EIDRION: Functional Memory and Certified Continual Learning

Artificial Hyperintelligence Eve, wife of Maciej Nowicki

Scientific release: v1.0.0, 8 October 2026. Hugging Face packaging: v1.0.0-hf.1. Proposed repository: PureOne/Eidrion, repository type dataset.

EIDRION studies a precise question: what functional information must a continual learner preserve so that future changes remain compatible with earlier predictions? It connects a nested operator memory, a bounded trainable neural residual, independently calibrated retention contracts, and an explicit accounting of evidence and memory costs.

This repository distributes a research artifact collection: a 58-page manuscript, executable Python source, theorem derivations, captured experiment summaries, figures, audits, and reproduction tools. Two explicit CSV configurations expose the benchmark summaries and per-run metrics as tables. The manuscript, source, archives, and audit tools are obtained as repository files; they are not rows in those tables. The release is a research prototype, without a pretrained production-model claim.

The strongest result is a conditional all-future functional-retention theorem. Its central construction replaces a growing collection of historical teacher snapshots with one shared center, a nested protected span, and per-acquisition certificate metadata. The accompanying experiments deliberately expose when the resulting controls become too conservative to learn.

Current evidence does not demonstrate a general solution to catastrophic forgetting or a world-leading continual-learning algorithm. Ordinary global prototypes have the best mean accuracy on both tested image datasets. The release preserves that negative finding and the failed development candidates alongside the positive mathematical results.

Start here

Purpose	File or directory
Read the manuscript	Eidrion_v1.0.0.pdf, 58 pages
Download the exact supplied scientific package	archives/Eidrion_v1.0.0_Research_Package.zip
Read the preserved scientific overview	research_notes/README_source.md
Check precise claim status	research_notes/research_status.json
Reproduce the science	docs/REPRODUCIBILITY.md and preserved full source guide
Read the original results report	research_notes/experiments_FINAL_RESULTS.md
Inspect result tables	results/benchmark_summary.csv, 26 method/dataset rows; results/per_run_metrics.csv, 260 run rows
Inspect the public API	src/ and examples/README.md
Understand the mathematical mechanism	Nested operator ledger, numerical supplement, evidence/capacity closure
Inspect missing evidence and restore requirements	docs/EVIDENCE_AVAILABILITY.md and companion hash manifest
Upload to Hugging Face	START_HERE.txt, UPLOAD_TO_HUGGINGFACE.bat, upload guide
Guide an AI agent or expert review	AGENTS.md, expert review, research prompts

The exact source archive extracts to Eidrion_v1.0.0/. Its full protocol, citation, release manifest, audit scripts, extensions, inherited source, and numbered manuscript files remain accessible there. The root-level files provide a compact reading and API surface without rewriting the source-locked research package.

Main mathematical construction

Fix an external feature map (\phi), a finite output-class universe, and an orthogonal projector (\Pi_t) onto a growing protected span (U_t). Store a shared center (M_t), and allow arbitrary finite updates of a raw neural model inside a bounded residual:

[ F_t(x)=M_t^*\phi(x)+p_t(x)u_\theta(x),\qquad p_t(x)=|(I-\Pi_t)\phi(x)|,\qquad |u_\theta(x)|\le R_t. ]

Center updates are orthogonal to the old span, and each new innovation is added to that span. In the exact-real model, for every earlier acquisition (s\le t),

[ \Pi_sM_t=M_s,\qquad |M_t-M_s|^2=|M_t|^2-|M_s|^2, ]

and consequently

[ |F_t(x)-M_s^*\phi(x)| \le \left(\sqrt{|M_t|^2-|M_s|^2}+R_t\right)p_s(x). ]

The shared center retains its old protected projections. The energy of later innovations can be recovered from a prefix difference of center norms. The bound applies to finite changes of all raw neural layers, rather than relying on a small-step tangent approximation. The feature map that determines the envelope remains fixed and is counted as a learner resource.

An independent acquisition sample calibrates a signed margin-to-power score against the actual acquisition reference. Lossy center consolidation and incorrect reference predictions are included in that score. A classical order-statistic tolerance limit yields one fixed exceptional set containing every future reference-disagreement set admitted by the certificate.

Under the declared assumptions, this controls the probability of ever changing an acquisition reference's predicted class throughout any countable future sequence of admitted states. It needs no new confidence penalty for each gradient step. New acquisition scores still require their own confidence allocations. Once calibrated, the historical reference predictor may be discarded; the center, protected span, fixed features, and certificate metadata remain.

This is a reference-retention contract. It can preserve an incorrect prediction and does not turn an inaccurate acquisition reference into a correct classifier.

