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In the article, we prove that for a line $l_0\\in T$ and any two points $P_1,P_2\\in C_1\\cap l_0$ there is a loop $l_t\\subset T$, $t\\in [0,1]$, such that the movement of the line $l_0$ along the loop $l_t$ induces the transposition of the points $P_1$, $P_2$ and the identity permutation of the other points of $C\\cap l_0$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.1426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-06T12:05:09Z","cross_cats_sorted":[],"title_canon_sha256":"93482b945c2e4103f984fa45e7f485fd7f12772e26763be6262ae76f10f19005","abstract_canon_sha256":"357d97662382e7cc2f86579a6c850270d78e143f850d61df727a55e39e4b365f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:59.056913Z","signature_b64":"r0xzUSkrmuQyMXOVp0LEaILlZ/9WE2lsOIQE3AyoSNcnYYgIUs9kGWF0JToNCANxqBU4EeYY6kIvy/m7HvwoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e53c80cc7bc701f827622b490a925a6d124d3575a26ea339f3a172ff98c55cba","last_reissued_at":"2026-05-18T02:56:59.056461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:59.056461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Galois groups of the dualizing coverings for plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vik.S. 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In the article, we prove that for a line $l_0\\in T$ and any two points $P_1,P_2\\in C_1\\cap l_0$ there is a loop $l_t\\subset T$, $t\\in [0,1]$, such that the movement of the line $l_0$ along the loop $l_t$ induces the transposition of the points $P_1$, $P_2$ and the identity permutation of the other points of $C\\cap l_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1426","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.1426","created_at":"2026-05-18T02:56:59.056530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.1426v1","created_at":"2026-05-18T02:56:59.056530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1426","created_at":"2026-05-18T02:56:59.056530+00:00"},{"alias_kind":"pith_short_12","alias_value":"4U6IBTD3Y4A7","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4U6IBTD3Y4A7QJ3C","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4U6IBTD3","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU","json":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU.json","graph_json":"https://pith.science/api/pith-number/4U6IBTD3Y4A7QJ3CFNEQVES2NU/graph.json","events_json":"https://pith.science/api/pith-number/4U6IBTD3Y4A7QJ3CFNEQVES2NU/events.json","paper":"https://pith.science/paper/4U6IBTD3"},"agent_actions":{"view_html":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU","download_json":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU.json","view_paper":"https://pith.science/paper/4U6IBTD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.1426&json=true","fetch_graph":"https://pith.science/api/pith-number/4U6IBTD3Y4A7QJ3CFNEQVES2NU/graph.json","fetch_events":"https://pith.science/api/pith-number/4U6IBTD3Y4A7QJ3CFNEQVES2NU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU/action/storage_attestation","attest_author":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU/action/author_attestation","sign_citation":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU/action/citation_signature","submit_replication":"https://pith.science/pith/4U6IBTD3Y4A7QJ3CFNEQVES2NU/action/replication_record"}},"created_at":"2026-05-18T02:56:59.056530+00:00","updated_at":"2026-05-18T02:56:59.056530+00:00"}