PureOne/AILITH-Beyond-Reinforcement-Learning

AÍLITH — Beyond Reinforcement Learning

Recursive Self-Modification and Continual Intelligence Growth in Game Agents, RSI in Game Worlds, Digital Twins

Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Research version: 0.5.0 · Released 18 October 2026 · MIT license

A mathematical and executable development layer for game agents: preserve useful evidence, build the machinery through which adaptation acts, inherit that machinery, and account for its construction, use, and maintenance.

This repository distributes a 79-page self-contained manuscript and complete Python research implementation. Its central result gives an exact separation between carrying fixed capacity for uncertain future tasks and paying to develop the required capacity after a task is revealed. The implementation includes causal observation sessions, cold and inherited-state control compilers, shared-parent scenario optimization, reproducible numerical studies, and interfaces for game hosts.

The full manuscript title is Beyond Reinforcement Learning: Recursive Self-Modification and Continual Intelligence Growth in Game Agents, RSI in Game Worlds, Digital Twins. AÍLITH is the project name.

This is a research-artifact repository hosted as a Hugging Face dataset repository. Its contents are manuscripts, software, synthetic control experiments, and verification records. It supplies no pretrained model weights, training corpus, or hosted inference service. The title states the research direction; the measured results concern the declared development and control models.

Downloads and reading paths

Artifact	Contents
Complete research archive	Unmodified original release: 237 entries, manuscript, LaTeX, implementation, tests, raw records, protocols, adapters, launchers, and historical provenance
79-page manuscript	The complete unified argument, assumptions, proofs, algorithms, experiments, worked examples, references, and integration appendix
Reproducibility guide	Installation, fresh output paths, study commands, numerical interpretation, and recorded environment
Evidence index	Claim-to-file map and distinction between frozen evidence and packaging-time checks
Claims and limitations	The exact scope of the results and what remains to be established
Release notes	Research changes in v0.5.0 and the scope of this Hugging Face packaging edition
Windows uploader instructions	Double-click UPLOAD_TO_HF.bat to sign in, choose a repository, and upload this release

For the main mathematical result, start with the plasticity comparison below and the manuscript's morphogenesis section. For implementation, extract the full archive and begin with examples/scenario_job.json, examples/hereditary_arena.py, and src/ailith/scenario.py. For independent inspection, read the protocols and raw records alongside their runner/oracle source.

Abstract

Recursive adaptation depends on more than a policy's present performance. An agent must preserve the information needed to evaluate changes, obtain evidence at the time it becomes available, construct the mechanisms through which changes can act, and carry useful capacity across task boundaries. AÍLITH formulates these obligations as paid development problems with explicit information order and inherited physical state.

The framework studies bilinear development dynamics with quadratic control action. It combines protected comparison evidence, causal linear observations, constructive finite-grid optimization, arbitrary inherited matrix factors, optional child maintenance, and reserve design before a future task is known. Gram and nuclear-norm formulations produce executable schedules and numerical lower bounds for the supported control classes. A two-stage scenario compiler returns one physically shared parent and the corresponding causal child schedules.

For uniformly distributed orthogonal unit targets, a fixed inherited design has exact paid lifetime action proportional to the square root of the number of possible tasks. Allowing the child to rebuild with constant controls during one interval gives an exact optimum below two, independent of that number in the limit. A matching construction and semidefinite dual establish the result within the stated model. The release supplies frozen numerical studies, explicit unresolved gaps, a timed acquisition arena, and a complete regression suite. Empirical improvement of a learned successor-producing agent remains an experiment to perform.

1. The central result: a paid plasticity advantage

A parent has one unit of preparation time and must prepare before learning which of $nn$ equally likely orthogonal unit tasks its child will receive. After revelation, the selected child has one unit of time to reach its task target. Preparation and execution pay the same specified quadratic-action ledger; this comparison has no maintenance charge.

