PureOne/Infinite-Players

Infinite Players

Self-Improving AI Agents In Video Games That Learn, Adapt, Remember, and Evolve Beyond Human Expertise

Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Research version: 3.0.0 · Hugging Face edition: 3.0.0-hf.2 · Date: 18 October 2026
Method family: AERÍN Continuation Algebra

A mathematical and executable framework for improving an agent while preserving a declared behavioral process, and for retaining evidence that can be reinterpreted when its world becomes better understood.

49-page manuscript · Technical overview · Claim ledger · Reproduction guide · Evidence and limitations

This repository contains the research manuscript, editable LaTeX sources, finite Python implementations, an original six-state tactical environment, synthetic experiment tables, seven figures, tests, and a record-to-capsule demonstration. It uses a Hugging Face dataset repository as a research archive. There are no pretrained model weights and no general-purpose training corpus. The heterogeneous tables are documented individually; they are not train/validation/test splits of one learning task.

The full title retains the long-term research objective. The demonstrated achievement is finite, known-model policy improvement with explicit semantic fidelity, revisable evidence, and auditable limits. Real human reconstruction, beyond-expert gameplay, GPU acceleration, commercial-engine integration, and sustained recursive self-improvement remain unevaluated.

Abstract

An agent can imitate a player's immediate action preferences while changing the situations the player would encounter. Preserving action classes at each state is therefore insufficient to preserve a session's behavioral process. Infinite Players protects the joint distribution of the next semantic action and next semantic state. Under a correct finite transition model and a realizable target kernel, all controllers inside the corresponding policy fiber generate the same semantic trajectory law at every finite horizon, even when the executor is revised between decisions.

The framework identifies reward improvement inside that fiber. Projection of exact action values into the transition-signature nullspace provides a feasible improving direction. An interior zero-projection criterion identifies the absence of compatible improvement. Constrained policy iteration with linear-programming subproblems supplies a stronger optimum and numerical primal/dual checks.

The evidence side asks what must survive consolidation when later measurements can change an old record's interpretation. A finite construction shows that a one-bit identity can require retaining n source bits to answer every future coordinate-specific calibration. An ordered operator tree implements exact fixed-catalog sequence inference and logarithmic-depth local factor replacement, with explicit preprocessing and storage costs. Persistent latent branches, approximation certificates, and lifetime promotion budgets connect evidence to control without treating generated alternatives as independent source observations.

Central questions

Which improvements can an artificial descendant make while preserving the behavior its source contract promises? The answer depends on what is protected. In the implemented arena, semantic posture and tactical choice are protected. Fine motor realization, ground microstate distribution, reward, and human reaction time are excluded. Some environments leave meaningful optimization freedom; others leave none.

What must remain in memory so that a later genuine measurement can correct an earlier interpretation? A small current posterior is not automatically a sufficient long-term archive. The package distinguishes the current answer, the supporting record, and the future queries that retained memory must support.

Main contributions

Component	Delivered result	Essential boundary
Semantic trajectory contract	Preserve a joint semantic action/state kernel and its finite-horizon path law	Correct dynamics, fixed maps, shared initial semantic law, nonempty feasible fibers
Compatible improvement	Projected exact-Q updates improve value while remaining feasible	Interior policy, controlled step size, exact finite model; numerical residuals checked
No-headroom criterion and ceiling	Zero nullspace projection characterizes interior optimality; LP policy iteration supplies a stronger constrained optimum	Nullity alone does not guarantee useful improvement
Future-calibration memory	One-bit identity construction requiring n retained bits; lossy entropy lower bound	Declared finite future-query contract, not universal memory compression
Revisable evidence tree	Ordered HMM factor products with source-indexed local replacement	Fixed hypothesis catalog and factor semantics; extra storage and build work
Evidence-to-execution composition	Calibrated coupled uncertainty passed through a persistent latent branch	Correct shared model and explicit approximation/fidelity errors
Lifetime promotion audit	Summable error allocation for successive fresh bounded-gain audits	Fresh conditionally independent sessions; no guarantee improving proposals exist

These results build on established constrained control, state abstraction, Bayesian inference, information theory, nullspace learning, and statistical error spending. Historical priority for those ingredients or for the combined framework has not been independently established.

