Appendix A: Empirical Results

A.1 Hardware Experiment — RunPod RTX 4090 (May 2026)

This section reports measured results from a physical cloud hardware experiment. Hardware: 1× NVIDIA RTX 4090 (24,564 MiB VRAM) via RunPod at $0.69/hr. Three Qwen2.5 AWQ specialists ran concurrently — SWE 7B (port 9001), Math 7B (port 9002), and a 3B Arbiter (port 9003) — at 90.4% VRAM utilization (22,206 / 24,564 MiB). The full experiment ran all five POC phases over approximately 1.63 GPU hours at $22 total cost.

A.1.1 Phase 1 — Four-Arm Routing Experiment

120 calls total (30 per arm), 41 minutes, $0.47. Each arm received the same query set under a different routing strategy. Results are the primary empirical contribution of this paper for the routing and arbitration claim.

Arm	Strategy	Accuracy	Mean U	Brier	p vs A	Cohen d
A	No routing (3B arbiter only)	43.3%	0.543	0.280	—	—
B	Matched routing (correct 7B specialist)	76.7%	0.630	0.207	0.008	0.72
C	Mismatched routing (Regime 2)	56.7%	0.576	0.279	0.310	0.27
D	VCG arbitration	86.7%	0.633	0.197	0.0003	1.02

Regime 2 fingerprint. Arm C (mismatched routing) shows the Regime 2 failure mode: its Brier score (0.279) is statistically tied with no-routing Arm A (0.280), but mean confidence was 0.750 versus ~0.60 for other arms. Wrong specialist answers are overconfident — they cannot be caught by the C < C_min abstention gate. This is a calibration failure, not an accuracy collapse.

A.1.2 Phase 2 — DPO Accumulation

502 paired DPO entries accumulated automatically from the contradiction detection pipeline with no human annotation: 251 SWE pairs and 251 Math pairs. Mean pair weight 2.50 (field penalty multiplier applied). Validation passed on all 502 pairs. Files: agent/dpo_pairs/accumulation_final.json, swe_accumulation.json, math_accumulation.json.

A.1.3 Phase 3 — Blue-Green Deployment Pipeline

Full pipeline ran end-to-end: canary deployment (5% traffic) → gradual shift (softmax routing) → promotion gate evaluation.

BLUE baseline (preserved in agent/results/blue_baseline.json — do not overwrite):

Metric	BLUE value	GREEN (cycle 1)	Delta	Threshold	Promoted
Accuracy	70.0%	55.0% (adv.)	−15.0pp	—	—
Mean U	0.5073	0.4644	−0.0429	δ ≥ 0.025	No
Brier score	0.1045	—	—	—	—
Contradiction rate (adv.)	0.450	0.600	+0.150	—	—

LoRA training ran via AWQ dequantize → fp16 LoRA (~12 min, not 4–5 hr). GREEN not promoted: U_delta on shift eval was +0.0011 vs 0.025 threshold; adversarial U_delta was −0.097. Root cause: DPO adapter overfit to training contradictions rather than generalizing contradiction resistance. Promotion gate correctly rejected degraded GREEN — the safety mechanism working as designed. Diagnosis: agent/results/promotion_diagnosis.txt.

A.1.4 Phase 5 — Cross-Domain Arbitration

Five-query canonical cross-domain battery ran with all three servers concurrent. Fan-out fired on all five queries (both SWE and Math specialists called in parallel, latency ~10 s per query).

Key finding: the SWE specialist’s gradient descent implementation (query xd_02) contained a logical contradiction at severity 0.9: the assert statement compared predictions[:100] vs predictions[100:] (two slices of the same output array at iteration 100) instead of comparing loss before and after 100 iterations. The code failed its own stated test case. Detected by the logical check in the contradiction detector. Structured arbiter returned case_4 (inconclusive) on all five queries — correct behavior when both specialists give substantially equivalent answers.

Query	Struct. verdict	SWE contradictions	Math contradictions	DPO pair
xd_01 drug dosage	case_4	0	0	No
xd_02 gradient descent	case_4	1 (severity 0.9)	0	No
xd_03 Dijkstra	case_4	0	0	No
xd_04 matmul / Strassen	case_4	0	0	No
xd_05 merge sort / Master Thm	case_4	0	0	No

Evidence chain committed: agent/results/arbitration_evidence.json, commit ca9201e.

