{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6FFK4CPESCAZM2ZG427K3ODJMO","short_pith_number":"pith:6FFK4CPE","canonical_record":{"source":{"id":"1402.0443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T17:39:23Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1ddaf246de10b1b59440cca68edde7d43f1a032bb973df7b7415aa99123059f4","abstract_canon_sha256":"0c6009928efa6a0225dfc86059e61394e9a53c4e4fe90dff183bd0aed0fa38a3"},"schema_version":"1.0"},"canonical_sha256":"f14aae09e49081966b26e6beadb869639d16603b40d3b7bb0d9b1f70b73403a9","source":{"kind":"arxiv","id":"1402.0443","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0443","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0443v2","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0443","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"6FFK4CPESCAZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6FFK4CPESCAZM2ZG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6FFK4CPE","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6FFK4CPESCAZM2ZG427K3ODJMO","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0443","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T17:39:23Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1ddaf246de10b1b59440cca68edde7d43f1a032bb973df7b7415aa99123059f4","abstract_canon_sha256":"0c6009928efa6a0225dfc86059e61394e9a53c4e4fe90dff183bd0aed0fa38a3"},"schema_version":"1.0"},"canonical_sha256":"f14aae09e49081966b26e6beadb869639d16603b40d3b7bb0d9b1f70b73403a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:32.716127Z","signature_b64":"OGuwrgQIHE0SL3KPs+fza8+8B37E9EZ4mY12MvtTtGQbpY6iyzOeV9zGmWB3XME4B3icIinhGgzMVf4WE3/6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f14aae09e49081966b26e6beadb869639d16603b40d3b7bb0d9b1f70b73403a9","last_reissued_at":"2026-05-18T02:46:32.715713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:32.715713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0443","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIAylih/YndGHgsKtgmPz2a/azBaA3qfHq5ONcnQ5N7l3lvEg9lVvaJF4dOPkMXLuXtzhRy/KMQtTCbX3BNUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:43:31.794345Z"},"content_sha256":"15d161bbc064eb0c12779a80462c2296d7e26ceeb287aead951f52f4faa0f95d","schema_version":"1.0","event_id":"sha256:15d161bbc064eb0c12779a80462c2296d7e26ceeb287aead951f52f4faa0f95d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6FFK4CPESCAZM2ZG427K3ODJMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Another product for a Borcherds form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Stephen Kudla","submitted_at":"2014-02-03T17:39:23Z","abstract_excerpt":"In his celebrated 1998 Inventiones paper, Borcherds constructed meromorphic automorphic forms Psi(F) for arithmetic subgroups associated to even integral lattices M of signature (n,2). The input to his construction is a vector valued weakly holomorphic modular form F of weight 1 - n/2, and the resulting Borcherds form has an explicit divisor on the arithmetic quotient X = Gamma_M\\ D. Most remarkably, in the neighborhood of each cusp (= rational point boundary component), there is a beautiful product formula for Psi(F), reminiscent of the classical product formula for the Dedekind eta-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0443","kind":"arxiv","version":2},"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":"2026-05-18T02:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUcOsiUKbz8LCj4gtg/EHiKfO66nRH35/6zvs8jUXTVJMlsWFAfWvcdg9bQ4DF8s1kKr9ir410YEEpi014woDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:43:31.794698Z"},"content_sha256":"4bc48d2e5327254d1057fc8eb4708883505ae6cadf2a5567a4696275978b083f","schema_version":"1.0","event_id":"sha256:4bc48d2e5327254d1057fc8eb4708883505ae6cadf2a5567a4696275978b083f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FFK4CPESCAZM2ZG427K3ODJMO/bundle.json","state_url":"https://pith.science/pith/6FFK4CPESCAZM2ZG427K3ODJMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FFK4CPESCAZM2ZG427K3ODJMO/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":"2026-06-27T07:43:31Z","links":{"resolver":"https://pith.science/pith/6FFK4CPESCAZM2ZG427K3ODJMO","bundle":"https://pith.science/pith/6FFK4CPESCAZM2ZG427K3ODJMO/bundle.json","state":"https://pith.science/pith/6FFK4CPESCAZM2ZG427K3ODJMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FFK4CPESCAZM2ZG427K3ODJMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6FFK4CPESCAZM2ZG427K3ODJMO","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":"0c6009928efa6a0225dfc86059e61394e9a53c4e4fe90dff183bd0aed0fa38a3","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T17:39:23Z","title_canon_sha256":"1ddaf246de10b1b59440cca68edde7d43f1a032bb973df7b7415aa99123059f4"},"schema_version":"1.0","source":{"id":"1402.0443","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0443","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0443v2","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0443","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"6FFK4CPESCAZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6FFK4CPESCAZM2ZG","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6FFK4CPE","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4bc48d2e5327254d1057fc8eb4708883505ae6cadf2a5567a4696275978b083f","target":"graph","created_at":"2026-05-18T02:46:32Z","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 his celebrated 1998 Inventiones paper, Borcherds constructed meromorphic automorphic forms Psi(F) for arithmetic subgroups associated to even integral lattices M of signature (n,2). The input to his construction is a vector valued weakly holomorphic modular form F of weight 1 - n/2, and the resulting Borcherds form has an explicit divisor on the arithmetic quotient X = Gamma_M\\ D. Most remarkably, in the neighborhood of each cusp (= rational point boundary component), there is a beautiful product formula for Psi(F), reminiscent of the classical product formula for the Dedekind eta-function.","authors_text":"Stephen Kudla","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T17:39:23Z","title":"Another product for a Borcherds form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0443","kind":"arxiv","version":2},"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":"sha256:15d161bbc064eb0c12779a80462c2296d7e26ceeb287aead951f52f4faa0f95d","target":"record","created_at":"2026-05-18T02:46:32Z","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":"0c6009928efa6a0225dfc86059e61394e9a53c4e4fe90dff183bd0aed0fa38a3","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T17:39:23Z","title_canon_sha256":"1ddaf246de10b1b59440cca68edde7d43f1a032bb973df7b7415aa99123059f4"},"schema_version":"1.0","source":{"id":"1402.0443","kind":"arxiv","version":2}},"canonical_sha256":"f14aae09e49081966b26e6beadb869639d16603b40d3b7bb0d9b1f70b73403a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f14aae09e49081966b26e6beadb869639d16603b40d3b7bb0d9b1f70b73403a9","first_computed_at":"2026-05-18T02:46:32.715713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:32.715713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OGuwrgQIHE0SL3KPs+fza8+8B37E9EZ4mY12MvtTtGQbpY6iyzOeV9zGmWB3XME4B3icIinhGgzMVf4WE3/6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:32.716127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0443","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15d161bbc064eb0c12779a80462c2296d7e26ceeb287aead951f52f4faa0f95d","sha256:4bc48d2e5327254d1057fc8eb4708883505ae6cadf2a5567a4696275978b083f"],"state_sha256":"768a220853213b4c437945a30d21582196a8b50a9fd94a3b3ed1f0f37af55848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MyiebUY0C+2amn5WwmdFdpHTtwMVQyM2VNlRPvH4EBpqGO/yl4MPy27XqRuilN+NDxi4KXcJFhkFLtkMY219DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:43:31.796615Z","bundle_sha256":"22a3902be676a6ff8bbdd95898dc75c72281afab79ef49d0c68eaa10358c9785"}}