{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DKTE2XLNKUWO5CK2BZIHRNAETB","short_pith_number":"pith:DKTE2XLN","canonical_record":{"source":{"id":"0902.4165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-24T14:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"47e1a0f5f975857ff256e024865bc82eff9cba907d9ac9c218fd3dbaf44d8ad0","abstract_canon_sha256":"a2e60adfc8ea460d4b91448b486f7c907f1332795ad58dc67cd21a43c813cf67"},"schema_version":"1.0"},"canonical_sha256":"1aa64d5d6d552cee895a0e5078b40498406876b077778cfb838472141fc8cc9b","source":{"kind":"arxiv","id":"0902.4165","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4165","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4165v1","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4165","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"DKTE2XLNKUWO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DKTE2XLNKUWO5CK2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DKTE2XLN","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DKTE2XLNKUWO5CK2BZIHRNAETB","target":"record","payload":{"canonical_record":{"source":{"id":"0902.4165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-24T14:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"47e1a0f5f975857ff256e024865bc82eff9cba907d9ac9c218fd3dbaf44d8ad0","abstract_canon_sha256":"a2e60adfc8ea460d4b91448b486f7c907f1332795ad58dc67cd21a43c813cf67"},"schema_version":"1.0"},"canonical_sha256":"1aa64d5d6d552cee895a0e5078b40498406876b077778cfb838472141fc8cc9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:56.335728Z","signature_b64":"4kbFZQbukUXAzEEamPioCU814i477UnLLcUzRpqvekj9NMiis5UbIATYnSWrQAZkIJof/X3dWM5BeGY6BdszCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aa64d5d6d552cee895a0e5078b40498406876b077778cfb838472141fc8cc9b","last_reissued_at":"2026-05-18T02:24:56.335027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:56.335027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.4165","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xYZdOz7uvRpoaNUuM0oYdskuSWOZYtXKvMP4X2ptYe9LjoU4IZ7nrUUhvq4WCZEuZc2U3XmIwIxY5n0e5fRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:09:09.408336Z"},"content_sha256":"a7a6d64d08bcabc37e44736657891be174f86203fce6c37208b628c4e1c5528a","schema_version":"1.0","event_id":"sha256:a7a6d64d08bcabc37e44736657891be174f86203fce6c37208b628c4e1c5528a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DKTE2XLNKUWO5CK2BZIHRNAETB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the average number of rational points on curves of genus 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Stoll","submitted_at":"2009-02-24T14:57:21Z","abstract_excerpt":"Based on computational evidence, we formulate a number of conjectures on the distribution of rational points on curves of genus 2 over the rational numbers, in terms of the size of the coefficients of an equation of the form y^2 = f(x) >."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4165","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TGJ/E4T2Ct3oEqQwoMO24CdYmzuQJw4iWG45Mjot0EW/G29Cc4T2Cd8rJ19NDRm7CwMc6jgVZTnzsSUjMpIiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:09:09.408679Z"},"content_sha256":"00cf4f083c952b3bfdb52e6b1de58d91afb9380756a84b918ccc412d582612ea","schema_version":"1.0","event_id":"sha256:00cf4f083c952b3bfdb52e6b1de58d91afb9380756a84b918ccc412d582612ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/bundle.json","state_url":"https://pith.science/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/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":"2026-06-22T04:09:09Z","links":{"resolver":"https://pith.science/pith/DKTE2XLNKUWO5CK2BZIHRNAETB","bundle":"https://pith.science/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/bundle.json","state":"https://pith.science/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKTE2XLNKUWO5CK2BZIHRNAETB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DKTE2XLNKUWO5CK2BZIHRNAETB","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":"a2e60adfc8ea460d4b91448b486f7c907f1332795ad58dc67cd21a43c813cf67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-24T14:57:21Z","title_canon_sha256":"47e1a0f5f975857ff256e024865bc82eff9cba907d9ac9c218fd3dbaf44d8ad0"},"schema_version":"1.0","source":{"id":"0902.4165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4165","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4165v1","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4165","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"DKTE2XLNKUWO","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DKTE2XLNKUWO5CK2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DKTE2XLN","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:00cf4f083c952b3bfdb52e6b1de58d91afb9380756a84b918ccc412d582612ea","target":"graph","created_at":"2026-05-18T02:24:56Z","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":"Based on computational evidence, we formulate a number of conjectures on the distribution of rational points on curves of genus 2 over the rational numbers, in terms of the size of the coefficients of an equation of the form y^2 = f(x) >.","authors_text":"Michael Stoll","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-24T14:57:21Z","title":"On the average number of rational points on curves of genus 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4165","kind":"arxiv","version":1},"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:a7a6d64d08bcabc37e44736657891be174f86203fce6c37208b628c4e1c5528a","target":"record","created_at":"2026-05-18T02:24:56Z","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":"a2e60adfc8ea460d4b91448b486f7c907f1332795ad58dc67cd21a43c813cf67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-24T14:57:21Z","title_canon_sha256":"47e1a0f5f975857ff256e024865bc82eff9cba907d9ac9c218fd3dbaf44d8ad0"},"schema_version":"1.0","source":{"id":"0902.4165","kind":"arxiv","version":1}},"canonical_sha256":"1aa64d5d6d552cee895a0e5078b40498406876b077778cfb838472141fc8cc9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aa64d5d6d552cee895a0e5078b40498406876b077778cfb838472141fc8cc9b","first_computed_at":"2026-05-18T02:24:56.335027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.335027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4kbFZQbukUXAzEEamPioCU814i477UnLLcUzRpqvekj9NMiis5UbIATYnSWrQAZkIJof/X3dWM5BeGY6BdszCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.335728Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7a6d64d08bcabc37e44736657891be174f86203fce6c37208b628c4e1c5528a","sha256:00cf4f083c952b3bfdb52e6b1de58d91afb9380756a84b918ccc412d582612ea"],"state_sha256":"e2c30f860a53b2f24355573066ee03e8a394a50b03c823f10752d34ea3cb8230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3Ea9Bg8ayrmqGiWHdTRWh1kuHwQbVjoBa9JS2NyC411gGo+IkT/qaAKQ8FrXvsayK9orH1Iccbwh8G2y1QkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T04:09:09.410609Z","bundle_sha256":"37560eec2a941a848511be8b7c3ff702a186149a7c95d46a1e4771399163fe3f"}}