{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7HI52MVXDDXQOFLGEI346AC5KD","short_pith_number":"pith:7HI52MVX","canonical_record":{"source":{"id":"1504.00852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T14:37:36Z","cross_cats_sorted":[],"title_canon_sha256":"60d7e00db41a151e40be24baf695f039b87b60c6028e5c0ffdfc884eb6cc91d3","abstract_canon_sha256":"ab906ddc57c1506fad6f2eeee88724caba48f74b380b9036c105a887365a740a"},"schema_version":"1.0"},"canonical_sha256":"f9d1dd32b718ef0715662237cf005d50d65a2b11b75725dc4492cd5b36ea8a52","source":{"kind":"arxiv","id":"1504.00852","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00852","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00852v3","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00852","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"7HI52MVXDDXQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7HI52MVXDDXQOFLG","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7HI52MVX","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7HI52MVXDDXQOFLGEI346AC5KD","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T14:37:36Z","cross_cats_sorted":[],"title_canon_sha256":"60d7e00db41a151e40be24baf695f039b87b60c6028e5c0ffdfc884eb6cc91d3","abstract_canon_sha256":"ab906ddc57c1506fad6f2eeee88724caba48f74b380b9036c105a887365a740a"},"schema_version":"1.0"},"canonical_sha256":"f9d1dd32b718ef0715662237cf005d50d65a2b11b75725dc4492cd5b36ea8a52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:13.884061Z","signature_b64":"Qxl/yBKXVHB/hsnBhqJ8WjrSgh0RvEfiQJI2yofZyATXJWZl5JMXmrOxIhG4Z2ZAO+EkuMLgjsMDK4Gm4vnKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9d1dd32b718ef0715662237cf005d50d65a2b11b75725dc4492cd5b36ea8a52","last_reissued_at":"2026-05-17T23:53:13.883422Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:13.883422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00852","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":"2026-05-17T23:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBbL4L3m+VrhKQSicJWRozRklOL9XYFNUwbwV75SHfz2xYs722WH/Yo3B5g7Tz9n/cpf+ETJ/IR/Q5tqr+hvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:40:13.550366Z"},"content_sha256":"bc4a4fa24eab23761ad5ad88af59f6eeb24196e6a54d83d35887b905a43ec3aa","schema_version":"1.0","event_id":"sha256:bc4a4fa24eab23761ad5ad88af59f6eeb24196e6a54d83d35887b905a43ec3aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7HI52MVXDDXQOFLGEI346AC5KD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Height pairings on orthogonal Shimura varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Howard, Eyal Z. Goren, Fabrizio Andreatta, Keerthi Madapusi Pera","submitted_at":"2015-04-03T14:37:36Z","abstract_excerpt":"Let $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of special divisors and CM points on $M$ to the central derivatives of certain $L$-functions. Each such $L$-function is the Rankin-Selberg convolution associated with a cusp form of half-integral weight $n/2 +1 $, and the weight $n/2$ theta series of a positive definite quadratic space of rank $n$.\n  When $n=1$ the Shimura variety $M$ is a classical quaternionic S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00852","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":"2026-05-17T23:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSEBgabw10DOWMqm4rBW66nMKO6EifFhIBQ3gQyzbl3STRND55ixfwfCnfHgFCjBJLOcyGBOoAAdhdW//gx/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:40:13.550717Z"},"content_sha256":"f8c5a4bc1c2212cc6ee42370ba8d32be6134475164f1a91e3619b03c499400b5","schema_version":"1.0","event_id":"sha256:f8c5a4bc1c2212cc6ee42370ba8d32be6134475164f1a91e3619b03c499400b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HI52MVXDDXQOFLGEI346AC5KD/bundle.json","state_url":"https://pith.science/pith/7HI52MVXDDXQOFLGEI346AC5KD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HI52MVXDDXQOFLGEI346AC5KD/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":"2026-06-03T08:40:13Z","links":{"resolver":"https://pith.science/pith/7HI52MVXDDXQOFLGEI346AC5KD","bundle":"https://pith.science/pith/7HI52MVXDDXQOFLGEI346AC5KD/bundle.json","state":"https://pith.science/pith/7HI52MVXDDXQOFLGEI346AC5KD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HI52MVXDDXQOFLGEI346AC5KD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7HI52MVXDDXQOFLGEI346AC5KD","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":"ab906ddc57c1506fad6f2eeee88724caba48f74b380b9036c105a887365a740a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T14:37:36Z","title_canon_sha256":"60d7e00db41a151e40be24baf695f039b87b60c6028e5c0ffdfc884eb6cc91d3"},"schema_version":"1.0","source":{"id":"1504.00852","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00852","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00852v3","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00852","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"7HI52MVXDDXQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7HI52MVXDDXQOFLG","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7HI52MVX","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:f8c5a4bc1c2212cc6ee42370ba8d32be6134475164f1a91e3619b03c499400b5","target":"graph","created_at":"2026-05-17T23:53:13Z","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 $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of special divisors and CM points on $M$ to the central derivatives of certain $L$-functions. Each such $L$-function is the Rankin-Selberg convolution associated with a cusp form of half-integral weight $n/2 +1 $, and the weight $n/2$ theta series of a positive definite quadratic space of rank $n$.\n  When $n=1$ the Shimura variety $M$ is a classical quaternionic S","authors_text":"Benjamin Howard, Eyal Z. Goren, Fabrizio Andreatta, Keerthi Madapusi Pera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T14:37:36Z","title":"Height pairings on orthogonal Shimura varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00852","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:bc4a4fa24eab23761ad5ad88af59f6eeb24196e6a54d83d35887b905a43ec3aa","target":"record","created_at":"2026-05-17T23:53:13Z","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":"ab906ddc57c1506fad6f2eeee88724caba48f74b380b9036c105a887365a740a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T14:37:36Z","title_canon_sha256":"60d7e00db41a151e40be24baf695f039b87b60c6028e5c0ffdfc884eb6cc91d3"},"schema_version":"1.0","source":{"id":"1504.00852","kind":"arxiv","version":3}},"canonical_sha256":"f9d1dd32b718ef0715662237cf005d50d65a2b11b75725dc4492cd5b36ea8a52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d1dd32b718ef0715662237cf005d50d65a2b11b75725dc4492cd5b36ea8a52","first_computed_at":"2026-05-17T23:53:13.883422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:13.883422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qxl/yBKXVHB/hsnBhqJ8WjrSgh0RvEfiQJI2yofZyATXJWZl5JMXmrOxIhG4Z2ZAO+EkuMLgjsMDK4Gm4vnKDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:13.884061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00852","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc4a4fa24eab23761ad5ad88af59f6eeb24196e6a54d83d35887b905a43ec3aa","sha256:f8c5a4bc1c2212cc6ee42370ba8d32be6134475164f1a91e3619b03c499400b5"],"state_sha256":"7a184bdd57d3f0ffaa4931ffa034cd1a0de01e7a05d3cae4ce8a8e456ecb7b5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WX43E6xOm3oibt7wceEKgdmMmhdkqkcwtHDdE58BKlFCCaljhwK/1EfsBRPrHbHpYAN4fYUvj/NjOIniJnqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:40:13.552670Z","bundle_sha256":"667c42a2163d312413b7080c57056cb6144a9f8a585e7d9f5f070dcbd25949d1"}}