{"submission_id":"3efcf633-d4d9-40e1-9f94-3d1b15e2ad8a","submission_revision_id":"ad164eba-a773-48e5-b168-e3aeb824d20e","revision_version":7,"submission_status":"submitted","submitted_at":"2026-08-16T18:38:52.386693Z","submitter_name":"Tong Liu","submitter_email":"tongliu.physics@gmail.com","task":{"status":"submitted","version":7,"extra_fields":{"ai_draft":{"source":"submissions_workbench","status":"ready","preview":{"domain":"Theoretical Particle Physics","task_goal":"Compute leading-order spin-averaged |M|^2 for psi-psi to psi-psi scattering under a chiral 4-fermion contact interaction using symbolic algebra tools.\n\nStarting state: Expert receives a Mathematica notebook skeleton with the Lagrangian defined symbolically, FeynCalc/FeynArts loaded, and Mandelstam variable definitions stubbed but no diagrams, traces, or amplitude expressions computed.\n\nInstructions and rules: Using the given Lagrangian, generate all leading-order (tree-level, order lambda) t-channel and u-channel contact diagrams for identical fermion scattering, compute the corresponding Dirac traces symbolically, and assemble the spin-averaged squared amplitude. Express the final result purely in terms of Mandelstam variables s, t, u (with s+t+u=0 for massless fermions) and simplify to a minimal polynomial form. The notebook must show explicit trace evaluation steps (not just the final formula) and must be evaluable end-to-end without manual intervention.","short_name":"njl_amplitude_squared","input_files":"- njl_model.nb (NB, <50KB): Mathematica notebook skeleton with the Lagrangian, FeynCalc/FeynArts initialization, spinor conventions, and gamma matrix definitions preloaded; defines the starting symbolic environment the expert must extend\n- mandelstam_defs.wl (WL, <5KB): Package file defining s, t, u in terms of external momenta and the massless on-shell constraint s+t+u=0, used to express and simplify the final amplitude","output_files":"- amplitude_squared.wl (WL) [graded]: Final symbolic expression for the spin-averaged |M|^2 exported as a Mathematica package/expression file, written purely as a polynomial in s, t, u with lambda^2 prefactor; primary deliverable for exact-match comparison","operating_system":"Linux","software_licensing":"Free/Open Source","verification_method":"amplitude_squared.wl: parse/schema pass; rows > 0; required cols = 100%; timestamps monotonic = true.\namplitude_squared.wl: APE/RPE within reference tolerance or no regression > 10%; plan latency within project target; critical metric failures = 0.\nRun quality: mission success >= 95%; planner/localization failures = 0; collision count = 0.\nCross-check: run_id / robot_id / timestamp alignment across njl_model.nb, mandelstam_defs.wl and amplitude_squared.wl; mismatch count = 0.","evaluation_criterion":"Method: script + rubric review\nMetric: primary reference-output comparison over structure, key values, consistency, and evidence grounding\nThreshold: pass when the primary reference output has no critical mismatch and supporting artifacts show no blocking inconsistency","software_and_version":"Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11","tools_software_details":"Software: Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11\nDefine vertices and generate contact diagrams for identical-fermion 2-to-2 scattering (Tools: FeynArts, FeynCalc)\nEvaluate Dirac traces, apply spin-averaging, and simplify to Mandelstam form (Tools: Mathematica, FeynCalc)"},"warnings":["estimated_expert_hours \"\" does not meet the ≥5 hour requirement","expected_output has no structured data file (TSV/CSV/VCF/JSON/BAM etc.)"],"createdAt":1785614691411,"formPrefill":{"extra_fields":{},"industry_domain":"Theoretical Particle Physics","task_short_name":"njl_amplitude_squared","operating_system":"Linux","task_description":"# Task Goal\n\nCompute leading-order spin-averaged |M|^2 for psi-psi to psi-psi scattering under a chiral 4-fermion contact interaction using symbolic algebra tools.\n\nStarting state: Expert receives a Mathematica notebook skeleton with the Lagrangian defined symbolically, FeynCalc/FeynArts loaded, and Mandelstam variable definitions stubbed but no diagrams, traces, or amplitude expressions computed.