{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BL637UK6C5IX5GROYN6GKDLMIO","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":"cdfe1797024958911e0f9863f3e67f8521b28efe729f0c953f9a3b9d47d42ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-21T09:00:27Z","title_canon_sha256":"5d15cf1a633f98e178ff10b9039c2753f92dfa3a5546c0fdc8f0ef39030c740e"},"schema_version":"1.0","source":{"id":"1211.4966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4966","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4966v2","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4966","created_at":"2026-05-18T03:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"BL637UK6C5IX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BL637UK6C5IX5GRO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BL637UK6","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:041fed2b20ba936a0c9df170a888fe9bfe90babc5e3896f286ef4cfc77fa0e29","target":"graph","created_at":"2026-05-18T03:29:37Z","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 distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. We investigate the properties of these mappings from the viewpoint of differential topology.","authors_text":"Shunsuke Ichiki, Takashi Nishimura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-21T09:00:27Z","title":"Distance-squared mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4966","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":"sha256:9fc8f07944761122a574034fc4c97c56c81b805766ecf07d5d6ee2d0d66150a0","target":"record","created_at":"2026-05-18T03:29:37Z","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":"cdfe1797024958911e0f9863f3e67f8521b28efe729f0c953f9a3b9d47d42ef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-11-21T09:00:27Z","title_canon_sha256":"5d15cf1a633f98e178ff10b9039c2753f92dfa3a5546c0fdc8f0ef39030c740e"},"schema_version":"1.0","source":{"id":"1211.4966","kind":"arxiv","version":2}},"canonical_sha256":"0afdbfd15e17517e9a2ec37c650d6c4387d2761fc51115df5996000a5b9e7235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0afdbfd15e17517e9a2ec37c650d6c4387d2761fc51115df5996000a5b9e7235","first_computed_at":"2026-05-18T03:29:37.482890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:37.482890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u4FP6Ow68nCihtDmiiWioUKBASQJ9UVVW0hEs3HdAYy9jtEPRDE2R4JlD90QMT567bIY384aDyvLIriJmUZEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:37.483740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fc8f07944761122a574034fc4c97c56c81b805766ecf07d5d6ee2d0d66150a0","sha256:041fed2b20ba936a0c9df170a888fe9bfe90babc5e3896f286ef4cfc77fa0e29"],"state_sha256":"e1827d62600c9ec566ab71fdfb2ed26d9ed28517b3cc9823098c1f8a01d2a929"}