{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YLTQHYQRAZOFVPWQLTAWFYDHSI","short_pith_number":"pith:YLTQHYQR","canonical_record":{"source":{"id":"2208.10587","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2022-08-22T20:38:56Z","cross_cats_sorted":["hep-ph","nucl-th"],"title_canon_sha256":"134dfaa26a17f60590acb63dffc515f2903a3fcf27ba1da84be3d7d2b4d4429e","abstract_canon_sha256":"675da2c54eb82d6124095d833e6e9d61401b23a76d433e8ccc869c07f9c9921d"},"schema_version":"1.0"},"canonical_sha256":"c2e703e211065c5abed05cc162e067920a601ea29c55eba73478aba5fbd71a0f","source":{"kind":"arxiv","id":"2208.10587","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.10587","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"2208.10587v1","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10587","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"YLTQHYQRAZOF","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_16","alias_value":"YLTQHYQRAZOFVPWQ","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_8","alias_value":"YLTQHYQR","created_at":"2026-07-05T04:50:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YLTQHYQRAZOFVPWQLTAWFYDHSI","target":"record","payload":{"canonical_record":{"source":{"id":"2208.10587","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2022-08-22T20:38:56Z","cross_cats_sorted":["hep-ph","nucl-th"],"title_canon_sha256":"134dfaa26a17f60590acb63dffc515f2903a3fcf27ba1da84be3d7d2b4d4429e","abstract_canon_sha256":"675da2c54eb82d6124095d833e6e9d61401b23a76d433e8ccc869c07f9c9921d"},"schema_version":"1.0"},"canonical_sha256":"c2e703e211065c5abed05cc162e067920a601ea29c55eba73478aba5fbd71a0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:50:37.127871Z","signature_b64":"beOtAgeBQ8PDZT7qn1zgPgJ2H40gDlc6bYDZ9ebr1MTOCQr5bn2cb79jaeBhwVR8f3+znDPzOicpfMbvQBcmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2e703e211065c5abed05cc162e067920a601ea29c55eba73478aba5fbd71a0f","last_reissued_at":"2026-07-05T04:50:37.127450Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:50:37.127450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.10587","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:50:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HChVBetJ4TAG2PSUVvUz5F2tILnqwBtT4RnFWCh8aZ7Q21aXctp4PtWuBPx7Zp/xJ8Sqdg40Je2NKR/l45U4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:00:59.729963Z"},"content_sha256":"dfee8162b83d0cc8e5aa5c90066c94bc9e084fae47f4a8717bfca153fe149530","schema_version":"1.0","event_id":"sha256:dfee8162b83d0cc8e5aa5c90066c94bc9e084fae47f4a8717bfca153fe149530"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YLTQHYQRAZOFVPWQLTAWFYDHSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-body scattering and quantization conditions from $S$ matrix unitarity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","nucl-th"],"primary_cat":"hep-lat","authors_text":"Andrew W. Jackura","submitted_at":"2022-08-22T20:38:56Z","abstract_excerpt":"Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10587","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/2208.10587/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:50:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8Nzj3rrfUqq7HYmw+CzYVajLjnalpWYhbsn2MHiDqcNwvzpZD/UO7bw7XBDiTjgY6SXj4abdDodCLJVnGazCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:00:59.730611Z"},"content_sha256":"7974f860415d6e2b73116aecdd28a2fd8377dd5d62a7083c861f0ce80169403d","schema_version":"1.0","event_id":"sha256:7974f860415d6e2b73116aecdd28a2fd8377dd5d62a7083c861f0ce80169403d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/bundle.json","state_url":"https://pith.science/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/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":"2026-08-04T17:00:59Z","links":{"resolver":"https://pith.science/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI","bundle":"https://pith.science/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/bundle.json","state":"https://pith.science/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLTQHYQRAZOFVPWQLTAWFYDHSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YLTQHYQRAZOFVPWQLTAWFYDHSI","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":"675da2c54eb82d6124095d833e6e9d61401b23a76d433e8ccc869c07f9c9921d","cross_cats_sorted":["hep-ph","nucl-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2022-08-22T20:38:56Z","title_canon_sha256":"134dfaa26a17f60590acb63dffc515f2903a3fcf27ba1da84be3d7d2b4d4429e"},"schema_version":"1.0","source":{"id":"2208.10587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.10587","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"2208.10587v1","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10587","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"YLTQHYQRAZOF","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_16","alias_value":"YLTQHYQRAZOFVPWQ","created_at":"2026-07-05T04:50:37Z"},{"alias_kind":"pith_short_8","alias_value":"YLTQHYQR","created_at":"2026-07-05T04:50:37Z"}],"graph_snapshots":[{"event_id":"sha256:7974f860415d6e2b73116aecdd28a2fd8377dd5d62a7083c861f0ce80169403d","target":"graph","created_at":"2026-07-05T04:50:37Z","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/2208.10587/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the fini","authors_text":"Andrew W. Jackura","cross_cats":["hep-ph","nucl-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2022-08-22T20:38:56Z","title":"Three-body scattering and quantization conditions from $S$ matrix unitarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10587","kind":"arxiv","version":1},"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:dfee8162b83d0cc8e5aa5c90066c94bc9e084fae47f4a8717bfca153fe149530","target":"record","created_at":"2026-07-05T04:50:37Z","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":"675da2c54eb82d6124095d833e6e9d61401b23a76d433e8ccc869c07f9c9921d","cross_cats_sorted":["hep-ph","nucl-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2022-08-22T20:38:56Z","title_canon_sha256":"134dfaa26a17f60590acb63dffc515f2903a3fcf27ba1da84be3d7d2b4d4429e"},"schema_version":"1.0","source":{"id":"2208.10587","kind":"arxiv","version":1}},"canonical_sha256":"c2e703e211065c5abed05cc162e067920a601ea29c55eba73478aba5fbd71a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2e703e211065c5abed05cc162e067920a601ea29c55eba73478aba5fbd71a0f","first_computed_at":"2026-07-05T04:50:37.127450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:50:37.127450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"beOtAgeBQ8PDZT7qn1zgPgJ2H40gDlc6bYDZ9ebr1MTOCQr5bn2cb79jaeBhwVR8f3+znDPzOicpfMbvQBcmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:50:37.127871Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.10587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfee8162b83d0cc8e5aa5c90066c94bc9e084fae47f4a8717bfca153fe149530","sha256:7974f860415d6e2b73116aecdd28a2fd8377dd5d62a7083c861f0ce80169403d"],"state_sha256":"d79670ff516c936447ce73d884cc9dafb27fbe48d2f10955f2683cf97a552db1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/67V3+HSSzNddCeVA53mmbmAc1ADBBjyE9fUV2PFXfIyowWsZUoVF2qODWFwTvKGd/Snsjeto+b0y99UQiPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:00:59.734885Z","bundle_sha256":"e1dda4422e28dc6a5b11803bd7148bfcec46d6231841dfa78c077f3c98b088e3"}}