# Infinite Players — Final research edition

**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**  
Version **3.0.0** · 18 October 2026  
Method family: **AERÍN Continuation Algebra**

## What this release contains

A self-contained final mathematical manuscript, runnable finite implementations, an original six-state tactical simulator, a record-to-capsule demonstration, raw synthetic results, proof-to-code claim mappings, and source-only reproduction. The supplied v1/v2 results are integrated and clearly separated from the new derivations. The untouched original v2 ZIP is included for provenance.

This is a completed **research handoff**, not a finished raw-video-to-commercial-game bot. No real person, video encoder, commercial engine, large-model training run, GPU benchmark, or beyond-expert performance has been evaluated. Continued analytic policy improvement is demonstrated; sustained improvement of the learning procedure itself is not.

## The main advance

The earlier same-state action-class contract does not preserve a whole session. Better motor actions can change which situations occur next. This edition instead constrains the **joint next semantic action and semantic state distribution**. Every executor in that finite policy fiber generates the same declared semantic trajectory law at every finite horizon, even if its controller is updated between decisions.

Inside that fiber, projecting exact action values into the signature nullspace gives a feasible improving direction. At an interior policy, zero projection at every state is an exact no-headroom criterion. LP policy iteration supplies a stronger global optimum and dual checks. These use established projection, constrained-MDP, abstraction, and shielding foundations; world-first priority for those ingredients is not claimed.

A second result shows that a **one-bit identity may require n retained source bits** for every later coordinate-specific calibration. The current posterior can be tiny while future reinterpretation requires a large archive. The positive implementation is an ordered operator tree: full sequence inference is retained, and a local source interpretation can be replaced in logarithmic tree depth, at a disclosed storage/build cost.

## Quick start

Python 3.10+ is intended; the recorded environment is Python 3.13.5 on Linux.

```bash
python -m pip install -r requirements.txt
python RUN_DEMO.py --output demo_output
python REPRODUCE.py --output reproduced
```

`REPRODUCE.py` requires a **new** output directory. It executes the 50 new unit tests, all finite studies, exact audits, figures, and the demo, then compares deterministic bytes with `REFERENCE_HASHES.json`. It never overwrites the supplied reference results.

To also rerun the preserved v2 archive:

```bash
python REPRODUCE.py --output reproduced_with_legacy --legacy
```

To verify the release bytes:

```bash
python VERIFY_RELEASE.py
```

To rebuild the PDF, install a TeX distribution providing the packages in `manuscript/main.tex`, then run:

```bash
python build_pdf.py
```

An editable pre-rendered bibliography is supplied; BibTeX is not required. `sources.bib` is also included. PDF rebuild timestamps can change PDF hashes without changing content. Numerical reproduction is separate from PDF rebuilding.

The Windows BAT wrapper supplies a convenience command; it has not been tested against a native commercial-game engine. No network, credentials, model weights, or GPU are required after dependencies are installed.

## Executed results

The primary arena metric is normalized discounted value, averaged over six initial ground states. The path metric is exact enumeration of the six-step semantic law starting at state zero. Both are defined identically across compared policies.

| Controller | Mean normalized value, 16 seeds | Mean semantic path TV |
|---|---:|---:|
| Source anchor | 0.511568 | 0 |
| Exact path-shield optimum | 0.642583 | 4.30e-16 |
| 24 projected-Q updates | 0.605199 | 2.31e-14 |
| Same-state class constraint only | 0.731438 | 0.483658 |
| Unconstrained optimum | 0.823909 | 0.856473 |

The path-shield gain is **0.131014**, with paired descriptive 95% interval **[0.116649, 0.145380]** over 16 independently seeded arenas. Higher return under the weaker constraints comes with behavioral drift. The projected update remains below the stronger LP ceiling; it is not advertised as the best optimizer.

For 3,000 short sequence records, the operator tree agrees with independently implemented full-HMM replay within **5.33e-15** in posterior probability. With 32 events and an actual simulated mechanics calibration, both correctly classify **999/1000** synthetic binary types. This is neither raw-video reconstruction nor an improvement over the same exact Bayesian model.