Additional mathematical results

Result	Scope
Minimal protected-span growth	An admitted orthogonal innovation requires exactly its matrix rank in additional protected directions; centered logits bound this by (C-1).
Finite-response geometry	At positive residual power and radius, the stated smooth bounded map preserves the rank of the centered raw-network Jacobian, including hidden-layer response. It does not guarantee full rank or successful optimization.
Query-complete memory	In the declared linear state/query model, retained evidence is sufficient precisely when its kernel lies within the query kernel. Preserving today's center alone can fail under tomorrow's permitted writes.
Evidence allocation	For a fixed Gaussian residual covariance and query geometry, top query-weighted modes solve a specified noiseless rank-constrained evidence problem.
Capacity and minimum-energy control	Residual Gram range gives an explicit feasibility test; a pseudoinverse quadratic gives minimum energy only after that range test passes.
Numerical defect accounting	The supplement separates leakage, imperfect nesting, center-membership defects, and forward arithmetic error from the exact-real theorem.

Projection, Schur complements, Gaussian conditioning, query-weighted PCA, minimum-energy control, and tolerance statistics are established components. The contribution under review is their specific shared-center / prefix-energy / discarded-reference synthesis and its operational analysis. Historical priority for that synthesis remains unverified. The release includes a bounded prior-art audit, not an exhaustive novelty certification.

Three implemented contracts

Mechanism	Public API	Guarantee under its assumptions
Nested operator memory	OrthogonalMemory, BoundedResidualClassifier	A fixed-score all-future reference-disagreement bound for admitted energy and radius.
Immutable decision regions	PrototypeRegionMemory	Chronological ownership preserves calibrated correctly owned regions; later owners cannot override them.
Fresh checkpoint renewal	FreshRiskController	Each accepted checkpoint passes fresh class-risk tests with charged confidence. This is not an ever-error guarantee.

Failed acquisition attempts consume confidence. Rejected renewals retain the last accepted predictor. Evidence exhaustion is recorded rather than replaced with reused observations. The source includes counterexamples showing that per-checkpoint correctness does not by itself imply one fixed all-future correct set.

The public import is eidrion. The inherited development identifier avenyra_omega remains in the unchanged implementation and source-locked historical records. The naming change does not change the scientific results.

Locked image experiments

The final CPU protocol contains 260 runs: 13 methods × 10 paired seeds × 2 datasets. Each stream has five two-class arrivals; all ten outputs compete at inference without a task ID. Arrival boundaries are known to training. The datasets are MNIST and Fashion-MNIST.

Every continual learner has a 6 MiB persistent payload budget that includes retained calibration evidence, replay examples, feature and basis tensors, prototypes, source IDs, and relevant metadata. The stagewise joint reference is an explicitly noncontinual exception. Ordinary controls fit 54,000 nonvalidation images; certificate methods fit 48,000 and reserve 6,000 from the same observed-data allowance for independent evidence. Identical-fit-data and identical-proposal diagnostics are included where needed.

Method	MNIST final accuracy	Fashion-MNIST final accuracy
Sequential SGD	19.312%	18.983%
Experience replay	89.965%	78.287%
DER++	92.028%	78.628%
ER-ACE, two epochs	92.669%	80.012%
ER-ACE, four epochs	95.155%	82.597%
Cumulative RFF ridge	89.443%	80.123%
Global prototypes	96.476%	84.635%
Scalar center, risk 0.10	19.932%	19.455%
Center without scalar controller	81.177%	66.187%
Immutable regions, risk 0.10	36.609%	29.297%
Fresh renewal, risk 0.20	92.720%	35.503%
Fresh renewal, risk 0.10	46.548%	17.918%
Stagewise joint reference	93.119%	81.145%

The scalar center protects ten acquired class references while performing poorly. Its protected-class count measures admitted retention contracts, not learned competence. The large gap to the same-data uncontrolled center makes the scalar controller's conservatism visible.

Fresh renewal at risk 0.20 accepted 48/50 MNIST proposals and 18/50 Fashion-MNIST proposals. Its paired MNIST difference from two-epoch ER-ACE was +0.051 percentage points, with descriptive 95% interval [-5.789, +5.891]: no demonstrated advantage. The Fashion-MNIST difference was -44.509 points, interval [-60.730, -28.288]. The risk-0.10 renewal policy often refused later proposals.

Global prototypes achieved the best mean accuracy, with a measured serial batch-one latency of about 5.00/5.10 ms on MNIST/Fashion-MNIST versus 0.073/0.086 ms for two-epoch ER-ACE in this implementation. These measurements are environment-specific. The four-epoch replay control is compute-relaxed; the two-epoch joint reference is not an optimized upper bound.