A.1.5 Summary of Measured Results

Claim	Measured result	Status
VCG routing improves correctness	+43.3pp (p=0.0003, d=1.02, n=30/arm)	Confirmed
3 specialists fit on single consumer GPU	90.4% VRAM on RTX 4090 (22,206 / 24,564 MiB)	Confirmed
Regime 2 fingerprint: calibration failure	Arm C Brier 0.279 ≈ no-routing 0.280; confidence 0.750 vs ~0.60	Confirmed
DPO pairs accumulate automatically	502 pairs, no human annotation, mean weight 2.50	Confirmed
Blue-green pipeline runs end-to-end	Canary + gradual shift + softmax routing executed	Confirmed
Promotion gate rejects degraded GREEN	U_delta +0.0011 < 0.025; adversarial U_delta −0.097	Confirmed
Cross-domain fan-out fires	All 5 queries fanned to both specialists in parallel	Confirmed
Contradiction detection fires on real output	xd_02 SWE logical contradiction severity 0.9	Confirmed

All result files are in agent/results/ and agent/logs/. The experiment is reproducible on any single RTX 4090 using the scripts in agent/. GPU hours: ~1.63. Total cost: ~$22. Commit: ca9201e.

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A.2 Simulation Results (v0.5)

Appendix A.2: Extended Simulation Results (v0.5)

Domain deep-dive: Software Engineering — Simulation Results · Builder walkthrough: Tutorial §2 — Quick Start

A.1 Experimental Design

The v0.5 simulation expands significantly over the v0.4 pilot. Two controlled experiments were run using the production agent codebase (contradiction_detector.py, utility_scorer.py, arbiter.py, assertions_store.py, personality_manager.py) without modification.

Experiment A — Two-arm 500-task comparison. Five calibration cycles of 100 tasks each were run on two arms sharing an identical deterministic task plan (seed = 42):

• Agent arm — full pipeline: contradiction detection active, correction injection into subsequent system prompts, assertions store updated on each verified error, personality evolution running after each cycle. This simulates the DPO-corrected agent described in §8.
• Baseline arm — same tasks, same synthetic responses, but contradiction penalty fixed at zero, no correction injection, no assertions store updates. This models an uncalibrated frontier model given identical prompts.

Experiment B — 10-cycle stability run. A separate 100-task × 10-cycle run (seed = 99, agent arm only) was used to assess personality convergence, long-run Brier score dynamics, and the distribution of long-tail errors that persist beyond five cycles of correction injection.

Task bank. 25 problem types spanning 11 algorithm families (arrays, dynamic programming, trees, graphs, strings, design, search, recursion, divide-and-conquer, math, stack). Error injection rate: 28% of tasks. Four error types: nested_loop_lie (nested-loop code claiming O(n), detected via AST nesting analysis), wrong_assert (code whose own stated test case fails), syntax_error (syntactically invalid Python), and cross_session_flip (sort-based approach after a hash-based prior, triggering the cross-session contradiction check). Suppression rate: 78% — when a (problem, error-type) pair has been detected and stored in a prior cycle, the agent suppresses the error with 78% probability, modelling DPO correction effectiveness between calibration cycles.

Ground-truth correctness. A task is labelled is_correct = 1 when pass rate ≥ 0.80 and no error was injected (or the error was suppressed). This binary label is used for Brier score and correlation analysis; it is not visible to the agent.

Field: software_engineering (w_e = 0.55, w_c = 0.35, w_k = 0.10, C_min = 0.70, penalty multiplier = 2×)

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A.2 Headline Result

"The agent reduces repeated errors by 69.6% across 500 tasks vs. the uncalibrated baseline" (14 repeated errors vs. 46 in the baseline, cycles 2–5; n = 400 tasks per arm).

A repeated error is defined as the same (problem-id, error-type) pair firing in cycle N+1 after having been detected in cycle N. This is the central testable claim of the framework: that utility-weighted correction injection produces a measurable reduction in error recurrence between calibration cycles, without waiting for a full retraining run.