\n\nInstructions and rules: Using the given Lagrangian, generate all leading-order (tree-level, order lambda) t-channel and u-channel contact diagrams for identical fermion scattering, compute the corresponding Dirac traces symbolically, and assemble the spin-averaged squared amplitude. Express the final result purely in terms of Mandelstam variables s, t, u (with s+t+u=0 for massless fermions) and simplify to a minimal polynomial form. The notebook must show explicit trace evaluation steps (not just the final formula) and must be evaluable end-to-end without manual intervention.\n\n# Input Files\n\n- njl_model.nb (NB, <50KB): Mathematica notebook skeleton with the Lagrangian, FeynCalc/FeynArts initialization, spinor conventions, and gamma matrix definitions preloaded; defines the starting symbolic environment the expert must extend\n- mandelstam_defs.wl (WL, <5KB): Package file defining s, t, u in terms of external momenta and the massless on-shell constraint s+t+u=0, used to express and simplify the final amplitude\n\n# Output Files\n\n- amplitude_squared.wl (WL) [graded]: Final symbolic expression for the spin-averaged |M|^2 exported as a Mathematica package/expression file, written purely as a polynomial in s, t, u with lambda^2 prefactor; primary deliverable for exact-match comparison\n\n# Tools / Software Details\n\nSoftware: Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11\nDefine vertices and generate contact diagrams for identical-fermion 2-to-2 scattering (Tools: FeynArts, FeynCalc)\nEvaluate Dirac traces, apply spin-averaging, and simplify to Mandelstam form (Tools: Mathematica, FeynCalc)\n\n# Evaluation Criterion\n\nMethod: script + rubric review\nMetric: primary reference-output comparison over structure, key values, consistency, and evidence grounding\nThreshold: pass when the primary reference output has no critical mismatch and supporting artifacts show no blocking inconsistency","software_licensing":"Free/Open Source","verification_method":"amplitude_squared.wl: parse/schema pass; rows > 0; required cols = 100%; timestamps monotonic = true.\namplitude_squared.wl: APE/RPE within reference tolerance or no regression > 10%; plan latency within project target; critical metric failures = 0.\nRun quality: mission success >= 95%; planner/localization failures = 0; collision count = 0.\nCross-check: run_id / robot_id / timestamp alignment across njl_model.nb, mandelstam_defs.wl and amplitude_squared.wl; mismatch count = 0.","software_and_version":"Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11"},"draftSession":"3633c495-6abb-4eb5-9c82-e57ef1a742fe"}},"submitted_at":"2026-08-16T18:38:52.386693+00:00","industry_domain":"Theoretical Particle Physics","task_short_name":"Psi-Psi to Psi-Psi Scattering","operating_system":"Linux","task_description":"• # Task Goal\n\nCompute leading-order spin-averaged |M|^2 for psi-psi to psi-psi scattering under a chiral 4-fermion contact interaction using symbolic algebra tools.\n\nThe interaction is of Nambu–Jona-Lasinio (NJL) type, a four-fermion model commonly used to study phenomena such as dynamical mass generation and spontaneous chiral symmetry breaking.\n\nStarting state: Expert receives a Mathematica notebook skeleton with the Lagrangian defined symbolically, FeynCalc/FeynArts loaded, and Mandelstam variable definitions stubbed but no diagrams, traces, or amplitude expressions computed. The completed Mathematica solution must be saved as `njl_scattering_complete.wl`.\n\nInstructions and rules: Using the given Lagrangian, generate all leading-order (tree-level, order lambda) t-channel and u-channel contact diagrams for identical fermion scattering, compute the corresponding Dirac traces symbolically, and assemble the spin-averaged squared amplitude. Express the final result purely in terms of Mandelstam variables s, t, u (with s+t+u=0 for massless fermions) and simplify to a minimal polynomial form. The completed solution must show explicit trace evaluation steps (not just the final formula) and must be evaluable end-to-end without manual intervention.