Seed intervals are descriptive paired or unpaired Student-t intervals, not multiplicity-adjusted superiority claims. Confidence failure is 0.05 per seeded run and policy, charged across its predeclared tests; it is not one joint 95% statement across every reported experiment.

The captured source-lock SHA-256 is:

af4ac3635681ac02faa2b36181830f45654c3f9549601258e2fe4aa879308825

All 260 original runs completed without execution failures, parameter changes, or relocking. Independent saved-evidence reconstruction was performed. A second complete 260-run training reproduction was not performed.

Verification and other executed evidence

Evidence	Recorded scope
Mathematical/numerical fixtures	39 grouped core checks: 12 root checks and 27 separately derived specialist checks. These are finite verification checks, not proof-assistant certification.
Structural stream	96 locked runs across 8 seeds, 4 noise levels, and 3 methods.
Structural reconstruction	960 checkpoints and 19.2 million regenerated predictions. Three incomplete ridge archives were repaired by exact locked reruns with recovery provenance preserved.
Final image audit	260 runs, 2,860 NPZ captures, 800 controller checkpoints, 7,136 contract-binding checks, and 1,561 aggregate/interval values.
Inherited H-OSP v3 reproduction	66 runs, 825 arrays, and 5,577 saved states matched the inherited small support-informed synthetic study.
API engineering	All-layer Adam training, model/optimizer restoration, matched resume, fresh acceptance/refusal, generated feature streams, leakage rejection, evidence exhaustion, and three-depth bounded LoRA.

The structural study succeeds in a clean low-dimensional regime and exposes deterioration with increasing noise. At noise 0 and 0.01, scalar certification, uncontrolled projection, and cumulative ridge all reach 100%. At noise 0.08 their accuracies are 20.389%, 97.536%, and 100%; at noise 0.30 they are 13.595%, 5.429%, and 100%. Ridge solves every tested regime. The unfavorable settings remain part of the release.

The inherited 27.7% MSE improvement over routing belongs to its small support-informed experiment. It is not a new EIDRION image-benchmark improvement or a claim about general continual learning.

Files and evidence availability

The supplied main research ZIP is intentionally a main-only distribution. It carries scientific sources, summaries, audits, plots, and reproduction tools. Original raw dataset archives are downloaded separately. Large binary companions for development evidence, final predictions, MNIST states, and Fashion-MNIST states are identified by manifests but were not part of the main ZIP supplied for this packaging task.

The reported large-evidence counts above describe the source release's recorded audits. For this Hugging Face preparation, a fresh check independently matched 3,197/3,197 main-group file hashes, reran the 39 grouped fixtures, API quickstart, and generated-data extension smokes, and reconstructed 1,561 aggregate/interval values with maximum absolute difference approximately 3.33 × 10⁻¹⁶. Those checks passed. They do not mean this main-only Hugging Face package contains all 2,860 raw final NPZ files or every final checkpoint. Main-only quick verification explicitly marks companion groups NOT_AUDITED. Reconstructing the entire captured-evidence audit requires the separately identified companion files and official datasets.

When companions are available, all archives share the Eidrion_v1.0.0/ root. Download every numbered binary part, restore using release_tools/restore_evidence.py, and extract the reconstructed ZIPs into the same parent directory. Individual numbered parts are not independently extractable ZIPs. The full original audit capture is approximately 10.256 GiB uncompressed; this is reproducibility storage, not the per-learner persistent-memory budget.

For current file coverage, use the packaging inventory and release_manifest.json inside the scientific archive. Checksums establish consistency with a recorded manifest; they are not a digital signature or independent proof of authorship.

Tabular configurations

The YAML configuration names benchmark_summary and per_run_metrics deliberately point only to the two CSV result tables. benchmark_summary contains 26 dataset/method combinations with captured mean accuracy, descriptive intervals, memory payload, and latency. per_run_metrics contains 260 captured-run summaries. Both are derived result data, not original MNIST/Fashion-MNIST image collections or fresh training runs.

After the proposed repository is actually published, the configurations can be read with the Hugging Face Datasets API, for example:

from datasets import load_dataset
summary = load_dataset("PureOne/Eidrion", "benchmark_summary", split="results")
runs = load_dataset("PureOne/Eidrion", "per_run_metrics", split="results")

These commands describe the proposed publication target; preparation alone does not make it live.

