| \chapter{An executable architecture and its interfaces} |
| \label{ch:architecture} |
| \section{The delivered finite pipeline} |
| The reference implementation has an original six-state stochastic arena, a four-hypothesis temporal inference catalog, a source-indexed operator memory, exact constrained planning, a persistent branch, and a capsule exporter. It performs the following complete finite workflow: |
| \begin{enumerate} |
| \item Generate an explicitly synthetic 32-event action/context recording under the declared model. |
| \item Validate unique source IDs, monotone simulation ticks, and the sign observation vocabulary. |
| \item Compile the sequence likelihood for every source/world hypothesis and retain the coupled posterior. |
| \item Read the actual simulated world calibration from the fixture, rather than sampling a world explanation and calling it a measurement. |
| \item Choose a persistent source-type branch from the calibrated posterior. |
| \item Construct its fixed semantic target and optimize a feasible descendant inside the path shield. |
| \item Execute 1,000 simulator steps and export the source reference, posterior, policies, protected/excluded observables, numerical checks, and descendant trace. |
| \end{enumerate} |
| This is an end-to-end finite mechanism demonstration. Its synthetic sign events are not video frames, its 32 events are not a measured clip duration, and its actor has an explicitly known small transition model. The fixture decoder rejects actual-human labels because it has not been validated as a real-data decoder. |
|
|
| \section{An evidence ledger, not an autobiographical generator} |
| Each source event carries an epoch and ID. A later annotation can replace the corresponding conditional factor after its model assumptions are checked. It does not append a second historical choice. A real-game implementation should preserve a record of the previous annotation, new decoder version, reason for change, and any affected behavior certificates. The prototype records revision identity and kind, but it does not implement a production authentication service or a complete immutable database. |
|
|
| A branch's experience can teach it to navigate, anticipate opponents, or allocate compute. Those skills belong in competence memory. A historical source inference is updated only from a suitable source or mechanics channel with the relevant conditional likelihood. This prevents an increasingly competent descendant from treating its own preferred moves as proof that the person always preferred them. |
|
|
| \section{Five runtime roles} |
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}p{.19\textwidth}XX@{}}\toprule |
| Role & Delivered finite realization & Proposed larger realization\\\midrule |
| Capture & Synthetic categorical event packets with IDs and shared ticks & Synchronized video, physical inputs, audio, player-visible state, and calibrated clocks.\\ |
| Inference & Known four-hypothesis HMM and operator tree & Learned perception plus calibrated joint hypotheses or particles, retaining source links.\\ |
| Actor & Known finite policy and simulator step interface & A game-capable reactive controller with action deadlines and authorized engine access.\\ |
| Proposer & Analytic projected-value update or LP optimization & Local language model, world model, or learned optimizer proposing typed changes.\\ |
| Verifier & Signature feasibility, value comparison, independent finite tests & Held-out real sessions, simultaneous model bounds where available, and rollback evaluation.\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| The full neural/engine integration is specified, not delivered. A code interface is not a working Unity, Unreal, Godot, Windows input, or anti-cheat-compatible adapter. The release makes no commercial-game control claim. |
|
|
| \section{GPU and local-model integration} |
| The finite arrays are deliberately small and execute on CPU without downloaded weights. Their matrix products are batchable over catalog hypotheses, but GPU launch and transfer overhead can dominate for $K=2$. The present study contains no GPU throughput or latency measurement. |
|
|
| A practical extension would keep large visual encoders and a game-capable backbone on an accelerator while batching source-factor production asynchronously. The lightweight actor would not wait for a language model at every motor tick. A local language model could propose a revised hypothesis, test scenario, memory schema, or skill; a typed bridge would prevent its text from directly overriding the source archive or protected motor gate. Such a proposal must declare which source, catalog, dynamics, or behavioral contract it changes. |
