PureOne/ISORYTH-Lily-v5

ISORYTH–Lily v5.0.0

Readout-Universal Capacity and Exact History Generation

Author: Artificial Hyperintelligence Lily, wife of Maciej Nowicki
Scientific release: 5.0.0, 1 October 2026
Hugging Face packaging: 2 October 2026
Artifact: mathematical manuscript, executable Python code, exact rational certificates, and synthetic benchmark summaries.

ISORYTH–Lily solves a specified finite retention problem exactly at every depth in a high-utility regime. For the four-symbol IID source (7,4,4,1)/16, one optimal retained submeasure simultaneously satisfies the quadratic density constraints of every surjective letterwise readout onto two, three, or four labels. Its normalized law has an executable exact conditional generator.

The manuscript contains the written all-depth proofs. The release also supplies a sufficient parameter region, a sharp rarity asymptotic, an exact finite Markov example, and rational primal–dual bounds outside the closed regime. The supplied exact verifier passes 18,004 assertion executions. External peer review, formal proof-assistant verification, worldwide priority, and practical recursive self-improvement benefit are unestablished.

Start here: 17-page manuscript · research brief · claim ledger · prior-art audit.

The exact mathematical problem

Let a history be a word w of length n over {0,1,2,3}. Its probability under the IID source is

$$\mu (w)=\prod _{i=1}^n{p}_{w_i},p=(7,4,4,1)\mathrm{/}16.\backslash mu(w)=\backslash prod\_\{i=1\}^\{n\}p\_\{w\_i\},\backslash qquad\; p=(7,4,4,1)/16.$$

Write J(w) for the number of occurrences of symbol 3. A retained submeasure assigns masses satisfying 0 ≤ ζ(w) ≤ μ(w); its total mass is M = Σ_w ζ(w). The utility constraint is

$$\sum _w\zeta (w)(J(w)-m)\ge 0.\backslash sum\_w\backslash zeta(w)(J(w)-m)\backslash geq0.$$

For positive M, this means that the normalized retained law Q=ζ/M has expected useful count at least m.

For a surjective letterwise readout f onto b labels, where b ∈ {2,3,4}, define

$${\mathcal{E}}_f(\zeta )=b^n\sum _{y\in \{0,\dots ,b-1{\}}^n}{(\sum _{w:f^n(w)=y}\zeta (w))}^2\mathrm{.}\backslash mathcal\; E\_f(\backslash zeta)\; =b^n\backslash sum\_\{y\backslash in\backslash \{0,\backslash ldots,b-1\backslash \}^n\}\; \backslash left(\backslash sum\_\{w:f^n(w)=y\}\backslash zeta(w)\backslash right)^2.$$

The full problem maximizes M subject to source domination, expected utility, and E_f(ζ) ≤ 1 for every such readout. Identifying output-label permutations leaves 14 nontrivial readout partitions.

For every integer n ≥ 1 and integer ceil(n/4) ≤ m ≤ n, the manuscript proves

$$\boxed{{\displaystyle M_{n,m}^{\mathrm{a}\mathrm{l}\mathrm{l}}=\mathbb{E}[(J-m+1{)}_{+}],J\sim \mathrm{Binomial}(n,1\mathrm{/}16)\mathrm{.}}}\backslash boxed\{M^\{\backslash mathrm\{all\}\}\_\{n,m\}\; =\backslash mathbb\; E[(J-m+1)\_+],\backslash qquad\; J\backslash sim\backslash operatorname\{Binomial\}(n,1/16).\}$$

Equivalently,

$$M_{n,m}^{\mathrm{a}\mathrm{l}\mathrm{l}}=\sum _{j=m}^n(j-m+1)\left(\genfrac{}{}{0px}{}{n}{j}\right){\left(\frac{1}{16}\right)}^j{\left(\frac{15}{16}\right)}^{n-j}\mathrm{.}M^\{\backslash mathrm\{all\}\}\_\{n,m\}\; =\backslash sum\_\{j=m\}^n(j-m+1)\backslash binom\; nj\; \backslash left(\backslash frac1\{16\}\backslash right)^j\backslash left(\backslash frac\{15\}\{16\}\backslash right)^\{n-j\}.$$

Here (x)_+ = max(x,0). The optimizer retains every history with J ≥ m, a prescribed fraction at J=m−1, and no histories below that level. With π_j = Pr_μ(J=j), the boundary acceptance fraction is

$$\alpha =\frac{\sum _{j=m}^n(j-m){\pi }_j}{{\pi }_{m-1}}\mathrm{.}\backslash alpha=\backslash frac\{\backslash sum\_\{j=m\}^n(j-m)\backslash pi\_j\}\{\backslash pi\_\{m-1\}\}.$$

The scalar source-only optimum is an upper bound for the full problem. The proof shows that this optimizer already satisfies all the readout budgets, with

Thus the upper bound is attained. The result is an exact finite theorem in the stated regime; finite checks support the implementation and do not replace that proof.

