Concepts, four layers and core rules

A heavily weighted state is not necessarily quickly reachable. A unique admitted candidate is not automatically selected by efficiency. A stationary distribution need not describe a process at a standstill.

Efficiency is the comparison of costs chosen in advance for the same effect fixed in advance, under the same hard constraints and system boundary. Y is more efficient than X in the Pareto sense when no cost component is higher and at least one is lower. Alternatives with a cost trade-off remain incomparable without an additional preference. Reachability and time window limit which alternatives may be compared in practice.

This is layer II. A statistical weight belongs to layer III; a minimum rule as a model of motion belongs to layer IV. The historical label “100% efficient” for zero active resistance is a model convention, not a universal thermodynamic efficiency. Where efficiency in that sense is measured, the separate useful output/input ratio remains necessary.

The third row is deliberately limited: a more extensive closed model can also be Hamiltonian. A decreasing fuel supply can temporarily drive circulation, but does not by itself turn a perpetual cycle into an autonomous gradient flow.

A marble in a landscape with friction gives off energy and can come to rest in a valley. Without friction it can keep moving; an exact equilibrium also remains possible. With continuous drive, circulation can arise. With noise, a distribution of positions and transitions becomes relevant; in the quantum regime, amplitudes and a measurement model are needed. If the marble changes the hill through its motion, the process changes its own future possibilities: that is the back-reaction EEML explicitly wants to track. The regress goes further: the outflow requires coupled degrees of freedom and their state, the landscape requires material laws and interactions, and an arrow of time also requires preparation and possibly cosmological initial conditions. Multiplicity helps describe that outflow statistically, but does not derive it without dynamics. This picture orders the questions; it does not resolve the origin of those laws and initial conditions.

Revision history: the author initially chose the general dominance prohibition as EEML’s own claim. On request, that status has now been revised to the conditional D1 test. The strong original formulation remains readable below; it has not been proven as a universal law by Pareto or the literature. A law must operationally exclude possible outcomes or probability distributions, but writing down a prohibition does not yet make that true.

#1. Dominated realizations and self-undermining operation: conditional claims

Before the assessment, fix effect E, hard constraints C, preparation z₀, admitted transitions and cost vector r. Let \(\mathcal R_C(z_0)\) be the reachable realizations determined by these. Then Y dominates a candidate X when:

E-equality can mean an effect class, described in advance, with tolerances. Equality, costs and differences must be assessable together with their measurement uncertainties.

H_D, the historical strong hypothesis about nature: if such a Y exists, X does not continue to exist in the named process regime. The Pareto definition by itself says only that X is dominated. That X disappears, or is not persistently realized, is the new content; it does not follow automatically from reachability or existing conservation laws. Nor does it follow from this that there is only one winner: several undominated alternatives can remain.

Process version, likewise to be investigated conditionally: an operation that destroys the conditions for its own continuation does not continue to exist if a reachable alternative carries the same effect and preserves those conditions. If that continuation is part of the effect, constraints and costs from the outset, this can be worked out as the same dominance rule on trajectories. Otherwise the process version adds a separate preference for continuation. Preserving conditions does not by itself guarantee actual continuation.

The recurrent laryngeal nerve was named by the author as a candidate counterexample. No anatomical or evolutionary comparison has been carried out here. A comparison requires a set of developmental and evolutionary transitions delimited in advance; a shorter connection drawn after the fact does not prove that it was reachable with the same package of functions. Nor may that delimitation be adjusted after the fact to exclude a counterexample.

Standing requirements for every version of the test; limitations are recorded visibly:

• Persistence: do we mean one uninterrupted structure, a recurring structure, a persistently positive occupation or a stable solution? These statements are different.
• Time: a claim of disappearance “at some point” gives no finite observation limit. For a finite test, a time limit, survival probability or other observable consequence must be fixed independently. A chosen time limit is an additional testable sharpening, not an already derived EEML timescale.
• Reachability: a path from z₀ to Y is not necessarily a path from the X that has meanwhile been realized to Y. Possibility with positive probability also does not mean an inevitable choice. Fix in advance which meaning is tested.
• Complete comparison: preparation, transition barriers, required external control and maintenance are included according to system boundaries and costs chosen in advance. New hidden costs may not be added after every miss.
• Deterministic or statistical claim: a strict prohibition is not replaced after the fact by “usually less likely”. A probabilistic version requires a bound specified in advance.