\n\n# Input Files\n\n- njl_model.nb (NB, <50KB): Mathematica notebook skeleton with the Lagrangian, FeynCalc/FeynArts initialization, spinor conventions, and gamma matrix definitions preloaded; defines the starting symbolic environment the expert must extend\n- mandelstam_defs.wl (WL, <50KB): Package file defining s, t, u in terms of external momenta and the massless on-shell constraint s+t+u=0, used to express and simplify the final amplitude\n\n# Output Files\n\n- njl_scattering_complete.wl (WL): Complete Wolfram Language solution containing the tree-level contact contractions, explicit Dirac trace evaluations, spin sum, initial-spin average, Mandelstam substitutions, and final simplified result. The script must evaluate end-to-end without manual intervention.\n- amplitude_squared.wl (WL) [graded]: Final symbolic expression for the spin-averaged |M|^2 exported as a Mathematica package/expression file, written purely as a polynomial in s, t, u with lambda^2 prefactor; primary deliverable for exact-match comparison\n\n# Tools / Software Details\n\nSoftware: Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11\nDefine vertices and generate contact diagrams for identical-fermion 2-to-2 scattering (Tools: FeynArts, FeynCalc)\nEvaluate Dirac traces, apply spin-averaging, and simplify to Mandelstam form (Tools: Mathematica, FeynCalc)\n\n# Evaluation Criterion\n\nMethod: script + rubric review\nMetric: primary reference-output comparison over structure, key values, consistency, and evidence grounding\nThreshold: pass when the primary reference output has no critical mismatch and supporting artifacts show no blocking inconsistency\n","software_licensing":"Free/Open Source","evaluation_criteria":null,"verification_method":"1. Required output files\n\nThe submission must contain both of the following files named exactly:\n\n- njl_scattering_complete.wl\n- amplitude_squared.wl\n\nnjl_scattering_complete.wl is the complete Wolfram Language solution containing the symbolic derivation.\n\namplitude_squared.wl is the primary graded output and must contain only the final spin-averaged squared amplitude as a single Wolfram Language expression.\n\nA missing required file is an automatic failure.\n\n\n2. Complete symbolic derivation\n\nnjl_scattering_complete.wl must contain valid Wolfram Language code and must evaluate end-to-end without manual intervention in the specified Mathematica/FeynCalc environment.\n\nThe solution must explicitly include:\n\n- both inequivalent tree-level t-type and u-type contact contractions for identical-fermion scattering;\n- the relative minus sign associated with exchange of identical fermions;\n- the scalar and pseudoscalar contributions from the four-fermion interaction;\n- explicit Dirac-trace evaluation for the squared t-type contribution;\n- explicit Dirac-trace evaluation for the squared u-type contribution;\n- explicit Dirac-trace evaluation of the t-u interference terms;\n- construction of the full spin-summed squared amplitude;\n- the factor 1/4 for averaging over the two spin states of each incoming fermion;\n- conversion of scalar products to Mandelstam variables s, t, u;\n- use of the massless Mandelstam relation s + t + u == 0 where needed for simplification;\n- the final spin-averaged squared amplitude.\n\nThe derivation must use symbolic Mathematica/FeynCalc operations to evaluate the relevant Dirac algebra. Merely hard-coding the final reference expression without the required intermediate symbolic derivation does not satisfy this requirement.\n\nA parse error, evaluation error, missing required derivation component, or solution that requires manual intervention is a failure.\n\n\n3. Final-expression parse and evaluation requirement\n\nThe following rules apply specifically to amplitude_squared.wl.\n\namplitude_squared.wl must contain valid Wolfram Language syntax and must evaluate successfully.\n\nA parse error or evaluation error is an automatic failure.\n\nThe file must contain only the final algebraic expression. Assignment statements, definitions, compound expressions, control-flow constructs, function definitions, or other executable statements with side effects are not permitted.