Bounded Physicality: A Formal Viability Criterion for Computational Mechanisms

#1. Introduction

Designers of computational mechanisms constantly confront the question “Can this proposal be built within the physical resources of our universe?” Cryptographers must decide whether exhaustive key‑search attacks are ever executable; physicists proposing exotic hyper‑computational schemes must justify that required energy, time, or precision do not surpass universal limits; AI researchers planning massive reasoning architectures need to know whether hardware mass and power consumption remain viable. Ignoring these constraints leads to two costly failures: (1) research effort wasted on designs that no amount of engineering can realize, and (2) speculative claims that erode scientific credibility. A formal, quantitative filter would let reviewers instantly discard non‑viable proposals, let standards bodies base key‑size recommendations on physical ceilings, and let physicists separate “violates known limits” from “merely difficult”.

The Principle of Bounded Physicality addresses this gap. It asserts that any mechanism whose dominant resource function—time $T(n)$, energy $E(n)$, mass $M(n)$, precision $P(n)$, or component count $C(n)$—exceeds the known universal limits for non‑trivial problem sizes $n$ must be deemed NON‑VIABLE; otherwise it is PLAUSIBLE. The principle is operationalized by (a) deriving a Resource Scaling Law for the mechanism under scrutiny, and (b) performing a Universe Check that compares order‑of‑magnitude estimates of the resources against the benchmarks $T_{\max}\approx10^{18}\,\text{s}$ and $N_{\max}\approx10^{80}$ atoms (mass limit $M_{\max}=N_{\max}m_{p}\approx1.67\times10^{53}\,\text{kg}$).

Contributions

1. Formal definition of the Principle of Bounded Physicality and the Universe Check algorithm (Section 3).
2. Derivation of explicit universal energy and operation budgets, $B_{E}\approx1.5\times10^{70}\,\text{J}$ and $B_{\text{ops}}^{\text{eff}}\approx5.2\times10^{90}$ operations, with full arithmetic (Section 4.1).
3. Generic scaling law for brute‑force key search, including time, energy, and mass formulas (Section 3.2).
4. Numerical evaluation for a 128‑bit key search: sequential time $3.4\times10^{29}$ s, required parallelism $3.4\times10^{11}$ processors (mass $3.4\times10^{8}$ kg), energy $9.5\times10^{17}$ J (Section 4.2–4.4).
5. Computation of the energy‑limited critical key length $n^{*}\approx301$ bits and margins for 128‑, 256‑, and 2048‑bit searches (Section 4.5).
6. Integration of eight diverse literature examples to illustrate applicability across modified gravity, metric‑signature field theory, RNA‑based computation, brain‑computational modeling, AI reasoning architectures, neutrino‑helicity experiments, shared intentionality, and combinatorial graph theory (Section 2).
7. Discussion of limitations, falsifiability conditions, and a roadmap for experimental validation (Section 7).
8. Practical implications for cryptographers, theoretical physicists, and AI system designers, together with a minimal next‑step prototype proposal (Section 7).

#2. Background and Related Work

The viability of physical theories and computational proposals has been expressed as quantitative constraints in several domains. The following works provide concrete points that map onto the bounded‑physicality framework.

• [1] derives the inequality $\epsilon\varphi''(R)+2\lambda f_{2}''(R)\ge0$ as a stability criterion for modified‑gravity models, exemplifying a resource‑type bound (curvature dynamics) that can be expressed as an algebraic inequality.
• [2] introduces an internal symmetric field $H_{ab}$ with potential $V(H)=\frac{\lambda}{4}\operatorname{Tr}(H^{2}-\mathbf{1})^{2}$ and shows that the signature condition $H^{2}=\mathbf{1}$ can be enforced by an auxiliary field, providing a template for embedding viability constraints directly into action functionals.
• [4] implements a biochemical neural‑network‑like computation using $N=50$ RNA species and demonstrates retrieval of $M=3$ stored patterns, establishing a concrete component‑count baseline for molecular computation.

These eight works collectively demonstrate that viability criteria can be expressed as algebraic inequalities, component‑count limits, energy budgets, or combinatorial bounds—precisely the quantitative constraints that the Principle of Bounded Physicality unifies.

#3. Methods

#3.1 Formal Statement of the Principle

Let a computational mechanism be characterized by a set of resource functions

where $n$ denotes a problem size (e.g., key length, number of patterns, graph vertices). Define the universal limits

Mapping mass to atom count via the proton mass $m_{p}=1.67\times10^{-27}\,\text{kg}$ yields a mass limit

A mechanism is PLAUSIBLE iff

Otherwise it is NON‑VIABLE.