|
|
| A new hypothesis outside the existing catalog cannot simply receive a probability through normalization of the old posterior. The relevant original source must be reinterpreted under the new model. Similarly, a change to semantic labels requires a new contract or a validated transport map; reusing the same label string does not prove meaning preservation. |
|
|
| \section{From the finite actor to an instrumented game} |
| The proposed engine contract requires a build identifier, monotone event clock, reset/checkpoint semantics, action vocabulary, actor observation boundary, and explicit acknowledgment of which world fields are privileged analyst information. It must distinguish physical controls from inferred controls. Delayed or out-of-order packets should be retained as timing uncertainty or rejected according to the capture model, not silently assigned to the nearest convenient action. |
|
|
| For each candidate executor, a verified model would construct or bound its semantic signature. If an exact finite signature is unavailable, the gate is an empirical test with stated coverage rather than a global theorem-backed shield. A fallback executor must itself satisfy the declared contract; replacing a missed deadline with a generic emergency action can alter the output law. Safety constraints and historical style can conflict and must be prioritized explicitly rather than hidden in a fidelity score. |
|
|
| Human recordings and behavior replicas should be permissioned and clearly labeled as reconstructions. An observer's recognition of a style is an empirical endpoint, not proof of psychological identity. The delivered simulator is an original local environment and does not automate a third-party online game. |
|
|
| \section{The exported player capsule} |
| The capsule's six persistent components are: source record and digest; coupled catalog posterior; source epoch and selected branch; semantic target and exclusions; executor and model versions; and evaluation/lineage records. The supplied JSON example records the precise claim scope. |
|
|
| In the demonstration run, the source-anchor normalized value is $0.53785$ and the constrained descendant's value is $0.66667$. Their enumerated six-step semantic path TV is $3.23\times10^{-16}$. The 1,000-step sampled reward mean is $0.676$. This latter number is one stochastic rollout, not a confidence interval or proof of improvement. The exact finite value and signature calculation are the relevant model-based evidence. |
|
|
| \chapter{Executed studies and strong controls} |
| \label{ch:experiments} |
| \section{Design and interpretation} |
| \status{executed, synthetic, known-model} |
| All new studies are generated from the fixed configuration and seed recorded in \texttt{results/config.json}. The master seed is 1,860,317, with independently specified offsets for the study families. The designs were written and executed within this research session; they are not an externally preregistered study. No participant, human video, brain recording, pretrained model, or commercial game is included. |
|
|
| The benchmark does not reward the method for making its comparator artificially uninformed. The operator tree is compared with independently implemented full vector-forward HMM inference. The projected update is compared with an exact LP-based constrained optimum, a weaker class-preserving policy, and an unrestricted optimum. Memory comparisons explicitly identify the lossy source information removed from each representation. Known true-family assumptions are shared where the comparison requires them. |
|
|
| Binomial accuracies use Wilson 95\% intervals over independently generated source records or trajectories. The arena gain intervals are paired Student-$t$ descriptive intervals over 16 independently seeded small arenas. They are conditional on the constructed arena family and are not multiplicity-adjusted claims over arbitrary games. Thousands of within-trajectory events are not counted as independent human participants. |
|
|
| \section{Continuous-trajectory timing} |
| The lag study generates 16,000 independent complete trajectories for each lag in $\{0,1,2,3,4,6,9\}$, with 64 valid pairs, $\alpha=0.6$, $\beta=0.75$, and $\rho=0.72$. Within each trajectory, overlapping lagged products retain the dependence in Theorem~\ref{thm:lag-cov}. They are not generated as independent endpoint pairs. |
|
|
| \begin{center}\smalltable |
| \begin{tabular}{@{}rrrrr@{}}\toprule |
| Lag & Accuracy & Observed score variance & Exact variance & Error upper bound\\\midrule |
