{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:H322LDSQZIOXLSUYOI3AIQPZ55","short_pith_number":"pith:H322LDSQ","canonical_record":{"source":{"id":"1512.05032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-16T02:41:37Z","cross_cats_sorted":[],"title_canon_sha256":"9660ab7d533088ae4e2dfa3d4df762a4b7209567c0ff3ea2d8c66b630a51edf6","abstract_canon_sha256":"2057f978870898095d411a7a827e691a724536675d4e968f2841a7088b51b3f5"},"schema_version":"1.0"},"canonical_sha256":"3ef5a58e50ca1d75ca9872360441f9ef498f362d511831d80a13770a96ff3187","source":{"kind":"arxiv","id":"1512.05032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05032","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05032v1","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05032","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"H322LDSQZIOX","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H322LDSQZIOXLSUY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H322LDSQ","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:H322LDSQZIOXLSUYOI3AIQPZ55","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-16T02:41:37Z","cross_cats_sorted":[],"title_canon_sha256":"9660ab7d533088ae4e2dfa3d4df762a4b7209567c0ff3ea2d8c66b630a51edf6","abstract_canon_sha256":"2057f978870898095d411a7a827e691a724536675d4e968f2841a7088b51b3f5"},"schema_version":"1.0"},"canonical_sha256":"3ef5a58e50ca1d75ca9872360441f9ef498f362d511831d80a13770a96ff3187","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:08.757241Z","signature_b64":"58uNZK4GmTdrGKY0+pyRJOxoYR0S59W4G/Wojfx42t+iOD6UFK4zC9kMDC3qUbsGEBi+speICYTLnSLwkvTTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ef5a58e50ca1d75ca9872360441f9ef498f362d511831d80a13770a96ff3187","last_reissued_at":"2026-05-18T01:18:08.756793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:08.756793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05032","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":"2026-05-18T01:18:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fa3bBX2AEbevSQlfNezj1m+BIuxw/H+AWNmVcTWoampsS/01IYtUwNLWuYuXgjuV56CYEuMOPyIn8XDuEOW3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:19:46.251436Z"},"content_sha256":"1c9ec86381cead3ff50f91ef45cacb8ab63f5bfdf00999729dd405e5adea9367","schema_version":"1.0","event_id":"sha256:1c9ec86381cead3ff50f91ef45cacb8ab63f5bfdf00999729dd405e5adea9367"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:H322LDSQZIOXLSUYOI3AIQPZ55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Heegner cycles at Eisenstein primes and the Katz $p$-adic $L$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Kriz","submitted_at":"2015-12-16T02:41:37Z","abstract_excerpt":"In this paper, we consider normalized newforms $f\\in S_k(\\Gamma_0(N),\\varepsilon_f)$ whose non-constant term Fourier coefficients are congruent to those of an Eisenstein series modulo some prime ideal above a rational prime $p$. In this situation, we establish a congruence between the anticyclotomic $p$-adic $L$-function of Bertolini-Darmon-Prasanna and the Katz two-variable $p$-adic $L$-function. From this, we derive congruences between images under the $p$-adic Abel-Jacobi map of certain generalized Heegner cycles attached to $f$ and special values of the Katz $p$-adic $L$-function.\n  In par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05032","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":"2026-05-18T01:18:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+X5rmBotlv3EQ/7zO7n37dKQ2XVtZRQxPnbIwtQnT5RxWorFrwOo73RfZctA1ZtHrTjSJRikbpGbiRlCbpH/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:19:46.251813Z"},"content_sha256":"3d6d38f3e9e25d25751c1ec8d2ee918ac219e55e857e65e16e3f00e49ca59b91","schema_version":"1.0","event_id":"sha256:3d6d38f3e9e25d25751c1ec8d2ee918ac219e55e857e65e16e3f00e49ca59b91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H322LDSQZIOXLSUYOI3AIQPZ55/bundle.json","state_url":"https://pith.science/pith/H322LDSQZIOXLSUYOI3