{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JD4MMASBRMY2XEPFG7RFONDJWU","short_pith_number":"pith:JD4MMASB","schema_version":"1.0","canonical_sha256":"48f8c602418b31ab91e537e2573469b51c1bb03ed2f1358ff86891176307ea25","source":{"kind":"arxiv","id":"1901.09172","version":1},"attestation_state":"computed","paper":{"title":"Galois quotients of metric graphs and invariant linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"JuAe Song","submitted_at":"2019-01-26T08:02:15Z","abstract_excerpt":"For a map $\\varphi : \\varGamma \\rightarrow \\varGamma^{\\prime}$ between metric graphs and an isometric action on $\\varGamma$ by finite group $K$, $\\varphi$ is a $K$-Galois covering on $\\varGamma^{\\prime}$ if $\\varphi$ is a morphism, the degree of $\\varphi$ coincides with the order of $K$ and $K$ induces a transitive action on every fibre. We prove that for a metric graph $\\varGamma$ with an isometric action by finite group $K$, there exists a rational map, from $\\varGamma$ to a tropical projective space, which induces a $K$-Galois covering on the image. By using this fact, we also prove that fo"},"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":"1901.09172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-26T08:02:15Z","cross_cats_sorted":[],"title_canon_sha256":"038241f6fd3fa7539a32de4030ee589e0998c00612b249c30110958d2a096419","abstract_canon_sha256":"65af4781ad81b9000a57f500c8b913d62606a42e971f29e9e062052ce723b740"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:26.699657Z","signature_b64":"pTCdAwRDD562mWB+Vl9/UTgTtRG8VWEGqE0Rd87nWJLKw3IQKd04eOrR3y2JAlD+F/b4Xw9h9aGTkcc/ixglCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48f8c602418b31ab91e537e2573469b51c1bb03ed2f1358ff86891176307ea25","last_reissued_at":"2026-05-17T23:55:26.699157Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:26.699157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Galois quotients of metric graphs and invariant linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"JuAe Song","submitted_at":"2019-01-26T08:02:15Z","abstract_excerpt":"For a map $\\varphi : \\varGamma \\rightarrow \\varGamma^{\\prime}$ between metric graphs and an isometric action on $\\varGamma$ by finite group $K$, $\\varphi$ is a $K$-Galois covering on $\\varGamma^{\\prime}$ if $\\varphi$ is a morphism, the degree of $\\varphi$ coincides with the order of $K$ and $K$ induces a transitive action on every fibre. We prove that for a metric graph $\\varGamma$ with an isometric action by finite group $K$, there exists a rational map, from $\\varGamma$ to a tropical projective space, which induces a $K$-Galois covering on the image. By using this fact, we also prove that fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09172","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":"1901.09172","created_at":"2026-05-17T23:55:26.699220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.09172v1","created_at":"2026-05-17T23:55:26.699220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09172","created_at":"2026-05-17T23:55:26.699220+00:00"},{"alias_kind":"pith_short_12","alias_value":"JD4MMASBRMY2","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JD4MMASBRMY2XEPF","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JD4MMASB","created_at":"2026-05-18T12:33:18.533446+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/JD4MMASBRMY2XEPFG7RFONDJWU","json":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU.json","graph_json":"https://pith.science/api/pith-number/JD4MMASBRMY2XEPFG7RFONDJWU/graph.json","events_json":"https://pith.science/api/pith-number/JD4MMASBRMY2XEPFG7RFONDJWU/events.json","paper":"https://pith.science/paper/JD4MMASB"},"agent_actions":{"view_html":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU","download_json":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU.json","view_paper":"https://pith.science/paper/JD4MMASB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.09172&json=true","fetch_graph":"https://pith.science/api/pith-number/JD4MMASBRMY2XEPFG7RFONDJWU/graph.json","fetch_events":"https://pith.science/api/pith-number/JD4MMASBRMY2XEPFG7RFONDJWU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU/action/storage_attestation","attest_author":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU/action/author_attestation","sign_citation":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU/action/citation_signature","submit_replication":"https://pith.science/pith/JD4MMASBRMY2XEPFG7RFONDJWU/action/replication_record"}},"created_at":"2026-05-17T23:55:26.699220+00:00","updated_at":"2026-05-17T23:55:26.699220+00:00"}