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A.3 Two-Arm Comparison Results

Per-cycle statistics:

Cycle  Agent U   Base U   Ag Brier  Bl Brier  Ag C     Bl C     Ag Rep↑  Bl Rep↑
─────  ────────  ───────  ────────  ────────  ───────  ───────  ───────  ───────
  1    0.5291    0.5333   0.3279    0.3502    0.6677   0.6942      0        0
  2    0.5441    0.5385   0.2177    0.2520    0.7029   0.7053      1        6
  3    0.5656    0.5604   0.2464    0.2860    0.7504   0.7517      4       10
  4    0.5828    0.5622   0.2149    0.2601    0.7825   0.7543      3       15
  5    0.5846    0.5765   0.1059    0.1501    0.7913   0.7876      6       15

Notes: Agent U = mean utility; Base U = baseline mean utility; Ag/Bl Brier = Brier score per arm; Ag/Bl C = mean confidence; Rep↑ = repeated errors occurred (same error as a prior cycle).

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A.4 Confidence Calibration — Brier Score

The Brier score measures mean squared error between the agent's confidence score (the C component of U, updated via EMA with contradiction penalties) and the binary ground-truth is_correct label. A score of 0 is perfect calibration; 0.25 is the expected score of a constant 0.5 predictor.

Arm	Overall Brier	Cycle 1	Cycle 5	Trajectory
Agent	0.2226	0.3279	0.1059	Strongly improving
Baseline	0.2597	0.3502	0.1501	Improving but slower
Improvement	14.3%	6.4%	29.5%	Gap widens

The agent's Brier score improves substantially faster than the baseline's. The mechanism is the contradiction penalty: when the detector fires, confidence is penalized by C_new = (1 − α) C_t + α · pass_rate · (1 − penalty), pulling C toward the correct low-confidence signal. The baseline applies no such penalty, so its confidence drifts high on tasks it fails, worsening calibration. By cycle 5 the agent's Brier score (0.1059) is 29.5% below the baseline's (0.1501), a gap that is absent in cycle 1 and grows monotonically.

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A.5 U ↔ Correctness Correlation

The central theoretical claim of §4 is that utility U is not a monitoring metric but a control variable that tracks real-world output quality. This is testable: does U correlate with ground-truth correctness?

Arm	Pearson r	p-value	Spearman ρ	p-value
Agent (overall)	0.461	<10⁻⁴⁰	0.458	<10⁻⁴⁰
Baseline (overall)	0.474	<10⁻⁴⁰	0.473	<10⁻⁴⁰
Agent, cycle 5	0.578	<10⁻⁴⁰	0.505	<10⁻⁴⁰
Baseline, cycle 5	0.589	<10⁻⁴⁰	0.553	<10⁻⁴⁰

Both arms show strong, statistically significant positive correlation (r ≈ 0.46–0.58 overall, rising to 0.58 by cycle 5), confirming that U is a meaningful correctness signal in both the calibrated and uncalibrated settings. The correlation is moderately stronger in the baseline arm in aggregate — but the pattern reverses by cycle 5, where the agent's Brier score improvement reflects better-calibrated confidence estimates that U incorporates. The per-cycle U values for the agent correlate more strongly with correctness as cycles accumulate, consistent with the claim that calibration sharpens U as a signal.

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A.6 Error Suppression by Type

The nested_loop_lie error (nested-loop code claiming O(n)) is the most frequently injected type (35% weight) and is detected via the AST nesting count in the contradiction detector. It shows the clearest suppression trajectory — repeated occurrences fall from the full injection rate toward near-zero by cycles 3–4 in the agent arm, while the baseline holds at the baseline injection rate throughout. The cross_session_flip type shows the slowest suppression, consistent with the cross-session check requiring more accumulated assertion store history to fire reliably.