| 0 & 1.00000 & 50.307 & 51.040 & 0.001534\\ |
| 1 & 0.99575 & 57.011 & 57.282 & 0.034762\\ |
| 2 & 0.96463 & 66.399 & 66.887 & 0.418653\\ |
| 3 & 0.89075 & 74.486 & 75.117 & 0.740138\\ |
| 4 & 0.80019 & 82.625 & 81.040 & 0.889588\\ |
| 6 & 0.66081 & 86.689 & 87.417 & 0.979257\\ |
| 9 & 0.56138 & 90.562 & 90.316 & 0.998055\\\bottomrule |
| \end{tabular} |
| \end{center} |
| At lag zero all 16,000 trials were correct; the Wilson lower limit is approximately 0.999760, not a population error of exactly zero. At lag four the accuracy interval is approximately $[0.79392,0.80631]$. The variance comparison supports the finite dependence calculation. The concentration bound is conservative and becomes nearly vacuous at large lags; no claim of a sharp learning curve is made. |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{01_lag_variance.png} |
| \caption{A single continuous recording generates correlated lagged evidence. Dots are sample variances across 16,000 independently generated trajectories per lag; the line is the exact variance formula. No biological frequency is used as a fitted AI parameter.}\end{figure} |
| The independent exact arithmetic audit enumerates 2,550 noise/increment atoms across 16 small $(n,\ell)$ cases and verifies both means and variances as rational numbers. This audit is stronger than a simulation match for those cases, but it is not a proof of correctness for an arbitrary real sensor process. |
|
|
| \section{Short sequence inference and genuine calibration} |
| The four catalog entries are $(\theta,w)\in\{-1,+1\}^2$. Observations satisfy |
| \begin{equation} |
| A_t=\theta wZ_tF_t,\qquad B_t=Z_tG_t. |
| \end{equation} |
| The source record identifies the product $\theta w$, while the prior symmetry leaves the marginal source type fair before a world measurement. A genuine fixture observation then reveals the actual $w$. For each of 8, 16, and 32 events, the study generates 1,000 independent records under the correct HMM family. |
|
|
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}rXXX@{}}\toprule |
| Events & Operator tree & Full-HMM replay & Product likelihood\\\midrule |
| 8 & $936/1000$; 93.6\% & $936/1000$; 93.6\% & $910/1000$; 91.0\%\\ |
| 16 & $975/1000$; 97.5\% & $975/1000$; 97.5\% & $962/1000$; 96.2\%\\ |
| 32 & $999/1000$; 99.9\% & $999/1000$; 99.9\% & $997/1000$; 99.7\%\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| The largest absolute tree/replay posterior discrepancy is $5.33\times10^{-15}$. Before calibration, the largest departure of the identity marginal from $1/2$ is $1.78\times10^{-15}$. The 32-event tree accuracy interval is approximately $[0.99436,0.99982]$. |
|
|
| The full sequence model can use context persistence that the product statistic discards. Its advantage over the product estimator is not a new superiority over Bayesian inference: the tree implements the same sequence model. The numbers are not directly comparable to the balanced-context v2 experiment because the context-generating law and trial counts differ. No reconstruction time in seconds or accuracy on real players follows from these event counts. |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{02_sequence_inference.png} |
| \caption{The operator tree and strong full-HMM comparator coincide. Error bars are Wilson intervals over 1,000 independent records per size. All methods receive the declared observation family; the product baseline intentionally restricts its retained statistic.}\end{figure} |
|
|
| \section{Sparse repairs in a long evidence archive} |
| For lengths 256, 2,048, and 16,384, the study compiles a fixed four-hypothesis/two-state workload and applies 16 distinct local source reannotations. Each reannotation replaces an existing contextual-sign likelihood. The workload tests likelihood maintenance; its random sign sequence is not asserted to be a correctly modeled human record. |
|
|
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}rXXXX@{}}\toprule |
| Events & Tree compositions / repair & Full forward steps / repair & Tree array payload & Maximum centered log-score error\\\midrule |
| 256 & 8 & 256 & 81,920 bytes & $3.98\times10^{-13}$\\ |
| 2,048 & 11 & 2,048 & 655,360 bytes & $6.82\times10^{-12}$\\ |
| 16,384 & 14 & 16,384 & 5,242,880 bytes & $6.18\times10^{-11}$\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| Centered log-score error compares log likelihoods after subtracting one common catalog entry. It remains meaningful when posterior probabilities saturate. The largest local-repair posterior discrepancy is below $7.46\times10^{-18}$ in these particular workloads; the log-score comparison is the more informative numerical stress check. |
