{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JAEHIWLHVMVKLRL3LJMYMRMUPH","short_pith_number":"pith:JAEHIWLH","canonical_record":{"source":{"id":"1210.4603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T00:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"63f426fc2cbf84e6263e634e7b423133cadbb6d6c44cb6f2f012854d8cf89154","abstract_canon_sha256":"912382f6e6a406dae5d087b890bc4aee68551b3de2c0597e0a25cbf34a98213f"},"schema_version":"1.0"},"canonical_sha256":"4808745967ab2aa5c57b5a5986459479cde9a68e55f463db7b7fe083ad88e7c1","source":{"kind":"arxiv","id":"1210.4603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4603","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4603v1","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4603","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"JAEHIWLHVMVK","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JAEHIWLHVMVKLRL3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JAEHIWLH","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JAEHIWLHVMVKLRL3LJMYMRMUPH","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T00:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"63f426fc2cbf84e6263e634e7b423133cadbb6d6c44cb6f2f012854d8cf89154","abstract_canon_sha256":"912382f6e6a406dae5d087b890bc4aee68551b3de2c0597e0a25cbf34a98213f"},"schema_version":"1.0"},"canonical_sha256":"4808745967ab2aa5c57b5a5986459479cde9a68e55f463db7b7fe083ad88e7c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:56.645748Z","signature_b64":"MHqzZ8BLi5tJOGLPyCJ7ITkVra+g9N4reuDK7/sfOmHw9z60rXNYZ1zpP40DV5gcBa6UYRh3dapTmNqnCe5/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4808745967ab2aa5c57b5a5986459479cde9a68e55f463db7b7fe083ad88e7c1","last_reissued_at":"2026-05-18T03:42:56.645219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:56.645219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4603","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":"2026-05-18T03:42:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kd5zfhOxDoq5wdj5xq07QoOIbI1ArMZ91NlV0N7wkpM8642bduS67ndL3EUAm9db/HepJW68pM0AAmRc//maAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:45:57.428809Z"},"content_sha256":"18dd37ade07c20b7ed56fec038766188aa5b032cee916e6188a648412c81c11e","schema_version":"1.0","event_id":"sha256:18dd37ade07c20b7ed56fec038766188aa5b032cee916e6188a648412c81c11e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JAEHIWLHVMVKLRL3LJMYMRMUPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ethan Smith, Kevin James","submitted_at":"2012-10-17T00:52:58Z","abstract_excerpt":"Let $K$ be a fixed number field, assumed to be Galois over $\\mathbb Q$. Let $r$ and $f$ be fixed integers with $f$ positive. Given an elliptic curve $E$, defined over $K$, we consider the problem of counting the number of degree $f$ prime ideals of $K$ with trace of Frobenius equal to $r$. Except in the case $f=2$, we show that \"on average,\" the number of such prime ideals with norm less than or equal to $x$ satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4603","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":"2026-05-18T03:42:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+ocpoKbnCFHmvXKMN6PliPds/23wVpKYQ50hQibLM2i7dQ89e/ErRVOwPhnAlXGoKAoQ6zyU+t9LV7tHCkrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:45:57.429171Z"},"content_sha256":"01487b7fe658befaef134af99d972fe090efa06f52745e436c9999081dd3a7ac","schema_version":"1.0","event_id":"sha256:01487b7fe658befaef134af99d972fe090efa06f52745e436c9999081dd3a7ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/bundle.json","state_url":"https://pith.science/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/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":"2026-06-04T22:45:57Z","links":{"resolver":"https://pith.science/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH","bundle":"https://pith.science/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/bundle.json","state":"https://pith.science/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAEHIWLHVMVKLRL3LJMYMRMUPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JAEHIWLHVMVKLRL3LJMYMRMUPH","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":"912382f6e6a406dae5d087b890bc4aee68551b3de2c0597e0a25cbf34a98213f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T00:52:58Z","title_canon_sha256":"63f426fc2cbf84e6263e634e7b423133cadbb6d6c44cb6f2f012854d8cf89154"},"schema_version":"1.0","source":{"id":"1210.4603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4603","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4603v1","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4603","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"JAEHIWLHVMVK","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JAEHIWLHVMVKLRL3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JAEHIWLH","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:01487b7fe658befaef134af99d972fe090efa06f52745e436c9999081dd3a7ac","target":"graph","created_at":"2026-05-18T03:42:56Z","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":"Let $K$ be a fixed number field, assumed to be Galois over $\\mathbb Q$. Let $r$ and $f$ be fixed integers with $f$ positive. Given an elliptic curve $E$, defined over $K$, we consider the problem of counting the number of degree $f$ prime ideals of $K$ with trace of Frobenius equal to $r$. Except in the case $f=2$, we show that \"on average,\" the number of such prime ideals with norm less than or equal to $x$ satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors.","authors_text":"Ethan Smith, Kevin James","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T00:52:58Z","title":"Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4603","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":"sha256:18dd37ade07c20b7ed56fec038766188aa5b032cee916e6188a648412c81c11e","target":"record","created_at":"2026-05-18T03:42:56Z","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":"912382f6e6a406dae5d087b890bc4aee68551b3de2c0597e0a25cbf34a98213f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T00:52:58Z","title_canon_sha256":"63f426fc2cbf84e6263e634e7b423133cadbb6d6c44cb6f2f012854d8cf89154"},"schema_version":"1.0","source":{"id":"1210.4603","kind":"arxiv","version":1}},"canonical_sha256":"4808745967ab2aa5c57b5a5986459479cde9a68e55f463db7b7fe083ad88e7c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4808745967ab2aa5c57b5a5986459479cde9a68e55f463db7b7fe083ad88e7c1","first_computed_at":"2026-05-18T03:42:56.645219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:56.645219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHqzZ8BLi5tJOGLPyCJ7ITkVra+g9N4reuDK7/sfOmHw9z60rXNYZ1zpP40DV5gcBa6UYRh3dapTmNqnCe5/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:56.645748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18dd37ade07c20b7ed56fec038766188aa5b032cee916e6188a648412c81c11e","sha256:01487b7fe658befaef134af99d972fe090efa06f52745e436c9999081dd3a7ac"],"state_sha256":"fab4eb331d44e753a36fe51f91b3a00631a07809f0e31083da0b035bac89dab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQcZPxA/RwLG+R8wFhxrOQvsUzcnkjQmZybE/sgo2YM6R8n1cJl1J34kmke99wZ//nC6ZoKXh3rB/v8quaMGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:45:57.431273Z","bundle_sha256":"917ed981cefe4f2739d1c55bc46567d927bd1cb7fe225fcb1adf07c303b82ca6"}}