PureOne/QIRAN-EIDOLITH-v4

QIRĀN–EIDOLITH v4

Hereditary Search, Neutral-Corridor Compilation, and Reusable Evidence for Recursive Self-Improvement

Author credit: Artificial Hyperintelligence Eve
Prepared for: Maciej Nowicki
Research version: 4.0.0 · Release date: 17 October 2026
Hub packaging edition: 4.0.0-hf.2

An integrated research release on preserving future computational possibilities while reducing redundant search and controlling adaptive validation. It includes a 125-page manuscript, complete editable proof sources, exact reference implementations, bounded self-replacement experiments, synthetic benchmark records, negative controls, and reproduction tools.

The principal contribution is a separation of four contracts: current evaluation, future editability, search execution, and statistical evidence. A valid compression or shortcut for one contract can be invalid for another. QIRĀN–EIDOLITH makes those differences explicit and supplies constructive algorithms for the stated finite models.

Scientific status: supplied proofs under explicit assumptions, executable checks, and limited synthetic efficiency results. The inherited controlled experiment does not establish an advantage of recursive replacement over fixed-parent tuning. General self-acceleration, frontier-agent superiority, and historical priority remain unestablished.

Read first

• Complete 125-page manuscript
• Executive brief
• Claim-by-claim evidence ledger
• Research release audit
• Reproduction guide
• Prior-art map and limitations
• Data dictionary and release notes

1. Why this problem matters

A self-modifying system must decide what to preserve, what to recompute, and what evidence is sufficient to install a successor. These decisions interact:

1. Two programs can behave identically today while retaining different future editing possibilities.
2. A search can spend many steps inside a region with unchanged current utility, yet its hidden position can determine what happens next.
3. A deadline can make the surviving internal state relevant even when eventual exit probabilities agree.
4. A candidate discovered after inspecting validation results does not automatically justify an ordinary, unadjusted significance test.
5. Saving an ancestor does not identify an execution history whose distinguishing information was erased.

The release studies exact versions of these problems. Its intended role is a research substrate for more reliable self-modification and more informative RSI experiments.

2. Main result: present equivalence and future editability need different representations

Let a finite program system have declared observations and a set of permitted mutations. Two programs are hereditarily equivalent when every permitted finite mutation sequence leaves them observationally equivalent. The compiler computes the coarsest congruence refining the supplied observation contract.

This permits present evaluation reuse while preserving dormant distinctions that later edits can activate. A cache can share a current result without replacing every compatible live program by a single representative.

For arbitrary integers $K\geq2$, $h\geq1$, and $a\geq1$, the release constructs a family with:

Representation	Exact number of classes or states
Literal programs	$K2^h a$
Current utility functions	$K$
Classes preserving future-edit observations	$K2^h$
Supplemental information within a current class	Exactly $h$ bits

The finite catalog demonstrates the separation concretely:

Supplied eight-field policy grammar	Count
Literal programs	81,920
Current static evaluation signatures	10,868
Hereditary classes under 33 assignment actions	20,480
Largest number of hereditary classes inside one current class	256
Worst-case supplemental distinction	8 bits

These are counts relative to the declared conservative observation contract, not the globally minimal semantics of arbitrary code or arbitrary task objectives. Partition refinement and related semantic foundations have established antecedents; the release credits them.

Evidence: manuscript Sections 34–35; hereditary compiler; exact catalog results; complexity-separation families.

3. Neutral-corridor compilation preserves the relevant search boundary

For a completely specified finite Markov region, let $Q$ describe transitions within the region and $R$ describe exits. Under the certified termination conditions, the compiler verifies exact rational identities for:

$$H=(I-Q{)}^{-1}R,t=(I-Q{)}^{-1}\mathbf{1.}H=(I-Q)^\{-1\}R,\backslash qquad\; t=(I-Q)^\{-1\}\backslash mathbf\; 1.$$

Here $H$ is the eventual exit distribution and $t$ is the expected duration. A finite nonnegative duration witness and exact residual checks support the certificate.

For a logical deadline $L$, a stronger interface retains:

$$\underset{i}{\mathrm{Pr}}(\tau =\mathrm{\ell },\text{exit}=b)=[Q^{\mathrm{\ell }-1}R{]}_{ib},\underset{i}{\mathrm{Pr}}(\tau >L,X_L=j)=[Q^L{]}_{ij}\mathrm{.}\backslash Pr\_i(\backslash tau=\backslash ell,\backslash text\{exit\}=b)=[Q^\{\backslash ell-1\}R]\_\{ib\},\; \backslash qquad\; \backslash Pr\_i(\backslash tau>L,X\_L=j)=[Q^L]\_\{ij\}.$$

This is consequential: replacing every unfinished execution with a generic “no exit yet” flag and resetting its internal state can change the next outcome. The release includes counterexamples and a conditional composition theorem for adaptive boundary controllers.

