{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:US2RPEUBRVFRZVS7BPVJEON55H","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":"ddb576255e1836e00d616b3db9793c986017094110e11413803779548ee2ee18","cross_cats_sorted":[],"license":"","primary_cat":"math.MG","submitted_at":"2004-05-07T16:40:21Z","title_canon_sha256":"b80fb08bf59b3b8d16e933963bcd5f04b66ee6e9cd59ce6a0f1cd1a2edda91b5"},"schema_version":"1.0","source":{"id":"math/0405130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405130","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405130v1","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405130","created_at":"2026-05-18T04:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"US2RPEUBRVFR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"US2RPEUBRVFRZVS7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"US2RPEUB","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6bc14b35e90976e3cea389695169f8c4c207ec923a7f003e5385406e0b215a76","target":"graph","created_at":"2026-05-18T04:39:18Z","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":"There are two natural metrics defined on an arbitrary convex cone: Thompson's part metric and Hilbert's projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.","authors_text":"Cormac Walsh, Roger D. Nussbaum","cross_cats":[],"headline":"","license":"","primary_cat":"math.MG","submitted_at":"2004-05-07T16:40:21Z","title":"A Metric Inequality for the Thompson and Hilbert Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405130","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:fe60a3014abbfe2712354c3a70f7f8ce8d0067d3a43a07388b75b2e455e2af60","target":"record","created_at":"2026-05-18T04:39:18Z","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":"ddb576255e1836e00d616b3db9793c986017094110e11413803779548ee2ee18","cross_cats_sorted":[],"license":"","primary_cat":"math.MG","submitted_at":"2004-05-07T16:40:21Z","title_canon_sha256":"b80fb08bf59b3b8d16e933963bcd5f04b66ee6e9cd59ce6a0f1cd1a2edda91b5"},"schema_version":"1.0","source":{"id":"math/0405130","kind":"arxiv","version":1}},"canonical_sha256":"a4b51792818d4b1cd65f0bea9239bde9fd2ffbf57260ed923a3e8ab7178b91c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4b51792818d4b1cd65f0bea9239bde9fd2ffbf57260ed923a3e8ab7178b91c3","first_computed_at":"2026-05-18T04:39:18.624951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:18.624951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P4cfDEpIBsmOeqfebSCLBdKS8A7ceZaJMf2oNNoCTA4VGxTc6Bvw9iOe9Ly7WB/h+PQdIeaYBD6VFFvfqlyiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:18.625690Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe60a3014abbfe2712354c3a70f7f8ce8d0067d3a43a07388b75b2e455e2af60","sha256:6bc14b35e90976e3cea389695169f8c4c207ec923a7f003e5385406e0b215a76"],"state_sha256":"7b17a70cd87f042fd87b56234697478d2f200426bd3452e68c4f7bde78ee04e8"}