{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:FAH33SYVQIXC26HBMOXWZ7NN2E","short_pith_number":"pith:FAH33SYV","canonical_record":{"source":{"id":"0810.4562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-25T03:55:02Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"a6919b66bf6ec4e3f051d19158780bfb488e50fbee7a72f8b526a2c9525bddfc","abstract_canon_sha256":"153f426debf2fef21c4f3ad04a006edc1d3c36cd329222654b6b46ad80700fcc"},"schema_version":"1.0"},"canonical_sha256":"280fbdcb15822e2d78e163af6cfdadd13cb7716d9be32134a6e0b277bfce0251","source":{"kind":"arxiv","id":"0810.4562","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4562","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4562v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4562","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"FAH33SYVQIXC","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FAH33SYVQIXC26HB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FAH33SYV","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:FAH33SYVQIXC26HBMOXWZ7NN2E","target":"record","payload":{"canonical_record":{"source":{"id":"0810.4562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-25T03:55:02Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"a6919b66bf6ec4e3f051d19158780bfb488e50fbee7a72f8b526a2c9525bddfc","abstract_canon_sha256":"153f426debf2fef21c4f3ad04a006edc1d3c36cd329222654b6b46ad80700fcc"},"schema_version":"1.0"},"canonical_sha256":"280fbdcb15822e2d78e163af6cfdadd13cb7716d9be32134a6e0b277bfce0251","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.997907Z","signature_b64":"FF1B08A7Z91tjXtNb7UdgZ8LxLMs47v81sRH/HwRxIk2ooD5AmemdGsKJac0GstEKhrgLUAUcMF5Ym5Gb2GjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"280fbdcb15822e2d78e163af6cfdadd13cb7716d9be32134a6e0b277bfce0251","last_reissued_at":"2026-05-18T02:58:10.997403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.997403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.4562","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":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQzGekg27c0Ra4tJSznPD1QrKz319N+CKgK5u9EnHdUA2lAmBa72uxjmLSQkdTsE+3vpdYqVQ8AiU5HgPUF8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:09.637499Z"},"content_sha256":"708c9694e47947c6499a1bba7528c5934813794e3900f2b4b0c2fda2310b40e5","schema_version":"1.0","event_id":"sha256:708c9694e47947c6499a1bba7528c5934813794e3900f2b4b0c2fda2310b40e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:FAH33SYVQIXC26HBMOXWZ7NN2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Manifolds of semi-negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DG","authors_text":"Cristian Conde, Gabriel Larotonda","submitted_at":"2008-10-25T03:55:02Z","abstract_excerpt":"The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces. Infinite dimensional manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class on nonpositively curved spaces, and several well-known results, such as existence and uniqueness of best approximations from convex closed sets, or the Bruhat-Tits fixed point theorem, are shown to hold in this setting, without dimension restrictions. Homogeneous spaces G/K of Banach-Lie groups of semi-negative curvature are also studied, explicit estimates on the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4562","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":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nz0mn7H0cl1LvnOOXJbbtMqfUTbyKXTsI5nz+AxFx1BmaQ0gyCwYNRn27jamndy4wDkX/AZE1aINy4Iq7IdfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:09.637860Z"},"content_sha256":"afa042bfe56b89aa16d61d67a133beba8965b43e90fe5f85bf8a778408eda330","schema_version":"1.0","event_id":"sha256:afa042bfe56b89aa16d61d67a133beba8965b43e90fe5f85bf8a778408eda330"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/bundle.json","state_url":"https://pith.science/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/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":"2026-06-11T16:36:09Z","links":{"resolver":"https://pith.science/pith/FAH33SYVQIXC26HBMOXWZ7NN2E","bundle":"https://pith.science/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/bundle.json","state":"https://pith.science/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FAH33SYVQIXC26HBMOXWZ7NN2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FAH33SYVQIXC26HBMOXWZ7NN2E","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":"153f426debf2fef21c4f3ad04a006edc1d3c36cd329222654b6b46ad80700fcc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-25T03:55:02Z","title_canon_sha256":"a6919b66bf6ec4e3f051d19158780bfb488e50fbee7a72f8b526a2c9525bddfc"},"schema_version":"1.0","source":{"id":"0810.4562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4562","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4562v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4562","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"FAH33SYVQIXC","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FAH33SYVQIXC26HB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FAH33SYV","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:afa042bfe56b89aa16d61d67a133beba8965b43e90fe5f85bf8a778408eda330","target":"graph","created_at":"2026-05-18T02:58:10Z","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 notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces. Infinite dimensional manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class on nonpositively curved spaces, and several well-known results, such as existence and uniqueness of best approximations from convex closed sets, or the Bruhat-Tits fixed point theorem, are shown to hold in this setting, without dimension restrictions. Homogeneous spaces G/K of Banach-Lie groups of semi-negative curvature are also studied, explicit estimates on the ge","authors_text":"Cristian Conde, Gabriel Larotonda","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-25T03:55:02Z","title":"Manifolds of semi-negative curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4562","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":"sha256:708c9694e47947c6499a1bba7528c5934813794e3900f2b4b0c2fda2310b40e5","target":"record","created_at":"2026-05-18T02:58:10Z","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":"153f426debf2fef21c4f3ad04a006edc1d3c36cd329222654b6b46ad80700fcc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-25T03:55:02Z","title_canon_sha256":"a6919b66bf6ec4e3f051d19158780bfb488e50fbee7a72f8b526a2c9525bddfc"},"schema_version":"1.0","source":{"id":"0810.4562","kind":"arxiv","version":1}},"canonical_sha256":"280fbdcb15822e2d78e163af6cfdadd13cb7716d9be32134a6e0b277bfce0251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"280fbdcb15822e2d78e163af6cfdadd13cb7716d9be32134a6e0b277bfce0251","first_computed_at":"2026-05-18T02:58:10.997403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:10.997403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FF1B08A7Z91tjXtNb7UdgZ8LxLMs47v81sRH/HwRxIk2ooD5AmemdGsKJac0GstEKhrgLUAUcMF5Ym5Gb2GjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:10.997907Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.4562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:708c9694e47947c6499a1bba7528c5934813794e3900f2b4b0c2fda2310b40e5","sha256:afa042bfe56b89aa16d61d67a133beba8965b43e90fe5f85bf8a778408eda330"],"state_sha256":"026a9ba939db803932232fa3b1be74a246ff95441710230d1dbb4d0d8d06538d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWsJ7BNtBmVhoqmxdMoMfzPiUXhu9Tm2xu/xAVDbKlTQVSV8lStBud+XvEaFKmc2qKidgUdX5Hn7dcnHKJEDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:36:09.639916Z","bundle_sha256":"bf33f949138a3a671a0711f10da8a3c8376571d8ac6d3b6792d5eccf9074a741"}}