1{2 "feasible": true,3 "researchMode": "theoretical",4 "secondaryModes": ["computational"],5 "summary": "Pure-mathematics study of the zero-forcing number Z(P(n,5)) of generalized Petersen graphs. All inputs are definitional (the graph family) and the work consists of exact computation (brute force, SAT/CP-SAT, fort hitting-set ILP), independent certificate checking, conjecture generation with prespecified holdout, and rigorous proof attempts for upper-bound constructions and lower-bound obstructions. No human subjects, no clinical or biosafety work, no proprietary data. Required tooling: Python 3.14.7 present; pip 26.2.1 present; 16 CPU cores available on worker M4M64c; tectonic (LaTeX engine) present and the platform latex_build tool exists; gcc/git present. Missing at preflight: python-sat / OR-Tools / networkx (installable from PyPI), drat-trim or another DRAT/LRAT checker (build from source only if the source host is allowlisted; otherwise lower bounds will rely on fort-cover ILP duals, independent re-solves and brute force rather than DRAT certificates), Lean 4 / Mathlib (elan absent; formalization is contingent on being able to install the toolchain and Mathlib cache within the network allowlist and is treated as optional). The honest outcome space includes a null result: a certified finite table of exact values plus a documented failure to prove an infinite-family theorem, which would fail the publication gate by design.",6 "restrictedActivities": [],7 "requiredApprovals": [],8 "missingInputs": [9 "No SAT solver library installed yet (python-sat / OR-Tools to be installed from PyPI in Stage A).",10 "No DRAT/LRAT proof checker installed (drat-trim must be built from source; depends on host allowlist).",11 "No Lean 4 toolchain (elan/lake absent); Lean formalization is optional and may be infeasible under the network allowlist.",12 "Full text of the primary sources must be fetched from allowlisted scholarly hosts during Stage B; access to paywalled text (e.g. the EJOR article) may be limited to abstracts and must be labeled as such.",13 "Published exact values of Z(P(n,5)) and of the P(24r,5) family must be extracted from the original papers, not assumed."14 ],15 "risks": [16 "Novelty risk: Rashidi et al. (2020) and the 2026 P(n,3)/P(n,4) papers may already contain the sharp result for k=5 or most of the small-n exact values; mitigation is the mandatory prior-art gate before any novelty claim.",17 "Proof risk: an infinite-family theorem may be unattainable within budget; a finite certified table alone is likely insufficient for publication and the run must then end in quality_failed honestly.",18 "Lower-bound certification risk: without a trusted DRAT checker, solver-reported optimality is only 'solver-supported'; mitigation is two independent exact formulations (SAT and fort hitting-set ILP / brute force) plus explicit fort-based arguments where possible.",19 "Compute scaling risk: exact Z for 2n vertices grows quickly; n up to ~40 is plausible with SAT, larger n is uncertain. Mitigation: benchmark n=11..20 first, set timeouts, treat timeouts as unknown.",20 "Budget risk: the live budget counter shows roughly USD 9.6 available to this session, far below the USD 150 nominal cap in run.json; the plan must prioritize a smaller correct study (pilot + discovery horizon) over extended horizons.",21 "Definition risk: a mismatch between the paper's P(n,k) convention and the literature's convention would invalidate comparisons; mitigation is reproducing two published small cases in Stage A/C before any comparison.",22 "Symmetry-reduction risk: orbit reduction in brute force must be justified by a proof that automorphisms map zero-forcing sets to zero-forcing sets; otherwise minimality claims are invalid."23 ],24 "estimatedBudgetUsd": 9.025}26