43.931002Z"},"content_sha256":"af22772c7f2e7690257eb39378d43b9fa44d63973bb4b6ad8cfe7bb81f7fdbd6","schema_version":"1.0","event_id":"sha256:af22772c7f2e7690257eb39378d43b9fa44d63973bb4b6ad8cfe7bb81f7fdbd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XF4EOMWYDMXKF6QEGPIJ7AC4N6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz retractions in Hadamard spaces via gradient flow semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Leonid V. Kovalev, Miroslav Bacak","submitted_at":"2016-03-07T07:00:18Z","abstract_excerpt":"Let $X(n),$ for $n\\in\\mathbb{N},$ be the set of all subsets of a metric space $(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped with the Hausdorff metric is called a finite subset space. In this paper we are concerned with the existence of Lipschitz retractions $r: X(n)\\to X(n-1)$ for $n\\ge2.$ It is known that such retractions do not exist if $X$ is the one-dimensional sphere. On the other hand L. Kovalev has recently established their existence in case $X$ is a Hilbert space and he also posed a question as to whether or not such Lipschitz retractions exist for $X$ being a Hadamard s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01836","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":"2026-05-18T00:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Egi/jXpq/m7X1+VTbBXmroy6uq8Rr45J+jO1njjuXPV33OxwrgYN+4xA9HpbC+cAq05D9uvHmTwIIxF1+B5ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:13:43.931672Z"},"content_sha256":"74a9c15ce9cc73956a921e5a44b494b07ca3d126fb19d4c7c675ca7565279b0e","schema_version":"1.0","event_id":"sha256:74a9c15ce9cc73956a921e5a44b494b07ca3d126fb19d4c7c675ca7565279b0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/bundle.json","state_url":"https://pith.science/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/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":"2026-06-09T06:13:43Z","links":{"resolver":"https://pith.science/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6","bundle":"https://pith.science/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/bundle.json","state":"https://pith.science/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XF4EOMWYDMXKF6QEGPIJ7AC4N6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XF4EOMWYDMXKF6QEGPIJ7AC4N6","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":"c1a1f8b8847437d48cb8ddc410d939a892c1c31738e9697f0165670e6d4b99d7","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-07T07:00:18Z","title_canon_sha256":"4660dc1b0edac33f8994dca0a985e920d10266e6953d991d89c151c87e71c9fd"},"schema_version":"1.0","source":{"id":"1603.01836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01836","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01836v1","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01836","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"XF4EOMWYDMXK","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XF4EOMWYDMXKF6QE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XF4EOMWY","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:74a9c15ce9cc73956a921e5a44b494b07ca3d126fb19d4c7c675ca7565279b0e","target":"graph","created_at":"2026-05-18T00:11:19Z","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 $X(n),$ for $n\\in\\mathbb{N},$ be the set of all subsets of a metric space $(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped with the Hausdorff metric is called a finite subset space. In this paper we are concerned with the existence of Lipschitz retractions $r: X(n)\\to X(n-1)$ for $n\\ge2.$ It is known that such retractions do not exist if $X$ is the one-dimensional sphere. On the other hand L. Kovalev has recently established their existence in case $X$ is a Hilbert space and he also posed a question as to whether or not such Lipschitz retractions exist for $X$ being a Hadamard s","authors_text":"Leonid V. Kovalev, Miroslav Bacak","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-07T07:00:18Z","title":"Lipschitz retractions in Hadamard spaces via gradient flow semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01836","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:af22772c7f2e7690257eb39378d43b9fa44d63973bb4b6ad8cfe7bb81f7fdbd6","target":"record","created_at":"2026-05-18T00:11:19Z","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":"c1a1f8b8847437d48cb8ddc410d939a892c1c31738e9697f0165670e6d4b99d7","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-07T07:00:18Z","title_canon_sha256":"4660dc1b0edac33f8994dca0a985e920d10266e6953d991d89c151c87e71c9fd"},"schema_version":"1.0","source":{"id":"1603.01836","kind":"arxiv","version":1}},"canonical_sha256":"b9784732d81b2ea2fa0433d09f805c6fb04ba4c49885dd3e8e3b8be909c11670","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9784732d81b2ea2fa0433d09f805c6fb04ba4c49885dd3e8e3b8be909c11670","first_computed_at":"2026-05-18T00:11:19.404296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:19.404296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HXTC0CrpKNUuRySOzcZAcVq0M1lgrz3gCUHJjVIeVe4QHGNe3CqPKG7GYK7EpfZz14PLira0+9/4L09R0PkyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:19.404828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af22772c7f2e7690257eb39378d43b9fa44d63973bb4b6ad8cfe7bb81f7fdbd6","sha256:74a9c15ce9cc73956a921e5a44b494b07ca3d126fb19d4c7c675ca7565279b0e"],"state_sha256":"e52bf24126957356071aa627458ad9262aea0da0b945abe0e42b794768ca3995"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSIjmW+pdKg5rubuFu4lfiOuwR9QZ6PqERxyhg5Y+6AQopCXCfVaOft7HOpPT6XECehG2VbAdGv3XiKA2gu9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:13:43.935536Z","bundle_sha256":"481ee83c535aa8485a31ca8e6bdf91fcc86d096294233934ec678f6ab0096c5e"}}