{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T2KI3LMVSJBX53ZQAJKTYBTHJD","short_pith_number":"pith:T2KI3LMV","schema_version":"1.0","canonical_sha256":"9e948dad9592437eef3002553c066748dbbc9eb8b5f38c36bc6cc8a1f734b72e","source":{"kind":"arxiv","id":"1707.04279","version":3},"attestation_state":"computed","paper":{"title":"Testing the threshold expansion for three-particle energies at fourth order in $\\phi^4$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Stephen R. Sharpe","submitted_at":"2017-07-13T18:40:29Z","abstract_excerpt":"A relativistic formalism for relating the the energies of the states of three scalar particles in finite volume to infinite volume scattering amplitudes has recently been developed. This formalism has been used to predict the energy of the state closest to threshold in an expansion in powers of $1/L$, with $L$ the box length. This expansion has been tested previously by a perturbative calculation of the threshold energy in $\\lambda \\phi^4$ theory, working to third order in $\\lambda$ and up to $\\mathcal O(1/L^6)$ in the volume expansion. However, several aspects of the predicted threshold behav"},"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":"1707.04279","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-07-13T18:40:29Z","cross_cats_sorted":[],"title_canon_sha256":"acecbb5a64f7858594d7b654cabe722d5ea91fcffb93e2ef920aa81d663c81ba","abstract_canon_sha256":"8e78f1f3daad63ef9280694d7223324feb40426c93207161ff3991b7e11f6a40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:45.659217Z","signature_b64":"u76naA95fV3ljyE/ghZGECC6kOvPnHbyYgd1g+lBCO2mZSz6jSx4vHbv2jbLBg4GrzR3ogQD46sQyO5CFqc/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e948dad9592437eef3002553c066748dbbc9eb8b5f38c36bc6cc8a1f734b72e","last_reissued_at":"2026-05-18T00:02:45.658814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:45.658814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing the threshold expansion for three-particle energies at fourth order in $\\phi^4$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Stephen R. Sharpe","submitted_at":"2017-07-13T18:40:29Z","abstract_excerpt":"A relativistic formalism for relating the the energies of the states of three scalar particles in finite volume to infinite volume scattering amplitudes has recently been developed. This formalism has been used to predict the energy of the state closest to threshold in an expansion in powers of $1/L$, with $L$ the box length. This expansion has been tested previously by a perturbative calculation of the threshold energy in $\\lambda \\phi^4$ theory, working to third order in $\\lambda$ and up to $\\mathcal O(1/L^6)$ in the volume expansion. However, several aspects of the predicted threshold behav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04279","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.04279","created_at":"2026-05-18T00:02:45.658871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04279v3","created_at":"2026-05-18T00:02:45.658871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04279","created_at":"2026-05-18T00:02:45.658871+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2KI3LMVSJBX","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2KI3LMVSJBX53ZQ","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2KI3LMV","created_at":"2026-05-18T12:31:43.269735+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/T2KI3LMVSJBX53ZQAJKTYBTHJD","json":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD.json","graph_json":"https://pith.science/api/pith-number/T2KI3LMVSJBX53ZQAJKTYBTHJD/graph.json","events_json":"https://pith.science/api/pith-number/T2KI3LMVSJBX53ZQAJKTYBTHJD/events.json","paper":"https://pith.science/paper/T2KI3LMV"},"agent_actions":{"view_html":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD","download_json":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD.json","view_paper":"https://pith.science/paper/T2KI3LMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04279&json=true","fetch_graph":"https://pith.science/api/pith-number/T2KI3LMVSJBX53ZQAJKTYBTHJD/graph.json","fetch_events":"https://pith.science/api/pith-number/T2KI3LMVSJBX53ZQAJKTYBTHJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD/action/storage_attestation","attest_author":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD/action/author_attestation","sign_citation":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD/action/citation_signature","submit_replication":"https://pith.science/pith/T2KI3LMVSJBX53ZQAJKTYBTHJD/action/replication_record"}},"created_at":"2026-05-18T00:02:45.658871+00:00","updated_at":"2026-05-18T00:02:45.658871+00:00"}