{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UIX24P5OOW3ISD5IXUTOKPILWG","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":"5067e88baf084bc2f7f9a87bd332e6e730fbf32c84a106523a3d0c23e38b9935","cross_cats_sorted":["math.CT","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-15T05:41:06Z","title_canon_sha256":"bc780e78cfbc548bcf152aa09eed9d62b0c2f034772ccea2cd58bd96b6d25795"},"schema_version":"1.0","source":{"id":"1810.06188","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06188","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06188v4","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06188","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"UIX24P5OOW3I","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UIX24P5OOW3ISD5I","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UIX24P5O","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:3e7e653a334f4aa14f8d47f3c89e33899491ddf770a2832db0e5c6d164b97961","target":"graph","created_at":"2026-05-18T00:01:52Z","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":"We discuss a new pseudometric on the space of all norms on a finite-dimensional vector space (or free module) $\\mathbb{F}^k$, with $\\mathbb{F}$ the real, complex, or quaternion numbers. This metric arises from the Lipschitz-equivalence of all norms on $\\mathbb{F}^k$, and seems to be unexplored in the literature. We initiate the study of the associated quotient metric space, and show that it is complete, connected, and non-compact. In particular, the new topology is strictly coarser than that of the Banach-Mazur compactum. For example, for each $k \\geqslant 2$ the metric subspace $\\{ \\| \\cdot \\","authors_text":"Apoorva Khare","cross_cats":["math.CT","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-15T05:41:06Z","title":"The non-compact normed space of norms on a finite-dimensional Banach space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06188","kind":"arxiv","version":4},"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":"sha256:02fee3acc01d77a1be9888ece73f557d805740823dcfe1938f1400ad4c9db9ad","target":"record","created_at":"2026-05-18T00:01:52Z","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":"5067e88baf084bc2f7f9a87bd332e6e730fbf32c84a106523a3d0c23e38b9935","cross_cats_sorted":["math.CT","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-15T05:41:06Z","title_canon_sha256":"bc780e78cfbc548bcf152aa09eed9d62b0c2f034772ccea2cd58bd96b6d25795"},"schema_version":"1.0","source":{"id":"1810.06188","kind":"arxiv","version":4}},"canonical_sha256":"a22fae3fae75b6890fa8bd26e53d0bb1a7f07fd9572194aeee790e66d4a7eaec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a22fae3fae75b6890fa8bd26e53d0bb1a7f07fd9572194aeee790e66d4a7eaec","first_computed_at":"2026-05-18T00:01:52.743879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:52.743879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQ5fc2bPGqrJ5QzJrDOu3ebnYV5s3iXFJ5t1nSgM0kw1Ee8oi5kF4G6rbXz5CZ+j+k/bEsoLmItCKV8V8zxIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:52.744439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06188","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02fee3acc01d77a1be9888ece73f557d805740823dcfe1938f1400ad4c9db9ad","sha256:3e7e653a334f4aa14f8d47f3c89e33899491ddf770a2832db0e5c6d164b97961"],"state_sha256":"5bdbc0dcd7405024a799a0b999482e5c41358f8fc06b68e6908c6b68c6b1775c"}