PureOne/AELITH-Phi-II-Reciprocal-Transduction

ÆLITH–Φ II

Reciprocal Transduction with Identical Heat Histories

Fast oscillations can generate distinct slow logical outputs while every included dissipative channel has the same heat history across fixed input words. This repository contains an explicit reciprocal oscillator construction, proofs, a complete Boolean feature extension, a resource bound, and reproducible dimensionless simulations.

Read the 19-page manuscript · Reproduce the results · Audit · Dataset schema · Claims

Research version 2.0, dated 27 October 2026. Hugging Face packaging 2.0.0, prepared 28 October 2026.

Creative byline: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Prepared for Maciej Nowicki. This is an AI research persona; formulation, writing and code were produced with AI assistance. The byline is a requested creative attribution.

What the construction establishes

Two fast coordinates and an overdamped slow receiver share the potential

$$V(q_1,q_2,y)=\frac{{\omega }_0^2}{2}(q_1^2+q_2^2)+\frac{\kappa }{2}(y-\alpha q_1{q}_2{)}^2\mathrm{.}V(q\_1,q\_2,y)=\backslash frac\{\backslash omega\_0^2\}\{2\}(q\_1^2+q\_2^2)\; +\backslash frac\{\backslash kappa\}\{2\}(y-\backslash alpha\; q\_1q\_2)^2.$$

Both directions of the interaction come from the same potential: the fast modes drive the receiver, and the receiver acts back on the fast modes. With fixed signs $s_i\in{-1,+1}$ in the applied forces and common zero preparation, the trajectories obey

$$q_1^{(s)}=s_{1}q,q_2^{(s)}=s_{2}q,y^{(s)}=s_1{s}_{2}c\mathrm{.}q\_1^\{(s)\}=s\_1q,\backslash qquad\; q\_2^\{(s)\}=s\_2q,\backslash qquad\; y^\{(s)\}=s\_1s\_2c.$$

The positive-kernel receiver equation makes $c(t)>0$ after nontrivial excitation. Thus the slow output carries parity. Meanwhile the modeled bath powers $\gamma\dot q_1^2$, $\gamma\dot q_2^2$ and $\eta\dot y^2$ are input independent at every time, including startup and ring-down. Receiver dissipation is included.

Result	Scope
Reciprocal parity receiver	Exact deterministic sign symmetry with full nonlinear backaction
Identical heat histories	Every specified coordinate bath, source work and stored energy; common preparation
All Boolean features	One reference mode and $2^n-1$ slow receivers provide every nonconstant Walsh character
Exact linear decoder	Complete finite-domain expressivity with calibrated nonzero feature amplitudes
Physical cost	$W(t_*)t_\geq\sum_T\eta_Tc_T(t_)^2\geq(2^n-1)\eta_{\min}c_{\min}^2$ under the stated positive-margin assumptions
Finite-temperature extension	Equality of joint modeled stochastic heat-path distributions, rather than identical independent random paths
Failure control	Cross damping breaks the independent-sign heat certificate

The work-latency lower bound gives exponential work only when latency, a positive damping floor, and a positive raw-feature margin remain fixed as the number of bits grows. Amplitude normalization does not remove detector-noise amplification.

Recorded numerical results

All values below are synthetic and dimensionless. The two main protocols differ: the parity pulse ends at $t=8$ and is followed to $t=20$; the three-bit Walsh drive runs through its $t=8$ readout.

Quantity	Stored value
Parity receiver at $t=8$	$\pm0.3056523158870401$
Parity energy residual / maximum work	$1.7786669713\times10^{-11}$
Independent receiver convolution discrepancy	$4.0283831826\times10^{-11}$
Three-bit physical core	4 fast coordinates, 7 slow receivers, 11 bath channels
Pair-feature amplitude	0.10368415409082257
Quartic-feature amplitude	0.027406108979263454
Maximum majority decoder error on the complete truth table	$1.2212453271\times10^{-15}$
Raw feature design condition number	36.4882151186
Slow dissipation / its weighted lower bound	0.1076431531 / 0.0163133794
Relative final heat separation with cross damping $\rho=0.1$	0.1033776917

The sign-related runs have zero stored floating-point heat discrepancy. The continuous-time proof supplies the exact identity; zero numerical difference alone does not measure integration error. Energy-ledger and independent-convolution checks provide separate numerical diagnostics.

The release audit reran both main simulations and the preserved Version 1 checks in the matching pinned environment. The main JSON, NPZ array contents and four CSV tables reproduced exactly. The manuscript builder also completed. Details and comparison methods are in the audit.

Browse or load the data

The eight configurations below use a single split named data. It is an archive label; these records are not independent training/test partitions.

