{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WL22CRSBVHGOFUMZ7H5C7ILLBR","short_pith_number":"pith:WL22CRSB","canonical_record":{"source":{"id":"1309.3812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T01:06:19Z","cross_cats_sorted":[],"title_canon_sha256":"c668a62d99668f04b1ab7269407822eebaae01e760efd8c8214b9c29d38da9b5","abstract_canon_sha256":"066707e5a3eabd51994ffc569b76fd5961ad4c280457c821d78b37a453fd1eaa"},"schema_version":"1.0"},"canonical_sha256":"b2f5a14641a9cce2d199f9fa2fa16b0c5a5125c87d57b808f37c79df51069030","source":{"kind":"arxiv","id":"1309.3812","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3812","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3812v1","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3812","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"pith_short_12","alias_value":"WL22CRSBVHGO","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WL22CRSBVHGOFUMZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WL22CRSB","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WL22CRSBVHGOFUMZ7H5C7ILLBR","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T01:06:19Z","cross_cats_sorted":[],"title_canon_sha256":"c668a62d99668f04b1ab7269407822eebaae01e760efd8c8214b9c29d38da9b5","abstract_canon_sha256":"066707e5a3eabd51994ffc569b76fd5961ad4c280457c821d78b37a453fd1eaa"},"schema_version":"1.0"},"canonical_sha256":"b2f5a14641a9cce2d199f9fa2fa16b0c5a5125c87d57b808f37c79df51069030","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:49.766208Z","signature_b64":"XLwdcXBe56p5wxbR/ADY3TFuaREtMXIcSuZT3pheLXiW8o4Lfhpx/xTkbZ/tjLJ+4oF2XwAyO3aX6mIqK8WkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2f5a14641a9cce2d199f9fa2fa16b0c5a5125c87d57b808f37c79df51069030","last_reissued_at":"2026-05-17T23:44:49.765653Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:49.765653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3812","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":"2026-05-17T23:44:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"naxCsvV+plAUpor1cHWLaJmpwBBuF5lS/cDM+T8eOawAewA4z+xNhBRmwktqgeqlQsdvTOzax1+EpkC78J0QDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:19:38.644424Z"},"content_sha256":"f679201596cb8f18b6499fece2d41c09291c6a75e774e0c3d38f7a7893b3fd42","schema_version":"1.0","event_id":"sha256:f679201596cb8f18b6499fece2d41c09291c6a75e774e0c3d38f7a7893b3fd42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WL22CRSBVHGOFUMZ7H5C7ILLBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Caleb Shor, Tony Shaska","submitted_at":"2013-09-16T01:06:19Z","abstract_excerpt":"In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same theta functions. We also look at a generalization of codes over imaginary quadratic fields, providing examples of non-equivalent pairs with the same theta function for $p=3$ and $p=5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3812","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":"2026-05-17T23:44:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFuK7TK6GlqvVI/g2aaIMiUml/w3K3b0i6iEH3IkWrGB4allAY99KgYPqLaDzinUY1elF5pL3kwIEi11/V1NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:19:38.645130Z"},"content_sha256":"cc1ce8afcbe34d5304c7c095e26262ceb83418edd8ec129919e20d194d1922e1","schema_version":"1.0","event_id":"sha256:cc1ce8afcbe34d5304c7c095e26262ceb83418edd8ec129919e20d194d1922e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/bundle.json","state_url":"https://pith.science/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/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":"2026-06-08T04:19:38Z","links":{"resolver":"https://pith.science/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR","bundle":"https://pith.science/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/bundle.json","state":"https://pith.science/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WL22CRSBVHGOFUMZ7H5C7ILLBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WL22CRSBVHGOFUMZ7H5C7ILLBR","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":"066707e5a3eabd51994ffc569b76fd5961ad4c280457c821d78b37a453fd1eaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T01:06:19Z","title_canon_sha256":"c668a62d99668f04b1ab7269407822eebaae01e760efd8c8214b9c29d38da9b5"},"schema_version":"1.0","source":{"id":"1309.3812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3812","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3812v1","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3812","created_at":"2026-05-17T23:44:49Z"},{"alias_kind":"pith_short_12","alias_value":"WL22CRSBVHGO","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WL22CRSBVHGOFUMZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WL22CRSB","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:cc1ce8afcbe34d5304c7c095e26262ceb83418edd8ec129919e20d194d1922e1","target":"graph","created_at":"2026-05-17T23:44:49Z","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 continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same theta functions. We also look at a generalization of codes over imaginary quadratic fields, providing examples of non-equivalent pairs with the same theta function for $p=3$ and $p=5$.","authors_text":"Caleb Shor, Tony Shaska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T01:06:19Z","title":"Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3812","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:f679201596cb8f18b6499fece2d41c09291c6a75e774e0c3d38f7a7893b3fd42","target":"record","created_at":"2026-05-17T23:44:49Z","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":"066707e5a3eabd51994ffc569b76fd5961ad4c280457c821d78b37a453fd1eaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T01:06:19Z","title_canon_sha256":"c668a62d99668f04b1ab7269407822eebaae01e760efd8c8214b9c29d38da9b5"},"schema_version":"1.0","source":{"id":"1309.3812","kind":"arxiv","version":1}},"canonical_sha256":"b2f5a14641a9cce2d199f9fa2fa16b0c5a5125c87d57b808f37c79df51069030","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2f5a14641a9cce2d199f9fa2fa16b0c5a5125c87d57b808f37c79df51069030","first_computed_at":"2026-05-17T23:44:49.765653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:49.765653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLwdcXBe56p5wxbR/ADY3TFuaREtMXIcSuZT3pheLXiW8o4Lfhpx/xTkbZ/tjLJ+4oF2XwAyO3aX6mIqK8WkAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:49.766208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f679201596cb8f18b6499fece2d41c09291c6a75e774e0c3d38f7a7893b3fd42","sha256:cc1ce8afcbe34d5304c7c095e26262ceb83418edd8ec129919e20d194d1922e1"],"state_sha256":"715a5f86b3d67f5f4c6fff63410e431d82d778bdd321253f416b83a32efbbef1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUHg1FWUGPOf/TFZr/Ejkl2MgMyFjLZNebDCS+QF6oQ8fEo9zPWwgbEhtuUUWGXh9FEdvqq3rPq0ahPqDb7YBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:19:38.649877Z","bundle_sha256":"6d5f703873a81c5915b4b78b6a38acccf73b21156cb34e069edfd31cda96217b"}}