|
|
| The reported operation units differ: a tree composition is a batch of matrix products, whereas a replay step is a batch of vector products. Figure~\ref{fig:repair} includes the corresponding dense arithmetic factors. Hardware timings and build cost are retained in a nondeterministic telemetry file, not used as deterministic reproduction hashes or a universal speed guarantee. The largest tree is much larger than the 32,768-byte two-sign raw payload; no memory-compression advantage is claimed for this fixture. |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{06_local_repair_work.png} |
| \caption{Arithmetic scaling for one sparse correction after compilation, with $H=4,K=2$. The tree pays a larger build and storage cost. This is not a measured GPU chart, and replacing most of an archive can favor a rebuild.}\label{fig:repair}\end{figure} |
|
|
| \section{Retrospective memory and a tiny source identity} |
| For the one-bit construction, exact small graph checks cover source records of one to four bits. Requiring every future coordinate yields $2^n$ memory states; restricting the allowed queried coordinates gives the corresponding smaller answer partition. The exact arithmetic audit additionally examines all 276 binary encoders for histories of one, two, and three bits. With three source bits and only one retained bit, the best average recovery accuracy is exactly $3/4$ under a uniform coordinate query. |
|
|
| The larger demonstration uses 256-bit records, 16,000 independently generated future queries, and a prefix-storage baseline. Stored coordinates are answered exactly after the genuine $W_J$ observation; other coordinates are guessed with an independent fair bit. Its expected accuracy is $1/2+b/(2n)$, while its evidence-based coverage is only $b/n$. |
|
|
| \begin{center}\smalltable |
| \begin{tabular}{@{}rrrr@{}}\toprule |
| Retained bits & Observed accuracy & Exact expected accuracy & Evidence-based coverage\\\midrule |
| 0 & 0.498125 & 0.500000 & 0\\ |
| 8 & 0.513938 & 0.515625 & 0.03125\\ |
| 32 & 0.560938 & 0.562500 & 0.12500\\ |
| 64 & 0.625688 & 0.625000 & 0.25000\\ |
| 128 & 0.751063 & 0.750000 & 0.50000\\ |
| 256 & 1.000000 & 1.000000 & 1.00000\\\bottomrule |
| \end{tabular} |
| \end{center} |
| The prefix scheme is not asserted optimal at every rate. The separate universal lower bound gives at least 235.317 retained bits for average error at most 1\% in the 256-bit family, hence at least 236 fixed-length bits. This is a necessary condition, not a claim that every 236-bit scheme achieves that error. |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{03_retrospective_memory.png} |
| \caption{One later mechanics query recovers the same one-bit source identity, but the selected old relationship may lie anywhere in the archive. Current identity marginals remain identical before calibration.}\end{figure} |
|
|
| \section{The six-state sequential arena} |
| There are six ground microstates grouped into two semantic postures. Two tactical action classes each have three motor realizations, for six available actions. The three motor realizations switch semantic posture with probabilities $0.1,0.5,0.9$. Conditional transitions among the three microstates within a posture are independently seeded Dirichlet draws with concentration two. Rewards are independently drawn from $[0.05,0.95]$ and depend on the ground state and motor action. |
|
|
| A persistent source type determines tactic probabilities $0.7/0.3$ or their reversal by posture. The source anchor uses a uniform mixture of the three motor realizations. Consequently every source-conditioned tactic has a 0.5 semantic posture-switch probability. That joint tactic/posture kernel is the protected target. The microstate and motor dimensions are deliberately unprotected. |
|
|
| All policies use the same known ground-state observation and transition model. Discount is $0.9$. Reported normalized value is $(1-\gamma)$ times the value averaged uniformly over all six initial states. The separate semantic-path metric enumerates the six-step joint tactic/posture law starting from ground state zero. Signature checks cover all six ground states, not only the path-evaluation start. The experiment does not claim to learn an unknown transition model. |
|
|
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}p{.30\textwidth}XXX@{}}\toprule |
| Method & Normalized value & Gain over anchor & Mean six-step semantic TV\\\midrule |
| Source anchor & 0.511568 & 0 & 0\\ |
| Exact path shield / LP & 0.642583 & 0.131014 & $4.30\times10^{-16}$\\ |