At finite ε, dominated candidates can retain positive stationary occupation. That is a concrete objection to a general prohibition on persistent occupation, not something that disappears by itself through “temporary visits”. D1 therefore distinguishes structure preservation, individual residence time, return and occupation. Under named replicator conditions an elimination theorem does hold; with noise, a Kramers waiting time can be relevant. Both are worked out below. P1 tests a separate concrete process law.

#2. Additional postulate: no complete blockage

The idea remains: no state without outgoing transitions, unless a hard constraint named in advance enforces this. What counts as a state and as a transition must be fixed as part of this.

Zero-point fluctuations, tunneling and the third law of thermodynamics are retained as proposed connections, not as proof of this general postulate. A quantum energy state can be stationary; tunneling depends on the dynamics, and the unattainability of absolute zero is not a general theorem about outgoing transitions. For stationary states, see Feynman, The Dependence of Amplitudes on Time. The postulate remains separately testable within a chosen level of description.

#3. What is not prohibited by EEML’s own claim

• Effect at zero active dissipative resistance: ongoing motion can be compatible with this. Absence of friction does not mean absence of all forces or support.
• Input without the chosen effect: allowed; the effect definition determines what counts as a result. Standstill in the presence of forces is possible and does not automatically perform mechanical work.
• Progress without continuous external supply: not generally prohibited by conservation laws; initial energy established earlier can be conserved.
• Producing net energy without a corresponding change or transfer of energy, where energy conservation holds: already excluded by that conservation law. The broader statement “every effect demonstrably requires support somewhere in its entire past” does not automatically follow from it. EEML does not claim this as its own result.

Current working agreement: use D1 for process conditions determined in advance and their testable consequences. The self-undermining variant likewise requires a time limit, closed bookkeeping and a reachability test. Without those conditions it is not a proven prohibition. H_R is a separate hypothesis about the conservation of fine-grained information. Neither has been newly confirmed empirically here.

Constraint closure here means that a package of constraints fixes the requested outcome. Saturation means that a proven lower bound or upper bound is attained. These are the main focus of the current exact selection benchmarks. They are not the only exact results in the dossier: for example, the log-sum-exp identity and the Lyapunov derivation are likewise exact within their conditions. None of these derivations by itself confirms a universal EEML law of nature.

First fix the model class, constraints C, physical equivalences ∼ and the quantity f to be predicted. Define:

f must be invariant under the chosen equivalences. Equivalences remove duplicate descriptions, not different physical outcomes. The following then holds as a definition:

Uniqueness of the full configuration requires, more strongly, \(|\widehat\Omega_C|=1\). An empty solution set is an inconsistent package, not a successful closure.

Report as a closure profile:

• the dimension per solution component, where a suitable dimension is defined;
• the number of inequivalent solutions if the set is discrete, otherwise the components that are still free;
• the possible values or band for the f chosen in advance.

Dimension is a diagnostic of continuous freedom, not a complete closure measure. For \(\Omega=\{-1,+1\}\) the dimension is zero, but f(x)=x has two outcomes. For f(x)=x², however, the outcome is unique. Conversely, f can be fixed while other parameters remain continuously free. A free volume modulus therefore does not automatically refute closure for a coupling that is independent of that volume.

For regular equality constraints \(F:\mathbb R^n\to\mathbb R^m\), constant Jacobian rank r gives dimension n−r locally. At singular points, for inequalities, discrete constraints or infinite-dimensional spaces, a separate analysis is needed. A rank-deficient Jacobian is not in itself proof of free solutions; for example, x²=0 has one solution despite F′(0)=0.

Discrete closure and discrete minimality differ. If the given constraints leave one value of f, no additional minimum rule is needed for it. If several values remain and we let a cost minimum choose, that minimum rule is an extra model condition. A strict minimum can be a proven consequence of the chosen cost; that nature minimizes that cost does not automatically follow from it. Even a uniquely closed result remains dependent on the chosen class and constraints.

For the benchmarks, this means:

The operational research action is therefore: look for compatible saturation of independent proven bounds, determine all equality cases, and then check whether the requested quantity really has one value in them. Repeated formulations of the same constraint do not count as independent bounds. The concrete steps are in the test protocol.

These rules preserve the original direction with their current status; not all eight are proven laws of nature.