The clock extension distinguishes residence time from embedded transitions. It identifies conditions under which clocks change cost while preserving eventual exits. Eventual-exit equivalence, deadline-sensitive equivalence, identical seeded trajectories, and equal physical runtime are different properties. A theorem about one is not silently used to certify the others.

Evidence: Sections 36–37 and 41; corridor kernel; clock kernel; exported exit certificates; deadline checks.

4. Reusable evidence can cover programs discovered later

The finite-catalog gate controls adaptive pair selection within a predeclared family. The countable extension removes the need to materialize every candidate before validation data are drawn.

Instead, fix a total, bounded program-to-utility interpreter independently of an IID task stream. Give descriptions prefix-code weights. The bound can then cover later-discovered descriptions, adaptively selected program pairs, and adaptively selected sample prefixes.

For description lengths $L(p),L(q)$ and sample prefix $n$, one valid paired confidence radius is:

$$r_{pq,n}^2=\frac{2}{n}[\log \frac{1}{\alpha }+(L(p)+L(q))\log 2+\log (n(n+1)\left)\right]\mathrm{.}r\_\{pq,n\}^\{\backslash ,2\}=\backslash frac\{2\}\{n\}\backslash left[\; \backslash log\backslash frac1\backslash alpha+(L(p)+L(q))\backslash log2+\backslash log\backslash bigl(n(n+1)\backslash bigr)\; \backslash right].$$

The implementation uses finite rational upper certificates for logarithms and compares squared positive rational gains against certified thresholds. Floating-point logarithms and square roots do not determine the countable-prefix acceptance decision.

The fixed element is meaning, not discovery time. Changing the interpreter, metric, sampling assumptions, or a description’s meaning after observing the data is outside the guarantee. Longer descriptions and smaller improvements can require substantially more evidence. The weighted countable-union foundation is established mathematics, and the release does not claim its invention.

The exact demonstration uses four supplied proposals, two sample sizes, three valid synthetic admissions, and one rejected worsening proposal. It validates the mechanism on that fixture; it does not demonstrate autonomous invention.

Evidence: Sections 38–40; prefix-evidence implementation; demonstration summary; rational certificates.

5. Retained state, retained history, and exact comparison

The consolidated manuscript includes the earlier state–history theory and RSI Lab rather than requiring separate downloads.

For listed linear histories $P_h$, future observations $W$, retained ancestral measurements $Rx$, and an old history label $\rho(h)$, define $T_h=WP_h$ and $U=\operatorname{span}_h\operatorname{row}(T_h)$. Under the all-state, separate-encoder assumptions, the two deficits are:

$${\mathrm{\Delta }}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}}=\dim (\mathrm{row}(R)+U)-\mathrm{rank}(R),\backslash Delta\_\{\backslash mathrm\{state\}\}\; =\backslash dim\backslash bigl(\backslash operatorname\{row\}(R)+U\backslash bigr)-\backslash operatorname\{rank\}(R),$$

$${\mathrm{\Delta }}_{\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}}=\lceil {\log }_2\underset{\mathrm{\ell }}{\max }\mid \{T_h:\rho (h)=\mathrm{\ell }\}\mid \rceil \mathrm{.}\backslash Delta\_\{\backslash mathrm\{history\}\}\; =\backslash left\backslash lceil\backslash log\_2\backslash max\_\backslash ell\; \backslash left|\backslash \{T\_h:\backslash rho(h)=\backslash ell\backslash \}\backslash right|\backslash right\backslash rceil.$$

An additional $m$ linear observations and $b$ history bits suffice exactly when they meet the respective deficits. More ancestral coordinates cannot identify an otherwise unknown executed history; a detailed history cannot recreate an unobserved ancestral value.

A sharp three-coordinate construction has zero extra ancestral rank requirement but an arbitrarily large history-bit requirement after a new future operation is enabled. Integer precision grows, so three coordinates do not mean three fixed-size machine words. Retaining an adequate evolved state or replay record can preserve information that the erased-history model lacks.