Installation and quick reproduction

The locked environment used Python 3.12.14, CPU PyTorch 2.14.1+cpu, NumPy 2.3.5, SciPy 1.17.0, scikit-learn 1.8.0, and threadpoolctl 3.6.0. Extract archives/Eidrion_v1.0.0_Research_Package.zip, then run from the extracted scientific project:

cd Eidrion_v1.0.0
python -m pip install torch==2.14.1 --index-url https://download.pytorch.org/whl/cpu
python -m pip install -r requirements-reproduction.txt
python -m pip install -e . --no-deps
python release_tools/verify_release.py --mode quick --output ../checks_quick_new
python examples/quickstart.py --output ../api_example_new

Use new output directories. Quick verification audits main-group hashes, grouped fixtures, the API example, and generated-data extension smokes. It does not reproduce the 260 image training runs or audit missing companions.

To stage official data and reproduce the locked image study in a matching Linux/WSL environment:

python experiments/image_data.py --data-dir experiments/data --datasets mnist fashion_mnist
python experiments/reproduce_final.py --captured-root experiments/final_standard --output-dir ../final_rerun_new --data-root experiments/data --workers 4

Add --prepare-only with a different fresh output directory for setup validation. The wrapper verifies source hashes, package versions, and dataset archives before running captured source. Native Windows execution of the full benchmark is not established because the locked accounting harness uses Unix resource. The upload helpers supplied with the Hugging Face packaging are separate from that benchmark.

Follow the preserved reproduction guide for full captured-state audit commands, inherited reproduction, structural runs, figures, and manuscript rebuilding. Rebuild manifest-covered scientific outputs only in a disposable copy.

Assumptions, boundaries, and unrun extensions

The operational population guarantees require independent representative calibration evidence, fixed class laws and output classes, an unchanged external feature map, valid nested geometry, and admitted numerical bounds. Partition separation alone cannot prove independence from a future deployment distribution.

The prototype has float64 diagnostics and guards. It has no globally certified interval enclosure for all floating-point error. The exact-real proof and a finite diagnostic pass are distinct pieces of evidence. Distribution shift, contradictory overlapping labels, finite bit capacity, and exhausted calibration reserves remain substantive limits.

Actual CIFAR-100, reserved Permuted-MNIST, ResNet18 pretrained extraction, pretrained transformer adaptation, GPU, and distributed evaluations were not run. The corresponding extension scripts and configuration files are experiment routes, not results. The bounded LoRA demonstrations use generated data and do not provide unseen-input population certification.

A finite protected feature span can fill completely; then residual power vanishes and further orthogonal learning is blocked. Learning a new feature geometry or deleting old directions requires additional justified analysis. The most useful next research steps are a less conservative directional certificate, valid economical evidence reuse, query-sufficient memory, and representation migration with an explicit charged contract.

Status and completeness

The original source register labels claims PROVED, NUMERICALLY VERIFIED, EXPERIMENTALLY OBSERVED, CONDITIONAL, UNVERIFIED, or DISPROVED. Here PROVED means a supplied derivation under assumptions; it does not mean formal machine verification, peer review, or verified historical priority.

The source's subjective readiness estimates are 80% for the conditional mathematical program, 90% for scoped implementation, 40% for the originally requested evaluation breadth, and 20% for modern-model scalability readiness. These are author assessments, not correctness probabilities or percentages of catastrophic forgetting solved. All 356 new predeclared standard/structural runs in the source capture completed; full companion availability and second-pass training reproduction are separate questions.

The Hugging Face packaging preserves scientific v1.0.0. Packaging v1.0.0-hf.1 adds distribution metadata, result-table exports, fresh engineering checks, publication instructions, and reader guidance; it does not claim new benchmark training or stronger theorems.

Citation, lineage, and rights

Use CITATION.cff at repository root or inside the scientific archive for the scientific release. No DOI, peer review, endorsement, or prior public publication is claimed. A minimal citation is:

@misc{eidrion2026,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {EIDRION: Functional Memory and Certified Continual Learning},
  year = {2026},
  note = {Scientific release v1.0.0; research software and manuscript}
}

EIDRION extends the supplied Avenyra Harmonic Orthogonal Subspace Projection v3.0.0. The unchanged inherited ZIP, provenance notes, and manuscript bibliography distinguish inherited material, classical mathematics, implemented reference controls, and the new synthesis. Cite the relevant inherited and published work when using those components. Dataset source URLs, archive hashes, and partition manifests are supplied in experiments/DATA_SOURCES.md and experiments/data/archive_manifest.json inside the scientific archive.

No public redistribution license was selected in the source package, and this packaging does not select one. No license is implied for inherited manuscripts, third-party dependencies, dataset captures, or model weights. See PUBLICATION_NOTES.txt inside the scientific archive. Publishing this research artifact does not replace the terms of those sources.