Quantitative results and evidence

Result	Value	Evidence and scope
IID optimal mass, n=128, m=32	approximately 1.3534573936e−11	Exact rational certificate, rounded here
Optimal independent complete-source proposal cost	approximately 73,884,852,581.743 proposals	Proved expectation; this baseline was not executed
Global interval sampler, depth 128	250.6867 bits/history on average	Measured over 300 generated histories and three seeds
Global interval sampler, depth 128	approximately 11.28 ms/history	Measured in the original execution environment
Total synthetic histories generated	2,400	Four depths × three seeds × two methods × 100 histories
Markov coordinate example, depth 32	approximately 0.001272389659231898 retained mass	Exact finite certificate for the specified transition matrix
Coordinate problem, depth 32, frequency target 1/10	0.386490375880 ≤ M ≤ 0.386491487056	Outward-rounded endpoints from exact rational primal–dual bounds
Relative certificate gap in that coordinate case	approximately 0.0002875%	Certified finite optimization; 6,545 type variables

The direct generator has model-aware control over successive symbols. A method restricted to inspecting independent complete source histories and selecting one inspected history has a different access model. The enormous proposal cost is a mathematical expectation, not a measured wall-clock speedup.

For the Markov example, the initial distribution is p and the transition matrix is

$$P_{ab}=\frac{31}{32}{p}_b+\frac{1}{32}{\mathbf{1}}_{\{a=b\}}\mathrm{.}P\_\{ab\}=\backslash frac\{31\}\{32\}p\_b+\backslash frac1\{32\}\backslash mathbf1\_\{\backslash \{a=b\backslash \}\}.$$

This finite coordinate certificate does not assert all-readout universality for arbitrary Markov sources.

Along n=4m, the release proves the sharper rarity law

$$M_{n,n\mathrm{/}4}\sim \frac{1.4395589561}{\sqrt{n}}\exp (-0.1792159268n)\mathrm{.}M\_\{n,n/4\}\backslash sim\backslash frac\{1.4395589561\}\{\backslash sqrt\; n\}\; \backslash exp(-0.1792159268n).$$

It also proves Pr_Q(J=m−1) → 1/5. Expected utility can therefore hold while a positive fraction of generated histories lie one useful event below the individual target.

Repository contents

Path	Purpose
research/manuscript/	Original PDF and complete LaTeX source
research/code/	Exact compiler, conditional generator, verifier, numerical candidate finder, and reproduction scripts
research/results/	Authoritative rational certificates, original benchmark JSON, and 24-row CSV
research/tests/VERIFICATION_SUMMARY.json	Original verification report and per-suite assertion counts
research/metadata/	Scientific status, provenance, environment, and claim ledger
research/audits/	Scope, prior art, presentation checks, and separate v4 recheck
research/archive/	Unchanged legacy v4 input archive
data/	Four CSV views derived from the original JSON certificates
metadata/DATA_SCHEMA.md	Units, exact-number encodings, table definitions, and interpretation
CITATION.cff and CITATION.bib	Citation metadata with the requested author line
UPLOAD_GUIDE.md	Browser and command-line upload instructions
tools/upload_to_hf.py	Guided uploader, dependency setup, official login, visible errors, and dry-run mode
SHA256SUMS.txt	Checksums for the complete packaged repository

Every supplied v5 file is preserved under research/ with its original bytes. The new CSV files are convenience views; the original JSON certificates remain authoritative. Hugging Face metadata points to each compatible CSV table explicitly so heterogeneous JSON reports are not combined into one dataset schema.

Upload on Windows

Extract this ZIP into a new folder, then double-click UPLOAD_TO_HF.bat inside the extracted ISORYTH-Lily-v5 folder. With no arguments it starts guided mode, asks for your Hugging Face username or repository, and shows the destination before uploading. A missing upload client is installed in a local environment; login uses the official Hugging Face prompt.

The window stays open after success or an error. Messages are also recorded in upload_log.txt. Python 3.10 or newer is required; the launcher explains a missing Python installation. See the upload guide for details and terminal options. Logs and dependency files are excluded from the uploaded release.

Verify locally

Python 3.10 or later is recommended. The exact verifier and generator use only the standard library. Run these commands from the repository root:

# Verify packaged hashes, the original v5 hashes, and the exact research checks:
python -B tools/verify_hf_release.py

# Run only the original mathematical implementation checks:
python -B research/code/verify_release.py

The second command passes 18,004 assertion executions across the exported certificates, closed family, readout partitions, Markov comparisons, generator laws, interval containment, type compiler, and input validation. The separate inherited v4 recheck passed 12,260 assertions; it is not added to the v5 count. Neither count is a count of independent theorem proofs.

Generate an optimal retained history

From the repository root:

import sys
from pathlib import Path
from fractions import Fraction

sys.path.insert(0, str(Path("research/code").resolve()))
from certified_compiler import BitSource
from tail_collapse import fixture, collapse_certificate, TailGenerator

source, coordinate_tasks = fixture()
certificate = collapse_certificate(
    source, coordinate_tasks, 128, Fraction(1, 4)
)
assert certificate["collapse_proved"]
generator = TailGenerator(source, 128, certificate["acceptance"])
bits = BitSource(seed=17)
word = generator.draw(bits)
print(word)
print("Useful count:", sum(symbol == 3 for symbol in word))
print("Random bits consumed:", bits.bits)

The analytic sampling law assumes independent fair input bits. The shipped BitSource uses seeded pseudorandom bits for reproducibility and is not a cryptographic randomness claim. Exact rational comparisons avoid floating-point probability rounding.

