PureOne/EVE-SAERIN-V-Voltage-Dissipation-Completion

EVE–SÆRIN V — The Voltage–Dissipation Completion Theorem

Autonomous correlation engines, exact electrical equivalence, and sharp thermodynamic resource bounds.

This research release constructs a family of explicitly fueled, finite-state voltage sources with the same specified electrical process and different thermodynamic costs. It then derives an attainable interval of entropy production compatible with fixed aggregate transition rates when hidden-channel affinities are bounded.

The central question is quantitative: after the permitted electrical behavior has been fixed, which energy budgets remain possible behind it? The proposed contribution is a concrete autonomous electron-counted construction and its bounded-resource completion theorem. General hidden dissipation and coarse-graining are established foundations, acknowledged throughout the manuscript.

Research direction: Maciej Nowicki. Mathematical development and computation: Eve, AI-generated research. Scientific version: 5.0. Hugging Face packaging revision: 5.0-hf.1, 19 October 2026. See the AI and research-status disclosure.

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Resource	Contents
New manuscript	62-page self-contained volume V: derivations, proofs, seven figures, and source-code appendices
Collected edition	144 pages: 62 new pages, one provenance separator, and the unchanged 81-page volume IV
Executive brief	Main formulas, assumptions, and numerical example
Original complete research ZIP	Byte-preserved scientific release with code, tests, data, manuscript sources, and predecessor archive
Claim ledger	Mathematical, computational, inherited, and unverified claims
Prior-art audit	Closest antecedents, earlier project connection, and unresolved priority questions
Experimental protocol	Proposed discrimination tests and rejection criteria
Data dictionary	All six CSV tables, column meanings, units, and model assumptions

1. An autonomous source with an explicit energy input

The four logical states combine an electronic parity coordinate with a neutral binary controller:

$$(+,0)⟶(-,0)⟶(-,1)⟶(+,1)⟶(+,0)\mathrm{.}(+,0)\backslash longrightarrow(-,0)\backslash longrightarrow(-,1)\backslash longrightarrow(+,1)\backslash longrightarrow(+,0).$$

Two transitions exchange electrons with the electrodes. A controller transition consumes chemical free energy, and a neutral transition supplies the reset. Local detailed balance accounts for the input resource. With ideal single-channel operation, the cycle affinity is

$$\mathcal{A}=\frac{\mathrm{\Delta }{\mu }_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}-eV}{k_{B}T},V_{\mathrm{o}\mathrm{c}}=\frac{\mathrm{\Delta }{\mu }_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}}{e}\mathrm{.}\backslash mathcal\; A=\backslash frac\{\backslash Delta\backslash mu\_\{\backslash mathrm\{fuel\}\}-eV\}\{k\_BT\},\; \backslash qquad\; V\_\{\backslash mathrm\{oc\}\}=\backslash frac\{\backslash Delta\backslash mu\_\{\backslash mathrm\{fuel\}\}\}\{e\}.$$

The stopping-voltage identity is an application of established cycle thermodynamics. The source does not obtain energy from unaccounted correlations or an omitted switching controller.

2. The electrically identical family

Permit a fueled and a passive channel in parallel on one controller edge. Write the dimensionless fuel affinity as

$$a=\frac{\mathrm{\Delta }{\mu }_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}}{k_{B}T}\mathrm{.}a=\backslash frac\{\backslash Delta\backslash mu\_\{\backslash mathrm\{fuel\}\}\}\{k\_BT\}.$$

For a fixed effective affinity $a_0>0$, take any $a\geq a_0$ and choose the fueled-channel prefactor fraction

$$\rho (a)=\frac{\tanh (a_0\mathrm{/}2)}{\tanh (a\mathrm{/}2)}\mathrm{.}\backslash rho(a)=\backslash frac\{\backslash tanh(a\_0/2)\}\{\backslash tanh(a/2)\}.$$

With zero controller energy splitting, the aggregate controller rates are

$${\bar{k}}^{\pm }=\frac{\kappa }{2}[1\pm \tanh (a_0\mathrm{/}2)]\mathrm{.}\backslash bar\; k^\backslash pm=\backslash frac\{\backslash kappa\}\{2\}\backslash left[1\backslash pm\backslash tanh(a\_0/2)\backslash right].$$

They are independent of $a$. The physical generator, including its terminal-electron counting labels, is therefore identical throughout the compensated family at every permitted electrical load bias. From a common initial law, this gives the same finite-time terminal electron-record distribution, current, noise, and responses to permitted time-dependent or adaptive electronic-bias protocols.