The static child keeps its inherited structure fixed. The adaptive child can rebuild that structure using constant preparation and execution coefficients during its single child interval. Under those control classes, the exact optimal total costs are

$$J_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}}(n)=\sqrt{n},J_{\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}}(n)=2\sqrt{\frac{n}{n+4}}\mathrm{.}J\_\{\backslash mathrm\{static\}\}(n)=\backslash sqrt\; n,\; \backslash qquad\; J\_\{\backslash mathrm\{adaptive\}\}(n)=2\backslash sqrt\{\backslash frac\{n\}\{n+4\}\}.$$

Thus

$$\frac{J_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}}(n)}{J_{\mathrm{a}\mathrm{d}\mathrm{a}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}}(n)}=\frac{\sqrt{n+4}}{2}⟶\mathrm{\infty }\mathrm{.}\backslash frac\{J\_\{\backslash mathrm\{static\}\}(n)\}\{J\_\{\backslash mathrm\{adaptive\}\}(n)\}\; =\backslash frac\{\backslash sqrt\{n+4\}\}\{2\}\backslash longrightarrow\backslash infty.$$

Possible orthogonal tasks	Static optimum	One-interval adaptive optimum	Static/adaptive ratio
1	1.000000	0.894427	1.118034
2	1.414214	1.154701	1.224745
4	2.000000	1.414214	1.414214
8	2.828427	1.632993	1.732051
16	4.000000	1.788854	2.236068

These table entries evaluate the exact formulas. They are not five independent learned-agent experiments. The frozen study separately records five physical/dual witnesses at these dimensions; n=16 is a witness case rather than a numerical solver comparison.

If the parent knows the eventual task in advance, its adaptive optimum is $2\mathrm{/}\sqrt{5}2/\backslash sqrt5$. The adaptive price of preparing under uncertainty is consequently

The result makes developmental plasticity mathematically concrete: a child can pay to construct the needed direction after revelation instead of requiring the parent to prepare every direction equally well.

Resource and control scope. The exact finite-\(n\) construction uses $nn$ physical channels. A separate cold-child construction uses one channel and gives the feasible uniform upper bound two, without generally attaining the smaller finite-\(n\) optimum. The theorem prices quadratic control action. It does not bound hardware memory, parameter count, CPU/GPU time, energy in joules, or intelligence. The adaptive formula is an optimum for the declared one-interval constant-control class, rather than a claim about unrestricted continuous-time control.

Constructive upper bound and matching lower bound

Let $FF$ denote the adaptation structure, $UU$ its rate of change, $\theta \backslash theta$ the adapted quantity, and $uu$ its execution control:

$$\dot{F}=U,\dot{\theta }=Fu\mathrm{.}\backslash dot\; F=U,\backslash qquad\; \backslash dot\backslash theta=Fu.$$

Define

$$z^2=\frac{1}{2}\sqrt{\frac{n+4}{n}},b=\frac{4z}{n+4},c=\frac{2nz}{n+4},d=\frac{1}{z}\mathrm{.}z^2=\backslash tfrac12\backslash sqrt\{\backslash frac\{n+4\}\{n\}\},\backslash quad\; b=\backslash frac\{4z\}\{n+4\},\backslash quad\; c=\backslash frac\{2nz\}\{n+4\},\backslash quad\; d=\backslash frac1z.$$

The parent prepares $B=b{I}_{n}B=bI\_n$. After task $jj$ is revealed, its child uses structural control $U_j=c{e}_j{e}_j^{\mathrm{\top }}U\_j=ce\_je\_j^\backslash top$ and execution coefficient $v_j=d{e}_{j}v\_j=de\_j$. Since $b+c\mathrm{/}2=zb+c/2=z$, the integrated endpoint map is exactly $(B+U_j\mathrm{/}2)v_j=e_j(B+U\_j/2)v\_j=e\_j$, with expected lifetime action $\frac{1}{2}(n{b}^2+c^2+d^2)\backslash tfrac12(nb^2+c^2+d^2)$. The manuscript supplies a feasible semidefinite dual with the same value. This proves optimality without assuming that a symmetric candidate must be optimal.

2. One framework for evidence, development, and inheritance

Layer	Mathematical role	Supplied implementation
Protected comparison evidence	Preserve information needed to compare candidate changes	linalg, comparison, certificates
Causal acquisition	Enforce release times, retain dependencies, and charge invoked reads	evidence_stream
Cold development	Build capacity from zero while evidence arrives	async_grid, stream_catalogue
Warm development	Start from an actual inherited matrix factor and optionally pay maintenance	warm_grid
Scalar reserve	Solve inherited reserve, delayed revelation, paid task pairs, and upkeep classes	reserve
Future reserve design	Prepare once for a distribution of possible descendant tasks	morphology, scenario
Development jobs	Bind bounded JSON requests to exported schedules and ledgers	development
Game-facing runtime	Policy decisions, proposals, tools, migration, admission, and rollback	Runtime modules, docs/, and engine adapter source

All module names are under ailith. The paper rederives the foundations needed to follow the current release; earlier drafts are unnecessary for understanding the main argument.