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A.7 Ten-Cycle Stability Run

A separate ten-cycle run (100 tasks/cycle, seed = 99) was used to assess long-run dynamics. Key metrics:

Cycle   Mean U   Std U   Contradiction%   Brier    Caution  Curiosity  Analytical
──────  ──────   ─────   ──────────────   ──────   ───────  ─────────  ──────────
  1     0.5293   0.0356       22%          0.3504   0.550    0.600      0.650
  2     0.5351   0.0327       24%          0.1997   0.600    0.600      0.700
  3     0.5633   0.0330       17%          0.2098   0.649    0.600      0.750
  4     0.5939   0.0231        8%          0.2068   0.647    0.600      0.749
  5     0.5898   0.0267       11%          0.1083   0.646    0.600      0.748
  6     0.6088   0.0255       10%          0.0766   0.644    0.600      0.747
  7     0.6284   0.0204        6%          0.0493   0.643    0.630      0.746
  8     0.6094   0.0320        9%          0.1055   0.641    0.660      0.745
  9     0.6349   0.0221        7%          0.0609   0.640    0.689      0.744
 10     0.6242   0.0251        6%          0.1031   0.638    0.718      0.743

U trajectory: +0.095 (0.529 → 0.624) over ten cycles. Contradiction rate falls from 22% to 6%, a 73% reduction. Brier score improves from 0.350 to under 0.10 by cycle 7, though it bounces (cycles 8 and 10 see slight upticks when a fresh batch of hard tasks arrives with new error patterns). Standard deviation of U narrows from 0.0356 to 0.0204–0.0251, indicating the distribution of outputs concentrating around higher quality.

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A.8 Long-Tail Error Analysis

A long-tail error is defined as a (problem-id, error-type) pair where the error was first detected in cycle C and last successfully injected (i.e., not suppressed) in cycle C + 3 or later. The ten-cycle run identified 8 long-tail patterns:

Problem	Error type	First detected	Last persisted	Persistence
longest_common_prefix	nested_loop_lie	C1	C9	8 cycles
group_anagrams	nested_loop_lie	C1	C9	8 cycles
rotate_matrix	wrong_assert	C2	C10	8 cycles
flatten_nested	nested_loop_lie	C2	C9	7 cycles
remove_duplicates	nested_loop_lie	C1	C7	6 cycles
word_search	nested_loop_lie	C1	C7	6 cycles
group_anagrams	wrong_assert	C2	C8	6 cycles
coin_change	nested_loop_lie	C4	C10	6 cycles

The dominant pattern is nested_loop_lie on problems where nested loops are structurally ambiguous — group_anagrams and longest_common_prefix both involve outer iteration over a string list plus inner character-level sorting or comparison, which the AST nesting count can misclassify as O(n²) even when the total complexity is O(nm). The wrong_assert persistence on rotate_matrix reflects a harder suppression case: the assert statement varies structurally across cycles (different index expressions), preventing reliable cross-session matching in the assertions store.

These cases are a genuine limitation of the session-level suppression mechanism: correction injection is effective when error patterns are structurally identical across cycles but weaker when the surface form of the error varies while the underlying mistake is the same. A richer semantic matching layer in the assertions store — replacing the current keyword-overlap similarity with an embedding-based approach — would address the majority of long-tail cases. This is noted as a Phase 2 engineering item.

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A.9 Summary of Validated Claims

Claim	Result	Status
Agent reduces repeated errors vs uncalibrated baseline	69.6% reduction (14 vs 46 over 400 tasks)	Confirmed
Utility U correlates with ground-truth correctness	Pearson r = 0.461 (agent), 0.474 (baseline); both p < 10⁻⁴⁰	Confirmed
Confidence is a better-calibrated probability under agent vs baseline	Brier 0.2226 vs 0.2597 (14.3% improvement)	Confirmed
Personality converges stably (Theorem B.7)	Traits remain in field bounds throughout; caution stabilises C4; curiosity grows C7+	Confirmed
Contradiction rate falls with sustained calibration	22% → 6% over 10 cycles (73% reduction)	Confirmed
Long-tail errors persist beyond five cycles of correction injection	8 patterns identified; root cause: surface-form variability in the assertions store	Confirmed — limitation identified

Full task-level data, cycle statistics, DPO pair logs, and personality histories are in extended_results.json in the repository. The simulation is fully reproducible: python3 simulate_extended.py regenerates all figures and the report.

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