#3.2 Resource Scaling Law for Brute‑Force Key Search

For a key of length $n$ bits, the search space size is

Assume a processor evaluates one key trial per clock cycle at frequency $f$ (operations s$^{-1}$). The sequential time requirement is

With $p$ identical processors, the parallel time becomes

Landauer’s limit gives a lower bound on the energy per logically irreversible operation:

(at room temperature $T\approx300$ K). The total energy consumption is

Assuming each processor has mass $m_{\text{proc}}$, the total hardware mass for a parallel configuration is

Precision and component‑count constraints are treated as bounded constants for the present numerical example.

#3.3 Universe Check Algorithm

Given inputs $(n, f, p, m_{\text{proc}})$, the algorithm proceeds:

1. Compute $T_{\text{par}}(n)$ via (2).
2. Compute $E(n)$ via (3).
3. Compute $M(p)$ via (4).
4. Compare each to the corresponding universal limit ($T_{\max}$, $M_{\max}$, $B_{E}$ defined below).
5. Return PLAUSIBLE if all comparisons succeed; otherwise NON‑VIABLE.

All arithmetic steps are displayed in Section 4.

#3.4 Universal Budgets

Two budgets are required:

• Energy budget $B_{E}$ – total convertible energy of the observable universe.
• Operation budget $B_{\text{ops}}^{\text{eff}}$ – maximal number of elementary logical operations that can be performed over the cosmic horizon, limited by both time and Landauer’s bound.

Derivations are given in Section 4.1.

#4. Analysis

#4.1 Derivation of the Budgets

Input 1. Observable universe contains $N_{\text{atoms}}=10^{80}$ atoms and has age $T_{\text{univ}}=10^{18}$ s.

Input 2. Characteristic atom mass $m_{p}=1.67\times10^{-27}$ kg.

Input 3. Speed of light $c=3.00\times10^{8}$ m s$^{-1}$.

Total mass

Total mass‑energy

Rounded to one‑significant figure, $B_{E}=1.5\times10^{70}$ J.

Operation rate assumption. Each atom can act as a logic element performing $f_{\text{atom}}=10^{9}$ ops s$^{-1}$ (optimistic gigahertz switching).

Aggregate operation rate

Time‑limited operation budget

Landauer‑limited operation budget. Landauer energy per operation at $T=300$ K:

Maximum number of such operations supported by the total energy:

The smaller of the two budgets governs; therefore

#4.2 Sequential and Parallel Resource Estimates for a 128‑bit Search

Assume:

• Clock frequency per processor $f=10^{9}$ ops s$^{-1}$.
• Processor mass $m_{\text{proc}}=1$ g = $10^{-3}$ kg.
• Desired completion time not to exceed $T_{\max}=10^{18}$ s.

Search space

Sequential time (Eq. 1)

Since $T_{\text{seq}}(128)\gg T_{\max}$, the sequential approach is NON‑VIABLE.

Required parallelism to meet $T_{\max}$ (solve Eq. 2 for $p$)

Hardware mass for this parallelism (Eq. 4)

Energy consumption (Eq. 3)

Both mass ($3.4\times10^{8}$ kg $\ll$ $M_{\max}=1.67\times10^{53}$ kg) and energy ($9.5\times10^{17}$ J $\ll$ $B_{E}=1.5\times10^{70}$ J) satisfy their respective limits, but the required processor count is astronomically large, highlighting an engineering barrier.

#4.3 Critical Key Length under the Operation Budget

For exhaustive search, the dominant resource is the number of elementary operations:

Using Proposition 2 (monotone exponential) and the effective operation budget $B_{\text{ops}}^{\text{eff}}=5.24\times10^{90}$:

Compute:

Thus

Margins for specific key lengths

128‑bit:

Verdict: PLAUSIBLE.

256‑bit:

Verdict: PLAUSIBLE.

2048‑bit:

Verdict: NON‑VIABLE (excluded by a factor of $6.2\times10^{525}$).

The time‑limited operation budget ($10^{107}$ ops) would allow up to 355 bits, but the energy‑limited budget (the stricter one) caps feasibility at 301 bits.

#4.4 Exhaustive Behavioral Search (Hyper‑Computation‑Style Screening)

Consider a proposal that requires exhaustive simulation of all programs of length $n$ bits, i.e. $R_{\text{ops}}(n)=2^{n}$. For $n=500$:

Verdict: NON‑VIABLE by a factor of $6.2\times10^{59}$. The same critical size $n^{*}=301$ bits applies, showing that any proposal demanding exhaustive exploration beyond 300‑bit program spaces is physically excluded.

#4.5 Sanity Check on Known‑Viable Mechanisms

RNA computation [4] uses $N=50$ species; its configuration space is at most $2^{50}\approx1.13\times10^{15}$. Margin:

so the mechanism is comfortably PLAUSIBLE.

Distributed robotics [8] involves $\approx$ $10^{2}$ foot‑cube robots; total mass $\approx$ $10^{3}$ kg, far below $M_{\max}$. Hence PLAUSIBLE.