| 24 projected-Q updates & 0.605199 & 0.093631 & $2.31\times10^{-14}$\\ |
| Conditional classes only & 0.731438 & 0.219870 & 0.483658\\ |
| Unconstrained optimum & 0.823909 & 0.312340 & 0.856473\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| Across 16 arena seeds, the path-shield gain has paired descriptive 95\% interval $[0.116649,0.145380]$. Its maximum signature residual is $8.33\times10^{-16}$. The projected-Q update gain has interval $[0.083067,0.104195]$ and maximum signature residual $3.44\times10^{-14}$. |
|
|
| The analytic update improves return while remaining feasible, but it falls below the stronger exact constrained optimum after 24 steps. The class-only comparator achieves greater return and retains its same-state tactic probabilities, yet its semantic path changes materially. The unrestricted policy gains still more by abandoning both constraints. These are tradeoffs, not a scoreboard declaring one method universally superior. |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{04_style_return_frontier.png} |
| \caption{Sixteen-seed means. Return can increase inside the exact path fiber, but constraining a richer behavioral process costs some unrestricted reward. No axis measures human recognizability or expert gameplay.}\end{figure} |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{05_horizon_fidelity.png} |
| \caption{A single declared arena seed, evaluated over multiple exact finite path lengths. Matching conditional tactics does not control the accumulated semantic law; the exact path shield remains at numerical roundoff.}\end{figure} |
|
|
| \begin{figure}[H]\centering\includegraphics[width=.94\textwidth]{07_nullspace_learning.png} |
| \caption{Twenty-four analytic projected-Q updates, each evaluated in the known finite MDP. The shaded interval is a descriptive pointwise standard-error band across the 16 arenas. The stronger LP ceiling remains above the update curve. This is controller improvement, not demonstrated optimizer self-modification.}\end{figure} |
|
|
| \section{Calibration and no-headroom controls} |
| The three-action fixture in Example~\ref{ex:unlock} is solved before and after a real read of the simulated mechanics variable. The robust policy has expected reward 0.4. Revealing world 0 unlocks reward 0.85 while preserving the exact stay/switch distribution. Revealing world 1 leaves reward 0.4 despite the same nominal nullity increase. This negative case separates linear degrees of freedom from a feasible positive-probability improvement. |
|
|
| A separate six-state control sets every action reward to 0.4. Its maximum absolute value change after path-constrained optimization is $6.66\times10^{-15}$, numerical roundoff around a true zero gain. The code therefore does not report every refinement or policy revision as an improvement. |
|
|
| \section{Rare-calibration approximation checks} |
| One thousand independently seeded positive-operator fixtures use eight factors, four catalog hypotheses, and two hidden states. Every factor is multiplied by a known entrywise perturbation within its prescribed log-error budget. Initial/terminal conditions, priors, and common probe weights vary; probe log weights span $[-650,0]$, explicitly stressing rare common outcomes. |
|
|
| No posterior TV exceeds the theoretical certificate within tolerance $10^{-12}$. The maximum observed TV is 0.0108104 and the largest error-to-bound ratio is 0.220499. These are implementation checks of an assumed multiplicative certificate. They do not show that a trained neural memory satisfies that certificate or that a missing-support model is safe. |
|
|
| \section{Lifetime auditing} |
| For each of true gains 0 and 0.3, the study generates 10,000 audit histories, each with 40 candidate versions and 256 independent bounded paired outcomes per version. The total budget is $\delta=0.05$. Under the zero-gain null, 60 histories accept any candidate: an observed lifetime false-promotion rate 0.006 with Wilson interval $[0.004665,0.007715]$, below but not equal to the theoretical upper bound 0.05. Under gain 0.3 every history accepts at least one candidate, with a mean 29.5762 accepted versions. |
|
|
| This controls a constructed conditional-independent audit model. It does not establish that language-model-generated candidates, reused game tests, or correlated clip fragments satisfy the assumptions. Nor does the positive-gain condition demonstrate recursive improvement; its true gain is fixed by the simulator. |
|
|
| \chapter{Verification, reproducibility, and release contents} |
| \label{ch:reproduce} |
| \section{New executable tests} |
