{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:KTF6B2CQQG7AE4UPTM6QMBVCLW","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":"611c7751cff03c6c1f4673243e0416b8d1427dc5bb06eab3f06963d22eddd3d5","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2005-04-25T08:32:34Z","title_canon_sha256":"dca9ef55d959e5957965bc483d0b1e0e63f3f6fd6a0d8c952eb7acc2f50d2fc3"},"schema_version":"1.0","source":{"id":"hep-lat/0504019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/0504019","created_at":"2026-07-04T17:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/0504019v2","created_at":"2026-07-04T17:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/0504019","created_at":"2026-07-04T17:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"KTF6B2CQQG7A","created_at":"2026-07-04T17:20:47Z"},{"alias_kind":"pith_short_16","alias_value":"KTF6B2CQQG7AE4UP","created_at":"2026-07-04T17:20:47Z"},{"alias_kind":"pith_short_8","alias_value":"KTF6B2CQ","created_at":"2026-07-04T17:20:47Z"}],"graph_snapshots":[{"event_id":"sha256:be31c4749b69b39d71d608c0dc728e234cc672d6881f85ef832c5fb2afa606c9","target":"graph","created_at":"2026-07-04T17:20:47Z","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/hep-lat/0504019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\\\"uscher's formula which establishes a similar relation in elastic scattering.","authors_text":"Chuan Liu, Song He, Xu Feng","cross_cats":[],"headline":"","license":"","primary_cat":"hep-lat","submitted_at":"2005-04-25T08:32:34Z","title":"Two Particle States and the $S$-matrix Elements in Multi-channel Scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/0504019","kind":"arxiv","version":2},"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:a8812fb7708fdb7c2b514b6d06a8b653420f6aebe9d247c0c6638a7e81f9fccc","target":"record","created_at":"2026-07-04T17:20:47Z","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":"611c7751cff03c6c1f4673243e0416b8d1427dc5bb06eab3f06963d22eddd3d5","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2005-04-25T08:32:34Z","title_canon_sha256":"dca9ef55d959e5957965bc483d0b1e0e63f3f6fd6a0d8c952eb7acc2f50d2fc3"},"schema_version":"1.0","source":{"id":"hep-lat/0504019","kind":"arxiv","version":2}},"canonical_sha256":"54cbe0e85081be02728f9b3d0606a25db2715916d247fff606789e440524b86f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54cbe0e85081be02728f9b3d0606a25db2715916d247fff606789e440524b86f","first_computed_at":"2026-07-04T17:20:47.601534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:20:47.601534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6g3F6h86sNsRbX2zgDF7MIzzUb/oUkVR0LFdrh6WGRUCPhtb8T5pm5XWgHkgq2h6yS4LIcd1K438lOp0gz8ACw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:20:47.601968Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-lat/0504019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8812fb7708fdb7c2b514b6d06a8b653420f6aebe9d247c0c6638a7e81f9fccc","sha256:be31c4749b69b39d71d608c0dc728e234cc672d6881f85ef832c5fb2afa606c9"],"state_sha256":"929b92a70cbe1b701c29172558aaae99e636a6e004a40f871d78ddfbf67a1c34"}