AIQPZ55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H322LDSQZIOXLSUYOI3AIQPZ55/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":"2026-06-22T13:19:46Z","links":{"resolver":"https://pith.science/pith/H322LDSQZIOXLSUYOI3AIQPZ55","bundle":"https://pith.science/pith/H322LDSQZIOXLSUYOI3AIQPZ55/bundle.json","state":"https://pith.science/pith/H322LDSQZIOXLSUYOI3AIQPZ55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H322LDSQZIOXLSUYOI3AIQPZ55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H322LDSQZIOXLSUYOI3AIQPZ55","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":"2057f978870898095d411a7a827e691a724536675d4e968f2841a7088b51b3f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-16T02:41:37Z","title_canon_sha256":"9660ab7d533088ae4e2dfa3d4df762a4b7209567c0ff3ea2d8c66b630a51edf6"},"schema_version":"1.0","source":{"id":"1512.05032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05032","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05032v1","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05032","created_at":"2026-05-18T01:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"H322LDSQZIOX","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H322LDSQZIOXLSUY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H322LDSQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:3d6d38f3e9e25d25751c1ec8d2ee918ac219e55e857e65e16e3f00e49ca59b91","target":"graph","created_at":"2026-05-18T01:18:08Z","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":"In this paper, we consider normalized newforms $f\\in S_k(\\Gamma_0(N),\\varepsilon_f)$ whose non-constant term Fourier coefficients are congruent to those of an Eisenstein series modulo some prime ideal above a rational prime $p$. In this situation, we establish a congruence between the anticyclotomic $p$-adic $L$-function of Bertolini-Darmon-Prasanna and the Katz two-variable $p$-adic $L$-function. From this, we derive congruences between images under the $p$-adic Abel-Jacobi map of certain generalized Heegner cycles attached to $f$ and special values of the Katz $p$-adic $L$-function.\n  In par","authors_text":"Daniel Kriz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-16T02:41:37Z","title":"Generalized Heegner cycles at Eisenstein primes and the Katz $p$-adic $L$-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05032","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":"sha256:1c9ec86381cead3ff50f91ef45cacb8ab63f5bfdf00999729dd405e5adea9367","target":"record","created_at":"2026-05-18T01:18:08Z","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":"2057f978870898095d411a7a827e691a724536675d4e968f2841a7088b51b3f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-16T02:41:37Z","title_canon_sha256":"9660ab7d533088ae4e2dfa3d4df762a4b7209567c0ff3ea2d8c66b630a51edf6"},"schema_version":"1.0","source":{"id":"1512.05032","kind":"arxiv","version":1}},"canonical_sha256":"3ef5a58e50ca1d75ca9872360441f9ef498f362d511831d80a13770a96ff3187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ef5a58e50ca1d75ca9872360441f9ef498f362d511831d80a13770a96ff3187","first_computed_at":"2026-05-18T01:18:08.756793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:08.756793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58uNZK4GmTdrGKY0+pyRJOxoYR0S59W4G/Wojfx42t+iOD6UFK4zC9kMDC3qUbsGEBi+speICYTLnSLwkvTTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:08.757241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c9ec86381cead3ff50f91ef45cacb8ab63f5bfdf00999729dd405e5adea9367","sha256:3d6d38f3e9e25d25751c1ec8d2ee918ac219e55e857e65e16e3f00e49ca59b91"],"state_sha256":"be7506a5f9ab8214dc03415be31ef26dd3b629a8ec3b7e8633bb9188b32d45ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kBGVolSI/DXtQak7Dyqz1Mqz8veQMKpE6nK9CuUcVzFRng9FgMIE8nqOPtzieKszifoSfXxPJui4HbHzMT+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:19:46.253647Z","bundle_sha256":"0e63363c1a55a11e743ff11f51507252b21b2bb69abae196057036d51d3a6450"}}