{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AXPRRS5735X7BAVIJXSO3USOWF","short_pith_number":"pith:AXPRRS57","canonical_record":{"source":{"id":"1408.5933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-08-25T21:37:51Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"5785f939c4f30012cdcb0436408896a1aa6f96eac0b06e31ed97b6b493cc9a63","abstract_canon_sha256":"6305418b923b52b1ded937b8940aebce4cc74b1dcc4ff6e7eafbff8c4e21ed71"},"schema_version":"1.0"},"canonical_sha256":"05df18cbbfdf6ff082a84de4edd24eb16b8fac1eab722eb4db63bc16c01fdd79","source":{"kind":"arxiv","id":"1408.5933","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5933","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5933v3","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5933","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"AXPRRS5735X7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AXPRRS5735X7BAVI","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AXPRRS57","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AXPRRS5735X7BAVIJXSO3USOWF","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-08-25T21:37:51Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"5785f939c4f30012cdcb0436408896a1aa6f96eac0b06e31ed97b6b493cc9a63","abstract_canon_sha256":"6305418b923b52b1ded937b8940aebce4cc74b1dcc4ff6e7eafbff8c4e21ed71"},"schema_version":"1.0"},"canonical_sha256":"05df18cbbfdf6ff082a84de4edd24eb16b8fac1eab722eb4db63bc16c01fdd79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:39.938627Z","signature_b64":"pq2XwUGLXLRouVB/rBTsAVz6H1y+Hu1mMJgD2mCHeGglbvBsbauOmUlZhawKT8BT0R9QiU+SPO7cP9c4xf4FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05df18cbbfdf6ff082a84de4edd24eb16b8fac1eab722eb4db63bc16c01fdd79","last_reissued_at":"2026-05-18T02:30:39.938088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:39.938088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5933","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDspgkR3cS6BftaFPcSpPgEiti+WxYsVCW6A0scvb5kjl+QAFN2OwILYF0b1DRn+iTlufr2lAU2suJeIkrN+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:51:36.210029Z"},"content_sha256":"95ce205dd6c17e83d9e1a7e419266ee931035dc668c0660c848353566a95538e","schema_version":"1.0","event_id":"sha256:95ce205dd6c17e83d9e1a7e419266ee931035dc668c0660c848353566a95538e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AXPRRS5735X7BAVIJXSO3USOWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A relativistic, model-independent, three-particle quantization condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-lat","authors_text":"Maxwell T. Hansen, Stephen R. Sharpe","submitted_at":"2014-08-25T21:37:51Z","abstract_excerpt":"We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles. We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a Z2 symmetry that removes vertices with an odd number of particles. The theory is assumed to have two-particle phase shifts that are bounded by \\pi/2 in the regime of elastic scattering. We determine the spectrum of the finite-volume theory from the poles in the odd-particle-number finite-volume correlator, which we analyze to all orders in perturbation theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5933","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3p7jlcGePC1Q4YqtUT+Eyn2fNGXxLhTl2ErWDFRXqljqLrrxbH5BsYesErD7Vc/QIJqNXDdPN5DVmkBSYIwsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:51:36.210388Z"},"content_sha256":"fe34254d633a9998429418f05987e621834d2ac17443b828454e19bdc108db9a","schema_version":"1.0","event_id":"sha256:fe34254d633a9998429418f05987e621834d2ac17443b828454e19bdc108db9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXPRRS5735X7BAVIJXSO3USOWF/bundle.json","state_url":"https://pith.science/pith/AXPRRS5735X7BAVIJXSO3USOWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXPRRS5735X7BAVIJXSO3USOWF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T08:51:36Z","links":{"resolver":"https://pith.science/pith/AXPRRS5735X7BAVIJXSO3USOWF","bundle":"https://pith.science/pith/AXPRRS5735X7BAVIJXSO3USOWF/bundle.json","state":"https://pith.science/pith/AXPRRS5735X7BAVIJXSO3USOWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXPRRS5735X7BAVIJXSO3USOWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AXPRRS5735X7BAVIJXSO3USOWF","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":"6305418b923b52b1ded937b8940aebce4cc74b1dcc4ff6e7eafbff8c4e21ed71","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-08-25T21:37:51Z","title_canon_sha256":"5785f939c4f30012cdcb0436408896a1aa6f96eac0b06e31ed97b6b493cc9a63"},"schema_version":"1.0","source":{"id":"1408.5933","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5933","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5933v3","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5933","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"AXPRRS5735X7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AXPRRS5735X7BAVI","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AXPRRS57","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:fe34254d633a9998429418f05987e621834d2ac17443b828454e19bdc108db9a","target":"graph","created_at":"2026-05-18T02:30:39Z","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"},"paper":{"abstract_excerpt":"We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles. We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a Z2 symmetry that removes vertices with an odd number of particles. The theory is assumed to have two-particle phase shifts that are bounded by \\pi/2 in the regime of elastic scattering. We determine the spectrum of the finite-volume theory from the poles in the odd-particle-number finite-volume correlator, which we analyze to all orders in perturbation theo","authors_text":"Maxwell T. Hansen, Stephen R. Sharpe","cross_cats":["nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-08-25T21:37:51Z","title":"A relativistic, model-independent, three-particle quantization condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5933","kind":"arxiv","version":3},"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":"sha256:95ce205dd6c17e83d9e1a7e419266ee931035dc668c0660c848353566a95538e","target":"record","created_at":"2026-05-18T02:30:39Z","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":"6305418b923b52b1ded937b8940aebce4cc74b1dcc4ff6e7eafbff8c4e21ed71","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2014-08-25T21:37:51Z","title_canon_sha256":"5785f939c4f30012cdcb0436408896a1aa6f96eac0b06e31ed97b6b493cc9a63"},"schema_version":"1.0","source":{"id":"1408.5933","kind":"arxiv","version":3}},"canonical_sha256":"05df18cbbfdf6ff082a84de4edd24eb16b8fac1eab722eb4db63bc16c01fdd79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05df18cbbfdf6ff082a84de4edd24eb16b8fac1eab722eb4db63bc16c01fdd79","first_computed_at":"2026-05-18T02:30:39.938088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:39.938088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pq2XwUGLXLRouVB/rBTsAVz6H1y+Hu1mMJgD2mCHeGglbvBsbauOmUlZhawKT8BT0R9QiU+SPO7cP9c4xf4FAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:39.938627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5933","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95ce205dd6c17e83d9e1a7e419266ee931035dc668c0660c848353566a95538e","sha256:fe34254d633a9998429418f05987e621834d2ac17443b828454e19bdc108db9a"],"state_sha256":"e0e5ecf503d447edeffb051764a3655c1f7a42ec806c46f1b50d14b3959c3461"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FbJmDOZLUL8evah7gvIO4NI534tHBXjj5ncwr1xUt2tVb1UqWdS9EnEOXn7Pc8SCDbTGKLRLukNfDo8j56FzDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:51:36.212429Z","bundle_sha256":"bc93b943a15be7865c8b2d838c327dad39a12c57ccf0806f94da4df8c1c4b270"}}