{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CZBQ3QNGYO7RDRWBMNGCES5TE4","short_pith_number":"pith:CZBQ3QNG","schema_version":"1.0","canonical_sha256":"16430dc1a6c3bf11c6c1634c224bb32723cd031602bdefd316a34ff2aac57408","source":{"kind":"arxiv","id":"1412.2970","version":2},"attestation_state":"computed","paper":{"title":"Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Pieter Naaijkens, Sven Bachmann, Wojciech Dybalski","submitted_at":"2014-12-09T14:35:16Z","abstract_excerpt":"We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding $S$-matrix. We also obtain some general restrictions on the shape of the energy-momentum spectrum. For the purpose of our analysis we adapt the concepts of almost local observables and energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the la"},"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":"1412.2970","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T14:35:16Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"4bb7f65853dd96bf3145e39926ecb61a04c2d78e35c29649b643c73fdaa37292","abstract_canon_sha256":"c72c7ed6b2c671757e61e242381159ebffffe72e6979228403d8da623a417938"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:18.658179Z","signature_b64":"mXimKWw6Zmga+lCTfgsf2Il5Beq3/q0iCAAO+xypRUpYd/8+U3xjrWkyU6YVHqil6p5RRRiz8qTWB/BCUar8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16430dc1a6c3bf11c6c1634c224bb32723cd031602bdefd316a34ff2aac57408","last_reissued_at":"2026-05-18T02:19:18.657666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:18.657666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Pieter Naaijkens, Sven Bachmann, Wojciech Dybalski","submitted_at":"2014-12-09T14:35:16Z","abstract_excerpt":"We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding $S$-matrix. We also obtain some general restrictions on the shape of the energy-momentum spectrum. For the purpose of our analysis we adapt the concepts of almost local observables and energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2970","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":"1412.2970","created_at":"2026-05-18T02:19:18.657744+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2970v2","created_at":"2026-05-18T02:19:18.657744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2970","created_at":"2026-05-18T02:19:18.657744+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZBQ3QNGYO7R","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZBQ3QNGYO7RDRWB","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZBQ3QNG","created_at":"2026-05-18T12:28:25.294606+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/CZBQ3QNGYO7RDRWBMNGCES5TE4","json":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4.json","graph_json":"https://pith.science/api/pith-number/CZBQ3QNGYO7RDRWBMNGCES5TE4/graph.json","events_json":"https://pith.science/api/pith-number/CZBQ3QNGYO7RDRWBMNGCES5TE4/events.json","paper":"https://pith.science/paper/CZBQ3QNG"},"agent_actions":{"view_html":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4","download_json":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4.json","view_paper":"https://pith.science/paper/CZBQ3QNG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2970&json=true","fetch_graph":"https://pith.science/api/pith-number/CZBQ3QNGYO7RDRWBMNGCES5TE4/graph.json","fetch_events":"https://pith.science/api/pith-number/CZBQ3QNGYO7RDRWBMNGCES5TE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4/action/storage_attestation","attest_author":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4/action/author_attestation","sign_citation":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4/action/citation_signature","submit_replication":"https://pith.science/pith/CZBQ3QNGYO7RDRWBMNGCES5TE4/action/replication_record"}},"created_at":"2026-05-18T02:19:18.657744+00:00","updated_at":"2026-05-18T02:19:18.657744+00:00"}