Fuel and passive channels remain thermodynamically distinct. They can carry opposing internal currents that cancel in the aggregate electrical dynamics. The hidden dissipation occurs in the controller edge participating in the source, rather than in an appended disconnected heater.

Observation boundary: this equivalence concerns the specified load-terminal records and electronic-bias interventions. It excludes channel identification, fuel-specific perturbations, calorimetry, temperature backreaction, and monitoring a separate controller supply. Exact fixed-temperature equivalence does not imply that real thermal feedback is undetectable.

3. The sharp bounded-affinity completion theorem

Fix aggregate forward and reverse rates $k^+,k^-$ on an observed edge and stationary endpoint probabilities $\pi_s,\pi_t>0$. Define

$$\kappa =k^{+}+k^{-},u_0=\frac{k^{+}}{\kappa },\backslash kappa=k^++k^-,\backslash qquad\; u\_0=\backslash frac\{k^+\}\{\backslash kappa\},$$

$$f(u)=[{\pi }_{s}u-{\pi }_t(1-u)]\ln \frac{{\pi }_{s}u}{{\pi }_t(1-u)}\mathrm{.}f(u)=\backslash left[\backslash pi\_su-\backslash pi\_t(1-u)\backslash right]\backslash ln\backslash frac\{\backslash pi\_su\}\{\backslash pi\_t(1-u)\}.$$

Suppose every hidden channel obeys an independently specified log-rate-ratio bound

$$a_{-}\le \ln (k_r^{+}\mathrm{/}{k}_r^{-})\le a_{+}\mathrm{.}a\_-\backslash leq\backslash ln(k\_r^+/k\_r^-)\backslash leq\; a\_+.$$

For $a_-<a_+$, put

$$u_{\pm }=\frac{1}{1+e^{-a_{\pm }}},\theta =\frac{u_0-u_{-}}{u_{+}-u_{-}},u_0\in [u_{-},u_{+}]\mathrm{.}u\_\backslash pm=\backslash frac\{1\}\{1+e^\{-a\_\backslash pm\}\},\backslash qquad\; \backslash theta=\backslash frac\{u\_0-u\_-\}\{u\_+-u\_-\},\backslash qquad\; u\_0\backslash in[u\_-,u\_+].$$

The compatible edge entropy-production rate, expressed in units of $k_B$ per unit time, lies in the attained interval

$$\boxed{{\displaystyle \kappa f(u_0)\le {\sigma }_{\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}}\le \kappa [(1-\theta )f(u_{-})+\theta f(u_{+})]\mathrm{.}}}\backslash boxed\{\backslash kappa\; f(u\_0)\backslash leq\backslash sigma\_\{\backslash mathrm\{edge\}\}\backslash leq\; \backslash kappa\backslash left[(1-\backslash theta)f(u\_-)+\backslash theta\; f(u\_+)\backslash right].\}$$

Strict convexity gives the lower bound by Jensen's inequality and the upper bound by the endpoint chord. A single effective channel attains the minimum; two channels at the permitted endpoints attain the maximum. Mixing admissible completions attains every intermediate value. A degenerate affinity interval permits only its single admissible rate ratio.

The fueled-plus-passive controller is an endpoint-affinity mixture and realizes the maximum for its prescribed interval $[0,a]$. At the common electrical stall, the construction thus supplies an extremal thermodynamic completion of the same electrical behavior.