| The v3 suite contains 50 new unit tests covering temporal formulas, impossible clock intervals, exact-model tree/replay agreement, rare probes, long likelihood scaling, atomic replacement, generated-source rejection, duplicate IDs, query graphs, source-memory bounds, semantic feasibility, full path laws, nullspace gains, zero headroom, calibration, LP dual residuals, lifetime budgets, and the integrated finite demo. |
|
|
| The independent small arithmetic audits use separate implementations and exact fractions where specified: |
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}p{.28\textwidth}XX@{}}\toprule |
| Audit & Scope & Result\\\midrule |
| Continuous lag & 16 cases, 2,550 increment/noise atoms & Exact means and variances agree.\\ |
| Operator likelihood & 16 complete hidden paths & Rational likelihood $17879/176400$; floating result differs by $5.55\times10^{-17}$.\\ |
| Retrospective encoders & 276 deterministic binary encoders & Complete query graphs and best one-bit recovery checked.\\ |
| Semantic preservation & 2,046 semantic words through length ten & Exact equality under baseline and improved mixture.\\ |
| Persistent composition & 72 posterior/horizon cases & Conditional common-kernel TV contraction holds.\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| These audits were written and executed in the same research session. They are not independent external replication or proof-assistant verification. An exhaustive finite fixture is not a statistical benchmark on real gameplay. |
|
|
| \section{Legacy reproduction and source integrity} |
| The original supplied v2 ZIP is preserved unchanged as an archival input. It was separately extracted and its supplied reproduction runner was executed. All 22 v2 unit tests passed. All 14 deterministic result and figure files matched their original recorded SHA-256 hashes. The comparison report records every expected and observed hash. |
|
|
| The supplied ZIP contains a v1 PDF but not the original v1 executable package. Consequently the v1 results described in the source are not labeled as newly reproduced. The final edition rederives the foundations needed for its new theorems and evaluates its own implementations independently. |
|
|
| The neuroscience PDF is retained only inside the untouched legacy archive with its original attribution and source terms. The current work does not claim its data, text, or biological discoveries as new Infinite Players results. The Cohen--Fausti reference is normalized to the verified author names Samuel N. Cohen and Eliana Fausti; archival documents themselves remain unchanged. |
|
|
| \section{Running the release} |
| From the final release root, install the numerical requirements and run: |
| \begin{lstlisting} |
| python -m pip install -r requirements.txt |
| python REPRODUCE.py --output reproduced |
| python RUN_DEMO.py --output demo_output |
| \end{lstlisting} |
| The runner uses a new output directory and does not overwrite the supplied reference results. It executes tests, all finite studies, exact audits, figures, and the end-to-end demo, then compares deterministic outputs with their recorded reference hashes. An optional legacy check re-extracts and reproduces the original v2 package. Timing telemetry and test-run wall times are intentionally excluded from deterministic equality. |
|
|
| The recorded numerical environment uses Python 3.13.5, NumPy 2.3.5, SciPy 1.17.0, and Matplotlib 3.10.8 on Linux. No network, model weights, API key, or GPU is needed once these dependencies are installed. The included Windows command wrapper is not a claim of native Windows or commercial-engine testing. Reproduction across different BLAS, optimizer, font, or numerical library versions may require tolerance-based examination instead of byte identity. |
|
|
| \section{Package map} |
| \begin{center}\smalltable |
| \begin{tabularx}{\textwidth}{@{}p{.39\textwidth}X@{}}\toprule |
| Path & Purpose\\\midrule |
| \texttt{src/infinite\_players/} & Temporal model, operator archive, query graph, finite actor, fidelity optimizer, audit gate, demo.\\ |
| \texttt{tests/} & New unit and integration tests.\\ |
| \texttt{experiments/} & Fixed-design studies, independent exact audits, plot generation.\\ |
| \texttt{results/} & Raw trial tables, summaries, configuration, audits, legacy comparison, and separate timing telemetry.\\ |
| \texttt{examples/demo/} & Synthetic recording, descendant trace, portable player capsule.\\ |
| \texttt{schemas/} & Capture and capsule contract documentation.\\ |
| \texttt{manuscript/} & Complete editable LaTeX source and references.\\ |
