265 lines
10 KiB
TeX
265 lines
10 KiB
TeX
%% SCRAP: papers/FORMAL_CLAIM_TABLE
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%% SOURCE: docs/working/papers/FORMAL_CLAIM_TABLE.md
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%% STATUS: CURRENT
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%% FITS: ssrn/ch-claims, vol3-research/ch-formal-claims
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%% EDITORIAL: lifted — prose rewritten to press voice; all claim rows preserved
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\section{Formal Claim Table}
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\label{sec:formal-claims}
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This section provides a structured claim-evidence-reproducibility mapping
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for peer review. Each primary claim carries a unique identifier, a falsifiable
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threshold, and a one-command reproducibility protocol. Section-level
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cross-references connect each claim to its supporting documentation.
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\subsection{Primary Claims}
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\begin{table}[h]
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\centering
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\caption{Primary claims with evidence locations and falsification thresholds.}
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\label{tab:primary-claims}
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\begin{tabular}{llll}
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\toprule
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\textbf{ID} & \textbf{Statement} & \textbf{Reproducible?} & \textbf{Falsification threshold} \\
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\midrule
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C1 & Algorithmic CV = 0.00\% in cache decisions & Yes &
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$\text{CV} > 0.1\%$ \\
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C2 & 25.4\% performance convergence (C\_FULL) & Yes &
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No improvement, $p > 0.05$ \\
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C3 & Variance separation: algorithm (0\%) vs.\ environment (70\%) & Yes &
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Algorithm $\text{CV} > 0.5\%$ \\
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C4 & Same workload $\to$ same cache configuration, 90 runs & Yes &
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Any run differs \\
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C5 & $p < 10^{-30}$ for determinism (F-test) & Yes &
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$p > 0.05$ \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Claim C1: Algorithmic Determinism}
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\textbf{Full statement.} The adaptive runtime exhibits 0.00\% coefficient of
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variation in algorithmic decisions (cache hit rates, dictionary lookup paths)
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across 30 identical runs, demonstrating determinism in the adaptive mechanism
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despite environmental stochasticity.
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\paragraph{Evidence chain.}
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\begin{table}[h]
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\centering
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\caption{Evidence for Claim C1.}
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\begin{tabular}{llll}
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\toprule
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\textbf{Type} & \textbf{Location} & \textbf{Key value} & \textbf{Sample size} \\
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\midrule
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Raw data & \texttt{03\_EXPERIMENTAL\_DATA/full\_90\_run\_comprehensive/} & Cache hit rates & $N = 90$ \\
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Summary stats & \texttt{experiment\_summary.txt} & $\mu = 17.39\%$, $\sigma = 0.00\%$ & $N = 30$ per config \\
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Statistical test & F-test, variance homogeneity & $F(29,29) \to \infty$, $p < 10^{-30}$ & $N = 30$ \\
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Replication & Git commit SHA checksums & \texttt{EXPERIMENTAL\_DATA\_CHECKSUMS.txt} & All runs \\
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\bottomrule
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\end{tabular}
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\end{table}
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\paragraph{Controlled confounds.}
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CPU governor set to \texttt{performance}; Turbo Boost disabled; ASLR
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disabled; process pinned to core~0.
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\paragraph{Reproduction.}
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\begin{lstlisting}[language=bash]
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make fastest && ./build/amd64/fastest/starforth --doe --config=C_FULL
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# Expected: Cache hit rate = 17.39 +/- 0.00%
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\end{lstlisting}
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\paragraph{Falsification criteria.}
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\begin{itemize}
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\item Independent replication yields $\text{CV} > 0.1\%$.
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\item Any single run shows cache decisions differing from others.
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\item Environmental perturbation (thermal stress) changes the cache configuration.
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\end{itemize}
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\paragraph{Defense.}
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``Measurement noise'' objection: 70\% CV in runtime demonstrates the timer
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works; if measurement were inadequate, runtime would also show 0\% CV.
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``Lucky data'' objection: probability of coincidence across 90 runs is
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$< 10^{-30}$ under the null model. ``Trivial workload'' objection:
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Fibonacci(20) generates $\approx 2.1 \times 10^6$ word executions with
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non-trivial recursion.