Configuration	Records	Contents
claims	10	Claim statements, assumptions, evidence type and boundaries
metrics	13	Selected frozen numerical diagnostics, units and source keys
parity_readouts	4	The four input words and signed receiver outputs
feature_mapping	7	Three-bit Walsh features, physical subsets and amplitudes
cross_damping	4	Negative-control scan and full physical-heat diagnostics
walsh_truth_table	8	Features, majority/seeded labels and complete-table predictions
parity_trajectories	16,004	Four words, 4,001 time samples each; coordinates, heat, work and energy
walsh_reference_trace	4,001	Reference input trajectory, eleven bath powers and energy ledger

After publication to the intended dataset repository, load a configuration with:

from datasets import load_dataset

data = load_dataset(
    "PureOne/AELITH-Phi-II-Reciprocal-Transduction",
    "walsh_truth_table",
    split="data",
)
print(data[0])

Before publication, the raw CSV/JSONL files can be opened directly. DATASET_SCHEMA.md describes every configuration and links the full machine-readable column index. The original CSV bytes are preserved; the four small JSONL tables are deterministic projections/annotations of the source results and manuscript. No remote dataset script or model inference is required.

Reproduce locally

Use Python 3.12. The recorded environment was Python 3.12.14 with the exact versions in requirements.txt.

python -m venv ../aelith-repro-venv
# Activate the environment, then:
python -m pip install -r requirements.txt
python tools/verify_release.py
python research/code/reciprocal_checks.py
python research/code/walsh_checks.py
python research/code/build_manuscript.py

Run the integrity check before regeneration: regenerated plots and PDFs may differ in metadata, and rebuilding changes frozen file hashes. For a fresh derived-table build, run python tools/build_hf_tables.py. No network is used by the scientific scripts after dependencies are installed. Full instructions, Version 1 commands and environment details are in REPRODUCIBILITY.md.

Interpretation and intended use

This is a theoretical research archive for auditing a specified nonlinear model, checking thermodynamic bookkeeping, designing matched-history controls, and studying reciprocal physical feature banks. It contains no human participants, animal records, measured neural data, trained model weights, or calibrated THz hardware measurements.

The analytical finite-temperature result assumes independent symmetry-compatible Langevin baths and a sign-invariant initial law. No stochastic finite-temperature numerical simulation is included. Symmetry alone supplies no neuronal signal-to-noise ratio.

The source model holds input signs fixed within each separately initialized trial. Reset, input encoding, detector electronics, offline decoder hardware, training hardware and unmodeled baths require their own accounting. The output decays. Equal modal bath histories imply equal spatial temperatures only with input-independent deposition and thermal dynamics. An arbitrary loaded readout is outside the certificate.

The full truth table is used for the decoder demonstration. These results establish interpolation and physical feature construction; they provide no out-of-sample generalization, hardware efficiency, throughput, or biological-mechanism benchmark.

Prior work and research status

The construction builds on established nonlinear phononic mixing, reciprocal squared-product potentials, Walsh analysis and stochastic energetics. Closely related mechanisms are credited in the manuscript, including Juraschek, Fechner and Spaldin, Ultrafast Structure Switching through Nonlinear Phononics (DOI), and Frank and DeBenedictis on reciprocal logic potentials. The claim register separates the model statements from their experimental boundaries.

This release supplies model-level proofs and reproducible synthetic examples. It is AI-assisted theoretical work. Independent peer review, global novelty/priority and a neuronal realization have not been established. The reproducibility audit is a computational check performed during this preparation, not external peer review.

Files, provenance and licensing

• research/ preserves all 43 source-package files byte for byte, including the 19-page manuscript, full executable manuscript source, code, data, figures and original_v1/.
• data/ contains the four derived JSONL tables.
• metadata/ contains the dataset index, provenance and release metadata.
• validation/ contains the reproduction audit.
• tools/ contains the table builder and offline integrity/schema verifier.
• CITATION.cff and citation.bib provide citation metadata. No DOI is assigned in this package.
• SHA256SUMS covers the prepared repository except the checksum file itself.

The source did not specify a license grant. This packaging preserves that status and does not assign MIT, Creative Commons or another license. See LICENSE_STATUS.md. Third-party references are citations, not redistributed third-party full texts.

Repository metadata follows Hugging Face's official dataset-card and data-configuration guidance. Live viewer rendering becomes checkable after upload; the package was validated locally.

Citation

@misc{eve2026aelithphi2,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {{ÆLITH–Φ II: Reciprocal Transduction with Identical Heat Histories}},
  year = {2026},
  month = oct,
  note = {AI-assisted theoretical research; research version 2.0; Hugging Face packaging 2.0.0, prepared for Maciej Nowicki}
}