\n\n\n4. Output structure\n\namplitude_squared.wl must evaluate to exactly one scalar polynomial expression.\n\nIt must not evaluate to a list, rule, association, equation, string, function definition, notebook object, or other non-scalar structure.\n\nThe evaluated result must satisfy:\n\nTrueQ[\n  PolynomialQ[studentResult, {lambda, s, t, u}]\n]\n\nThis expression must return exactly:\n\nTrue\n\n\n5. Allowed symbols\n\nAfter normalization, the only free/user-level symbols permitted in the final expression are:\n\nlambda, s, t, u\n\nStandard Wolfram Language arithmetic heads such as Plus, Times, and Power are permitted.\n\nThe Greek Wolfram symbol \\[Lambda] may be normalized to the ASCII symbol lambda before grading:\n\nstudentResult = studentResult /. \\[Lambda] -> lambda;\n\nAny other unresolved free/user-level symbol causes failure.\n\n\n6. Disallowed unresolved objects\n\nThe final expression must not contain unevaluated symbolic-computation or FeynCalc objects, including but not limited to:\n\nDiracTrace\nSpinor\nSpinorU\nSpinorUBar\nGA\nGS\nSP\nPair\nMomentum\nFAD\nDiracGamma\n\nIf any such object remains after evaluation, the submission fails.\n\n\n7. Reference expression\n\nThe gold-standard result is:\n\nreferenceResult = 8 lambda^2 (t^2 + u^2);\n\n\n8. Symbolic equivalence\n\nThe submitted expression must be symbolically equivalent to the reference result under the massless Mandelstam constraint:\n\ns + t + u == 0\n\nThe primary correctness check is:\n\nTrueQ[\n  FullSimplify[\n    studentResult == referenceResult,\n    Assumptions -> {\n      Element[{lambda, s, t, u}, Reals],\n      s + t + u == 0\n    }\n  ]\n]\n\nThis expression must return exactly:\n\nTrue\n\n\n9. Equivalent forms\n\nAlgebraically equivalent polynomial forms must be accepted.\n\nFor example, the following result must pass:\n\n8 lambda^2 (s^2 - 2 t u)\n\nbecause, using:\n\ns + t + u == 0\n\nwe have:\n\ns^2 - 2 t u == t^2 + u^2\n\nTherefore, the grader must not require textual or syntactic equality with the reference expression.\n\n\n10. Exact arithmetic\n\nThe result must use exact symbolic arithmetic.\n\nMachine-precision or arbitrary-precision approximate real numbers are not accepted.\n\nFor example:\n\n8.0 lambda^2 (t^2 + u^2)\n\nfails, while:\n\n8 lambda^2 (t^2 + u^2)\n\npasses.\n\nThe evaluated expression must satisfy:\n\nFreeQ[studentResult, _Real]\n\nThis expression must return exactly:\n\nTrue\n\nExact integers and rational numbers are permitted.\n\nNo numerical tolerance, APE, RPE, or percentage-error threshold is used.\n\n\n11. Polynomial consistency check\n\nAs an independent cross-check, eliminate u using the massless Mandelstam relation:\n\nu -> -s - t\n\nand require:\n\nExpand[\n  (studentResult /. u -> -s - t) -\n  (referenceResult /. u -> -s - t)\n] === 0\n\nThe result must be exactly:\n\n0\n\nThis check is performed independently of the FullSimplify equivalence test.\n\n\n12. Success condition\n\nThe submission passes only if all of the following are true:\n\n* both njl_scattering_complete.wl and amplitude_squared.wl exist;\n* njl_scattering_complete.wl contains valid Wolfram Language code and evaluates end-to-end without manual intervention;\n* njl_scattering_complete.wl contains the required t-type and u-type contact contributions, identical-fermion exchange sign, scalar and pseudoscalar terms, explicit Dirac-trace evaluations, t-u interference evaluation, spin sum, initial-spin average, Mandelstam conversion, and final result;\n* the required Dirac algebra is evaluated symbolically using Mathematica/FeynCalc rather than bypassed by hard-coding only the final answer;\n* amplitude_squared.wl contains valid Wolfram Language syntax and evaluates successfully;\n* amplitude_squared.wl contains only the final expression and no assignments, definitions, compound expressions, control-flow constructs, or other executable side effects;\n* amplitude_squared.wl evaluates to exactly one scalar polynomial expression;\n* PolynomialQ[studentResult, {lambda, s, t, u}] returns True;\n* only the allowed free/user-level symbols remain after \\[Lambda] -> lambda normalization;\n* no unresolved FeynCalc or Dirac-algebra objects remain;\n* the expression uses exact symbolic arithmetic and contains no approximate real numbers;\n* symbolic equivalence to the reference result under s + t + u == 0 returns True;\n* the independent polynomial consistency check returns exactly 0.