| \texttt{legacy/} & Untouched supplied v2 research ZIP.\\ |
| \texttt{CLAIMS.json} & Theorem, implementation, result, and limitation mapping.\\\bottomrule |
| \end{tabularx} |
| \end{center} |
| Checksums establish byte correspondence with a reference, not who produced a source or whether a theorem premise holds. A successful reproduction establishes the supplied finite computation in the recorded environment, not the real-world validity of its likelihood model. |
|
|
| \chapter{Boundaries and the decisive next experiments} |
| \label{ch:limits} |
| \section{What has been completed} |
| The final research edition supplies the promised finite source/evidence model, dependence-aware temporal derivations, future-memory obstruction, revisable likelihood implementation, full semantic-path control constraint, exact compatible ceiling, projected improvement mechanism, composition theorem, runnable finite demonstration, quantitative controls, and reproducibility materials. These components form a coherent research result rather than a loose collection of proposed analogies. |
|
|
| The theoretical novelty claim is deliberately narrower than the product ambition. The known foundations are openly credited. A full historical-priority review, external proof audit, independent reproduction, and matched contemporary real-game comparison remain outstanding. The package does not use an internal synthetic score as evidence of a field-wide landmark. |
|
|
| \section{Failure cases that matter} |
| A source recording may not distinguish the desired player traits even with correct mechanics. Engine legality may differ from the player's understanding. An unknown latency may be indistinguishable from an individual reaction delay without an independent clock anchor. Unmodeled nonstationarity can make old evidence predict the wrong source epoch. A new capability can make an old memory summary insufficient. A new game patch can invalidate both inference factors and actor signatures. |
|
|
| The operator tree requires a fixed finite catalog and costs storage. The approximate certificate requires common support and controlled multiplicative error; average neural reconstruction loss does not provide it. Exact semantic preservation can be infeasible or leave no reward headroom. A rank drop can fail to create an admissible improving action at a boundary. A policy can preserve its narrow semantic law while changing unprotected motor behavior substantially. |
|
|
| The projected-Q procedure uses exact model-based action values and can be less efficient than the LP reference. The arena supplies known ground states to all compared policies; it is not a pixel-control benchmark. The finite audit gate requires fresh independent session outcomes and can be invalidated by evaluator reuse or model-dependent leakage. None of these failures is eliminated by a more elaborate name or by routing more text through a language model. |
|
|
| \section{A real-player reconstruction study} |
| A decisive next study should compare nested 30-second, 2-minute, and 10-minute personal recordings, while keeping shared game competence and population pretraining fixed. These are proposed experimental arms, not achieved reconstruction durations. Separate video-only, synchronized-input, and authorized engine-instrumented conditions. Count decision opportunities and actual human effort as well as clip length. |
|
|
| Split by person before representation fitting and keep each evaluation player's personal evidence restricted to the declared clip. Later sessions and novel scenarios from that person provide the target data. Adjacent frames, duplicate exports, and multiple annotations of one episode remain in the same partition. A source appearing in undisclosed pretraining cannot be treated as an unseen individual without a contamination analysis. |
|
|
| Use strong implementation-matched baselines: an unpersonalized competent agent, a player-conditioned behavioral clone, an inverse-dynamics video model, a latent player model, a memory-equipped controller with the same sources, and a direct style-conditioned game system such as Robo-Saber where the domain and interfaces permit \cite{robosaber}. Full-source replay or exact inference in tractable subproblems is a necessary reference for memory mechanisms. |
|
|
| \section{Recognizability, semantics, and competence} |
| Measure proper prediction scores, calibrated uncertainty, error--coverage curves, response-time distributions, and source-supported adaptation separately. Blind human judges should compare the source and reconstructed behavior with appropriately skill-matched distractors. Familiarity with the source is a separate factor. Repeated human sessions provide a within-person variability reference, not an absolute identity ceiling. |
