{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MB2UBY4FQHWVLGCBDQ6OXM3H6Q","short_pith_number":"pith:MB2UBY4F","canonical_record":{"source":{"id":"1806.10875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-28T10:54:52Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"9e31748faf462821354193df88a90bd4a2854db9a59d63949eccb4a24f4efaaf","abstract_canon_sha256":"357cb7b81bcf4b01c0d57c6f004f3e4ef2e746117fb85d3915c21c69840fbc8a"},"schema_version":"1.0"},"canonical_sha256":"607540e38581ed5598411c3cebb367f42803b2881b3eef1bce2c7f25949cd873","source":{"kind":"arxiv","id":"1806.10875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10875","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10875v1","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10875","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"MB2UBY4FQHWV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MB2UBY4FQHWVLGCB","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MB2UBY4F","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MB2UBY4FQHWVLGCBDQ6OXM3H6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-28T10:54:52Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"9e31748faf462821354193df88a90bd4a2854db9a59d63949eccb4a24f4efaaf","abstract_canon_sha256":"357cb7b81bcf4b01c0d57c6f004f3e4ef2e746117fb85d3915c21c69840fbc8a"},"schema_version":"1.0"},"canonical_sha256":"607540e38581ed5598411c3cebb367f42803b2881b3eef1bce2c7f25949cd873","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:15.990777Z","signature_b64":"O8cG+iHB4Z6O6vQ2QpITHj7U9KE/TzWPTFHaDYVs2QBfdTDbvslkRQah1vl2w7ftU9m8iyKk0YdYTztm10h7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"607540e38581ed5598411c3cebb367f42803b2881b3eef1bce2c7f25949cd873","last_reissued_at":"2026-05-17T23:52:15.990129Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:15.990129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10875","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":"2026-05-17T23:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5PYtb/1ERxppYKjH82dwY/GvDPJ2LrjOaPUpNp/DPDrtGPoYyVRThQsYvdyLt9FinOVwzRDnJpHfjNGNpn/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:40:32.535718Z"},"content_sha256":"542ef576d9eb7490c934664dcecde07bcc9905225634f5522f87dede75b3d81b","schema_version":"1.0","event_id":"sha256:542ef576d9eb7490c934664dcecde07bcc9905225634f5522f87dede75b3d81b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MB2UBY4FQHWVLGCBDQ6OXM3H6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entanglement-assisted quantum error-correcting codes from units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Barry Hurley, Donny Hurley, Ted Hurley","submitted_at":"2018-06-28T10:54:52Z","abstract_excerpt":"Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$ errors, mds (maximum distance separable) EAQECCs of the form $[[n,r,d;c]]$ with $R=\\frac{r}{n}, d\\geq (2t+1), c = (n-r), d= (n-r+1)$ are constructed. Series of such codes may be constructed where the rate and the relative distance approach non-zero constants as $n$ approaches infinity. The codes may also be constructed over prime order fields in which modular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10875","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":"2026-05-17T23:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPE8C7iskPQxEiiEfJ/1GbGQQdMHC495JsoYK7RNGdNEzKnKs3O88DhpgVAZ1Ezzf5P+PacDm33rObaK+NB+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:40:32.536516Z"},"content_sha256":"a0f641beba8ed138d44e930dd9d9e264e98d3b6a3416768eb796279ec7d49585","schema_version":"1.0","event_id":"sha256:a0f641beba8ed138d44e930dd9d9e264e98d3b6a3416768eb796279ec7d49585"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/bundle.json","state_url":"https://pith.science/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/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":"2026-05-31T12:40:32Z","links":{"resolver":"https://pith.science/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q","bundle":"https://pith.science/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/bundle.json","state":"https://pith.science/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MB2UBY4FQHWVLGCBDQ6OXM3H6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MB2UBY4FQHWVLGCBDQ6OXM3H6Q","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":"357cb7b81bcf4b01c0d57c6f004f3e4ef2e746117fb85d3915c21c69840fbc8a","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-28T10:54:52Z","title_canon_sha256":"9e31748faf462821354193df88a90bd4a2854db9a59d63949eccb4a24f4efaaf"},"schema_version":"1.0","source":{"id":"1806.10875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10875","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10875v1","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10875","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"MB2UBY4FQHWV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MB2UBY4FQHWVLGCB","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MB2UBY4F","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:a0f641beba8ed138d44e930dd9d9e264e98d3b6a3416768eb796279ec7d49585","target":"graph","created_at":"2026-05-17T23:52:15Z","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":"Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$ errors, mds (maximum distance separable) EAQECCs of the form $[[n,r,d;c]]$ with $R=\\frac{r}{n}, d\\geq (2t+1), c = (n-r), d= (n-r+1)$ are constructed. Series of such codes may be constructed where the rate and the relative distance approach non-zero constants as $n$ approaches infinity. The codes may also be constructed over prime order fields in which modular","authors_text":"Barry Hurley, Donny Hurley, Ted Hurley","cross_cats":["math.IT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-28T10:54:52Z","title":"Entanglement-assisted quantum error-correcting codes from units"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10875","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":"sha256:542ef576d9eb7490c934664dcecde07bcc9905225634f5522f87dede75b3d81b","target":"record","created_at":"2026-05-17T23:52:15Z","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":"357cb7b81bcf4b01c0d57c6f004f3e4ef2e746117fb85d3915c21c69840fbc8a","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-28T10:54:52Z","title_canon_sha256":"9e31748faf462821354193df88a90bd4a2854db9a59d63949eccb4a24f4efaaf"},"schema_version":"1.0","source":{"id":"1806.10875","kind":"arxiv","version":1}},"canonical_sha256":"607540e38581ed5598411c3cebb367f42803b2881b3eef1bce2c7f25949cd873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607540e38581ed5598411c3cebb367f42803b2881b3eef1bce2c7f25949cd873","first_computed_at":"2026-05-17T23:52:15.990129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:15.990129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O8cG+iHB4Z6O6vQ2QpITHj7U9KE/TzWPTFHaDYVs2QBfdTDbvslkRQah1vl2w7ftU9m8iyKk0YdYTztm10h7Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:15.990777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:542ef576d9eb7490c934664dcecde07bcc9905225634f5522f87dede75b3d81b","sha256:a0f641beba8ed138d44e930dd9d9e264e98d3b6a3416768eb796279ec7d49585"],"state_sha256":"23d8ef3256056babb5d5cd5f7b0ebbbe109dcfd49851bb7a0415ddeacc75832c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXzx5ptHz5PlWw1gNTsSBy8sypF16Jw5PMCs6+BQbXPEfF252um4mpAsUDEU3Wql6MvbZEV5oyNwkbF7nPVmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:40:32.540999Z","bundle_sha256":"514f9a5f9c28d4675c48b8bfb2ab1021b69b4464496d2dbb96b5b84e82f391a5"}}