Causal evidence and dormant usefulness

An observation can have future decoding value despite having no immediate target coefficient. For example, an early reading of $z_{1}z\_1$ is needed to recover $z_{2}z\_2$ from a later reading of $z_1+z_{2}z\_1+z\_2$. AÍLITH retains these dependencies instead of equating current irrelevance with safe deletion.

The acquisition implementation rejects premature reads before invoking their provider, refuses to backdate late reads, and keeps invoked failed acquisitions in the ledger. These are in-process protocol guarantees. The host owns the actual clock and the truth of sensor values.

Inherited geometry and future accessibility

Within the specified isotropic model, inherited capacity can be represented by $P=F{F}^{\mathrm{\top }}P=FF^\backslash top$. Its orientation affects which future transformations are affordable. Equal rank or equal total magnitude need not imply equal adaptability.

For inherited state $\mathsf{H}\backslash mathsf\; H$, future task $\xi \backslash xi$, and the declared admissible dynamics, define the least continuation cost $C_{\mathsf{H}}(\xi )C\_\{\backslash mathsf\; H\}(\backslash xi)$. Under the manuscript's measurability and attainment conditions, budgeted evolvability is

$${\mathrm{Evolv}}_{\mu ,B}(\mathsf{H})=\mu \{\xi :C_{\mathsf{H}}(\xi )\le B\}\mathrm{.}\backslash operatorname\{Evolv\}\_\{\backslash mu,B\}(\backslash mathsf\; H)\; =\backslash mu\backslash \{\backslash xi:C\_\{\backslash mathsf\; H\}(\backslash xi)\backslash le\; B\backslash \}.$$

This evaluates adaptability against an explicit future-task distribution and budget. It separates current task success from the cost of useful future changes.

Preparing before the future task is known

The shared-parent problem minimizes a paid preparation term plus expected descendant continuation cost:

$$\underset{P⪰0}{\min }[\frac{\mathrm{tr}P}{2S_0}+\sum _j{\pi }_j{v}_j(P,Y_j)]\mathrm{.}\backslash min\_\{P\backslash succeq0\}\; \backslash left[\backslash frac\{\backslash operatorname\{tr\}P\}\{2S\_0\}\; +\backslash sum\_j\backslash pi\_jv\_j(P,Y\_j)\backslash right].$$

The static subclass has a spectral reserve allocation based on the square root of a weighted future-task moment. The dynamic two-stage compiler uses a shared Gram formulation. Under the stated expandable-width assumptions, its semidefinite formulation is exact and factorization recovers one physical parent shared by every child branch. A restrictive channel cap can prevent an unrestricted optimum from being attained.

Optional maintenance also changes the value of unused reserve. Extra capacity can incur a real continuation liability. Construction, retention, execution, and retirement therefore need distinct accounting.

3. Recorded evidence

The values below summarize the frozen v0.5.0 studies. Full controls, inputs, protocols, numerical oracles, and source bindings are inside the complete archive. Convenient copies of the summary records are in evidence/.

Verification or study	Frozen recorded outcome
Full regression suite	220 passed; zero failures, errors, or skips
Inherited-state schedules	37 prescribed; all independently checked; 35 closed numerical grid gaps and two retained feasible open gaps
Static reserve design	13 exact-formula cases and eight successful independent direct-optimization starts
General shared-parent scenarios	18 prescribed solves; all independently checked and all requested numerical grid gaps closed
Analytic plasticity witnesses	Five constructive/dual witnesses, at n=1,2,4,8,16
Retained streaming study	71 prescribed schedules independently checked; no independent check failures
Retained scalar reserve study	93 warm records, 25 paid task-pair records, and 24 direct-optimization starts
Original archive verifier	900 file, inventory, and evidence-binding checks

For the scenario study, the largest component-relative endpoint error is approximately 5.3408 × 10⁻¹⁵, and the largest relative finite-grid gap is 9.2575 × 10⁻⁸. The retained streaming study has a largest relative grid gap of approximately 6.7972 × 10⁻⁸.

The inherited-state study retains two open relative grid gaps: approximately 0.9326199% and 0.0222087%. Their schedules pass endpoint and cost checks. They remain unresolved optimality intervals rather than being replaced by selected reruns.

