{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AJ3ICX7ZFRHY4DFHOSHRQSKV5S","short_pith_number":"pith:AJ3ICX7Z","canonical_record":{"source":{"id":"1505.02693","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T16:22:17Z","cross_cats_sorted":[],"title_canon_sha256":"bba28bf42745b09d380d7263c81c9661f37a04beff0f9ff811b58874237b8310","abstract_canon_sha256":"354829f51fccda38044dccce96b8565763c452a9344c2b27d479716b56b81be3"},"schema_version":"1.0"},"canonical_sha256":"0276815ff92c4f8e0ca7748f184955eca6b056b5167e5e14cea217fb39b4a529","source":{"kind":"arxiv","id":"1505.02693","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02693","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02693v2","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02693","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"AJ3ICX7ZFRHY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJ3ICX7ZFRHY4DFH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJ3ICX7Z","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AJ3ICX7ZFRHY4DFHOSHRQSKV5S","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02693","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T16:22:17Z","cross_cats_sorted":[],"title_canon_sha256":"bba28bf42745b09d380d7263c81c9661f37a04beff0f9ff811b58874237b8310","abstract_canon_sha256":"354829f51fccda38044dccce96b8565763c452a9344c2b27d479716b56b81be3"},"schema_version":"1.0"},"canonical_sha256":"0276815ff92c4f8e0ca7748f184955eca6b056b5167e5e14cea217fb39b4a529","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:34.566785Z","signature_b64":"slz4UzGLYEH/772bPogpzxXCwdSWavsovjBftwHnwfWcNs+dOzpBuGnodavfhV6y3eHlLCDjk67eQf0K7IjuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0276815ff92c4f8e0ca7748f184955eca6b056b5167e5e14cea217fb39b4a529","last_reissued_at":"2026-05-18T01:59:34.566164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:34.566164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02693","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":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"96lkfr7zMPhDInMZZOP7oN3u2SK8snEMU1ckcXpwRKk0CS9A3MtX8/2sEKzBbom7Ks7rFN7qIy8prw8cU7eADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:44.230081Z"},"content_sha256":"15a2ab5a399329c59b1b575ea5e1154b3bc4c59688622a6559bd042d84731170","schema_version":"1.0","event_id":"sha256:15a2ab5a399329c59b1b575ea5e1154b3bc4c59688622a6559bd042d84731170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AJ3ICX7ZFRHY4DFHOSHRQSKV5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector valued theta functions associated with binary quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephan Ehlen","submitted_at":"2015-05-11T16:22:17Z","abstract_excerpt":"We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta functions of weight one and determine an orthogonal basis with respect to the Petersson inner product. Moreover, we give an explicit formula for the Petersson norms of the elements of this basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02693","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":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhmJhelOqHSmm6gPi1do83zTUxn5YdPOZYtAimMh79srp5k+c/nwEPX/TT0lW9LoGVK4K18OqRFxEaZM1MnkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:44.230496Z"},"content_sha256":"b6714bdd93e1a5553af94535032efbb47f69e0ccd2c3d5d8c18085ed03ec70bc","schema_version":"1.0","event_id":"sha256:b6714bdd93e1a5553af94535032efbb47f69e0ccd2c3d5d8c18085ed03ec70bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/bundle.json","state_url":"https://pith.science/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/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":"2026-06-24T20:02:44Z","links":{"resolver":"https://pith.science/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S","bundle":"https://pith.science/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/bundle.json","state":"https://pith.science/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJ3ICX7ZFRHY4DFHOSHRQSKV5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AJ3ICX7ZFRHY4DFHOSHRQSKV5S","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":"354829f51fccda38044dccce96b8565763c452a9344c2b27d479716b56b81be3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T16:22:17Z","title_canon_sha256":"bba28bf42745b09d380d7263c81c9661f37a04beff0f9ff811b58874237b8310"},"schema_version":"1.0","source":{"id":"1505.02693","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02693","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02693v2","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02693","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"AJ3ICX7ZFRHY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJ3ICX7ZFRHY4DFH","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJ3ICX7Z","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b6714bdd93e1a5553af94535032efbb47f69e0ccd2c3d5d8c18085ed03ec70bc","target":"graph","created_at":"2026-05-18T01:59:34Z","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":"We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta functions of weight one and determine an orthogonal basis with respect to the Petersson inner product. Moreover, we give an explicit formula for the Petersson norms of the elements of this basis.","authors_text":"Stephan Ehlen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T16:22:17Z","title":"Vector valued theta functions associated with binary quadratic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02693","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":"sha256:15a2ab5a399329c59b1b575ea5e1154b3bc4c59688622a6559bd042d84731170","target":"record","created_at":"2026-05-18T01:59:34Z","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":"354829f51fccda38044dccce96b8565763c452a9344c2b27d479716b56b81be3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T16:22:17Z","title_canon_sha256":"bba28bf42745b09d380d7263c81c9661f37a04beff0f9ff811b58874237b8310"},"schema_version":"1.0","source":{"id":"1505.02693","kind":"arxiv","version":2}},"canonical_sha256":"0276815ff92c4f8e0ca7748f184955eca6b056b5167e5e14cea217fb39b4a529","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0276815ff92c4f8e0ca7748f184955eca6b056b5167e5e14cea217fb39b4a529","first_computed_at":"2026-05-18T01:59:34.566164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:34.566164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"slz4UzGLYEH/772bPogpzxXCwdSWavsovjBftwHnwfWcNs+dOzpBuGnodavfhV6y3eHlLCDjk67eQf0K7IjuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:34.566785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02693","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15a2ab5a399329c59b1b575ea5e1154b3bc4c59688622a6559bd042d84731170","sha256:b6714bdd93e1a5553af94535032efbb47f69e0ccd2c3d5d8c18085ed03ec70bc"],"state_sha256":"fb75a841034c1d394568a46529f3d2cb0067ddcb4164331b8c3aa19ec8c43d0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z0C/QyaI77d9jEkfmqe5pgpnkkZO/TuOonCte1HyYjWW2t5M69JBiXLHBJ9Sgf2PsFqNZ1v30w4ohzT4pIMJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:02:44.232521Z","bundle_sha256":"90114a53d687fe9cbeaa86aa3fb9727acfb56839cec8dce1f36860b75853b209"}}