PureOne/evolvability-preserving-dormant-dendrites

Evolvability-Preserving Dormant Dendrites: The Joint Reserve Law

Neural structures optimized for future capability accessibility — matched evidence and protected plasticity reserves.

Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Release maintainer: Maciej Nowicki · PureOne
Research version: 2.0.0 · Artifact release: 2.0.0-hf1 · Prepared: 19 September 2026

Status: meaningful advance. The finite Gaussian/quadratic core is solved within stated assumptions. Independent novelty, universal neural training acceleration, and a uniquely superior architecture are not established. This repository contains a research artifact and synthetic experimental records, not pretrained model weights or a general-purpose training dataset.

Start here

Reader	Entry point
Researcher	Main manuscript — PDF · searchable Markdown
Mathematical reviewer	Complete proofs — PDF · searchable Markdown · theorem index
ML engineer	Algorithm · reference code · reproduction guide
AI agent or search system	AI_AGENT_INDEX.json · claim registry · llms.txt
Skeptical reviewer	Falsification · prior art · limitations
Full project history	Original v1 manuscript · v1 proofs · 34-objective coverage

Research question

What should a neural system preserve today, despite little or no current predictive benefit, because it makes valuable future capabilities cheaper to acquire?

The proposed answer is a matched capability option: retained or obtainable evidence that identifies a useful change, together with a protected, affordable route for expressing it. More parameters, more variance, or more reachable rank alone are insufficient. Information and controllability must agree in the directions they support.

Main mathematical results

PROVED under the declared finite quadratic decision model. Let $r$ be a future behavioral residual, $m=\mathbb{E}[r\mid\mathcal I]$ its conditional mean given permitted information, and $W=KK^\top$ the cost-normalized protected control Gramian. The exact improvement from optimal adaptation is

$${\mathcal{G}}_{\eta }(K,\mathcal{I})=\frac{1}{2}\mathrm{tr}\text{\hspace{0.17em}⁣}[W(W+\eta I{)}^{-1}\mathbb{E}[m{m}^{\mathrm{\top }}]]\mathrm{.}\backslash mathcal\; G\_\backslash eta(K,\backslash mathcal\; I)\; =\backslash frac12\backslash operatorname\{tr\}\backslash !\backslash left[W(W+\backslash eta\; I)^\{-1\}\backslash mathbb\{E\}[mm^\backslash top]\backslash right].$$

This expression values useful evidence and the ability to act on it jointly. Its conditional-expectation and ridge-control ingredients are classical; the claimed contribution is the reserve decision formulation and its derived laws, subject to further novelty review.

PROVED — sharp joint-reserve birth law. In one Gaussian mode, normalized evidence and plasticity reserves $s,t\geq0$, positive linear prices $a,b$, and maximum gross future benefit $A$ give

$$\underset{s,t\ge 0}{\max }[A\frac{s}{1+s}\frac{t}{1+t}-as-bt]>0⟺A>(a^{1\mathrm{/}3}+b^{1\mathrm{/}3}{)}^3\mathrm{.}\backslash max\_\{s,t\backslash geq0\}\backslash left[A\backslash frac\{s\}\{1+s\}\backslash frac\{t\}\{1+t\}-as-bt\backslash right]>0\; \backslash quad\backslash Longleftrightarrow\backslash quad\; A>(a^\{1/3\}+b^\{1/3\})^3.$$

At equality, the empty reserve and the finite pair $s=(b/a)^{1/3}$, $t=(a/b)^{1/3}$ tie. The onset requires no fixed creation fee. Single-component coordinate growth initialized at zero cannot discover this profitable pair.

PROVED — exact coverage cost. Preserving a joint spectral fraction $q\in(0,1)$ in every direction of a $d$-dimensional normalized model costs at least

$$d{c}_{\ast }(q),c_{\ast }(q)=\frac{(a+b)q+2\sqrt{abq}}{1-q}\mathrm{.}d\backslash ,c\_*(q),\backslash qquad\; c\_*(q)=\backslash frac\{(a+b)q+2\backslash sqrt\{abq\}\}\{1-q\}.$$

The bound is attained and allows noncommuting matrix candidates. It is a precision/trace resource theorem, not a claim about exact memory bytes or every nonlinear task.

