{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2RYLR372G6HLI6QTQH4BH376WB","short_pith_number":"pith:2RYLR372","canonical_record":{"source":{"id":"2412.05867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"06bc7c92069bee75f1a4ebc3fd773cc385582b04de75a1a4feaa5cc6cb55ccb7","abstract_canon_sha256":"63bd797a9c3e345027feb92db6809b6fd267a0244ccc93bb0db7d0cb91c88505"},"schema_version":"1.0"},"canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","source":{"kind":"arxiv","id":"2412.05867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.05867","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"arxiv_version","alias_value":"2412.05867v1","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.05867","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_12","alias_value":"2RYLR372G6HL","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_16","alias_value":"2RYLR372G6HLI6QT","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_8","alias_value":"2RYLR372","created_at":"2026-07-05T09:46:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2RYLR372G6HLI6QTQH4BH376WB","target":"record","payload":{"canonical_record":{"source":{"id":"2412.05867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"06bc7c92069bee75f1a4ebc3fd773cc385582b04de75a1a4feaa5cc6cb55ccb7","abstract_canon_sha256":"63bd797a9c3e345027feb92db6809b6fd267a0244ccc93bb0db7d0cb91c88505"},"schema_version":"1.0"},"canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:46:10.903483Z","signature_b64":"X4d8ASK4/L8jnRyhd9DHZRymL+sr3T1lXMU+LVUA7vpcJuKntLI0ZENhfI1Kk1L+SS3Dhcr8CWUs+w22RGtiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","last_reissued_at":"2026-07-05T09:46:10.902931Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:46:10.902931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.05867","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":"2026-07-05T09:46:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sH7/PX7PMYCLSByKxgcQ217qLzV5RBAH97uq6iYupfO0EJBFFPwB54mHU/CxFKD4KJgGVJ3GVEfqoFPam3HWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:13:04.013668Z"},"content_sha256":"4f35129ee6c8ad11f8ab4f3dfc4cb4eaff2f26afc35fef469fe189c705c3bce8","schema_version":"1.0","event_id":"sha256:4f35129ee6c8ad11f8ab4f3dfc4cb4eaff2f26afc35fef469fe189c705c3bce8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2RYLR372G6HLI6QTQH4BH376WB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $L$-functions of Hecke characters and anticyclotomic towers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Haijun Jia","submitted_at":"2024-12-08T09:15:17Z","abstract_excerpt":"In this paper, we generalize a work of Rohrlich. Let $K/\\mathbb{Q}$ be an imaginary quadratic field and $\\phi$ be a Hecke character of $K$ of infinite type (1,0) whose restriction to $\\mathbb{Q}$ is the quadratic character corresponding to $K/\\mathbb{Q}$. We consider a class of Hecke characters $\\chi$, which are anticyclotomic twists of $\\phi$ with ramification in a prescribed finite set of primes. We shall prove the central vanishing order of the Hecke $L$-function $L(s,\\chi$) attached to each $\\chi$ is 0 or 1 depending on the root number $W(\\chi)$ for all but finitely many such $\\chi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.05867","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.05867/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":"2026-07-05T09:46:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"418v0kFGPdFe2WA8LLIkKgoJrWh9bClEWZZhLIvDK/C6rv2N1CdHUWm1I/xYkPoEA8eHwOVpBZbjCsA0cT0bCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:13:04.014776Z"},"content_sha256":"5de100b821208cbb01514ae48961a259f016d3556f457e33f6a2fe56ab374b69","schema_version":"1.0","event_id":"sha256:5de100b821208cbb01514ae48961a259f016d3556f457e33f6a2fe56ab374b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2RYLR372G6HLI6QTQH4BH376WB/bundle.json","state_url":"https://pith.science/pith/2RYLR372G6HLI6QTQH4BH376WB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2RYLR372G6HLI6QTQH4BH376WB/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":"2026-08-12T15:13:04Z","links":{"resolver":"https://pith.science/pith/2RYLR372G6HLI6QTQH4BH376WB","bundle":"https://pith.science/pith/2RYLR372G6HLI6QTQH4BH376WB/bundle.json","state":"https://pith.science/pith/2RYLR372G6HLI6QTQH4BH376WB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2RYLR372G6HLI6QTQH4BH376WB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2RYLR372G6HLI6QTQH4BH376WB","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":"63bd797a9c3e345027feb92db6809b6fd267a0244ccc93bb0db7d0cb91c88505","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","title_canon_sha256":"06bc7c92069bee75f1a4ebc3fd773cc385582b04de75a1a4feaa5cc6cb55ccb7"},"schema_version":"1.0","source":{"id":"2412.05867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.05867","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"arxiv_version","alias_value":"2412.05867v1","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.05867","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_12","alias_value":"2RYLR372G6HL","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_16","alias_value":"2RYLR372G6HLI6QT","created_at":"2026-07-05T09:46:10Z"},{"alias_kind":"pith_short_8","alias_value":"2RYLR372","created_at":"2026-07-05T09:46:10Z"}],"graph_snapshots":[{"event_id":"sha256:5de100b821208cbb01514ae48961a259f016d3556f457e33f6a2fe56ab374b69","target":"graph","created_at":"2026-07-05T09:46:10Z","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/2412.05867/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we generalize a work of Rohrlich. Let $K/\\mathbb{Q}$ be an imaginary quadratic field and $\\phi$ be a Hecke character of $K$ of infinite type (1,0) whose restriction to $\\mathbb{Q}$ is the quadratic character corresponding to $K/\\mathbb{Q}$. We consider a class of Hecke characters $\\chi$, which are anticyclotomic twists of $\\phi$ with ramification in a prescribed finite set of primes. We shall prove the central vanishing order of the Hecke $L$-function $L(s,\\chi$) attached to each $\\chi$ is 0 or 1 depending on the root number $W(\\chi)$ for all but finitely many such $\\chi$.","authors_text":"Haijun Jia","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","title":"On $L$-functions of Hecke characters and anticyclotomic towers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.05867","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":"sha256:4f35129ee6c8ad11f8ab4f3dfc4cb4eaff2f26afc35fef469fe189c705c3bce8","target":"record","created_at":"2026-07-05T09:46:10Z","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":"63bd797a9c3e345027feb92db6809b6fd267a0244ccc93bb0db7d0cb91c88505","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","title_canon_sha256":"06bc7c92069bee75f1a4ebc3fd773cc385582b04de75a1a4feaa5cc6cb55ccb7"},"schema_version":"1.0","source":{"id":"2412.05867","kind":"arxiv","version":1}},"canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","first_computed_at":"2026-07-05T09:46:10.902931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:46:10.902931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X4d8ASK4/L8jnRyhd9DHZRymL+sr3T1lXMU+LVUA7vpcJuKntLI0ZENhfI1Kk1L+SS3Dhcr8CWUs+w22RGtiDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:46:10.903483Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.05867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f35129ee6c8ad11f8ab4f3dfc4cb4eaff2f26afc35fef469fe189c705c3bce8","sha256:5de100b821208cbb01514ae48961a259f016d3556f457e33f6a2fe56ab374b69"],"state_sha256":"081ef4b7cf13b22ee1d47a54c27d19d2ae1e4610281d79e0a486adc0142237b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mkcLcRsHVnTJMY5uBwJtPPA25CsIaX2278iVRPoOLP4ZCG7anooE+crMARsLnwzAED2JJ4uMYy6RklW315P+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:13:04.022069Z","bundle_sha256":"83d564779eaab6cf94b5a0e48167a954791d2025008c7eb9913733d349131e2f"}}