{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5DDJSFRPRLVQPGQ6T3MENCYN5L","short_pith_number":"pith:5DDJSFRP","canonical_record":{"source":{"id":"1211.2681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T16:20:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3eb0d4f26831be1f285d9fff14c22c08263d542f8dc4af66cdacf360bbe4a57e","abstract_canon_sha256":"364a64aff36b818401019bf3e28922f5b1b8ea80440fd771d97019af4f496a74"},"schema_version":"1.0"},"canonical_sha256":"e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08","source":{"kind":"arxiv","id":"1211.2681","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2681","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2681v3","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2681","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"5DDJSFRPRLVQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5DDJSFRPRLVQPGQ6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5DDJSFRP","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5DDJSFRPRLVQPGQ6T3MENCYN5L","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T16:20:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3eb0d4f26831be1f285d9fff14c22c08263d542f8dc4af66cdacf360bbe4a57e","abstract_canon_sha256":"364a64aff36b818401019bf3e28922f5b1b8ea80440fd771d97019af4f496a74"},"schema_version":"1.0"},"canonical_sha256":"e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:01.610094Z","signature_b64":"PMhX3i6xgkEICWfTtsJTns3kMyYA3/lJ6H+sAoBMmmQvm6HSEOOFfcTbm6uAYKZfmL8zboittwDpYN6ehW3qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08","last_reissued_at":"2026-05-18T03:05:01.609570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:01.609570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2681","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KReTI6pkJhRZGmIGLzrfSianiF9PXryMycjKVgEtfw+zSXBwplPD6xMAcgko8pqbGQXY6c04leWEfbbkjYkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:49:27.129791Z"},"content_sha256":"ab0828a8b0227520de1a879686a714963f6271fe26442c99e23f53e01126e692","schema_version":"1.0","event_id":"sha256:ab0828a8b0227520de1a879686a714963f6271fe26442c99e23f53e01126e692"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5DDJSFRPRLVQPGQ6T3MENCYN5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A combinatorial Li-Yau inequality and rational points on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Fumiharu Kato, Gunther Cornelissen, Janne Kool","submitted_at":"2012-11-12T16:20:08Z","abstract_excerpt":"We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field. We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2681","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG48yboJwcGo5lI1DuShX0oG0adqhYPcikFpskUm+9CTovuQ1pD/6bfbp6STs8W7WAUiA33St1mhqUPg/1ZCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:49:27.130424Z"},"content_sha256":"fac044e85edfcd24ade7b6a7f05e45d38776479ef801011ec1408d67d9bf1a32","schema_version":"1.0","event_id":"sha256:fac044e85edfcd24ade7b6a7f05e45d38776479ef801011ec1408d67d9bf1a32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/bundle.json","state_url":"https://pith.science/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T18:49:27Z","links":{"resolver":"https://pith.science/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L","bundle":"https://pith.science/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/bundle.json","state":"https://pith.science/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DDJSFRPRLVQPGQ6T3MENCYN5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5DDJSFRPRLVQPGQ6T3MENCYN5L","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":"364a64aff36b818401019bf3e28922f5b1b8ea80440fd771d97019af4f496a74","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T16:20:08Z","title_canon_sha256":"3eb0d4f26831be1f285d9fff14c22c08263d542f8dc4af66cdacf360bbe4a57e"},"schema_version":"1.0","source":{"id":"1211.2681","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2681","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2681v3","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2681","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"5DDJSFRPRLVQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5DDJSFRPRLVQPGQ6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5DDJSFRP","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:fac044e85edfcd24ade7b6a7f05e45d38776479ef801011ec1408d67d9bf1a32","target":"graph","created_at":"2026-05-18T03:05:01Z","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 present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field. We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplac","authors_text":"Fumiharu Kato, Gunther Cornelissen, Janne Kool","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T16:20:08Z","title":"A combinatorial Li-Yau inequality and rational points on curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2681","kind":"arxiv","version":3},"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:ab0828a8b0227520de1a879686a714963f6271fe26442c99e23f53e01126e692","target":"record","created_at":"2026-05-18T03:05:01Z","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":"364a64aff36b818401019bf3e28922f5b1b8ea80440fd771d97019af4f496a74","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T16:20:08Z","title_canon_sha256":"3eb0d4f26831be1f285d9fff14c22c08263d542f8dc4af66cdacf360bbe4a57e"},"schema_version":"1.0","source":{"id":"1211.2681","kind":"arxiv","version":3}},"canonical_sha256":"e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08","first_computed_at":"2026-05-18T03:05:01.609570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:01.609570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMhX3i6xgkEICWfTtsJTns3kMyYA3/lJ6H+sAoBMmmQvm6HSEOOFfcTbm6uAYKZfmL8zboittwDpYN6ehW3qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:01.610094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2681","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab0828a8b0227520de1a879686a714963f6271fe26442c99e23f53e01126e692","sha256:fac044e85edfcd24ade7b6a7f05e45d38776479ef801011ec1408d67d9bf1a32"],"state_sha256":"bb76f9cec7001b6dd413a5ba972219e91640bd4fc252fe920f8debe711962fe2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"51TFKxD2ozzUrpuzNRHj5dQOOX27iDLol7J2J3CMCd5b9Qh5ImlNzIn+tUQsVE05UzpUlRTe/eoXnhOFXAnrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:49:27.133659Z","bundle_sha256":"e10eac72bd8b233dd8a2f82d308b4e782b196051458c70b4309a1a7cb63e2567"}}