At 16,384 archived events, one correction requires **14 batched tree compositions** instead of 16,384 full-forward vector steps. The units differ; the figures include H K³ and H K² arithmetic factors. The largest tree spends **5,242,880 array bytes**, excluding overhead, versus **32,768 raw two-sign bytes**. It is a local-update accelerator, not a compression win on this narrow fixture. Non-deterministic timings and preprocessing are disclosed separately.

Other studies include 112,000 continuous Markov trajectories across seven lags, 16,000 retrospective queries at each storage budget, 1,000 positive-circuit perturbation trials, a calibration-unlock fixture with a negative world control, a zero-headroom arena, and 10,000 lifetime audit histories per gain condition. Detailed configurations and raw trial tables are included.

## Verification

**50/50 new unit tests passed.** Independent in-session exact audits verify 16 lag cases across 2,550 atoms, 16 operator paths, 276 finite encoders, 2,046 semantic words, and 72 persistent-composition cases. The supplied v2 archive also reruns with **22/22 tests passed and 14/14 original result/figure hashes matched**. The v1 executable package was not supplied; its old numerical results have not been relabeled as freshly reproduced.

`QA_REPORT.json` records the final extracted-package reproduction and artifact checks. Matching hashes establish byte correspondence, not scientific authenticity or independent review. The mathematical proofs have not been proof-assistant verified or peer reviewed.

## Source and method boundaries

The uploaded Hesse et al. (2026) neuroscience preprint motivates preserving time-resolved relationships and validating inferred states on held-out information. It does not establish a consciousness implementation, a universal 15 Hz AI clock, or the adequacy of the binary game model. No raw primate data were reanalyzed.

Close prior work includes Robo-Saber's style-conditioned VR gameplay, VPT, ToMnet, Voyager, SIMA 2, programmatic style-consistency, nullspace imitation, probabilistic inference circuits, functional graph compression, and shielding. The manuscript identifies their contributions rather than claiming that personalized bots, hidden-state models, or nullspaces were invented here.

## Runtime modules

| Module | Delivered responsibility |
|---|---|
| `temporal.py` | Correct lag moments, one-trajectory bound, clock/response interval |
| `evidence_tree.py` | Fixed-catalog scaled operators, source replacement, strong vector-forward reference |
| `memory_contract.py` | Exact small confusability graphs and memory lower bound |
| `fidelity.py` | Signature fibers, LP policy iteration, nullspace updates, full small path enumeration |
| `arena.py` | Original finite environment with reset/step interface |
| `promotion.py` | Lifetime error allocation and fresh bounded-gain audit |
| `demo.py` | Synthetic record, real fixture calibration, persistent branch, optimization, execution, capsule |

All source-kind labels are **caller assertions, not cryptographic authentication**. Duplicate IDs are rejected, but distinct IDs do not prove independent observations. A likelihood model change requires recompilation or a separately justified transport; old factors cannot magically represent a new hypothesis.

## The demo

The demo produces `synthetic_recording.jsonl`, `descendant_trace.jsonl`, and `player_capsule.json`. It deliberately validates only its known synthetic sign family. The capsule records source identity, coupled posterior, protected semantic kernel, explicit exclusions, historical anchor, descendant policy, numerical audits, and source digest. Its sampled branch persists across execution; it is not independently redrawn before each action.

In the reference run, normalized source value is **0.537849**, descendant value **0.666669**, and six-step semantic TV **3.23e-16**. The 1,000-step stochastic reward mean is **0.676**. The latter is one trace, not a separate statistically validated performance claim.

## Scientific limitations

Raw gameplay capture, action decoding, actual player knowledge, learned world models, native engine adapters, local-LLM proposal services, human timing, cross-game transfer, expert comparison, and sustained recursive self-improvement are not implemented or validated. Exact path preservation requires a realizable semantic target and correct transition model. More protected detail can remove all improvement headroom. A small current posterior does not imply small future-sufficient memory. Extending a catalog or changing a source epoch can invalidate an old summary.

The manuscript gives an explicit real-player evaluation program and keeps these open tasks separate from the completed finite research. No ongoing background service or automatic publication has been created.