{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6IBT3KM66IKVNI5TUNHN2ZVAHF","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":"0acd4a58635263b9577502b528e92bb913b0d9cadd328a7e2f917037c3bfd4e0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-01-12T00:36:11Z","title_canon_sha256":"6c7d5be9f6bd17742f7a36db33375a3079f59175b608bfa7f84d88872893e4dd"},"schema_version":"1.0","source":{"id":"2601.07112","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.07112","created_at":"2026-05-26T01:03:22Z"},{"alias_kind":"arxiv_version","alias_value":"2601.07112v4","created_at":"2026-05-26T01:03:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.07112","created_at":"2026-05-26T01:03:22Z"},{"alias_kind":"pith_short_12","alias_value":"6IBT3KM66IKV","created_at":"2026-05-26T01:03:22Z"},{"alias_kind":"pith_short_16","alias_value":"6IBT3KM66IKVNI5T","created_at":"2026-05-26T01:03:22Z"},{"alias_kind":"pith_short_8","alias_value":"6IBT3KM6","created_at":"2026-05-26T01:03:22Z"}],"graph_snapshots":[{"event_id":"sha256:056b2091b90d4c2f0bb6a699942d7035a07f28b26dfc4f79bd339c4c7926c46d","target":"graph","created_at":"2026-05-26T01:03:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.07112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Anabelian geometry suggests that, for suitably geometric objects, their \\'etale fundamental groups determine the geometric objects up to isomorphism. From a group-theoretic viewpoint, this philosophy requires rigidity properties, which often follow from their center-freeness of the associated \\'etale fundamental groups. In fact, some profinite groups arising from anabelian geometry are center-free. For any integer $m\\geq 2$, we investigate how such center-freeness behaves under passage to the maximal $m$-step solvable quotients. In particular, we show that the maximal $m$-step solvable quotien","authors_text":"Naganori Yamaguchi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-01-12T00:36:11Z","title":"Center-freeness of finite-step solvable groups arising from anabelian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07112","kind":"arxiv","version":4},"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":"sha256:9893e9ffd402283c6097fe484ab257cf5101e432b6eecb30f290c5d8281c4c69","target":"record","created_at":"2026-05-26T01:03:22Z","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":"0acd4a58635263b9577502b528e92bb913b0d9cadd328a7e2f917037c3bfd4e0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-01-12T00:36:11Z","title_canon_sha256":"6c7d5be9f6bd17742f7a36db33375a3079f59175b608bfa7f84d88872893e4dd"},"schema_version":"1.0","source":{"id":"2601.07112","kind":"arxiv","version":4}},"canonical_sha256":"f2033da99ef21556a3b3a34edd66a0396e5b052fec5929c9a794e7320f0e6760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2033da99ef21556a3b3a34edd66a0396e5b052fec5929c9a794e7320f0e6760","first_computed_at":"2026-05-26T01:03:22.094847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:22.094847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zsaj1f7xIe/hi8a46NxYP1bXItt2i2+/FRxEeSovTdYz4FdC2df+lb6QmRXRIsANER4/UG/8JBUDwQF+5dbtAw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:22.095794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.07112","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9893e9ffd402283c6097fe484ab257cf5101e432b6eecb30f290c5d8281c4c69","sha256:056b2091b90d4c2f0bb6a699942d7035a07f28b26dfc4f79bd339c4c7926c46d"],"state_sha256":"255be2961903dcb6e829f00291c4eb0389a86294532f2fd5f7829288df033907"}