{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4BPRON7XLGN44EORHVSP676MOJ","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":"ee501a44f8ced573345a9129e223ec8488621ab570f84a6f383f4a320a4868cb","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-13T00:19:53Z","title_canon_sha256":"c6c7b2c81e396f8ca1276f2d4b15ad1bce7e7a2e33fdfd31441f8125d0d335f1"},"schema_version":"1.0","source":{"id":"1611.04057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04057","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04057v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04057","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"4BPRON7XLGN4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BPRON7XLGN44EOR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BPRON7X","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a9d352442c0aa1cf6c0071f198f05229714f1c95aeaec9e00c29baff272c5a83","target":"graph","created_at":"2026-05-18T00:59:17Z","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 the problem of deciding when a metrisable topological group $G$ has a canonically defined local Lipschitz geometry. This naturally leads to the concept of minimal metrics on $G$, that we characterise intrinsically in terms of a linear growth condition on powers of group elements.\n  Combining this with work on the large scale geometry of topological groups, we also identify the class of metrisable groups admitting a canonical global Lipschitz geometry.\n  In turn, minimal metrics connect with Hilbert's fifth problem for completely metrisable groups and we show, assuming that the set o","authors_text":"Christian Rosendal","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-13T00:19:53Z","title":"Lipschitz structure and minimal metrics on topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04057","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:cefbdbd18fdd64c0c443777ef5aed62c9312d13120e88e164659e4fa82a0383c","target":"record","created_at":"2026-05-18T00:59:17Z","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":"ee501a44f8ced573345a9129e223ec8488621ab570f84a6f383f4a320a4868cb","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-13T00:19:53Z","title_canon_sha256":"c6c7b2c81e396f8ca1276f2d4b15ad1bce7e7a2e33fdfd31441f8125d0d335f1"},"schema_version":"1.0","source":{"id":"1611.04057","kind":"arxiv","version":1}},"canonical_sha256":"e05f1737f7599bce11d13d64ff7fcc72764be2c384c1d3e1ace86af226e98c90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e05f1737f7599bce11d13d64ff7fcc72764be2c384c1d3e1ace86af226e98c90","first_computed_at":"2026-05-18T00:59:17.714677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:17.714677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3G0yQ4u7yB1KTpxUIXPIvxFIBpfIFKOzxsOBHzxst4/qTEz7g1x1jghsL2g72nWQKPGyOd17/B65gEyi5xSRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:17.715381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cefbdbd18fdd64c0c443777ef5aed62c9312d13120e88e164659e4fa82a0383c","sha256:a9d352442c0aa1cf6c0071f198f05229714f1c95aeaec9e00c29baff272c5a83"],"state_sha256":"274dd1efc9e535b68da47c08ccc7ceeb2e05979af496e66433b31b9dcd665695"}