{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ARQX7AKKCGWLEQPGC6NMFZZKNZ","short_pith_number":"pith:ARQX7AKK","canonical_record":{"source":{"id":"2009.10329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-09-22T05:44:50Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"cc2d7d8db38275bdad0651cac387f5b79d29a493a50c32b5a6dbddfa9f713d73","abstract_canon_sha256":"78e2afc2a939ab0f4f4a85294949984b45c35e49aade0ff9216ab15ecd9b5194"},"schema_version":"1.0"},"canonical_sha256":"04617f814a11acb241e6179ac2e72a6e72ce0773ffe49db74c45f487a209ef46","source":{"kind":"arxiv","id":"2009.10329","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.10329","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"2009.10329v1","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.10329","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"ARQX7AKKCGWL","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_16","alias_value":"ARQX7AKKCGWLEQPG","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_8","alias_value":"ARQX7AKK","created_at":"2026-07-05T03:01:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ARQX7AKKCGWLEQPGC6NMFZZKNZ","target":"record","payload":{"canonical_record":{"source":{"id":"2009.10329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-09-22T05:44:50Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"cc2d7d8db38275bdad0651cac387f5b79d29a493a50c32b5a6dbddfa9f713d73","abstract_canon_sha256":"78e2afc2a939ab0f4f4a85294949984b45c35e49aade0ff9216ab15ecd9b5194"},"schema_version":"1.0"},"canonical_sha256":"04617f814a11acb241e6179ac2e72a6e72ce0773ffe49db74c45f487a209ef46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:09.985473Z","signature_b64":"33kj07DOJNwbaOxs2vpkQGK3I3yC5S56uw15ySXxittWsQYApeSX4A37BZVJGGkTHhbdv2KHpiqb7X9Ivt0oDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04617f814a11acb241e6179ac2e72a6e72ce0773ffe49db74c45f487a209ef46","last_reissued_at":"2026-07-05T03:01:09.984963Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:09.984963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.10329","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":"2026-07-05T03:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQ/pWrXIcHx5DZs2AWBpBV8plAjBhiKlLjT6K/EAjg1iEX/DR81fTkGNPDjD9pLbmPhVixq9J9hnzgRzvsqTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:07:44.113417Z"},"content_sha256":"217760699781a3afab4491ce1cfedcf70a6fcaf33c995cc2a2f3cb5101c5afd3","schema_version":"1.0","event_id":"sha256:217760699781a3afab4491ce1cfedcf70a6fcaf33c995cc2a2f3cb5101c5afd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ARQX7AKKCGWLEQPGC6NMFZZKNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor-network codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Nathan A. McMahon, Robert J. Harris, Terry Farrelly, Thomas M. Stace","submitted_at":"2020-09-22T05:44:50Z","abstract_excerpt":"Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We also show that for holographic codes the exact tensor-network decoder (with no bond-dimension truncation) is efficient wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10329","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.10329/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhXnIUcfQyBJsmlnzwJpZ5niUieAZhYFCjzH0bGBJUt5j1vfLZZW7gBdtED1hPjZ9DboS5A+6vXJSEwa+jtBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:07:44.114225Z"},"content_sha256":"b83f7038b450d4cdf3970ba2ab65c160e92380f0cc4effe353b9db15e4ce1726","schema_version":"1.0","event_id":"sha256:b83f7038b450d4cdf3970ba2ab65c160e92380f0cc4effe353b9db15e4ce1726"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/bundle.json","state_url":"https://pith.science/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/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":"2026-08-13T17:07:44Z","links":{"resolver":"https://pith.science/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ","bundle":"https://pith.science/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/bundle.json","state":"https://pith.science/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARQX7AKKCGWLEQPGC6NMFZZKNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ARQX7AKKCGWLEQPGC6NMFZZKNZ","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":"78e2afc2a939ab0f4f4a85294949984b45c35e49aade0ff9216ab15ecd9b5194","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-09-22T05:44:50Z","title_canon_sha256":"cc2d7d8db38275bdad0651cac387f5b79d29a493a50c32b5a6dbddfa9f713d73"},"schema_version":"1.0","source":{"id":"2009.10329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.10329","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"2009.10329v1","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.10329","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"ARQX7AKKCGWL","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_16","alias_value":"ARQX7AKKCGWLEQPG","created_at":"2026-07-05T03:01:09Z"},{"alias_kind":"pith_short_8","alias_value":"ARQX7AKK","created_at":"2026-07-05T03:01:09Z"}],"graph_snapshots":[{"event_id":"sha256:b83f7038b450d4cdf3970ba2ab65c160e92380f0cc4effe353b9db15e4ce1726","target":"graph","created_at":"2026-07-05T03:01:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.10329/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We also show that for holographic codes the exact tensor-network decoder (with no bond-dimension truncation) is efficient wi","authors_text":"Nathan A. McMahon, Robert J. Harris, Terry Farrelly, Thomas M. Stace","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-09-22T05:44:50Z","title":"Tensor-network codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10329","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":"sha256:217760699781a3afab4491ce1cfedcf70a6fcaf33c995cc2a2f3cb5101c5afd3","target":"record","created_at":"2026-07-05T03:01:09Z","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":"78e2afc2a939ab0f4f4a85294949984b45c35e49aade0ff9216ab15ecd9b5194","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-09-22T05:44:50Z","title_canon_sha256":"cc2d7d8db38275bdad0651cac387f5b79d29a493a50c32b5a6dbddfa9f713d73"},"schema_version":"1.0","source":{"id":"2009.10329","kind":"arxiv","version":1}},"canonical_sha256":"04617f814a11acb241e6179ac2e72a6e72ce0773ffe49db74c45f487a209ef46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04617f814a11acb241e6179ac2e72a6e72ce0773ffe49db74c45f487a209ef46","first_computed_at":"2026-07-05T03:01:09.984963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:01:09.984963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33kj07DOJNwbaOxs2vpkQGK3I3yC5S56uw15ySXxittWsQYApeSX4A37BZVJGGkTHhbdv2KHpiqb7X9Ivt0oDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:01:09.985473Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.10329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217760699781a3afab4491ce1cfedcf70a6fcaf33c995cc2a2f3cb5101c5afd3","sha256:b83f7038b450d4cdf3970ba2ab65c160e92380f0cc4effe353b9db15e4ce1726"],"state_sha256":"a178ffcfe09ddd28024edd11a2b2146df30be9b3b62f2cfcc58e71f212acf830"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjS5MmClNr3hrsFPc1YkUhsBgtuU35LgXIre1lReXLf+1WrhiGEtvHQ2Ir6GGIVNOgv7/infkukZaTgr/l6VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:07:44.120506Z","bundle_sha256":"45f8d8967bee0cec290b005e74167c63ffd76401e4933ee00566c1b6b51e00a5"}}