{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CGGBOJX7CB7AXNICZMUCPQ3HDF","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":"5a59272d910039f14eb8b82bb75ab22e907a7906b2840bd61b716f3da99bbc9b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-12-20T12:06:33Z","title_canon_sha256":"2d85f391ad06f4d4ffc26dd2e215dd52f67cb38c019189d85910eaea9e2ab9e6"},"schema_version":"1.0","source":{"id":"1312.5906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5906","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5906v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5906","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"CGGBOJX7CB7A","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGGBOJX7CB7AXNIC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGGBOJX7","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:75b53259de8d08aa741f84e60d035a8bfeeb3d5b8e2058464d0eb78eb006b736","target":"graph","created_at":"2026-05-18T03:04:06Z","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":"Riemannian metrics on the unit ball of the quaternions, which are naturally associated with the reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex variable case, no Riemannian metric is invariant under regular self-maps of the quaternionic ball.","authors_text":"Giulia Sarfatti, Nicola Arcozzi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-12-20T12:06:33Z","title":"Invariant metrics for the quaternionic Hardy space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5906","kind":"arxiv","version":2},"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:a7324f8c1036baac5be690b6efee748d796620c2aef93ff2273adae8a5bb75a3","target":"record","created_at":"2026-05-18T03:04:06Z","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":"5a59272d910039f14eb8b82bb75ab22e907a7906b2840bd61b716f3da99bbc9b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-12-20T12:06:33Z","title_canon_sha256":"2d85f391ad06f4d4ffc26dd2e215dd52f67cb38c019189d85910eaea9e2ab9e6"},"schema_version":"1.0","source":{"id":"1312.5906","kind":"arxiv","version":2}},"canonical_sha256":"118c1726ff107e0bb502cb2827c3671969409dbf5a15506ee330213e9521439c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"118c1726ff107e0bb502cb2827c3671969409dbf5a15506ee330213e9521439c","first_computed_at":"2026-05-18T03:04:06.006639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:06.006639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXkpBZZp4exrjfQkqPlkENfrPJL5BGSM6TTZdRcK6EG+aLocfousVjjd4hju6bTF3DW7poSJqpLPerQ8+L9ICg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:06.007046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7324f8c1036baac5be690b6efee748d796620c2aef93ff2273adae8a5bb75a3","sha256:75b53259de8d08aa741f84e60d035a8bfeeb3d5b8e2058464d0eb78eb006b736"],"state_sha256":"1f338b65774c5496c2cbb3ad7b37b34aab95bf300de67b27e6e64e51c1f8c215"}