|
|
| A semantic contract must be defined before results are examined. Evaluate common held-out situations and free-running trajectories: the former isolates conditional decisions, while the latter reveals changed occupancy and temporal structure. Compare full motor traces alongside protected semantics. A lack of statistically detected difference is not evidence of practical equivalence without a declared equivalence margin and adequate precision. |
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| The memory experiment should consolidate an initially ambiguous event before revealing a genuine later calibration. Include rare outcomes, a misunderstood-mechanic control, wrong-build probes, duplicated annotations, and generated self-play masquerading as source evidence. Report all readable bytes, source retrieval cost, factor-repair cost, and missed control deadlines. Restricted answers should be labeled unresolved rather than confidently completed from a generic prior. |
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| \section{Beyond human expertise} |
| Outperforming the recorded individual is narrower than outperforming qualified experts. Expert comparison needs independent tasks and opponents, matched game rules, observation access, reaction constraints, control bandwidth, practice opportunities, and a predeclared source-fidelity contract. Privileged engine state or unrestricted motor speed must be reported separately. |
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| The formal ceiling identifies when unrestricted optimality is compatible with a chosen semantic law in a known finite model. It does not establish compatibility for a particular real person. If the protected behavioral process itself entails suboptimal decisions, a descendant must either retain that cost or explicitly obtain permission to relax the contract. The title states the research target, not an executed expert-level benchmark. |
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| \section{Recursive self-improvement} |
| Updating a policy is not the same as improving the procedure that learns future policies. A genuine recursive experiment should allow edits to the optimizer, memory representation, skill compiler, experiment selector, or hypothesis language. Evaluate the edited learner on fresh tasks from matched initial models and budgets against both a fixed learner and an equally resourced fixed search method. Include preprocessing, rejected proposals, validation, and retrieval costs. |
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| A useful future connection is that better competence may make a previously unreachable diagnostic situation accessible. If the historical person is available, that situation can acquire a targeted real preference observation. If not, it can support a genuine mechanics probe or remain an explicitly uncertain extrapolation. Self-generated choices do not fill the missing historical label. |
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| The lifetime audit theorem prevents one specific statistical failure mode under its assumptions. It does not prove that recursive edits will compound, escape a performance ceiling, or avoid distribution shifts. A stronger learner must demonstrate transfer of its improved learning procedure, not merely inherit a better already-trained policy. |
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| \section{Final assessment} |
| The completed contribution is a formal and executable separation of three questions: what the record identifies, what the memory must retain for future interpretation, and what performance improvements preserve the declared source process. The strongest new result is a compositional answer under finite assumptions: a source-conditioned evidence certificate can be carried through an exact semantic-path shield, while a computable nullspace/dual test determines whether faithful improvement is possible. |
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| That result makes the project more rigorous and more implementable than an unrestricted promise of a perfect eternal player. The remaining empirical task is concrete: connect the declared interfaces to real capture and strong game backbones, then test source fidelity and learning under the same accounting discipline. The present research does not claim that those experiments have already succeeded. |
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