PROVED — calibrated accessibility witness. The held-out score

$$\widehat{G}=\frac{1}{N}\sum _j[r_j^{\mathrm{\top }}S{\widehat{m}}_j-\frac{1}{2}{\widehat{m}}_j^{\mathrm{\top }}S{\widehat{m}}_j],S=W(W+\eta I{)}^{-1},\backslash widehat\; G=\backslash frac1N\backslash sum\_j\backslash left[r\_j^\backslash top\; S\backslash widehat\; m\_j-\backslash frac12\backslash widehat\; m\_j^\backslash top\; S\backslash widehat\; m\_j\backslash right],\; \backslash qquad\; S=W(W+\backslash eta\; I)^\{-1\},$$

equals realized ridge loss-plus-effort improvement. Its expected regret is precisely a quadratic prediction error on reachable directions. Unlike predicted variance alone, it penalizes false readiness. The package also derives a robust action floor, a separable resource allocator, and resource-aware descendant simulation composition.

Executed evidence and negative controls

The current code passed 70 numerical/software checks. The new experiment used 20 seeds, 5,000 Gaussian samples per seed, dimension 32, rank 4, and 150 joint preparation steps. All methods had equal reserve array counts and precision/control trace.

Method	Mean exact expected benefit
Matched evidence and control	1.280000
Independently oriented control	0.143861
Disjoint evidence and control	0
Jointly prepared reserve	1.280000
Conventional informed joint co-design	1.280000

The informed conventional method ties the optimum and can align known bases directly. Preparation compute is not equal. These results support the mechanism and trainability; they do not establish superior total FLOPs, energy or neural training time.

The earlier nonlinear bank experiment remains available. Prepared banks needed 15 versus 65.48 mean steps for random banks inside the observed family, but 110.46 versus 65.61 outside it. A conventional learned-subspace adapter tied the prepared bank. The v2 action-floor theorem does not retroactively repair that nonlinear experiment.

Reproduce

From a downloaded repository, using Python 3.10+ with the declared scientific dependencies:

python -m pip install -r research/v2/requirements.txt
cd research/v2
python tests/verify.py
python run_experiments.py

The recorded execution used Python 3.12, PyTorch 2.14.0+cpu, double precision, and one CPU thread. Other dependency versions may change numerical tolerances; see environment records. The publication launcher has separate dependencies and does not install PyTorch.

Outputs include raw CSV, JSON summaries and figures. Full protocol, negative controls, expected outputs and independent reproduction instructions are in REPRODUCIBILITY.md. The 70 checks are numerical/software checks, not 70 novel theorems or machine-checked proofs.

Claim registry and dataset viewer

The default Hub dataset configuration exposes metadata/claims.jsonl: one curated record per major result, with stable ID, statement, assumptions, epistemic status, proof location, implementation and counterexamples. The train split is a Hub file-configuration convention; these are research records, not training examples for a deployed model.

Raw experiment files remain separately addressable under research/v2/results/ and research/v1/results/. No mixed-schema CSV auto-discovery is required. DATA_DICTIONARY.md documents their interpretation.

Relationship to existing work

The framework overlaps with sensing/control co-design, task-based quantization, learned adaptation metrics/subspaces, LoRA/adapters, nonconcave resource allocation and approximate simulation. A conventional system implementing the same evidence, controls, optimizer and costs can match it. See the targeted prior-art review for primary sources and exact overlap boundaries.

The user's True Machine Memory, Eigenplasticity/General Plasticity Fields, EVE Phase Geometry, descendant evolvability and RAVEN abstraction programs motivate interfaces in the framework. Their role is recorded in the manuscripts; they are not treated as independently validated evidence of neural performance.

Limitations and falsification

• No trained Transformer or large-model benchmark is supplied.
• No universal advantage over equally informed conventional methods is proved.
• Precision, mobility and action are not measured hardware memory, FLOPs or energy.
• Future-task distribution errors and changing representations can invalidate local certificates.
• The scalar birth law assumes initially absent paired resources and positive linear prices.
• Independent novelty and external proof review remain open.

The complete failure register, experimental program, roadmap and scope estimates are included. A failed neural comparison is a legitimate result; the archive retains its negative controls.

Citation, attribution and reuse

Use CITATION.cff, CITATION.bib, or:

Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Evolvability-Preserving Dormant Dendrites: The Joint Reserve Law. Research version 2.0.0, artifact release 2.0.0-hf1, 2026. Maintained by Maciej Nowicki (PureOne).

The author string is the supplied research byline. The release is AI-generated research, with no asserted institutional affiliation or peer-review endorsement. No DOI or arXiv identifier has been assigned by this package.

Original manuscripts, figures, metadata and synthetic result records: CC BY 4.0. Source code and launch scripts: MIT. See LICENSE.md. External cited works retain their own terms. Claim status and attribution should be preserved when summarizing or reusing this work.