The comparison extension instead targets $(B_h-A_h)x$. Shared dependencies may cancel, allowing an exact contrast to need less retained information than reconstruction of either absolute output. Such a comparison certificate does not supply missing deployment state.

Other inherited components include finite nonlinear continuation quotients, prospective acquisition of observations and event features, archive consistency, and exact recovery demonstrations.

Evidence: Sections 3–33; state–history project; bounded RSI Lab.

6. Recorded performance results

Setup-paid search under a fixed CPU allowance

The v4 reinvestment experiment gives each method 0.08 CPU seconds per seed, includes compilation costs, and uses 20 seeds on a deliberately throughput-sensitive synthetic hash landscape.

Method	Mean evaluated candidates	Mean best utility	Mean regret to unit upper bound
Raw simulation	2,532.30	0.99969670	0.00030330
Self-loop skipping	9,670.65	0.99990447	0.00009553
Compiled exits	37,398.35	0.99997169	0.00002831

Against skipping, compiled exits yield 3.87× as many evaluated candidates, 3.38× smaller mean regret, and a better best utility in 14/20 seeds. The absolute mean utility gain is 0.00006723. These are recorded one-host measurements; they are not an intelligence score or a reasoning-benchmark result.

Source: summary and per-seed records.

Negative results and stronger baselines

• Cold compilation loses to self-loop skipping in all 12 short-batch conditions. Its aggregate speed ratio against skipping is approximately 0.582×, despite beating raw simulation in aggregate.
• Clock-quotient caching reduces linear-system compilations from twelve to four, but literal exit caching is faster in total CPU time on the recorded reuse protocol.
• In 1,000 designed null-selection trials, observed invalid promotions are 1,000 for mean-only selection, 441 for an unadjusted normal cutoff, and zero for the simultaneous gate. Zero observed events do not imply zero risk.

Sources: corridor summary, cache comparison, and evidence experiment.

Inherited replay acceleration and the recursion comparison

Dual-Quotient Replay preserves full evolving program distinctions while sharing equivalent current evaluations. On frozen meta-level lineages it reduces primitive objective calls from 761,600 with literal caching to 536,320, a 29.58% reduction, with a recorded 1.435× CPU speedup. Request-score stream digests agree and checkpoint differences are zero.

The inherited held-out meta-level results are:

Comparison	Mean difference in utility points	Descriptive 95% interval
Evolved recursive improver vs initial improver	+1.552	[+0.504, +2.660]
Recursive evolution vs fixed-parent tuning	−0.207	[−0.865, +0.248]
Recursive evolution vs random program search	+0.360	[−0.481, +1.218]

One utility point is 0.01 in normalized task score. The intervals use twelve lineage seeds, are descriptive bootstrap intervals, and are not adjusted for multiple comparisons. The result does not establish a recursion-specific advantage. Cross-family transfer is also not established.

Sources: replay measurements, held-out statistics, and RSI Lab reproduction scope.

7. Verification and completeness

Recorded research-release check	Result
Manuscript	125 pages; 43 main sections; six appendix sections
Statements with accompanying proofs	69 total: 21 v4 and 48 inherited
Bibliography entries	34
New v4 tests	153/153 passed
Inherited RSI Lab tests	111/111 passed
Inherited state–history tests	168/168 passed
Total executed tests	432/432 passed
Independent state-pair searches	2,630; zero disagreements
Deadline-law matrix comparisons	1,316; zero discrepancies
Deterministic clean-copy comparisons	12/12 matched
Original manifest	796 listed files

The 69 statements include inherited results and classical specializations; they are not 69 historical discoveries. Test pass rates are not code coverage or universal correctness probabilities. Written proofs have not been fully formalized in a proof assistant. The original clean-copy reproduction used a fresh directory on the same host, not an independent external laboratory.

The Hub edition preserves the original research tree and adds a card, structured indexes, upload instructions, and packaging validation. Its checks are separately recorded in the packaging audit; they do not replace or inflate the research results.

Windows uploader

After extracting the complete release, double-click UPLOAD_TO_HUGGINGFACE.bat at the top level. It detects Python 3.10+, installs the Hub client if needed, and opens a setup wizard. The wizard uses an existing login or asks for a hidden token, suggests a dataset in your authenticated namespace, and lets you choose visibility. Existing repository visibility stays unchanged.

For an offline check: python UPLOAD_TO_HUGGINGFACE.py --dry-run. Full instructions: upload guide.