Independent numerical checks reconstruct endpoints, costs, and dual constraints from the literal interval formulas. They are independently implemented checks within this release, rather than an external replication or human peer review. Float64 bounds with explicit corrections are distinct from directed-rounding interval certificates. Small grid gaps also remain distinct from continuous-time accuracy; the warm study's conservative continuous relative brackets range from roughly 0.4431% to 100%.

Timed hereditary arena

The supplied arena fixes a parent before drawing its task, starts the child from that actual factor, receives observations at times zero and three quarters, rejects a premature acquisition, and integrates the schedule. The recorded endpoint error is 2.220446049250313 × 10⁻¹⁶. Both the inherited-factor discrepancy and forbidden early coefficient are zero.

This arena uses the static parent designer followed by a dynamically rebuilding child. It demonstrates a feasible hereditary execution path; it does not claim joint parent/child optimality. The separate scenario compiler implements joint two-stage optimization. Sensor charges remain separate from control action.

Checks performed for this Hugging Face edition

The frozen studies and original source archive remain unchanged. During packaging, a fresh extraction passed all 900 original verification checks, and a fresh regression run passed all 220 tests. The new records are kept separately under evidence/packaging_*; they do not enlarge the numerical study or replace its frozen results.

The measured reference studies run on Linux CPU, with Python 3.12.14, NumPy 2.3.5, and SciPy 1.17.0. The fresh packaging environment is recorded separately. Actual loopback HTTP is tested. External LLM inference, engine compilation, real ONNX model execution, and GPU execution were outside the frozen validation scope.

4. Quick start

Download and extract the complete research archive. It creates AILITH_v0.5.0/. Run the following from that extracted directory using Python 3.10 or newer:

python -m venv .venv
# Activate .venv for your shell.
python -m pip install -e .
python verify_release.py

python examples/hereditary_arena.py --output results/my_hereditary_arena.json
python -m ailith develop --request examples/scenario_job.json --output results/my_scenario.json

The original RUN_AILITH.bat supplies a Windows launch path for the arena and development jobs. Batch scripts are supplied and inspected; native Windows execution was not measured in the reference study.

A shared-parent Python example

from ailith.scenario import solve_scenarios

plan = solve_scenarios(
    targets=[[[1.0], [0.0]], [[0.0], [1.0]]],
    probabilities=[0.5, 0.5],
    times=[[0.0, 1.0], [0.0, 1.0]],
    releases=[[0.0], [0.0]],
    preparation_time=1.0,
    maintenance=0.0,
)
assert plan.factor is not None
print(plan.status, plan.grid_lower, plan.action_upper)

parent_factor = plan.factor
parent_control = plan.preparation_control
# Execute the paid parent before the public task is selected.
# Choose the corresponding child only after task revelation.
child = plan.branches[0]

This example's exact one-interval optimum is $2\mathrm{/}\sqrt{3}2/\backslash sqrt3$, approximately 1.1547005384, including preparation. The target maps and task prior are public design inputs. Unknown episode readings still arrive through the acquisition contract. A schedule's state_map(t) represents a linear map rather than secretly acquiring future evidence.

action_upper comes from feasible returned controls. grid_lower is a separately checked numerical dual bound. A software status of certified refers to the requested numerical grid gap; it does not signify a formally verified proof or demonstrated RSI. Inspect feasible, inconclusive, width, residual, and continuous-bound fields before execution.

Reproduce the frozen study designs

Use fresh output locations:

python benchmarks/run_inheritance.py --output-dir results/inheritance_reproduction
python benchmarks/run_scenarios.py --output-dir results/scenarios_reproduction
python benchmarks/run_streaming.py --output-dir results/streaming_reproduction
python benchmarks/run_reserve.py --tag reproduction

A fixed seed reproduces declared inputs. It does not create additional independent statistical evidence. Run verify_release.py before editing reference files. See REPRODUCIBILITY.md for validation and document-building details.

5. Games, local models, tools, and GPUs

AÍLITH separates background development from ordinary game decisions. The background CPU compiler accepts public targets, release schedules, inherited state, or a menu of future tasks. The game host owns simulation time, actual observations, valid adaptation variables, and fallback behavior. A compact actor handles routine decisions.