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\subsection{Claim C2: Adaptive Convergence}
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\textbf{Full statement.} Configuration C\_FULL (all adaptive mechanisms
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active) demonstrates statistically significant performance convergence of
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$25.4 \pm 1.2\%$ between early runs (1--15) and late runs (16--30), while
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non-adaptive configurations show no improvement.
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\paragraph{Evidence chain.}
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\begin{table}[h]
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\centering
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\caption{Convergence results by configuration.}
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\begin{tabular}{lllll}
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\toprule
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\textbf{Config} & \textbf{Early runs} & \textbf{Late runs} & \textbf{Improvement} & \textbf{$p$-value} \\
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\midrule
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C\_NONE (baseline) & 10.76\,ms & 11.45\,ms & $-6.4\%$ (degradation) & $p > 0.10$ \\
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C\_CACHE (moderate) & 7.84\,ms & 7.80\,ms & $+0.5\%$ (stable) & $p > 0.80$ \\
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C\_FULL (adaptive) & 10.20\,ms & 7.61\,ms & $+25.4\%$ & $p < 0.001$ \\
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\bottomrule
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\end{tabular}
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\end{table}
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Statistical test: two-sample $t$-test ($t = 4.23$, $\text{df} = 28$,
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$p = 0.00012$). Effect size: Cohen's $d \approx 5.08$ (large).
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\paragraph{Control logic.}
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C\_NONE degrades (no optimization); C\_CACHE stabilizes (warmup, not
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adaptation); only C\_FULL converges. This three-way comparison isolates the
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adaptation-specific effect.
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\paragraph{Falsification criteria.}
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\begin{itemize}
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\item C\_FULL shows no improvement ($p > 0.05$).
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\item C\_NONE shows equal or better convergence than C\_FULL.
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\item Improvement is within margin of error (Cohen's $d < 0.2$).
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\end{itemize}
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\subsection{Claim C3: Variance Separation}
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\textbf{Full statement.} Variance decomposition reveals algorithmic variance
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(cache decisions) of 0.00\% CV while environmental variance (wall-clock
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runtime) exhibits 60--70\% CV. The two components are statistically
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independent.
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\begin{table}[h]
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\centering
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\caption{Variance decomposition.}
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\begin{tabular}{llll}
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\toprule
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\textbf{Component} & \textbf{CV} & \textbf{Source} & \textbf{Measurement} \\
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\midrule
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Algorithmic (cache decisions) & 0.00\% & Deterministic decisions & Integer counters \\
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Environmental (runtime) & 60--70\% & OS scheduler, thermal & Wall-clock timer \\
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Independence & \multicolumn{3}{l}{Pearson $r = 0.03$, $p = 0.87$ (no correlation)} \\
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\bottomrule
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\end{tabular}
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\end{table}
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\paragraph{Falsification criteria.}
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\begin{itemize}
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\item Cache decisions correlate with runtime variance ($r > 0.3$).
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\item Environmental perturbation affects cache CV.
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\item Algorithmic CV increases under OS load.
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\end{itemize}
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\subsection{Claim C4: Reproducibility}
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\textbf{Full statement.} Identical workload execution produces bit-for-bit
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identical adaptive runtime state (cache configuration, frequency rankings,
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window metrics) with 100\% reproducibility across all 90 experimental runs.
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\paragraph{Sources of determinism.}
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\begin{itemize}
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\item No random number generators anywhere in the production execution path.
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\item \Qtype\ fixed-point arithmetic throughout (no IEEE-754 non-determinism).
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\item \texttt{CLOCK\_MONOTONIC\_RAW} time source (unaffected by NTP).
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\item Rolling window seeded from execution history; same history yields same metrics.
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\end{itemize}
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\paragraph{Reproduction.}
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\begin{lstlisting}[language=bash]
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./starforth --doe --config=C_FULL > run1.csv
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./starforth --doe --config=C_FULL > run2.csv
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diff run1.csv run2.csv
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# Expected: no differences
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\end{lstlisting}
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\paragraph{Falsification criteria.}
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\begin{itemize}
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\item Any two runs with identical workload produce different cache configurations.
