{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OJVZGCFLRY22AN2SWVGNQ2GCPB","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":"51f26ed9f9ff67c88c5494f239b91e43eebeb92bd0b8dfcff053a5b6ab325a19","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-12-07T07:01:08Z","title_canon_sha256":"5b05a0abd5a6a5324a7588d414d25c022439da69795751726e9cb47390b0f712"},"schema_version":"1.0","source":{"id":"0912.1172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1172","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1172v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1172","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"OJVZGCFLRY22","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OJVZGCFLRY22AN2S","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OJVZGCFL","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:972c428cdedf473a55cea1588179fe6241180f243704472a9227c7fd88945bd6","target":"graph","created_at":"2026-05-18T04:40:54Z","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":"For a k-flat F inside a locally compact CAT(0)-space X, we identify various conditions that ensure that F bounds a (k+1)-dimensional half flat in X. Our conditions are formulated in terms of the ultralimit of X. As applications, we obtain (1) constraints on the behavior of quasi-isometries between tocally compact CAT(0)-spaces, (2) constraints on the possible non-positively curved Riemannian metrics supported by certain manifolds, and (3) a correspondence between metric splittings of a complete, simply connected, non-positively curved Riemannian manifold and the metric splittings of its asympt","authors_text":"J.-F. Lafont, S. Francaviglia","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-12-07T07:01:08Z","title":"Large scale detection of half-flats in CAT(0)-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1172","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":"sha256:6845658f5020e0cd0cdc9b4df40a49c4307041f271063889f0dbad31f8070ea1","target":"record","created_at":"2026-05-18T04:40:54Z","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":"51f26ed9f9ff67c88c5494f239b91e43eebeb92bd0b8dfcff053a5b6ab325a19","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-12-07T07:01:08Z","title_canon_sha256":"5b05a0abd5a6a5324a7588d414d25c022439da69795751726e9cb47390b0f712"},"schema_version":"1.0","source":{"id":"0912.1172","kind":"arxiv","version":1}},"canonical_sha256":"726b9308ab8e35a03752b54cd868c2784c518cb3bc2b2ba53c6f56e6ecf25ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"726b9308ab8e35a03752b54cd868c2784c518cb3bc2b2ba53c6f56e6ecf25ed4","first_computed_at":"2026-05-18T04:40:54.615027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.615027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OC9CZMOesvqEfS5rJJQLiIGgXVeoujZGcOjs07UrwyN9Q/UFJdTvV+6LQaxlm3006ar84LvQ/ng3m6VKGXtLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.615471Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6845658f5020e0cd0cdc9b4df40a49c4307041f271063889f0dbad31f8070ea1","sha256:972c428cdedf473a55cea1588179fe6241180f243704472a9227c7fd88945bd6"],"state_sha256":"71b9cb7c970161e158e0846079bb9b67b4c3dd1dceae729ec1a4aa91eb9c9263"}