{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4GTAATYCUZANOVEAA5Q75CZPAJ","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":"7f81079923732fb1456c1776ab3f3c063b9b194e30b062c8e5287e53f8f4e488","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-03-04T10:59:56Z","title_canon_sha256":"16569d4f411f53a2663bd788c00e8aebc67a1f6d391aad5958874c3ca3cea113"},"schema_version":"1.0","source":{"id":"1703.01439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01439","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01439v1","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01439","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"4GTAATYCUZAN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4GTAATYCUZANOVEA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4GTAATYC","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:f49f679171dd86805b0b1f4a93bc50bff659899163d21fc3128f06c02b309c0f","target":"graph","created_at":"2026-05-18T00:49:30Z","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":"If $\\varphi$ and $\\psi$ are two continuous real-valued functions defined on a compact topological space $X$ and $G$ is a subgroup of the group of all homeomorphisms of $X$ onto itself, the natural pseudo-distance $d_G(\\varphi,\\psi)$ is defined as the infimum of $\\mathcal{L}(g)=\\|\\varphi-\\psi \\circ g \\|_\\infty$, as $g$ varies in $G$. In this paper, we make a first step towards extending the study of this concept to the case of Lie groups, by assuming $X=G=S^1$. In particular, we study the set of the optimal homeomorphisms for $d_G$, i.e. the elements $\\rho_\\alpha$ of $S^1$ such that $\\mathcal{L","authors_text":"Alessandro De Gregorio","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-03-04T10:59:56Z","title":"On the set of optimal homeomorphisms for the natural pseudo-distance associated with the Lie group S^1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01439","kind":"arxiv","version":1},"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:e8feee038f05214a07c8e026ff1ef566ae2acecfc908e39e6d48cd4380aa09ff","target":"record","created_at":"2026-05-18T00:49:30Z","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":"7f81079923732fb1456c1776ab3f3c063b9b194e30b062c8e5287e53f8f4e488","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-03-04T10:59:56Z","title_canon_sha256":"16569d4f411f53a2663bd788c00e8aebc67a1f6d391aad5958874c3ca3cea113"},"schema_version":"1.0","source":{"id":"1703.01439","kind":"arxiv","version":1}},"canonical_sha256":"e1a6004f02a640d754800761fe8b2f024ad8e31bc2451ed72113624ed4a0ec11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1a6004f02a640d754800761fe8b2f024ad8e31bc2451ed72113624ed4a0ec11","first_computed_at":"2026-05-18T00:49:30.735111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:30.735111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sZvFhFWsvr3x+BiXZ7PAZKZPMNAm0CXzTKIi5oe0OM8Dp2gBJ9ciXKh2dlHhdf4i7Q+XvLiHuwfRrBJ0KGczCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:30.735697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8feee038f05214a07c8e026ff1ef566ae2acecfc908e39e6d48cd4380aa09ff","sha256:f49f679171dd86805b0b1f4a93bc50bff659899163d21fc3128f06c02b309c0f"],"state_sha256":"b04453d8e7f6f5ee04612c1799ae997b3b07f1be93048af35ff4371d69c94bd6"}