Mathematical mechanism

Let s be a ground state, a a motor action, φ(s) its semantic state, and ψ(s,a) its semantic action. A transition-signature column is

$$D_s[(c,q^{\mathrm{\prime }}),a]=\mathbf{1}\{\psi (s,a)=c\}\sum _{s^{\mathrm{\prime }}:\varphi (s^{\mathrm{\prime }})=q^{\mathrm{\prime }}}P(s^{\mathrm{\prime }}\mid s,a)\mathrm{.}D\_s[(c,q\text{'}),a]=\backslash mathbf\{1\}\backslash \{\backslash psi(s,a)=c\backslash \}\backslash sum\_\{s\text{'}:\backslash phi(s\text{'})=q\text{'}\}P(s\text{'}\backslash mid\; s,a).$$

For target semantic kernel Kθ, the admissible executors form the fiber

$${\mathcal{F}}_{\theta }(s)=\{p\ge 0:{\mathbf{1}}^{\mathrm{\top }}p=1,D_{s}p=K_{\theta }(\cdot ,\cdot \mid \varphi (s))\}\mathrm{.}\backslash mathcal\; F\_\backslash theta(s)=\backslash \{p\backslash ge0:\backslash mathbf1^\backslash top\; p=1,\backslash ;D\_sp=K\_\backslash theta(\backslash cdot,\backslash cdot\backslash mid\backslash phi(s))\backslash \}.$$

If every executed action distribution remains in this fiber, the joint law of

$$(q_0,c_0,q_1,c_1,\dots ,c_{T-1},q_T)(q\_0,c\_0,q\_1,c\_1,\backslash ldots,c\_\{T-1\},q\_T)$$

is fixed by Kθ at every finite horizon. The executor can change ground actions, optimize unprotected reward, and change internally. The theorem protects the declared process, not every aspect of a human player.

At an interior feasible policy, a compatible direction is

$$d_s=(I-D_s^{†}{D}_s)Q_s^{\pi }\mathrm{.}d\_s=(I-D\_s^\backslash dagger\; D\_s)Q\_s^\backslash pi.$$

A sufficiently small feasible positive step has Bellman advantage ηs‖ds‖² and yields nondecreasing value under the stated assumptions. If the projection vanishes at every state, that interior policy has no reward improvement available under the same contract. Boundary policies require feasible-cone or LP treatment; the interior criterion is not a universal stopping test.

For retained evidence, the finite identity construction yields

$$b\ge n[1-h_2(ϵ)],b\backslash ge\; n[1-h\_2(\backslash epsilon)],$$

where b is retained fixed-length memory and ε is average recovery error after a uniformly selected coordinate probe. At zero error all n source bits must remain distinguishable, although the unknown identity itself is one bit. This concerns future recoverability, not an identity containing n bits.

The manuscript and technical overview supply proofs, temporal-dependence calculations, approximation bounds, feasibility assumptions, and composition conditions.

Executed results

All comparisons below use synthetic fixtures and known finite models. Reference values come from the supplied v3 tables. A fresh preparation-time execution passed 50/50 v3 tests and matched 32/32 deterministic reference files, including figures and demo outputs. It used Python 3.12.14; the source recorded Python 3.13.5. Both used the locked numerical dependencies. See release validation.

Reward versus protected behavior

Value is normalized discounted value, (1−γ)V, with γ = 0.9, averaged over six initial ground states and then 16 seeded arenas. Drift is total variation between exactly enumerated six-step semantic laws starting at ground state zero. The two metrics have different declared initial-state conventions.

Controller	Mean normalized value	Gain over source	Mean six-step semantic TV
Source anchor	0.511568	0	0
Path-shield LP optimum	0.642583	+0.131014	4.30 × 10⁻¹⁶
24 projected-Q updates	0.605199	+0.093631	2.31 × 10⁻¹⁴
Same-state action-class constraint	0.731438	+0.219870	0.483658
Unconstrained optimum	0.823909	+0.312340	0.856473

The path-shield gain has a paired descriptive 95% interval of [0.116649, 0.145380] over 16 seeds. The projected procedure remains below the stronger LP ceiling. Higher-return policies under weaker constraints exhibit behavioral drift; they do not solve the same preservation problem. Near-machine-precision TV values are numerical residuals, not evidence of exact real-world fidelity.

Sequence inference and calibration

The operator tree and independently implemented full-HMM replay evaluate the same Bayesian sequence model. Their largest posterior discrepancy across 3,000 independent short records is 5.33 × 10⁻¹⁵. A genuine simulated mechanics calibration resolves an ambiguity not resolved by the pre-calibration identity posterior.

Events per record	Operator tree	Full HMM replay	Paired-product baseline	Records
8	93.6%	93.6%	91.0%	1,000
16	97.5%	97.5%	96.2%	1,000
32	99.9%	99.9%	99.7%	1,000

These are synthetic binary-type accuracies after calibration. The tree organizes inference and revision differently; it does not improve the accuracy of the same exact HMM. No raw video or real player is decoded.

Revising a long evidence archive

With H hypotheses, K hidden states, and n events, dense construction costs O(nHK³), one local replacement costs O(HK³ log n), and operator payload uses O(nHK²) storage. Full vector-forward replay costs O(nHK²) per evaluation.

