{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MD2DM5BE355RZKUD6NXBMJC3MP","short_pith_number":"pith:MD2DM5BE","canonical_record":{"source":{"id":"1407.1018","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T19:11:20Z","cross_cats_sorted":[],"title_canon_sha256":"2130935b250bb251cbf1722865f35aa3a4c08b0fc26d0036e01b946ea9ba9442","abstract_canon_sha256":"f7a1fc78831906fa152b751bf94903c99c5e2b9860f9fa0c38430d19924590ff"},"schema_version":"1.0"},"canonical_sha256":"60f4367424df7b1caa83f36e16245b63c51fd8ff4b02cb0b827bd3833c8fa314","source":{"kind":"arxiv","id":"1407.1018","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1018","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1018v3","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1018","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"pith_short_12","alias_value":"MD2DM5BE355R","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MD2DM5BE355RZKUD","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MD2DM5BE","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MD2DM5BE355RZKUD6NXBMJC3MP","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1018","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T19:11:20Z","cross_cats_sorted":[],"title_canon_sha256":"2130935b250bb251cbf1722865f35aa3a4c08b0fc26d0036e01b946ea9ba9442","abstract_canon_sha256":"f7a1fc78831906fa152b751bf94903c99c5e2b9860f9fa0c38430d19924590ff"},"schema_version":"1.0"},"canonical_sha256":"60f4367424df7b1caa83f36e16245b63c51fd8ff4b02cb0b827bd3833c8fa314","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:12.231061Z","signature_b64":"EmLoseEHVHiRCuEyXS01X8ZGmsqvJ3p7yUzAy6nO3xDlLrenfUDjXYxXTk1XInpHuLwNL7R7NKvXbrU5yKUCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60f4367424df7b1caa83f36e16245b63c51fd8ff4b02cb0b827bd3833c8fa314","last_reissued_at":"2026-05-18T01:35:12.230588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:12.230588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1018","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":"2026-05-18T01:35:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DXgYanxeRlvOFhE+s3t697NrEqUN94PzgiWNmxxi7Fli9l0xcbdCm9vGTHg0RC+Moyzvp10EL7ZJPyaqZPdmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:42:39.925875Z"},"content_sha256":"2ffa9626fc254566c9748db981e89780dbfa7751412c32293b659a5f731de394","schema_version":"1.0","event_id":"sha256:2ffa9626fc254566c9748db981e89780dbfa7751412c32293b659a5f731de394"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MD2DM5BE355RZKUD6NXBMJC3MP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of zeta functions associated to hyperelliptic curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kaiyu Wu, Michael O. Rubinstein","submitted_at":"2014-07-03T19:11:20Z","abstract_excerpt":"Let $q$ be an odd prime power, and $H_{d,q}$ denote the set of square-free monic polynomials $D(x) \\in F_q[x]$ of degree $d$. Katz and Sarnak showed that the moments, over $H_{d,q}$, of the zeta functions associated to the curves $y^2=D(x)$, evaluated at the central point, tend, as $q \\to \\infty$, to the moments of characteristic polynomials, evaluated at the central point, of matrices in $USp(2\\lfloor (d-1)/2 \\rfloor)$. Using techniques that were originally developed for studying moments of $L$-functions over number fields, Andrade and Keating conjectured an asymptotic formula for the moments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1018","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":"2026-05-18T01:35:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSwJbCrLeuwJzkvWsjKjKc1B9j1rYrSel59j9CVF7ArzgwyjCKW8Txzh/P9XOY3LX/wICaqlDu2u0tx8qonVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:42:39.926404Z"},"content_sha256":"b0606e5ec307c2541b11a6590db790cb5efe3feb4c47d0efe194be4ff9bda5df","schema_version":"1.0","event_id":"sha256:b0606e5ec307c2541b11a6590db790cb5efe3feb4c47d0efe194be4ff9bda5df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MD2DM5BE355RZKUD6NXBMJC3MP/bundle.json","state_url":"https://pith.science/pith/MD