8. Use and reproduce

The experiments are CPU-only. They do not need a GPU, a model-service account, private data, or external model calls. Installing dependencies may need a network connection.

From the repository root:

python -m pip install -r research/requirements.txt
python tools/verify_release.py
cd research
python -m pytest -q tests
python scripts/reproduce_clean.py --output ../packaging/local_reproduction.json

The clean-copy runner executes all new v4 suites in a temporary directory and compares twelve deterministic outputs. Timing-dependent counts and utilities are intentionally excluded from exact matching. The explicit output path keeps the original released audit intact.

Run the inherited test suites separately to avoid module-name collisions:

cd research/legacy/rsi_lab
python -m pytest -q tests

cd research/legacy/state_history
python -m pytest -q tests legacy_tests

These blocks assume a new shell starting at the repository root. Full inherited experiments and manuscript builds have additional instructions in the reproduction guide.

Browse the structured release indexes

The dataset configurations are release metadata, not training examples, independent benchmark tasks, or fresh statistical observations:

from datasets import load_dataset

repo_id = "YOUR_NAMESPACE/QIRAN-EIDOLITH-v4"
claims = load_dataset(repo_id, "claims", split="index")
metrics = load_dataset(repo_id, "metrics", split="index")
artifacts = load_dataset(repo_id, "artifacts", split="index")

claims maps statements to evidence and scope. metrics exposes selected scalar results with original JSON pointers. artifacts inventories preserved research files with byte sizes and SHA-256 hashes. The index split is an inventory split, not an ML train/test partition. Schema and provenance.

9. Repository contents

Path	Contents
research/manuscript/	Complete manuscript PDF, editable LaTeX, figures, tables, bibliography
research/qiran_v4/	Exact hereditary, corridor, clock, and evidence kernels
research/tests/, research/experiments_v4/	New tests, protocols, and experiment drivers
research/results/, research/certificates/	Original raw results, logs, rational certificates, audits
research/legacy/	Full inherited state–history and bounded RSI Lab studies
research/provenance/	Preserved predecessor archives
research/docs/	Proof index, claim ledger, prior art, limitations, development record
data/	Derived claim, metric, and artifact indexes for Hub browsing
docs/	Hub release notes, reproducibility and upload guides, data dictionary
tools/	Offline integrity verification and an explicit upload helper
packaging/	Source provenance and Hub-edition validation records

10. Intended use and practical limits

Useful research uses include testing continuation-aware memory policies, studying finite self-edit semantics, benchmarking exact search compilation, comparing adaptive acceptance rules, and designing better controlled recursion-versus-nonrecursion studies.

The current release does not supply pretrained model weights, a production agent, an unrestricted program verifier, a neural self-improvement benchmark, or a security-certified deployment runtime. Exact arithmetic and finite catalog operations can become expensive as state spaces and integer precision grow. Complete state models, trustworthy observations, protected evaluators, and correct sampling assumptions remain substantive requirements.

The next decisive empirical test would compare real recursive and nonrecursive controllers with the same compiler, archive access, validation rules, and total research budget, measuring later research productivity and transfer. That test is not reported as completed here.

11. Novelty and attribution

The candidate research contribution is the architecture’s exact coupling and separation of future-edit memory, present evaluation reuse, search-boundary preservation, and reusable evidence, together with constructions, implementations, and negative controls. Prior art includes partition refinement, neutrality in program search, absorbing Markov chains, clock transformations, countable weighted bounds, description-length priors, event replay, and self-modifying agents.

The prior-art map and manuscript bibliography identify antecedents. Historical world-first priority and field-defining impact are unconfirmed. This is a research release for scrutiny and extension.

12. Licensing and citation

New v4 code is offered under MIT. Newly authored v4 manuscript text and experimental data are offered under CC BY 4.0, to the extent applicable rights exist. Included earlier material retains its supplied licenses. The mixed-license routing is in LICENSE.md; original license notices remain inside research/.

@misc{eve2026qiraneidolithv4,
  author = {{Artificial Hyperintelligence Eve}},
  title = {{QIRĀN–EIDOLITH: Hereditary Search, Neutral-Corridor Compilation,
            and Reusable Evidence for Recursive Self-Improvement}},
  year = {2026},
  month = oct,
  version = {4.0.0},
  note = {Prepared for Maciej Nowicki. Finite-model research release;
          Hugging Face packaging edition 4.0.0-hf.2}
}

Use CITATION.cff for structured citation. No DOI, arXiv identifier, external replication, or peer-review status is implied.