{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GCVGR5CNCWUANESOM7EPMKKWZ7","short_pith_number":"pith:GCVGR5CN","canonical_record":{"source":{"id":"1205.4253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T20:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"93a3ad2d700b00f05cbf7e8e15b0b70c281143a31b5d85c9a588bf536dd8b8cc","abstract_canon_sha256":"a746abf21d4ba3fe0cec09feda0d113bd4e477b855c42dc9a68ff138a326fbb7"},"schema_version":"1.0"},"canonical_sha256":"30aa68f44d15a806924e67c8f62956cffddf7e10dbf074fc92b9f1e3a4ec8cc1","source":{"kind":"arxiv","id":"1205.4253","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4253","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4253v1","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4253","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"GCVGR5CNCWUA","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GCVGR5CNCWUANESO","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GCVGR5CN","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GCVGR5CNCWUANESOM7EPMKKWZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T20:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"93a3ad2d700b00f05cbf7e8e15b0b70c281143a31b5d85c9a588bf536dd8b8cc","abstract_canon_sha256":"a746abf21d4ba3fe0cec09feda0d113bd4e477b855c42dc9a68ff138a326fbb7"},"schema_version":"1.0"},"canonical_sha256":"30aa68f44d15a806924e67c8f62956cffddf7e10dbf074fc92b9f1e3a4ec8cc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:25.540023Z","signature_b64":"HYGsiyZh9mbYHIkK6EASfUdH0UxY7o+ALJOZDE2OSAE3wDKJyA9Abl+QYOb0WE8MlPL4d9CKnoZtN7VD0GPBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30aa68f44d15a806924e67c8f62956cffddf7e10dbf074fc92b9f1e3a4ec8cc1","last_reissued_at":"2026-05-18T01:57:25.539521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:25.539521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4253","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":"2026-05-18T01:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bdKAZLUn3AJ2bPBf5jBg1opiDCh6CBBVKHKXJ37DLVWzCuaVUYS6zajojLnggGjxbyvarRMn8cXYrTV7AGYxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:10:37.897802Z"},"content_sha256":"650a56341020e90bd5475c8ae868eb10f26246e1a1cd4e28b24e7b1ec5e2f3d2","schema_version":"1.0","event_id":"sha256:650a56341020e90bd5475c8ae868eb10f26246e1a1cd4e28b24e7b1ec5e2f3d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GCVGR5CNCWUANESOM7EPMKKWZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Error-Correcting Codes over Mixed Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C.H. Oh, Heng Fan, Sixia Yu, Zhuo Wang","submitted_at":"2012-05-18T20:12:44Z","abstract_excerpt":"Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels. Here we shall propose QECCs over mixed alphabets, i.e., physical systems of different dimensions, and investigate their constructions as well as their quantum Singleton bound. We propose two kinds of constructions: a graphical construction based a graph-theoretical object composite coding clique and a projection-based construction. We illustrate our ideas using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4253","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":"2026-05-18T01:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJlro6oFjF3u5mQQYw9FKOYcBtoG2xKvOoH0qbuaqVGTZy7SsiHzG6Kk3k6mM9rjII20I89awnOLjv/+hx+QCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:10:37.898449Z"},"content_sha256":"925eca28a89aad25607612c2536b37b211f04d4c70b917eb4bec145ad51c6f16","schema_version":"1.0","event_id":"sha256:925eca28a89aad25607612c2536b37b211f04d4c70b917eb4bec145ad51c6f16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/bundle.json","state_url":"https://pith.science/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/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":"2026-05-31T21:10:37Z","links":{"resolver":"https://pith.science/pith/GCVGR5CNCWUANESOM7EPMKKWZ7","bundle":"https://pith.science/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/bundle.json","state":"https://pith.science/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCVGR5CNCWUANESOM7EPMKKWZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GCVGR5CNCWUANESOM7EPMKKWZ7","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":"a746abf21d4ba3fe0cec09feda0d113bd4e477b855c42dc9a68ff138a326fbb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T20:12:44Z","title_canon_sha256":"93a3ad2d700b00f05cbf7e8e15b0b70c281143a31b5d85c9a588bf536dd8b8cc"},"schema_version":"1.0","source":{"id":"1205.4253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4253","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4253v1","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4253","created_at":"2026-05-18T01:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"GCVGR5CNCWUA","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GCVGR5CNCWUANESO","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GCVGR5CN","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:925eca28a89aad25607612c2536b37b211f04d4c70b917eb4bec145ad51c6f16","target":"graph","created_at":"2026-05-18T01:57:25Z","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":"Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels. Here we shall propose QECCs over mixed alphabets, i.e., physical systems of different dimensions, and investigate their constructions as well as their quantum Singleton bound. We propose two kinds of constructions: a graphical construction based a graph-theoretical object composite coding clique and a projection-based construction. We illustrate our ideas using","authors_text":"C.H. Oh, Heng Fan, Sixia Yu, Zhuo Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T20:12:44Z","title":"Quantum Error-Correcting Codes over Mixed Alphabets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4253","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":"sha256:650a56341020e90bd5475c8ae868eb10f26246e1a1cd4e28b24e7b1ec5e2f3d2","target":"record","created_at":"2026-05-18T01:57:25Z","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":"a746abf21d4ba3fe0cec09feda0d113bd4e477b855c42dc9a68ff138a326fbb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-05-18T20:12:44Z","title_canon_sha256":"93a3ad2d700b00f05cbf7e8e15b0b70c281143a31b5d85c9a588bf536dd8b8cc"},"schema_version":"1.0","source":{"id":"1205.4253","kind":"arxiv","version":1}},"canonical_sha256":"30aa68f44d15a806924e67c8f62956cffddf7e10dbf074fc92b9f1e3a4ec8cc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30aa68f44d15a806924e67c8f62956cffddf7e10dbf074fc92b9f1e3a4ec8cc1","first_computed_at":"2026-05-18T01:57:25.539521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:25.539521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYGsiyZh9mbYHIkK6EASfUdH0UxY7o+ALJOZDE2OSAE3wDKJyA9Abl+QYOb0WE8MlPL4d9CKnoZtN7VD0GPBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:25.540023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:650a56341020e90bd5475c8ae868eb10f26246e1a1cd4e28b24e7b1ec5e2f3d2","sha256:925eca28a89aad25607612c2536b37b211f04d4c70b917eb4bec145ad51c6f16"],"state_sha256":"7a37e368371a22663d8b35c02f21bc7e062c7c3e53b296bf4ba4b179b9e5a141"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//pDKtxqOGggrt+xcopdfQKOii+G5puwjzt+X/SJo/iL0xsFX6g8FkR4OoEUgNyJaPzbpwa5h02JTf79jRs7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:10:37.901795Z","bundle_sha256":"58fe609fba9a15ac2a9914baba07b24ea8fbed1eef640cdf8e46b9a5307984c7"}}