{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5VRC4YRZ5OE6LIJFG7VROR2N6Z","short_pith_number":"pith:5VRC4YRZ","schema_version":"1.0","canonical_sha256":"ed622e6239eb89e5a12537eb17474df64c65e33172a1a7d5a7e89f86e5d94d8d","source":{"kind":"arxiv","id":"1708.09213","version":4},"attestation_state":"computed","paper":{"title":"Lecture Notes of Tensor Network Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","physics.app-ph","quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"Cheng Peng, Emanuele Tirrito, Gang Su, Luca Tagliacozzo, Maciej Lewenstein, Shi-Ju Ran, Xi Chen","submitted_at":"2017-08-30T11:07:18Z","abstract_excerpt":"Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum information science, statistical physics, and so on. In this lecture notes, we focus on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems. Starting from basic concepts and definitions, we first explain the relations between TN and physical problems, including the TN representations of classica"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.09213","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2017-08-30T11:07:18Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","physics.app-ph","quant-ph"],"title_canon_sha256":"453b85129cbae38d1c942057d0d48165b6784cfaac2a960d51838958683a52d2","abstract_canon_sha256":"8377d28bac4164c258e9c10c082095d3fa1e8b4d5f21d4f40f478e6e73f2866b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:37:15.015521Z","signature_b64":"x0LxEtnRbO9lCyJDu9wQdHdr/PDeQpwmmC+n5kT73aI5gT443QWykBRGtIpFF38A9IPcHbP8Rt5VAFnJMKUnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed622e6239eb89e5a12537eb17474df64c65e33172a1a7d5a7e89f86e5d94d8d","last_reissued_at":"2026-07-05T00:37:15.015034Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:37:15.015034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lecture Notes of Tensor Network Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","physics.app-ph","quant-ph"],"primary_cat":"physics.comp-ph","authors_text":"Cheng Peng, Emanuele Tirrito, Gang Su, Luca Tagliacozzo, Maciej Lewenstein, Shi-Ju Ran, Xi Chen","submitted_at":"2017-08-30T11:07:18Z","abstract_excerpt":"Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum information science, statistical physics, and so on. In this lecture notes, we focus on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems. Starting from basic concepts and definitions, we first explain the relations between TN and physical problems, including the TN representations of classica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09213","kind":"arxiv","version":4},"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/1708.09213/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.09213","created_at":"2026-07-05T00:37:15.015091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.09213v4","created_at":"2026-07-05T00:37:15.015091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09213","created_at":"2026-07-05T00:37:15.015091+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VRC4YRZ5OE6","created_at":"2026-07-05T00:37:15.015091+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VRC4YRZ5OE6LIJF","created_at":"2026-07-05T00:37:15.015091+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VRC4YRZ","created_at":"2026-07-05T00:37:15.015091+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"1906.10929","citing_title":"Entanglement Certification $-$ From Theory to Experiment","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z","json":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z.json","graph_json":"https://pith.science/api/pith-number/5VRC4YRZ5OE6LIJFG7VROR2N6Z/graph.json","events_json":"https://pith.science/api/pith-number/5VRC4YRZ5OE6LIJFG7VROR2N6Z/events.json","paper":"https://pith.science/paper/5VRC4YRZ"},"agent_actions":{"view_html":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z","download_json":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z.json","view_paper":"https://pith.science/paper/5VRC4YRZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.09213&json=true","fetch_graph":"https://pith.science/api/pith-number/5VRC4YRZ5OE6LIJFG7VROR2N6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/5VRC4YRZ5OE6LIJFG7VROR2N6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z/action/storage_attestation","attest_author":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z/action/author_attestation","sign_citation":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z/action/citation_signature","submit_replication":"https://pith.science/pith/5VRC4YRZ5OE6LIJFG7VROR2N6Z/action/replication_record"}},"created_at":"2026-07-05T00:37:15.015091+00:00","updated_at":"2026-07-05T00:37:15.015091+00:00"}