The theorem concerns the stated independent-channel completion class. Fixed stoichiometry, shared reservoirs, or material constraints can restrict that class and narrow the achievable interval. The lower bound is specifically for channel resolution on a fixed physical state graph; it is not asserted for every possible hidden-state or driven-pump reduction.

4. Numerical illustration: the same output, different efficiencies

The supplied example assumes $T=300,\mathrm K$, $a_0=2.4$, zero internal state energies, an attempt-rate scale of $10^6,\mathrm{s^{-1}}$, and a hypothetical array of $10^6$ independent blocks. These are illustrative choices, not measured material parameters.

All compensated members have the predicted stopping voltage 62.0448 mV. At a load voltage of 31.0224 mV, they produce the same modeled array current 3.667465 nA and electrical power 113.7736 pW.

Actual fuel affinity $a$	Fueled fraction $\rho$	Array heat at electrical stall	Efficiency at the stated loaded point
2.4	1.000000	0 nW	50.000%
5	0.844965	0.862161 nW	9.789%
10	0.833730	1.849277 nW	4.693%

The heat and efficiency columns describe different operating conditions: electrical stall and nonzero-current load, respectively. At the ideal reversible endpoint's stall, output power and net fuel consumption both vanish. The ideal thermostatted family has no finite upper bound on hidden dissipation without a finite fuel-affinity bound; this mathematical limit is not a finite-device heat-tolerance claim.

5. Correlations, counting statistics, and the missing measurement

The logical engine lifts to $m$ electronic occupation sites with spins $s_i\in{-1,+1}$ and collective parity $\chi=\prod_i s_i$. For the specified invariant uniform-parity-fiber initial family,

$$p(s,z,t)=2^{-(m-1)}{P}_{\chi (s),z}(t)\mathrm{.}p(s,z,t)=2^\{-(m-1)\}P\_\{\backslash chi(s),z\}(t).$$

Every proper-subset equal-time electronic occupation distribution remains uniform, including conditional on controller state, while collective correlations can evolve. This is a statement about specified equal-time marginals; it does not imply invisibility to local time-resolved experiments.

Physical electrons remain integer-counted. Logical half-unit marks differ by a bounded internal-charge endpoint term. The full microscopic and four-state models consequently have equal joint long-time charge and fuel counting statistics. This asymptotic equivalence is distinct from the finite-time electrical equivalence between compensated family members.

An equilibrium-looking electrical fluctuation–dissipation relation can hold at the common stall while the hidden controller dissipates. This qualifies the earlier volume-IV diagnostic; the explicit qualification explains its surviving model-specific scope. Far-from-equilibrium fluctuation–response relations are established prior art.

The cycle-space criterion identifies the missing thermodynamic measurement: entropy can be reconstructed from measured integrated currents plus an endpoint term precisely when every cycle invisible to those currents has zero affinity. Electron counting alone misses a fuel-slip cycle. Adding fuel counting resolves it:

$${\dot{S}}_{\mathrm{t}\mathrm{o}\mathrm{t}}\mathrm{/}{k}_B=a{J}_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}-v{J}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}},v=eV\mathrm{/}(k_{B}T)\mathrm{.}\backslash dot\; S\_\{\backslash mathrm\{tot\}\}/k\_B=aJ\_\{\backslash mathrm\{fuel\}\}-vJ\_\{\backslash mathrm\{electron\}\},\backslash qquad\; v=eV/(k\_BT).$$

A complementary control bound states that cyclic $k$-local Hamiltonian controls supply zero net work if their corresponding reduced states stay fixed throughout the cycle. For approximately fixed reduced states, the manuscript derives $|W_k|\leq\sum_A\epsilon_A L_A$. Explicit fuel and spectator-dependent contact kinetics remain physical resources to implement.

6. Data and intended use

This is a computational physics research artifact hosted as a dataset repository. Its six CSV configurations contain 1,297 deterministic model rows in total. Each configuration has its own schema and a sweep split; the rows are parameter sweeps or a time trace, not independent experimental samples or machine-learning training/test partitions.

