{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:SWVPYSLSMFEXFESK52S3RMJAZN","short_pith_number":"pith:SWVPYSLS","canonical_record":{"source":{"id":"2002.02067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-06T02:02:13Z","cross_cats_sorted":[],"title_canon_sha256":"464e1a1dedbfd6b8b9007cb14ff0e0c6ecc2bc4ea16ec6cbb4c7a43c0b19103c","abstract_canon_sha256":"38e05903db8330c49e73984c4ced01b639b061854bc6a5ffa4d56e6f5b392f91"},"schema_version":"1.0"},"canonical_sha256":"95aafc4972614972924aeea5b8b120cb435f0da3f1ece77c4c68d019357642c3","source":{"kind":"arxiv","id":"2002.02067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02067","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02067v2","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02067","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"SWVPYSLSMFEX","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_16","alias_value":"SWVPYSLSMFEXFESK","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_8","alias_value":"SWVPYSLS","created_at":"2026-07-05T01:54:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:SWVPYSLSMFEXFESK52S3RMJAZN","target":"record","payload":{"canonical_record":{"source":{"id":"2002.02067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-06T02:02:13Z","cross_cats_sorted":[],"title_canon_sha256":"464e1a1dedbfd6b8b9007cb14ff0e0c6ecc2bc4ea16ec6cbb4c7a43c0b19103c","abstract_canon_sha256":"38e05903db8330c49e73984c4ced01b639b061854bc6a5ffa4d56e6f5b392f91"},"schema_version":"1.0"},"canonical_sha256":"95aafc4972614972924aeea5b8b120cb435f0da3f1ece77c4c68d019357642c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:54:27.479449Z","signature_b64":"qvV9n4xYQqgIis7/aLNWeq0RqIqPpJwAD24iyNmB+B+x075Dql/cAqHB3jjvSdYobM1LRuPqP644ZyWgbuutCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95aafc4972614972924aeea5b8b120cb435f0da3f1ece77c4c68d019357642c3","last_reissued_at":"2026-07-05T01:54:27.478954Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:54:27.478954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.02067","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":"2026-07-05T01:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NzG1j5mCPA9bG+R8Hz0N+IHBcKEJDFetbnB6ZbwHlmWZv8Ty5mO6Bvgrm0mYCkmCp1ShVUSIczNS2OFEhWZlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T09:16:13.990335Z"},"content_sha256":"7d6b65251fede8a0d9435e57d75e79d95e021dff963f56fae4047afd89bdfac8","schema_version":"1.0","event_id":"sha256:7d6b65251fede8a0d9435e57d75e79d95e021dff963f56fae4047afd89bdfac8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:SWVPYSLSMFEXFESK52S3RMJAZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restrictions on Weil polynomials of Jacobians of hyperelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Caleb Springer, Edgar Costa, Mckenzie West, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker","submitted_at":"2020-02-06T02:02:13Z","abstract_excerpt":"Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed ${g\\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\\to\\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.02067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKIQVCkzbZiAcXeeGjTST9uJOqxpzkLpDWxgPP0HF8dQ0zYmwMNXSGLvuV/vaKjlGZZfPN3ncMrj3xgjIuHaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T09:16:13.990720Z"},"content_sha256":"3c7667bea5284e602d5fb88bdb6daaf798143014e334602ed5e410a454f9ea2a","schema_version":"1.0","event_id":"sha256:3c7667bea5284e602d5fb88bdb6daaf798143014e334602ed5e410a454f9ea2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWVPYSLSMFEXFESK52S3RMJAZN/bundle.json","state_url":"https://pith.science/pith/SWVPYSLSMFEXFESK52S3RMJAZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWVPYSLSMFEXFESK52S3RMJAZN/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":"2026-07-10T09:16:13Z","links":{"resolver":"https://pith.science/pith/SWVPYSLSMFEXFESK52S3RMJAZN","bundle":"https://pith.science/pith/SWVPYSLSMFEXFESK52S3RMJAZN/bundle.json","state":"https://pith.science/pith/SWVPYSLSMFEXFESK52S3RMJAZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWVPYSLSMFEXFESK52S3RMJAZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:SWVPYSLSMFEXFESK52S3RMJAZN","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":"38e05903db8330c49e73984c4ced01b639b061854bc6a5ffa4d56e6f5b392f91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-06T02:02:13Z","title_canon_sha256":"464e1a1dedbfd6b8b9007cb14ff0e0c6ecc2bc4ea16ec6cbb4c7a43c0b19103c"},"schema_version":"1.0","source":{"id":"2002.02067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02067","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02067v2","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02067","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"SWVPYSLSMFEX","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_16","alias_value":"SWVPYSLSMFEXFESK","created_at":"2026-07-05T01:54:27Z"},{"alias_kind":"pith_short_8","alias_value":"SWVPYSLS","created_at":"2026-07-05T01:54:27Z"}],"graph_snapshots":[{"event_id":"sha256:3c7667bea5284e602d5fb88bdb6daaf798143014e334602ed5e410a454f9ea2a","target":"graph","created_at":"2026-07-05T01:54:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.02067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed ${g\\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\\to\\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of","authors_text":"Caleb Springer, Edgar Costa, Mckenzie West, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-06T02:02:13Z","title":"Restrictions on Weil polynomials of Jacobians of hyperelliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02067","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":"sha256:7d6b65251fede8a0d9435e57d75e79d95e021dff963f56fae4047afd89bdfac8","target":"record","created_at":"2026-07-05T01:54:27Z","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":"38e05903db8330c49e73984c4ced01b639b061854bc6a5ffa4d56e6f5b392f91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-06T02:02:13Z","title_canon_sha256":"464e1a1dedbfd6b8b9007cb14ff0e0c6ecc2bc4ea16ec6cbb4c7a43c0b19103c"},"schema_version":"1.0","source":{"id":"2002.02067","kind":"arxiv","version":2}},"canonical_sha256":"95aafc4972614972924aeea5b8b120cb435f0da3f1ece77c4c68d019357642c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95aafc4972614972924aeea5b8b120cb435f0da3f1ece77c4c68d019357642c3","first_computed_at":"2026-07-05T01:54:27.478954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:54:27.478954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qvV9n4xYQqgIis7/aLNWeq0RqIqPpJwAD24iyNmB+B+x075Dql/cAqHB3jjvSdYobM1LRuPqP644ZyWgbuutCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:54:27.479449Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.02067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d6b65251fede8a0d9435e57d75e79d95e021dff963f56fae4047afd89bdfac8","sha256:3c7667bea5284e602d5fb88bdb6daaf798143014e334602ed5e410a454f9ea2a"],"state_sha256":"4560157ccdb39fb223f8ff84df42d5715b4ec8c71ce800894eefd8b1fa50f2b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9xCkjBd0FFXmmtoumIiEjRnQaU5mQK/s4jV8sJ8rXoOwXdktmdteAEs2nRxGY9ALZyHW3Ifn/P1I1DdJAACDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T09:16:13.993245Z","bundle_sha256":"7de4bfdbcfefac085ae264cd9bea0b15bce735a3cb0b06c6ebd078516afd8579"}}