{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:XCYQYNP4F4TI2LE2H4DADFDRUB","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":"8f8d6a2b20904de51f2249c8243b2cb5a87fa0e0aa4d0fb15044f71464ff6a2a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2023-05-04T21:32:36Z","title_canon_sha256":"8ba92981f838b41bae8d6ba2b29f3a5df334d93137e941efa9b2ab819b40e9f7"},"schema_version":"1.0","source":{"id":"2305.03163","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.03163","created_at":"2026-07-05T08:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2305.03163v3","created_at":"2026-07-05T08:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.03163","created_at":"2026-07-05T08:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"XCYQYNP4F4TI","created_at":"2026-07-05T08:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"XCYQYNP4F4TI2LE2","created_at":"2026-07-05T08:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"XCYQYNP4","created_at":"2026-07-05T08:23:08Z"}],"graph_snapshots":[{"event_id":"sha256:8078d4d836f637f408710112a4fec372beafd0367794ffa89cf8864ac6e0c107","target":"graph","created_at":"2026-07-05T08:23:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.03163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to isometry as vector spaces over the two-element field, endowed with an injective norm. Using isosceles-free decompositions, we provide bounds on the maximal number of distances in arbitrary homogeneous finite metric spaces.","authors_text":"Adam Barto\\v{s}, Christian Bargetz, Franz Luggin, Wies{\\l}aw Kubi\\'s","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2023-05-04T21:32:36Z","title":"Homogeneous isosceles-free spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.03163","kind":"arxiv","version":3},"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":"sha256:34c9a2fdfd2e7c5ce7f59e196e9bdf1e4efc84ba5ba82331613b4eb868728422","target":"record","created_at":"2026-07-05T08:23:08Z","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":"8f8d6a2b20904de51f2249c8243b2cb5a87fa0e0aa4d0fb15044f71464ff6a2a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2023-05-04T21:32:36Z","title_canon_sha256":"8ba92981f838b41bae8d6ba2b29f3a5df334d93137e941efa9b2ab819b40e9f7"},"schema_version":"1.0","source":{"id":"2305.03163","kind":"arxiv","version":3}},"canonical_sha256":"b8b10c35fc2f268d2c9a3f06019471a05ab1cf9b557b24278adcc683efc24acb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8b10c35fc2f268d2c9a3f06019471a05ab1cf9b557b24278adcc683efc24acb","first_computed_at":"2026-07-05T08:23:08.813099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:08.813099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n1xcAYr4DcU70Fqxr0sFNAlF+cfbaEk/HU02jyI9u+hc31pDaGoCSpIV5r1txVwrNbR9F8e4pXBoB+enixyqBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:08.813594Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.03163","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34c9a2fdfd2e7c5ce7f59e196e9bdf1e4efc84ba5ba82331613b4eb868728422","sha256:8078d4d836f637f408710112a4fec372beafd0367794ffa89cf8864ac6e0c107"],"state_sha256":"d5aa8ae238d2add5f2c4088d37d0d06436018787018bbe9dcc3bfebe9e0b195b"}