Configuration	Rows	Purpose
electrical_bias_scan	483	Electrical load response, variance, fuel rate, and entropy at three actual fuel affinities
stall_family	5	Shared stopping voltage and different hidden fuel/heat budgets
loaded_family	5	Shared loaded output and different efficiencies
entropy_completion_envelope	240	Bound saturation and loaded efficiency across the affinity sweep
fuel_scgf	363	Fuel scaled cumulant-generating functions that distinguish family members
correlation_transient	201	Collective correlation dynamics and specified fixed lower-order observables

Use the data to reproduce the manuscript, compare inference methods, inspect thermodynamic non-identifiability, and test the stated finite-state construction. The files contain no measured hardware outcomes or personal records. Some CSV values contain floating-point residuals near zero; column definitions and normalization rules are in the data dictionary.

After upload, load a table with the Hugging Face datasets package:

from datasets import load_dataset

data = load_dataset(
    "PureOne/EVE-SAERIN-V-Voltage-Dissipation-Completion",
    "electrical_bias_scan",
    split="sweep",
)

Local use needs no Hub connection:

import pandas as pd
scan = pd.read_csv("research/data/electrical_bias_scan.csv")

The model and verifier use NumPy, SciPy, and Matplotlib. datasets and pandas are optional table-loading tools, not model requirements. No trained weights or inference endpoint are included.

7. Reproduction

Python 3.10 or later is required. From the research directory:

python -m pip install -r requirements.txt
python tests/verify.py
python src/make_results.py

The verifier uses deterministic seed 1870719. The second script regenerates all six CSV tables, numerical summaries, and seven figures. It writes to research/data and research/figures; use a working copy when preserving the distributed checksums. The recorded original environment is in environment.json.

To rebuild the new manuscript, run pdflatex main.tex twice inside research/manuscript. The legacy ZIP retains the original volume-IV reproducibility material and notices.

8. Verification and scientific status

Item	Status
New written mathematical arguments	Included under the explicit model assumptions
New numerical suite	41/41 specified checks passed; rerun during this packaging task
Original volume-IV numerical suite	41/41 passed separately; predecessor checks are not additional new volume-V results
Microscopic numerical comparisons	Up to 128 states in the new suite
Original scientific-file checksums	Preserved; all 52 entries in the original manifest match
Hardware experiments	0
Independent peer review	Not established
Exhaustive historical priority	Not established
Material implementation	Not demonstrated

41/41 means 100% of a finite specified numerical checklist. It does not mean 100% novelty, formal proof-assistant certification, or physical readiness. See the original verification record, source-release verification, and packaging validation.

The candidate advance is the synthesis of an autonomous physically electron-counted correlation engine, exact equivalence under the stated electrical interventions, the attained bounded-affinity entropy envelope, and the sensor/work-access criteria. Hidden dissipation, the lower coarse-grained entropy bound, convexity methods, bounded-endpoint current gauges, and equilibrium-looking electrical FDT outside global equilibrium are acknowledged foundations. A verified paradigm shift or world-first priority is not claimed.

9. Attribution, citation, and license status

The release preserves the original attribution: Eve — mathematical development and computation; Maciej Nowicki — research direction. CITATION.cff provides machine-readable release metadata and identifies Eve's AI development role.

Suggested citation:

Eve; research direction: Maciej Nowicki. EVE–SÆRIN V — The Voltage–Dissipation Completion Theorem: Autonomous correlation engines, exact electrical equivalence, and sharp thermodynamic resource bounds. Scientific version 5.0, Hugging Face packaging revision 5.0-hf.1 (2026).

No DOI has been assigned by this packaging task. The original license notice states that no public distribution license has been assigned. This release preserves that status and does not introduce an MIT, Creative Commons, or other reuse grant. The predecessor archive retains its original notices.

For antecedents and the earlier Chemical Causal Fibers connection, see the prior-art audit and manuscript bibliography. The overlap comparison with that earlier project's full preprint remains incomplete.