{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4STY5GLWR2WS2EVA7OC2XNKU26","short_pith_number":"pith:4STY5GLW","canonical_record":{"source":{"id":"1105.1715","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-09T16:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"611c46e6d1f02feca55e7e4afc9e2cecf4e14da5003d4ee7172033ce380b803f","abstract_canon_sha256":"7441358a72d44e381833a69e60fabe2868fdc56ff768019f374cd3552358361b"},"schema_version":"1.0"},"canonical_sha256":"e4a78e99768ead2d12a0fb85abb554d7aababef81364332c033d663d7bcc4b23","source":{"kind":"arxiv","id":"1105.1715","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1715","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1715v3","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1715","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"4STY5GLWR2WS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4STY5GLWR2WS2EVA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4STY5GLW","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4STY5GLWR2WS2EVA7OC2XNKU26","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1715","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-09T16:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"611c46e6d1f02feca55e7e4afc9e2cecf4e14da5003d4ee7172033ce380b803f","abstract_canon_sha256":"7441358a72d44e381833a69e60fabe2868fdc56ff768019f374cd3552358361b"},"schema_version":"1.0"},"canonical_sha256":"e4a78e99768ead2d12a0fb85abb554d7aababef81364332c033d663d7bcc4b23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:13.369576Z","signature_b64":"IBXA2n9iwPAz4R77C7zefUel72eXNZDQW1RLKcLCM3gTOu5zws1fhzdwc91ntshEFu3zFM8c5jj6GUcKTUVZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a78e99768ead2d12a0fb85abb554d7aababef81364332c033d663d7bcc4b23","last_reissued_at":"2026-05-18T02:42:13.369166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:13.369166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1715","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":"2026-05-18T02:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hg+1vRho1v88WIiyJBkVvlG+ffpgRJJ2Hxh88COQ1QRiLkmjzE3Qx4BqCXO7RuGbJgAbborXCTp6EGyZe/0kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:32:12.999534Z"},"content_sha256":"8d347ff92a4018cb2825c3641745feaa9818a77cdbc4ceb06071f32d76cd4458","schema_version":"1.0","event_id":"sha256:8d347ff92a4018cb2825c3641745feaa9818a77cdbc4ceb06071f32d76cd4458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4STY5GLWR2WS2EVA7OC2XNKU26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic fibrations on a generic Jacobian Kummer surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abhinav Kumar","submitted_at":"2011-05-09T16:17:47Z","abstract_excerpt":"We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1715","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":"2026-05-18T02:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K12YVpmvn0APfLrPHCGzu0LNyrHWaAWd/0G+bB+pdVgiGR7CLGJhBMJCz3gHwZSKth9PLn+uzajK8lzFLoS/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:32:13.000244Z"},"content_sha256":"127180e43951ffe2f4e53b456f24f03ec38b1cfdeda7cfa070dbda75a89b96b1","schema_version":"1.0","event_id":"sha256:127180e43951ffe2f4e53b456f24f03ec38b1cfdeda7cfa070dbda75a89b96b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4STY5GLWR2WS2EVA7OC2XNKU26/bundle.json","state_url":"https://pith.science/pith/4STY5GLWR2WS2EVA7OC2XNKU26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4STY5GLWR2WS2EVA7OC2XNKU26/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":"2026-05-29T14:32:13Z","links":{"resolver":"https://pith.science/pith/4STY5GLWR2WS2EVA7OC2XNKU26","bundle":"https://pith.science/pith/4STY5GLWR2WS2EVA7OC2XNKU26/bundle.json","state":"https://pith.science/pith/4STY5GLWR2WS2EVA7OC2XNKU26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4STY5GLWR2WS2EVA7OC2XNKU26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4STY5GLWR2WS2EVA7OC2XNKU26","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":"7441358a72d44e381833a69e60fabe2868fdc56ff768019f374cd3552358361b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-09T16:17:47Z","title_canon_sha256":"611c46e6d1f02feca55e7e4afc9e2cecf4e14da5003d4ee7172033ce380b803f"},"schema_version":"1.0","source":{"id":"1105.1715","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1715","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1715v3","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1715","created_at":"2026-05-18T02:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"4STY5GLWR2WS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4STY5GLWR2WS2EVA","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4STY5GLW","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:127180e43951ffe2f4e53b456f24f03ec38b1cfdeda7cfa070dbda75a89b96b1","target":"graph","created_at":"2026-05-18T02:42:13Z","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 describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008.","authors_text":"Abhinav Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-09T16:17:47Z","title":"Elliptic fibrations on a generic Jacobian Kummer surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1715","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":"sha256:8d347ff92a4018cb2825c3641745feaa9818a77cdbc4ceb06071f32d76cd4458","target":"record","created_at":"2026-05-18T02:42:13Z","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":"7441358a72d44e381833a69e60fabe2868fdc56ff768019f374cd3552358361b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-09T16:17:47Z","title_canon_sha256":"611c46e6d1f02feca55e7e4afc9e2cecf4e14da5003d4ee7172033ce380b803f"},"schema_version":"1.0","source":{"id":"1105.1715","kind":"arxiv","version":3}},"canonical_sha256":"e4a78e99768ead2d12a0fb85abb554d7aababef81364332c033d663d7bcc4b23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a78e99768ead2d12a0fb85abb554d7aababef81364332c033d663d7bcc4b23","first_computed_at":"2026-05-18T02:42:13.369166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:13.369166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBXA2n9iwPAz4R77C7zefUel72eXNZDQW1RLKcLCM3gTOu5zws1fhzdwc91ntshEFu3zFM8c5jj6GUcKTUVZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:13.369576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1715","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d347ff92a4018cb2825c3641745feaa9818a77cdbc4ceb06071f32d76cd4458","sha256:127180e43951ffe2f4e53b456f24f03ec38b1cfdeda7cfa070dbda75a89b96b1"],"state_sha256":"a3cf70090cd8f85db137beab73cd494bd3daac29c65da1b073e38396b331cfbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8Z9TGG5eg9JLRywH34Y4LFMPv3/FBs+YB5sTiaQ1POWCwWhTEd6iIdgOCude0Iw5m2B28LWQdLDVM23m6ldBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:32:13.003929Z","bundle_sha256":"718dd227d6c430849778e50d981a05bb4570d5b05df238463ab3c2332525d731"}}