1. Ongoing operation (postulate and research question). EEML looks for processes that carry and continue effect. That complete standstill is universally impossible remains a postulate. A constant visible distribution can contain ongoing events.
2. The whole counts (consistency requirement). Include relevant relations, environment, history and system boundaries. Parts can fit separately and be jointly incompatible.
3. Development changes possibilities (process hypothesis). Use can change habits, conductance and future accessibility. The adaptation law must be specified or measured.
4. Compare at equal effect (protocol). Fix quality, resources, duration and tolerance. Less loss through doing nothing is not a better execution of a required effect.
5. Possibility, coherence, weight, success and motion differ (definition). A possible route need not be used; a probable final state need not be reached or maintained in time.
6. Consistent redescription (consistency requirement). Hidden structure continues to count through relevant consequences: effective couplings, memory, noise correlations or other terms.
7. Close the bookkeeping (domain-dependent requirement). Include supply, output, storage, maintenance and damage. Conservation laws are used where they physically hold. There is no demonstrated universal conservation law for ‘resistance’.
8. Reconstruct and test, including EEML itself (protocol). Compare alternatives, remove constraints as a test, record failures and predict new circumstances without retuning.

Symbols are defined more precisely per example. Statistical cost, mechanical action and fluctuation rate functional are not the same quantity without a derivation. F is thermodynamic free energy only under additional physical identifications.

Proposal by the author, 28 September 2026: “effort = force, effect = motion”. This gives a concrete mechanical research branch. For a test, we operationalize effort as the required driving force, measured in newtons, and effect as a motion agreed in advance with initial conditions, load and duration. The magnitude of the force, its maximum and its time integral are different possible comparison measures; the choice must be fixed in advance. This does not tacitly replace the broader historical concepts with an already proven universal identification.

In classical mechanics with constant mass, in an inertial frame, the net force determines the acceleration: \(\sum\mathbf F=m\,d\mathbf v/dt\). Driving force, opposing force and their sum must therefore be kept separate. At zero net force the velocity stays constant; that can be ongoing motion or rest. A force can also change only the direction. See Feynman, Newton’s Laws of Dynamics.

An explicit model is a single rectilinear direction of motion with linear friction:

For the same constant velocity \(v_*>0\), the following holds:

Less friction here requires less driving force for the same motion effect. At γ=0 the velocity already present can be maintained without driving force; from rest, no acceleration follows without net force. The preparation that supplied the initial velocity belongs in the bookkeeping when we compare the full process.

Force is not the same as energy use. The transferred mechanical work is \(W=\int\mathbf F_{\rm drive}\cdot d\mathbf r\); the power is \(\mathbf F_{\rm drive}\cdot\mathbf v\). A smaller force over a longer path need not mean less work. These quantities may be tracked alongside force without swapping the definition of effort after the fact. See Feynman, Work and Potential Energy.

The relation above is a consequence of Newton plus the chosen friction law. An EEML claim of its own then asks which route, structure or adaptation lowers the required force, and which new outcome this predicts in advance. The identification “force/motion” does not by itself yet derive the costs \(c_i\), preferences or process parameters of P1.

CAN means that the required context is present; DOES names the executed transition; LEAVES names the context that remains. A seed is preparation, a cycle an executable sequence that restores a named context, and residual demand the additional support during execution.

A simple discrete translation uses a stock \(m\in\mathbb N^k\). An operation has required input u and output v:

A shortfall is componentwise \((u-m)_+\). Replenishment must be booked explicitly; the formula does not make it available by itself. This is related to a Petri net. A cycle must actually be executable. If every transition requires a missing seed, it does not start by itself.

Example: a direct operation consumes a and delivers one effect pulse. A cycle \(a\to b\to c\to a\) delivers one effect pulse at the last step. With one initial a and one time unit per step, ten direct pulses require nine replenishments and ten steps; the cycle requires no new a, but thirty steps. This is a trade-off between support and duration. Fuel or energy that is not included in the stock may not be regarded as free.

The kinship with Petri nets and chemical organization theory does not automatically make a cycle optimal, reachable or thermodynamically closed. See Dittrich and Speroni di Fenizio.

Retained as postulates: nothing does not exist; effortless effect is underlying; motivations, habits and goals co-determine the context; EEML must also be applied to its own formulation. The convention ‘100% effortless’ denotes zero active opposition with actual effect. It is not automatically the thermodynamic output/input efficiency or a proof of energy for free.

The original argument remains visible: assume total absence; then resistance is absent; add the founding rule that absent resistance necessarily implies an existing effortless state; that state is something; hence total absence conflicts with that founding rule. The transition from absence to the existence of a state is additional content. The argument does not independently prove the founding rule or a cosmic zero point.

‘Nothing’ as total absence and ‘naught’ as something present that has no effect within a context remain different concepts. Couplings that are present can be inactive; this is made operational further on with a damping matrix. The concrete models can be investigated without a theory of origin.