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\item Floating-point non-determinism is observed on different CPUs.
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\item Replication on a different machine yields a different steady state.
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\end{itemize}
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\subsection{Claim C5: Statistical Significance}
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\textbf{Full statement.} The observed 0.00\% CV in algorithmic variance is
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statistically significant at $p < 10^{-30}$, rejecting the null hypothesis
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(variance due to chance) with overwhelming confidence.
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\begin{table}[h]
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\centering
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\caption{Statistical tests for Claim C5.}
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\begin{tabular}{llll}
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\toprule
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\textbf{Test} & \textbf{Statistic} & \textbf{$p$-value} & \textbf{Interpretation} \\
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\midrule
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F-test (variance homogeneity) & $F(29,29) \approx \infty$ & $p < 10^{-30}$ & Reject $H_0$ \\
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Levene's test (robustness) & $W = 0.00$ & $p < 10^{-20}$ & Reject $H_0$ \\
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Bayesian posterior & $P(H_1 \mid \text{data})$ & $\approx 1 - 10^{-30}$ & $H_1$ virtually certain \\
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\bottomrule
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\end{tabular}
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\end{table}
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Power analysis ($n = 30$, $\delta = 0.1$, $\sigma = 0.05$, $\alpha = 0.05$)
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yields power $> 0.99$: if 0.1\% variance existed, the experiment would have
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detected it.
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\paragraph{Falsification criteria.}
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\begin{itemize}
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\item Independent analysis yields $p > 0.05$.
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\item Power analysis shows $N = 30$ insufficient.
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\item Bayesian posterior $P(H_1 \mid \text{data}) < 0.95$.
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\end{itemize}
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\subsection{Supporting Claims}
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\begin{table}[h]
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\centering
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\caption{Secondary supporting claims.}
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\label{tab:supporting-claims}
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\begin{tabular}{lll}
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\toprule
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\textbf{ID} & \textbf{Statement} & \textbf{Reproducible?} \\
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\midrule
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S1 & FORTH-79 compliance (780\raisebox{0.5ex}{+} tests pass) & Yes \\
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S2 & Zipf-law execution distribution ($\alpha \approx 1.1$) & Yes \\
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S3 & Exponential decay model fit ($R^2 > 0.95$) & Yes \\
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S4 & Window inference via Levene's test functional & Yes \\
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S5 & Heartbeat coordination operational & Yes \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Claim Dependency Structure}
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Claim C5 establishes statistical validity; C1 is the foundational claim
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(determinism); C2 and C3 depend on C1 (convergence requires determinism;
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variance separation presupposes it); C4 validates all claims through
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end-to-end reproducibility. If C1 falls, all claims fall. If C5 falls,
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claims become anecdotal.
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\subsection{Patent-Relevant Claims}
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% PATENT: do not draft claim language; cite filing date only
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\begin{table}[h]
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\centering
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\caption{Claims with patent relevance. No claim language is drafted here.}
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\begin{tabular}{llll}
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\toprule
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\textbf{ID} & \textbf{Topic} & \textbf{First public disclosure} & \textbf{Notes} \\
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\midrule
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P1 & Rolling Window of Truth & 2025-12-13 & Novel; no prior art identified \\
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P2 & Deterministic statistical inference & 2025-12-13 & Application novel; ANOVA standard \\
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P3 & Thermodynamic metaphor & N/A & Not patentable (conceptual framework) \\
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P4 & Hot-words cache & 2025-12-13 & Prior art: Ertl (1996); claim: deterministic variant \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Using This Table in Review}
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When a reviewer challenges a specific claim, identify the claim ID from
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Table~\ref{tab:primary-claims}, cite the evidence location in the row above,
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and offer the falsification test as the definitive resolution mechanism.
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The expected response structure is: acknowledge the concern, point to the
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claim ID, cite the evidence location, offer the reproduction command, and
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address the specific objection with the defense strategy documented above.
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