{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C5PQFQJ6V4HXANQX7O3Q256DSS","short_pith_number":"pith:C5PQFQJ6","canonical_record":{"source":{"id":"1503.05776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T14:20:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9f43848d2ba6c27835c3f61c823aa22adf068307a365aa26dac485fc22e9f02f","abstract_canon_sha256":"44847134983468dbd8991139c602662aa0b5d837621af2d68698445c25bc0db6"},"schema_version":"1.0"},"canonical_sha256":"175f02c13eaf0f703617fbb70d77c3948f1fa0bf71691e694e65f6cd001331ec","source":{"kind":"arxiv","id":"1503.05776","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05776","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05776v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05776","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"C5PQFQJ6V4HX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5PQFQJ6V4HXANQX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5PQFQJ6","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C5PQFQJ6V4HXANQX7O3Q256DSS","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T14:20:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9f43848d2ba6c27835c3f61c823aa22adf068307a365aa26dac485fc22e9f02f","abstract_canon_sha256":"44847134983468dbd8991139c602662aa0b5d837621af2d68698445c25bc0db6"},"schema_version":"1.0"},"canonical_sha256":"175f02c13eaf0f703617fbb70d77c3948f1fa0bf71691e694e65f6cd001331ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.368260Z","signature_b64":"FWYvgCvuPM4xTQSrNd/MCL7u5k11PnWoGvjBPi3axSDXJ+oqnLIGr1tRIwdcvSArMZ1/RXXRUx+8jZnInXF+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175f02c13eaf0f703617fbb70d77c3948f1fa0bf71691e694e65f6cd001331ec","last_reissued_at":"2026-05-18T00:52:02.367752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.367752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05776","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yVtuXK1ZvD1RKv9Yi/Bg7J+H+SnV/GAzKLhBTBjMlLEZhJKCB+anHYx0SgksgBJLzOPxeUnbymERaKr1SXmRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:18:20.242686Z"},"content_sha256":"7e8e207210ff2a1cadb31badb93857bd95b4b08e96712edc001f9aeb00b7d594","schema_version":"1.0","event_id":"sha256:7e8e207210ff2a1cadb31badb93857bd95b4b08e96712edc001f9aeb00b7d594"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C5PQFQJ6V4HXANQX7O3Q256DSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theta characteristics of tropical $K_4$-curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Melody Chan, Pakawut Jiradilok","submitted_at":"2015-03-19T14:20:47Z","abstract_excerpt":"A $K_4$-curve is a smooth, proper curve X of genus 3 over a nonarchimedean field whose Berkovich skeleton $\\Gamma$ is a complete graph on 4 vertices. The curve X has 28 effective theta characteristics, i.e. the 28 bitangents to a canonical embedding, while $\\Gamma$ has exactly seven tropical theta characteristics, as shown by Zharkov. We prove that the 28 effective theta characteristics of a $K_4$-curve specialize to the theta characteristics of its minimal skeleton in seven groups of four."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05776","kind":"arxiv","version":2},"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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGw/lMZaywEPMDbQd43WqIiJ9V8roYz7SCfNA8EJtm/2dS+/f+MqiYiFZzpM04qgl4sWlEWPuVEqh2HppO8yDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:18:20.243363Z"},"content_sha256":"4e802207fcc78c90f68c17d43c1f4408d85597b34a6a35f04a6ce5923084fceb","schema_version":"1.0","event_id":"sha256:4e802207fcc78c90f68c17d43c1f4408d85597b34a6a35f04a6ce5923084fceb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/bundle.json","state_url":"https://pith.science/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/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":"2026-05-28T21:18:20Z","links":{"resolver":"https://pith.science/pith/C5PQFQJ6V4HXANQX7O3Q256DSS","bundle":"https://pith.science/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/bundle.json","state":"https://pith.science/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5PQFQJ6V4HXANQX7O3Q256DSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C5PQFQJ6V4HXANQX7O3Q256DSS","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":"44847134983468dbd8991139c602662aa0b5d837621af2d68698445c25bc0db6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T14:20:47Z","title_canon_sha256":"9f43848d2ba6c27835c3f61c823aa22adf068307a365aa26dac485fc22e9f02f"},"schema_version":"1.0","source":{"id":"1503.05776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05776","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05776v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05776","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"C5PQFQJ6V4HX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5PQFQJ6V4HXANQX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5PQFQJ6","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:4e802207fcc78c90f68c17d43c1f4408d85597b34a6a35f04a6ce5923084fceb","target":"graph","created_at":"2026-05-18T00:52:02Z","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":"A $K_4$-curve is a smooth, proper curve X of genus 3 over a nonarchimedean field whose Berkovich skeleton $\\Gamma$ is a complete graph on 4 vertices. The curve X has 28 effective theta characteristics, i.e. the 28 bitangents to a canonical embedding, while $\\Gamma$ has exactly seven tropical theta characteristics, as shown by Zharkov. We prove that the 28 effective theta characteristics of a $K_4$-curve specialize to the theta characteristics of its minimal skeleton in seven groups of four.","authors_text":"Melody Chan, Pakawut Jiradilok","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T14:20:47Z","title":"Theta characteristics of tropical $K_4$-curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05776","kind":"arxiv","version":2},"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":"sha256:7e8e207210ff2a1cadb31badb93857bd95b4b08e96712edc001f9aeb00b7d594","target":"record","created_at":"2026-05-18T00:52:02Z","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":"44847134983468dbd8991139c602662aa0b5d837621af2d68698445c25bc0db6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T14:20:47Z","title_canon_sha256":"9f43848d2ba6c27835c3f61c823aa22adf068307a365aa26dac485fc22e9f02f"},"schema_version":"1.0","source":{"id":"1503.05776","kind":"arxiv","version":2}},"canonical_sha256":"175f02c13eaf0f703617fbb70d77c3948f1fa0bf71691e694e65f6cd001331ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"175f02c13eaf0f703617fbb70d77c3948f1fa0bf71691e694e65f6cd001331ec","first_computed_at":"2026-05-18T00:52:02.367752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.367752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FWYvgCvuPM4xTQSrNd/MCL7u5k11PnWoGvjBPi3axSDXJ+oqnLIGr1tRIwdcvSArMZ1/RXXRUx+8jZnInXF+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.368260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e8e207210ff2a1cadb31badb93857bd95b4b08e96712edc001f9aeb00b7d594","sha256:4e802207fcc78c90f68c17d43c1f4408d85597b34a6a35f04a6ce5923084fceb"],"state_sha256":"bcee46d2531bf8996c80286dbfb37327657fdc1f29272d56fe67ced85d6a0021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGMfq7kuNyejCSYayguG1bq3EwtBQTqk+2L05GDLB077RZ1GvkUic+jsmM615X7m0ymFkjGp9nweD+zoLMvNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:18:20.246832Z","bundle_sha256":"b1773585d164ae741907be2bb4187a3af1c6c2888c1f5edb36b070bc3897cf42"}}