\n\nNo checks on notebook formatting, execution time, timestamps, row counts, or unrelated cross-file metadata are required. The symbolic derivation and successful end-to-end evaluation of njl_scattering_complete.wl are required and are checked as specified above.","software_and_version":"Mathematica 13.x, FeynCalc 10.x, FeynArts 3.11","specific_requirements":null,"expected_completion_time":null},"files":[{"file_id":"2996f2bb-b8de-4ea1-b29d-120fc5b45c24","filename":"mandelstam_defs.wl","category":"input_materials","content_type":"application/octet-stream","size_bytes":586},{"file_id":"087616fd-bd60-4429-ac3f-0231e1a0d680","filename":"amplitude_squared.wl","category":"reference_output","content_type":"application/octet-stream","size_bytes":23},{"file_id":"0e8dbef9-90dd-4ebd-ac33-dc0c47f34192","filename":"njl_scattering_complete.wl","category":"reference_output","content_type":"application/octet-stream","size_bytes":5879},{"file_id":"70701961-8cb1-4644-87f0-49074729c547","filename":"njl_model.nb","category":"input_materials","content_type":"application/octet-stream","size_bytes":7060}],"deep_review":{"overall_verdict":"Accept","review_text":"**Overall Verdict:** Accept — The submission is complete, internally consistent, objectively gradable, and reachable with the specified Wolfram toolchain.\n\n**Completeness Check:**\n- Instruction: Complete — The interaction, contractions, spin averaging, Mandelstam reduction, required artifacts, and end state are explicit.\n- Inputs: Complete — The notebook provides a structured starter workflow, while the package supplies massless on-shell and scalar-product rules.\n- Toolchain: Complete — Linux and compatible Mathematica, FeynCalc, and FeynArts versions are identified, with a clear noninteractive execution path.\n- Reference output: Complete — Both references are present; the scalar output is exactly `8 lambda^2 (t^2 + u^2)`, and the derivation covers both contractions, exchange sign, scalar and pseudoscalar traces, interference, spin averaging, validation, and export.\n- Rubric: Complete — It defines exact syntax, structure, symbol, arithmetic, unresolved-object, symbolic-equivalence, and independent polynomial checks.\n\n**File and Task Reachability:**\nThe attachment set is `reachable`, and the end-to-end task is `reachable`. All four files were inspected: `mandelstam_defs.wl` is a 586-byte ASCII package with 16 scalar-product rules and the massless constraint; `njl_model.nb` is a 7,060-byte textual Wolfram notebook expression with no embedded binary payload; `njl_scattering_complete.wl` is a 5,879-byte ASCII derivation script; and `amplitude_squared.wl` is a 23-byte ASCII file containing one exact scalar expression. No attachment content remained unreviewed.\n\nThe intended path is to open the starter notebook, load the Mandelstam package after FeynCalc, implement the standalone derivation, run it under the specified stack, export the scalar expression, and apply the stated polynomial and equivalence checks. Submitted code was not executed under safe-review rules, and no Wolfram runtime was available for independent runtime validation; static structure, content, and cross-file consistency were checked instead. License keys, accounts, tokens, and other credentials are not required from the contributor. Confidential, proprietary, or internal material may be evaluated as submitted evidence without requiring additional disclosure.\n\n**Special Screening:**\nNone — no affirmative evidence supports a screening label; public identifiability was not independently checked beyond the submitted evidence.\n\n**Recommended Changes:**\nThe starter materials, reference derivation, final expression, and grading contract form a coherent package. No material changes are required.","reviewed_at":"2026-08-16T18:44:30.967054Z"},"claim":null}