{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HNQF26EUJ4XKR4Y2O5WQHGBCVO","short_pith_number":"pith:HNQF26EU","schema_version":"1.0","canonical_sha256":"3b605d78944f2ea8f31a776d039822ab821756c69937d4dafd7f13d64e925b88","source":{"kind":"arxiv","id":"1811.09899","version":2},"attestation_state":"computed","paper":{"title":"A Schr\\\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christoph Fischbacher","submitted_at":"2018-11-24T21:24:01Z","abstract_excerpt":"We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\\\"odinger type operators on what we call \"$N$-particle graphs with maximal local occupation number $M$\", where the kinetic term is described by a weighted Laplacian. Generalizing previous results for the spin-$1/2$ case, we give sufficient conditions for the existence of spectral gaps above the low-lying droplet band when the underlying graph $\\mathcal{G}$ is (i) the chain and (ii) a strip of width $L$."},"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":"1811.09899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-24T21:24:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1020243864ab1c5aec7f894ddaff310fa1c082f5a274b88783cfd09600db2099","abstract_canon_sha256":"efd5290884038579543404fb502d6a93e2863eb32e8a975a5ad9b1203e45cbdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:21.967770Z","signature_b64":"oRd756vNGK9Ihfp3fVhM2SgxTKy7gPjVX+WL1jA/dYpSrpyVZy8DWX0YgdEGoEfsIe1ng3oYvuF1OY3hxe2FBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b605d78944f2ea8f31a776d039822ab821756c69937d4dafd7f13d64e925b88","last_reissued_at":"2026-05-17T23:54:21.967216Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:21.967216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Schr\\\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christoph Fischbacher","submitted_at":"2018-11-24T21:24:01Z","abstract_excerpt":"We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\\\"odinger type operators on what we call \"$N$-particle graphs with maximal local occupation number $M$\", where the kinetic term is described by a weighted Laplacian. Generalizing previous results for the spin-$1/2$ case, we give sufficient conditions for the existence of spectral gaps above the low-lying droplet band when the underlying graph $\\mathcal{G}$ is (i) the chain and (ii) a strip of width $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09899","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.09899","created_at":"2026-05-17T23:54:21.967322+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.09899v2","created_at":"2026-05-17T23:54:21.967322+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09899","created_at":"2026-05-17T23:54:21.967322+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNQF26EUJ4XK","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNQF26EUJ4XKR4Y2","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNQF26EU","created_at":"2026-05-18T12:32:28.185984+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/HNQF26EUJ4XKR4Y2O5WQHGBCVO","json":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO.json","graph_json":"https://pith.science/api/pith-number/HNQF26EUJ4XKR4Y2O5WQHGBCVO/graph.json","events_json":"https://pith.science/api/pith-number/HNQF26EUJ4XKR4Y2O5WQHGBCVO/events.json","paper":"https://pith.science/paper/HNQF26EU"},"agent_actions":{"view_html":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO","download_json":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO.json","view_paper":"https://pith.science/paper/HNQF26EU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.09899&json=true","fetch_graph":"https://pith.science/api/pith-number/HNQF26EUJ4XKR4Y2O5WQHGBCVO/graph.json","fetch_events":"https://pith.science/api/pith-number/HNQF26EUJ4XKR4Y2O5WQHGBCVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO/action/storage_attestation","attest_author":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO/action/author_attestation","sign_citation":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO/action/citation_signature","submit_replication":"https://pith.science/pith/HNQF26EUJ4XKR4Y2O5WQHGBCVO/action/replication_record"}},"created_at":"2026-05-17T23:54:21.967322+00:00","updated_at":"2026-05-17T23:54:21.967322+00:00"}