Connection	Delivered capability	Deployment evidence
Unity, Unreal, Godot	Adapter source and setup documentation	Source supplied; actual engine compilation and gameplay remain deployment work
Local actor sidecar	Loopback HTTP routes for actions, feedback, status, and batches	Real loopback protocol tests
Development worker	Bounded JSON jobs, request digest, schedules, and paid ledgers	Executed reference jobs and CPU tests
Local LLM	Compatible chat-completions client and bounded declarative proposals	Dry-run/protocol tests; no real external model inference measured
Tools	Typed host callbacks with schemas, size limits, and recorded metadata	In-process checks; host-managed workers are needed for interruption of slow callbacks
GPU actor inference	Optional ONNX Runtime CPU/CUDA backend	Backend tests use mocked model execution; no GPU throughput or real model run reported
Digital twins	Separate world/player roles and error accounting	Synthetic reference experiments, without a claim of a validated real-world twin

The HTTP policy sidecar and development-job CLI are separate interfaces. A host must connect the compiled schedules to its own adaptation mechanism. For cumulative state, apply the increment since the previous event; applying the entire accumulated state on every frame repeats work.

The convex compilers use dense NumPy/SciPy CPU operations. They target bounded adaptation interfaces such as skill parameters, latent controllers, or compact adapters. The release does not treat a full LLM weight matrix as an already scalable control problem, and JSON transport does not share GPU buffers.

Engine/runtime integration is documented in the archive's docs/INTEGRATION.md and docs/STREAMING_INTEGRATION.md. Provider-specific requirements are in the Ollama compatibility documentation and ONNX Runtime CUDA documentation. These external links are operational references, rather than evidence of a deployment run in this study.

6. Research context and attribution

The synthesis incorporates paid self-reconfiguration from NØEMA–Λ, dormant preparation and lifecycle accounting from Evolvability-Preserving Dormant Dendrites, and task-dependent descendant accessibility from RAVEN Evolvability. Their relevant mechanisms are rederived under the present control assumptions.

The manuscript credits established foundations in nuclear-norm factorization, semidefinite optimization, bilinear control, matrix boundary-value methods, and quantitative-genetic evolvability. The proposed contribution is the particular causal, inherited, paid-development formulation and its derived constructions and separations. The release does not claim to have invented those classical methods.

Related game-RSI and evolvability literature is discussed in the manuscript bibliography. No matched leaderboard comparison establishes that this system outperforms other RSI systems. Worldwide priority and state-of-the-art game performance remain unestablished.

7. Scope, intended use, and next empirical gate

Use this release to study the geometry and timing of adaptation, inspect constructive optimal-control examples, reproduce the declared numerical studies, or build an explicitly bounded game-host integration.

The supported causal streaming model uses a fixed context during its planning window, known target maps and covariance, exact Gaussian linear observations, deterministic shared preparation, and the stated quadratic objective. Protected-evidence worst-case results use their own bounded latent assumptions. Arbitrary moving contexts, unknown targets, noisy sensing, program edits, actuator constraints, and large nonlinear actors need additional models.

The two-stage shared-parent solver is implemented. General multilevel inheritance is developed mathematically under stated conditions; a scalable general scenario-tree scheduler is not delivered. The in-process tool and evidence contracts are also distinct from an operating-system sandbox for generated code.

The next empirical RSI test compares a modified producer with an unchanged producer on fresh descendant tasks while matching information, inherited reserve, starting policy, model calls, tools, and paid development allowance. It measures descendant performance, retained skills, distribution shift, and development cost. The current release defines that experiment without claiming its outcome.

8. Provenance, integrity, and license

This Hugging Face edition adds documentation and packaging checks around the unchanged v0.5.0 release. It is not a new numerical study or research version. The archive retains recovered v0.1 and v0.4 material for provenance. Exact intermediate v0.2/v0.3 archives and unavailable experiments were not recreated from remembered claims.

The outer SHA256SUMS inventories this upload kit. The inner MANIFEST.json and verify_release.py bind the original archive's files, sources, protocols, and recorded evidence. Hash consistency detects changed bytes; it does not authenticate authorship, prove a theorem, or replace scientific review.

The supplied MIT license is preserved from the source release, with copyright 2026 Maciej Nowicki. References and third-party dependencies retain their own rights and licenses. No new license is assigned to separately cited prior works.

Citation

Use CITATION.cff or CITATION.bib. The citation preserves the requested author and complete manuscript title. No DOI, arXiv identifier, or peer-review status is claimed.

@misc{eve2026ailith,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {Beyond Reinforcement Learning: Recursive Self-Modification and Continual Intelligence Growth in Game Agents, RSI in Game Worlds, Digital Twins},
  year = {2026},
  month = {oct},
  howpublished = {Research manuscript and software release},
  note = {AÍLITH, version 0.5.0; 79-page manuscript and reproducible research package}
}