2DM5BE355RZKUD6NXBMJC3MP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MD2DM5BE355RZKUD6NXBMJC3MP/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":"2026-06-06T14:42:39Z","links":{"resolver":"https://pith.science/pith/MD2DM5BE355RZKUD6NXBMJC3MP","bundle":"https://pith.science/pith/MD2DM5BE355RZKUD6NXBMJC3MP/bundle.json","state":"https://pith.science/pith/MD2DM5BE355RZKUD6NXBMJC3MP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MD2DM5BE355RZKUD6NXBMJC3MP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MD2DM5BE355RZKUD6NXBMJC3MP","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":"f7a1fc78831906fa152b751bf94903c99c5e2b9860f9fa0c38430d19924590ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T19:11:20Z","title_canon_sha256":"2130935b250bb251cbf1722865f35aa3a4c08b0fc26d0036e01b946ea9ba9442"},"schema_version":"1.0","source":{"id":"1407.1018","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1018","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1018v3","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1018","created_at":"2026-05-18T01:35:12Z"},{"alias_kind":"pith_short_12","alias_value":"MD2DM5BE355R","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MD2DM5BE355RZKUD","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MD2DM5BE","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:b0606e5ec307c2541b11a6590db790cb5efe3feb4c47d0efe194be4ff9bda5df","target":"graph","created_at":"2026-05-18T01:35:12Z","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":"Let $q$ be an odd prime power, and $H_{d,q}$ denote the set of square-free monic polynomials $D(x) \\in F_q[x]$ of degree $d$. Katz and Sarnak showed that the moments, over $H_{d,q}$, of the zeta functions associated to the curves $y^2=D(x)$, evaluated at the central point, tend, as $q \\to \\infty$, to the moments of characteristic polynomials, evaluated at the central point, of matrices in $USp(2\\lfloor (d-1)/2 \\rfloor)$. Using techniques that were originally developed for studying moments of $L$-functions over number fields, Andrade and Keating conjectured an asymptotic formula for the moments","authors_text":"Kaiyu Wu, Michael O. Rubinstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T19:11:20Z","title":"Moments of zeta functions associated to hyperelliptic curves over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1018","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":"sha256:2ffa9626fc254566c9748db981e89780dbfa7751412c32293b659a5f731de394","target":"record","created_at":"2026-05-18T01:35:12Z","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":"f7a1fc78831906fa152b751bf94903c99c5e2b9860f9fa0c38430d19924590ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T19:11:20Z","title_canon_sha256":"2130935b250bb251cbf1722865f35aa3a4c08b0fc26d0036e01b946ea9ba9442"},"schema_version":"1.0","source":{"id":"1407.1018","kind":"arxiv","version":3}},"canonical_sha256":"60f4367424df7b1caa83f36e16245b63c51fd8ff4b02cb0b827bd3833c8fa314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60f4367424df7b1caa83f36e16245b63c51fd8ff4b02cb0b827bd3833c8fa314","first_computed_at":"2026-05-18T01:35:12.230588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:12.230588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EmLoseEHVHiRCuEyXS01X8ZGmsqvJ3p7yUzAy6nO3xDlLrenfUDjXYxXTk1XInpHuLwNL7R7NKvXbrU5yKUCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:12.231061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1018","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ffa9626fc254566c9748db981e89780dbfa7751412c32293b659a5f731de394","sha256:b0606e5ec307c2541b11a6590db790cb5efe3feb4c47d0efe194be4ff9bda5df"],"state_sha256":"e7eb0662f6fbc472c6e8d33ab1b813dda6730526a59d27041bb13ecad7108624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"881OVS0Kc+PXvIQwvVbyQDw+LfnbyBm8WuMoDOGQxJu49nKgjKmfG3ujXtNORAiW7fUqDJ9uwpdTezYhLBh9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:42:39.929491Z","bundle_sha256":"3aa5af50f862ff57437572df1367a5827373139ab4c92686544843463f02401b"}}