{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HCUOSYFT4PE2FEGVU2EIXF2L6R","short_pith_number":"pith:HCUOSYFT","schema_version":"1.0","canonical_sha256":"38a8e960b3e3c9a290d5a6888b974bf47b39a7f4a8eeb83d0f080a24981f279e","source":{"kind":"arxiv","id":"2607.22522","version":1},"attestation_state":"computed","paper":{"title":"Exact Neural-Network Representations of the Motzkin States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Chaohui Fan, Hai-Jun Liao, Jia-lin Chen, Runde Zha, Tao Xiang, Yuntian Gu","submitted_at":"2026-07-24T17:50:44Z","abstract_excerpt":"Motzkin spin chains are paradigmatic frustration-free one-dimensional quantum systems whose ground states feature exactly solvable combinatorial structures and exotic, area-law-violating entanglement scaling. Specifically, colorless Motzkin states exhibit critical logarithmic entanglement divergence \\(\\log N\\) with system size \\(N\\), while their colorful counterparts host supercritical sublinear \\(\\sqrt{N}\\) entanglement growth. Such unconventional entanglement behaviors place these states well beyond the expressive capability of standard matrix product states, which are fundamentally constrai"},"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":"2607.22522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-24T17:50:44Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"c456411fd1eddc42cb73510c76f348eb0864eaff7544e5b0de3e47173d413f86","abstract_canon_sha256":"d3f92d6329354cef1882bd63254667f2314a9b784e8373dafd5f2a5f430be622"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T01:21:31.954963Z","signature_b64":"b5ZghVeaOMEkCIk9HnJk/OVZWgBGt8fGu+rpyvPtDdbGMSnzAmHAvqrnn0/T8N4gSrYODu7SPtdSAdRPHywqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38a8e960b3e3c9a290d5a6888b974bf47b39a7f4a8eeb83d0f080a24981f279e","last_reissued_at":"2026-07-27T01:21:31.954163Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T01:21:31.954163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Neural-Network Representations of the Motzkin States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Chaohui Fan, Hai-Jun Liao, Jia-lin Chen, Runde Zha, Tao Xiang, Yuntian Gu","submitted_at":"2026-07-24T17:50:44Z","abstract_excerpt":"Motzkin spin chains are paradigmatic frustration-free one-dimensional quantum systems whose ground states feature exactly solvable combinatorial structures and exotic, area-law-violating entanglement scaling. Specifically, colorless Motzkin states exhibit critical logarithmic entanglement divergence \\(\\log N\\) with system size \\(N\\), while their colorful counterparts host supercritical sublinear \\(\\sqrt{N}\\) entanglement growth. Such unconventional entanglement behaviors place these states well beyond the expressive capability of standard matrix product states, which are fundamentally constrai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22522","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/2607.22522/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":"2607.22522","created_at":"2026-07-27T01:21:31.954596+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22522v1","created_at":"2026-07-27T01:21:31.954596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22522","created_at":"2026-07-27T01:21:31.954596+00:00"},{"alias_kind":"pith_short_12","alias_value":"HCUOSYFT4PE2","created_at":"2026-07-27T01:21:31.954596+00:00"},{"alias_kind":"pith_short_16","alias_value":"HCUOSYFT4PE2FEGV","created_at":"2026-07-27T01:21:31.954596+00:00"},{"alias_kind":"pith_short_8","alias_value":"HCUOSYFT","created_at":"2026-07-27T01:21:31.954596+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R","json":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R.json","graph_json":"https://pith.science/api/pith-number/HCUOSYFT4PE2FEGVU2EIXF2L6R/graph.json","events_json":"https://pith.science/api/pith-number/HCUOSYFT4PE2FEGVU2EIXF2L6R/events.json","paper":"https://pith.science/paper/HCUOSYFT"},"agent_actions":{"view_html":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R","download_json":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R.json","view_paper":"https://pith.science/paper/HCUOSYFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22522&json=true","fetch_graph":"https://pith.science/api/pith-number/HCUOSYFT4PE2FEGVU2EIXF2L6R/graph.json","fetch_events":"https://pith.science/api/pith-number/HCUOSYFT4PE2FEGVU2EIXF2L6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R/action/storage_attestation","attest_author":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R/action/author_attestation","sign_citation":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R/action/citation_signature","submit_replication":"https://pith.science/pith/HCUOSYFT4PE2FEGVU2EIXF2L6R/action/replication_record"}},"created_at":"2026-07-27T01:21:31.954596+00:00","updated_at":"2026-07-27T01:21:31.954596+00:00"}