Events	Batched tree compositions per correction	Forward vector steps per replay	Tree array bytes	Raw two-sign bytes
256	8	256	81,920	512
2,048	11	2,048	655,360	4,096
16,384	14	16,384	5,242,880	32,768

Here H = 4 and K = 2. A tree composition and a vector step have different arithmetic costs. Payload excludes object overhead. The tree accelerates repeated sparse corrections after compilation; it is not a compression win on this fixture. results/runtime_telemetry.json reports machine-dependent timings separately from deterministic outputs.

Additional studies

Study	Scope and finding	Interpretation
Dependence-aware lag	112,000 continuous Markov trajectories across seven lags	Overlapping temporal evidence is not independent sampling
Retrospective memory	16,000 queries per tested storage budget	Future-query recovery differs from present posterior size
Positive-circuit approximation	1,000 perturbation trials, zero bound violations	Constructed common-support certificate; no learned neural-calibration claim
Calibration unlock	Reward 0.4 → 0.85 in one world; 0.4 → 0.4 in the negative control	Reduced constraint rank alone does not imply gain
Lifetime audit, zero gain	Any promotion in 60/10,000 histories over 40 candidate versions	Empirical 0.6% under a 5% lifetime budget in this fixture
Lifetime audit, gain 0.3	At least one promotion in 10,000/10,000 histories	Toy detection result, not recursive intelligence growth
Exact arithmetic checks	2,550 lag atoms, 16 hidden paths, 276 encoders, 2,046 semantic words, 72 composition cases	Finite implementation checks alongside stated proofs

The source also includes a v2 reproduction record. The original v2 archive passed 22/22 tests and matched 14/14 hashes again during preparation. That nested archive is omitted from this focused edition. Those are legacy results, not additional v3 tests. Executable v1 source was not supplied and has not been freshly reproduced.

Upload to Hugging Face

Extract the release ZIP, then double-click UPLOAD_TO_HUGGINGFACE.bat on Windows. It prepares the uploader dependencies and opens the interactive uploader. Choose your repository, authenticate when prompted, and review the upload plan. The uploader transfers only verified release files and preserves an existing repository's visibility.

On other systems, install requirements-upload.txt and run python UPLOAD_TO_HUGGINGFACE.py. For a fully offline preview, run python UPLOAD_TO_HUGGINGFACE.py --dry-run without installing upload packages. See the upload guide.

Quick start

Use Python 3.11+ for the locked dependencies. Fresh execution used Python 3.12.14. A CPU is sufficient. No GPU, model downloads, credentials, or network connection are needed after installing dependencies.

From the repository root:

python -m pip install -r requirements-locked.txt
python VERIFY_RELEASE.py
python RUN_DEMO.py --output demo_output
python REPRODUCE.py --output reproduced

Choose a new, nonexistent output directory for REPRODUCE.py. It runs tests, studies, exact audits, figures, and the demo before comparing all 32 deterministic references. Generated artifacts go to the selected directory; supplied references are preserved. Nondeterministic timings are excluded from hash comparison.

The broader requirements.txt supplies version ranges. Python 3.10 is an intended lower bound in the original package metadata, not a freshly tested configuration of this edition. The locked NumPy and SciPy releases require Python 3.11+. See reproducibility.

For programmatic use, install with python -m pip install -e . and run:

python examples/minimal_policy.py

The example compares an anchor with its compatible LP descendant in one finite arena. It can also run directly from this source tree after numerical dependencies are installed.

Record-to-capsule demonstration

The demo generates a synthetic sign-family record, performs joint identity/world inference, applies an actual simulated-world calibration, samples one persistent identity branch, optimizes a compatible executor, executes 1,000 steps, and exports its contract.

Output	Contents
synthetic_recording.jsonl	32 source events, unique IDs, ticks, clock domain, epoch, and explicit synthetic labels
player_capsule.json	Source digest, coupled posteriors, persistent branch, protected kernel, source and descendant policies, exclusions, and numerical audits
descendant_trace.jsonl	Ground states, motor actions, semantic actions, next states, and rewards

The reference demo has normalized anchor value 0.537849, descendant value 0.666669, and six-step semantic TV 3.23 × 10⁻¹⁶. Its sampled reward mean is 0.676 over one stochastic trace. That trace is not a separate statistical performance study.

Source-kind labels are caller assertions. A SHA-256 digest checks correspondence to recorded bytes, not a real player's identity, observation independence, or consent. Duplicate IDs are rejected; distinct IDs alone do not establish independent evidence. Reannotation replaces an existing factor rather than manufacturing another observation.

