{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7DV4GFHAJPYUKYIVLJFBAXURKE","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":"e6feac46be9ee20ec156009ada073f3a90ae80b4dd2d0c11a7baedd6ab14ea74","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-09T16:52:12Z","title_canon_sha256":"506fc0851fce1e2d525e67e4b932b32b2de8422af11e8d08d77c10f5d4d58cd6"},"schema_version":"1.0","source":{"id":"1203.2131","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2131","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2131v3","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2131","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"7DV4GFHAJPYU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7DV4GFHAJPYUKYIV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7DV4GFHA","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:6f3585db38c8bf7325c3291a5721838e39d01c4441d92ac7eec41cd9205438e1","target":"graph","created_at":"2026-05-18T02:17:22Z","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":"A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry.","authors_text":"Hao Chen","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-09T16:52:12Z","title":"Distance Geometry for Kissing Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2131","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":"sha256:00b2cf8d2d1895152850e76ec454b3dfdb14a00c028c526a31eb5eccd65fddff","target":"record","created_at":"2026-05-18T02:17:22Z","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":"e6feac46be9ee20ec156009ada073f3a90ae80b4dd2d0c11a7baedd6ab14ea74","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-09T16:52:12Z","title_canon_sha256":"506fc0851fce1e2d525e67e4b932b32b2de8422af11e8d08d77c10f5d4d58cd6"},"schema_version":"1.0","source":{"id":"1203.2131","kind":"arxiv","version":3}},"canonical_sha256":"f8ebc314e04bf14561155a4a105e91510036b37f83a7af3bab6642ac02c3ff90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8ebc314e04bf14561155a4a105e91510036b37f83a7af3bab6642ac02c3ff90","first_computed_at":"2026-05-18T02:17:22.198355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:22.198355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XhfRBGQYo23UmZrJedwBynpmlK9UzUDDInTcXxbuXUXxHjLrBI/yffuJ6p1baN1+knbdZvHe8a2cxQdGzsKjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:22.199096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2131","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b2cf8d2d1895152850e76ec454b3dfdb14a00c028c526a31eb5eccd65fddff","sha256:6f3585db38c8bf7325c3291a5721838e39d01c4441d92ac7eec41cd9205438e1"],"state_sha256":"9ba955bc201368fc77de9f84ea5ffc19d94e777fbe9a56c98a5da25677b65985"}