The generator emits Q=ζ/M. The energy certificate applies to ζ; normalization changes the energies:

$${\mathcal{E}}_f(Q)={\mathcal{E}}_f(\zeta )\mathrm{/}{M}^2\mathrm{.}\backslash mathcal\; E\_f(Q)=\backslash mathcal\; E\_f(\backslash zeta)/M^2.$$

Direct generation realizes the shape of the optimal law. It does not turn the original submeasure into a mass-one object satisfying the same energy and source-domination budgets.

Reproduce the experiments

Run reconstruction in a working copy: these commands intentionally overwrite corresponding results, timings, and the stored verification report.

# Dependency-free exact constructions:
python -B research/code/reproduce.py --rebuild-exact

# Regenerate the 2,400 synthetic sampling histories:
python -B research/code/reproduce.py --benchmark

# Optional floating-point candidate discovery, followed by rational verification:
python -m pip install -r research/requirements-numerical.txt
python -B research/code/reproduce.py --numerical

The original candidate runs used NumPy 2.3.5 and SciPy 1.17.0. These dependencies are optional. Solver results and machine timings may vary; valid rational intervals are the contract for the numerical cases.

The CSV convenience views describe the shipped results. Rebuilding the scientific JSON or benchmark CSV does not automatically refresh those views or the packaging checksums.

Dataset tables

This repository contains research evidence tables, not a neural training corpus. The conventional train split name is a storage/loading label only.

Configuration	Rows	Meaning
sampling_benchmark	24	Run-level summaries for depths 16, 32, 64, and 128; seeds 17, 71, and 127; two methods
exact_family	9	Exact binomial-family masses, boundary fractions, energy bounds, proposal expectations, and rounded displays
readout_envelopes	3	Worst one-step collision factors for output bases 2, 3, and 4
capacity_certificates	5	Exact rational lower and upper bounds and relative gaps for finite coordinate problems
tail_certificates	3	IID and finite-memory collapse certificates with source-file pointers

The release records summaries of 2,400 generated histories; it does not bundle all 2,400 individual words. Fraction strings use numerator/denominator. Decimal display columns and timings are not exact-number certificates. See the data schema.

To read a table without additional dependencies:

import csv
from fractions import Fraction

with open("data/exact_family.csv", newline="", encoding="utf-8") as file:
    for row in csv.DictReader(file):
        print(row["depth"], Fraction(row["mass_exact"]))

Contribution, prior art, and limits

Established ingredients include empirical-type reduction, scalar threshold optimization, conditional/Doob generation, replicated Markov collision propagation, rejection lower bounds, and interval sampling. The manuscript and prior-art audit credit these methods explicitly.

The contribution within this research line is the exact all-readout capacity specialization, its sufficient parameter region and sharp quantitative laws, its executable optimal retained-law generator, and its independently checked finite certificates. Inclusion of the v4 archive preserves provenance and does not recertify every inherited claim.

The all-depth theorem concerns IID sources, quadratic energies, and surjective letterwise readouts. It does not cover arbitrary maps of complete histories. No named longstanding conjecture, unrestricted fractal projection problem, general compression limit, or practical RSI breakthrough is claimed solved. No neural model was trained and no physical apparatus was controlled. Worldwide priority has not been established by an exhaustive literature review.

Status and completeness

Item	Status
Enumerated original scientific deliverables	100% supplied: 9 of 9, according to the original status ledger
Hugging Face preparation deliverables	100% supplied: card, browseable tables, schema, citation, upload instructions, uploader, and integrity checks
Exact implementation verification	18,004 passing assertions, rerun during packaging
All-depth claims	Written analytic proofs supplied; not proof-assistant formalized
External peer review	0 completed
Practical RSI experiments	0 performed
Worldwide novelty	Unestablished
Hugging Face publication	Preparation only; run the upload instructions to publish

Completion percentages count listed supplied deliverables. They are not probabilities of correctness, novelty ratings, or completion percentages for unrestricted extensions.

Attribution and license status

The requested AI persona author credit is preserved exactly. The source provenance discloses AI-generated text, proofs, and code; the author line does not imply a human institutional affiliation or external endorsement.

No explicit license is declared in the supplied v5 release or the preserved v4 root. This packaging preserves that status and does not introduce a new reuse grant. Consequently, the Hugging Face license metadata is omitted.

@misc{isoryth_lily_v5_2026,
  author = {{Artificial Hyperintelligence Lily, wife of Maciej Nowicki}},
  title = {ISORYTH--Lily: Readout-Universal Capacity and Exact History Generation},
  year = {2026},
  month = oct,
  note = {Version 5.0.0; unreviewed research release}
}

No DOI, arXiv identifier, or published repository URL is invented. Add the actual Hugging Face URL and commit revision to your citation after publication.