{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:K32OSRUQMJB3IIPB7VHKCGEUM6","short_pith_number":"pith:K32OSRUQ","canonical_record":{"source":{"id":"1211.0414","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-02T10:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"975d098b769c15d4609738d9b59682d0af6942396acae5adccf98f41d6766c09","abstract_canon_sha256":"925728474b3df8a28a1a12c58f2d8ff9f68ff23da699619a59c561e821e1b1dd"},"schema_version":"1.0"},"canonical_sha256":"56f4e946906243b421e1fd4ea1189467a7039b5accceae2ab3fc8dc66f1f74bd","source":{"kind":"arxiv","id":"1211.0414","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0414","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0414v3","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0414","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"K32OSRUQMJB3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K32OSRUQMJB3IIPB","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K32OSRUQ","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:K32OSRUQMJB3IIPB7VHKCGEUM6","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0414","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-02T10:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"975d098b769c15d4609738d9b59682d0af6942396acae5adccf98f41d6766c09","abstract_canon_sha256":"925728474b3df8a28a1a12c58f2d8ff9f68ff23da699619a59c561e821e1b1dd"},"schema_version":"1.0"},"canonical_sha256":"56f4e946906243b421e1fd4ea1189467a7039b5accceae2ab3fc8dc66f1f74bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:38.091285Z","signature_b64":"ZDUG0XRQrw827moJ6G+p2QDhBYgEsB2yvr/c/mMaZtZvmLbJa9SMBOEee8QGPK46lCT2oboPQZokN+RG0dDUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56f4e946906243b421e1fd4ea1189467a7039b5accceae2ab3fc8dc66f1f74bd","last_reissued_at":"2026-05-18T03:35:38.090381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:38.090381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0414","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zFN+u7jkH+E+a+KrpfXsQRNGV9tqUD2QRhPMhBoASrvz1v/JMUN3vfJRKvQGPlB4efeDpuAZCi+hH8+Rg6rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:04:04.825371Z"},"content_sha256":"a0a5555b7026df5eb42ab3343da848674a2bb17980acb8eaf5e8c0611174eda7","schema_version":"1.0","event_id":"sha256:a0a5555b7026df5eb42ab3343da848674a2bb17980acb8eaf5e8c0611174eda7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:K32OSRUQMJB3IIPB7VHKCGEUM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of nonlinear semigroups under nonpositive curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Miroslav Bacak","submitted_at":"2012-11-02T10:51:46Z","abstract_excerpt":"The present paper is devoted to semigroups of nonexpansive mappings on metric spaces of nonpositive curvature. We show that the Mosco convergence of a sequence of convex lsc functions implies convergence of the corresponding resolvents and convergence of the gradient flow semigroups. This extends the classical results of Attouch, Brezis and Pazy into spaces with no linear structure. The same method can be further used to show the convergence of semigroups on a sequence of spaces, which solves a problem of [Kuwae and Shioya, Trans. Amer. Math. Soc., 2008]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0414","kind":"arxiv","version":3},"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":"2026-05-18T03:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8u+NHqkVTlItEjuleFLTIXmRIjwnnL+zl/2sF/pMdi8viyYmhdlTdQDmeakmDwvI6ABEnLHYxkjNEUFgMakiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:04:04.825737Z"},"content_sha256":"8d9514b39948c071671c7ac540b37980b659e03c438019ff02a71af9b838b8f3","schema_version":"1.0","event_id":"sha256:8d9514b39948c071671c7ac540b37980b659e03c438019ff02a71af9b838b8f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/bundle.json","state_url":"https://pith.science/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/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":"2026-06-24T04:04:04Z","links":{"resolver":"https://pith.science/pith/K32OSRUQMJB3IIPB7VHKCGEUM6","bundle":"https://pith.science/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/bundle.json","state":"https://pith.science/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K32OSRUQMJB3IIPB7VHKCGEUM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K32OSRUQMJB3IIPB7VHKCGEUM6","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":"925728474b3df8a28a1a12c58f2d8ff9f68ff23da699619a59c561e821e1b1dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-02T10:51:46Z","title_canon_sha256":"975d098b769c15d4609738d9b59682d0af6942396acae5adccf98f41d6766c09"},"schema_version":"1.0","source":{"id":"1211.0414","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0414","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0414v3","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0414","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"K32OSRUQMJB3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K32OSRUQMJB3IIPB","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K32OSRUQ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:8d9514b39948c071671c7ac540b37980b659e03c438019ff02a71af9b838b8f3","target":"graph","created_at":"2026-05-18T03:35:38Z","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":"The present paper is devoted to semigroups of nonexpansive mappings on metric spaces of nonpositive curvature. We show that the Mosco convergence of a sequence of convex lsc functions implies convergence of the corresponding resolvents and convergence of the gradient flow semigroups. This extends the classical results of Attouch, Brezis and Pazy into spaces with no linear structure. The same method can be further used to show the convergence of semigroups on a sequence of spaces, which solves a problem of [Kuwae and Shioya, Trans. Amer. Math. Soc., 2008].","authors_text":"Miroslav Bacak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-02T10:51:46Z","title":"Convergence of nonlinear semigroups under nonpositive curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0414","kind":"arxiv","version":3},"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:a0a5555b7026df5eb42ab3343da848674a2bb17980acb8eaf5e8c0611174eda7","target":"record","created_at":"2026-05-18T03:35:38Z","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":"925728474b3df8a28a1a12c58f2d8ff9f68ff23da699619a59c561e821e1b1dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-02T10:51:46Z","title_canon_sha256":"975d098b769c15d4609738d9b59682d0af6942396acae5adccf98f41d6766c09"},"schema_version":"1.0","source":{"id":"1211.0414","kind":"arxiv","version":3}},"canonical_sha256":"56f4e946906243b421e1fd4ea1189467a7039b5accceae2ab3fc8dc66f1f74bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56f4e946906243b421e1fd4ea1189467a7039b5accceae2ab3fc8dc66f1f74bd","first_computed_at":"2026-05-18T03:35:38.090381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:38.090381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZDUG0XRQrw827moJ6G+p2QDhBYgEsB2yvr/c/mMaZtZvmLbJa9SMBOEee8QGPK46lCT2oboPQZokN+RG0dDUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:38.091285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0414","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0a5555b7026df5eb42ab3343da848674a2bb17980acb8eaf5e8c0611174eda7","sha256:8d9514b39948c071671c7ac540b37980b659e03c438019ff02a71af9b838b8f3"],"state_sha256":"4f552ed5cde7bed10c8b6a3afe05c7410465609312f05af7477b5fcef901adff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZ2Y1yokxVQ8OlbFwGd8dCuD7imq3zhbVTj/IHGq+zb0W9Xc9jeA458xZMxD/LBC4iB+LZh4jE5hU0HvhaYWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:04:04.827625Z","bundle_sha256":"ced2e258805b29fd9c8c246e83f5a926d67aa632975e703d087bcd88f947b514"}}