{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2QUXFWBIGTD2UK6B2KCM5S5YAE","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":"4d71dda8b133988d9e54dc403a5f0ad2eb99cb2e0d7dc7395d7db2b5e9d19f9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-02T14:12:03Z","title_canon_sha256":"95aa7e304feb04bafbb5505c53323a822df671a11dff97249b49ab60ca5c22c1"},"schema_version":"1.0","source":{"id":"2607.02204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02204","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02204v1","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02204","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"2QUXFWBIGTD2","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"2QUXFWBIGTD2UK6B","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"2QUXFWBI","created_at":"2026-07-03T01:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:eda65c16a3ac583128ac090c3753d4bed029736669c4caf9a32b2ab98cfc6498","target":"graph","created_at":"2026-07-03T01:17:45Z","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/2607.02204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces relative versions of the inner automorphism group and the transvection group associated with surjective quandle homomorphisms.By using the relative inner automorphism group, we define a notion of \\emph{connectedness} for surjective homomorphisms. We characterize connected homomorphisms algebraically as quotient maps, and use the relative transvection group to establish a maximal \\emph{connected-covering} factorization for arbitrary surjections. Finally, we study surjective homomorphisms for which the relative inner automorphism group acts $2$-transitively on each fiber. U","authors_text":"Tomoki Yoshida, Yuki Imamura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-02T14:12:03Z","title":"Relativization of symmetries on quandles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02204","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":"sha256:47c3253a7d71a1a2024a749409e893a433645a1c4bb991f6318431724e2d1c3c","target":"record","created_at":"2026-07-03T01:17:45Z","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":"4d71dda8b133988d9e54dc403a5f0ad2eb99cb2e0d7dc7395d7db2b5e9d19f9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-02T14:12:03Z","title_canon_sha256":"95aa7e304feb04bafbb5505c53323a822df671a11dff97249b49ab60ca5c22c1"},"schema_version":"1.0","source":{"id":"2607.02204","kind":"arxiv","version":1}},"canonical_sha256":"d42972d82834c7aa2bc1d284cecbb8010d83bdaad3bd179edc08bd49a27771d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d42972d82834c7aa2bc1d284cecbb8010d83bdaad3bd179edc08bd49a27771d5","first_computed_at":"2026-07-03T01:17:45.050070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:45.050070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J6I0r27YG9bjxXx3q3KO0UPW9QoJAA9upXYTFErpMCi8GWM+vreUjMXAPJVWxJLdrIJLIloF6lQaHwn4/SyLAw==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:45.050465Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47c3253a7d71a1a2024a749409e893a433645a1c4bb991f6318431724e2d1c3c","sha256:eda65c16a3ac583128ac090c3753d4bed029736669c4caf9a32b2ab98cfc6498"],"state_sha256":"fe8dc197527a184789c9e35b0d2b694b3f623db5c9b920b73b6a8384a7ff8563"}