Repository guide

Path	Purpose
Infinite_Players_Final_Research.pdf	Original 49-page manuscript, unchanged
manuscript/	Editable LaTeX chapters, rendered references, bibliography source
src/infinite_players/	Temporal evidence, tree, memory contract, fidelity solver, arena, promotion, demo
UPLOAD_TO_HUGGINGFACE.bat, UPLOAD_TO_HUGGINGFACE.py	Windows launcher and portable manifest-verified uploader
tests/, experiments/	50 v3 tests, studies, exact audits, figures, optional legacy runner
results/, figures/	Reference summaries, trial tables, deterministic outputs, seven figures
examples/, schemas/	Reference capsule, synthetic records, contract, minimal policy example
docs/	Technical overview, evidence boundaries, integration, reproduction, upload guide, release description, data dictionary
CLAIMS.json	Ten claim families linked to proofs, implementations, tests, and results
REFERENCE_HASHES.json	Original 32 deterministic comparison targets, unchanged
FILE_MANIFEST.json	File hashes for this Hugging Face edition
provenance/	Original notices, QA/release records, source manifest, packaging inventory
validation/	Fresh execution and edition validation reports

docs/ORIGINAL_RESEARCH_README.md describes the complete original handoff, including its nested legacy archive. This card and current edition documents define which files are supplied here.

Intended uses and implementation path

The code supports finite semantic-control experiments, analysis of reward headroom under protected behavior, revisable fixed-catalog inference, and future-query memory research. It supplies a tractable reference for larger systems with explicit preservation and evidence obligations.

Unity, Unreal Engine, Godot, gameplay capture, action decoding, local-LLM proposal services, GPU inference, and cross-game transfer are future targets. The reset/step simulator is Gym-like, not a tested Gymnasium adapter. No commercial game plugin, unattended game-control service, pretrained player model, or measured VRAM requirement is delivered.

A future bridge must define observations, authorized actions, clock and source epochs, model validity, semantic targets, and fallback behavior before transferring any guarantee. The tiny K = 2 CPU products do not predict visual-encoder or large-model cost. See the integration contract.

Status and limitations

Status: complete finite research release; broader gameplay and recursive-improvement program open. All ten claim families have explicit evidence boundaries. Fresh execution passed 100% of 50 v3 tests and matched 100% of 32 deterministic references. These percentages describe delivered checks, not progress toward human reconstruction, expert superiority, or general RSI.

Exact semantic preservation assumes correct dynamics, fixed maps, realizable targets, and feasible execution. Protecting more detail can remove all reward headroom. Full path enumeration grows exponentially and is only a small-case audit; the theorem supplies the general finite-horizon argument.

The tree assumes a fixed catalog, hidden-state dimension, event semantics, and source order. New hypotheses or likelihood models require recompilation or separately justified transport. A compact current posterior does not justify discarding evidence needed for a wider future-query contract.

The proofs are not proof-assistant verified or externally peer reviewed. Experiments use synthetic data and supplied dynamics. Exact-Q policy improvement does not demonstrate model-free learning or improvement of the learning procedure itself. No state-of-the-art ranking or world-first priority has been established.

The neuroscience preprint discussed in the manuscript supplies motivation, not an implemented consciousness mechanism, universal neural clock, or validation of the binary game model. No raw biological data were reanalyzed. The nested source-paper archive and original seed image are excluded from this edition.

Related work

The manuscript discusses gameplay imitation and player modeling, including VPT, ToMnet, Robo-Saber, Voyager, and SIMA 2, alongside style consistency, nullspace imitation, inference circuits, functional graph compression, and shielding. Personalized agents, HMMs, constrained MDPs, and nullspace methods are established foundations.

The release emphasizes their explicit synthesis into a joint semantic path contract, compatible improvement and its stopping boundary, revisable evidence, and future-calibration obligations. Original attribution is retained in the references and bibliography. No new external novelty survey was conducted for this packaging edition.

License and citation

The source declares no additional public license for the new v3 materials. This edition preserves that status and adds no open-source or open-data grant. The YAML intentionally omits a license identifier. See LICENSE_STATUS.txt and provenance/SOURCE_LICENSE_STATUS.txt.

Please retain the supplied author line. No DOI or arXiv identifier has been assigned by this release.

@misc{eve2026infiniteplayers,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {Infinite Players: Self-Improving AI Agents In Video Games That Learn, Adapt, Remember, and Evolve Beyond Human Expertise},
  year = {2026},
  month = {oct},
  version = {3.0.0},
  note = {AERÍN Continuation Algebra. Finite research edition; Hugging Face packaging 3.0.0-hf.2}
}

CITATION.cff preserves the original citation metadata. Add the actual repository URL and pinned revision after publication.