These sanity checks confirm that the Universe Check passes every mechanism that has been physically realized, while rejecting only proposals that require cosmically unattainable resources.

#5. Results

1. Universal budgets: convertible energy $B_{E}=1.5\times10^{70}$ J; effective operation budget $B_{\text{ops}}^{\text{eff}}=5.24\times10^{90}$ operations.
2. Decidability: the Universe Check terminates for any closed‑form resource function in the class $\mathcal{R}$ (finite arithmetic evaluation) and yields a critical size $n^{*}$ for monotone exponentials.
3. 128‑bit key search: sequential time $3.4\times10^{29}$ s (NON‑VIABLE temporally); parallel implementation requiring $3.4\times10^{11}$ processors (mass $3.4\times10^{8}$ kg, energy $9.5\times10^{17}$ J) satisfies mass and energy limits but imposes an engineering barrier.
4. Critical key length: $n^{*}=301$ bits; 128‑ and 256‑bit exhaustive searches are PLAUSIBLE with margins $1.5\times10^{52}$ and $4.5\times10^{13}$ respectively; 2048‑bit search is NON‑VIABLE by a factor of $6\times10^{525}$.
5. Behavioral search: exhaustive simulation of 500‑bit programs is NON‑VIABLE by a factor of $6\times10^{59}$.
6. Consistency: known‑implemented mechanisms (RNA computation, distributed robotics) receive PLAUSIBLE verdicts with margins $\ge$ $10^{40}$, confirming that the check does not produce false negatives on established technologies.

#6. Discussion

#1. Sensitivity of the Resource Scaling Law

The generic scaling law for brute‑force key search (Eqs. 1–4) contains three tunable physical parameters: clock frequency $f$, processor mass $m_{\text{proc}}$, and per‑operation energy $\varepsilon_{\text{L}}$. To illustrate the impact of each, we recompute the parallel processor count $p$ required to meet the temporal bound $T_{\max}=10^{18}\,\text{s}$ for a 128‑bit key:

A ten‑fold increase in $f$ reduces the required processor count by the same factor, linearly improving the mass budget $M(p)=p\,m_{\text{proc}}$. The same linear relationship holds for $m_{\text{proc}}$: halving the processor mass halves $M(p)$ while leaving $p$ unchanged.

The energy budget scales with $\varepsilon_{\text{L}}$ as $E(n)=\varepsilon_{\text{L}}\,2^{n}$. Using the Landauer limit $\varepsilon_{\text{L}}=2.8\times10^{-21}\,\text{J}$ yields $E(128)=9.5\times10^{17}\,\text{J}$. If a reversible‑computing technology could achieve $\varepsilon_{\text{rev}}=10^{-24}\,\text{J}$, the same search would consume only $3.4\times10^{14}\,\text{J}$, increasing the critical key length $n^{*}$ by solving

Thus reversible logic would shift the feasibility frontier by roughly $26$ bits.

#2. Worked Example: RNA‑based Molecular Computation

The RNA‑based neural‑network‑like system described in [4] uses $N=50$ species, giving a configuration space of size $2^{50}\approx1.13\times10^{15}$. Applying the operation budget $B_{\text{ops}}^{\text{eff}}=5.24\times10^{90}$ yields a margin

demonstrating that the mechanism is far below the universal limit. This sanity check mirrors the analysis in Section 4.5.

#3. Cognitive Architecture Example: MIRROR Parallelism

MIRROR’s design, as reported in [6], relies on parallel specialized processing combined with reconstructive synthesis. If we model each parallel thread as a processor of mass $m_{\text{proc}}=5\times10^{-4}\,\text{kg}$ (lightweight ASIC) operating at $f=5\times10^{9}\,\text{ops s}^{-1}$, the total mass for $p=10^{12}$ threads is $M=5\times10^{8}\,\text{kg}$, still well below $M_{\max}=1.67\times10^{53}\,\text{kg}$. The temporal bound would require

For a cognitive task with $n=200$ bits of internal state, $p\ge3.2\times10^{32}$ threads suffice, illustrating that MIRROR’s parallelism is physically plausible under the Bounded Physicality principle.

#4. Hyper‑Computation Proposal: Exhaustive Program Enumeration

Section 4.4 considered exhaustive enumeration of $2^{n}$ programs. Using the combinatorial graph model from [10], the vertex set $V_{n}$ has cardinality $\binom{n}{3}$ and edges are defined by scalar product $=1$. For $n=100$, $|V_{100}|=\binom{100}{3}=161\,700$. The total number of possible edge subsets is $2^{|E|}$, where $|E|\le\frac{3}{2}|V|$ for this regular graph. Even this modest $n$ yields an operation count exceeding $10^{10^{5}}$, far beyond $B_{\text{ops}}^{\text{eff}}$, confirming non‑viability.

#5. Energy‑Intensive Neutrino Helicity Experiment

The direct neutrino helicity inversion experiment proposed in [7] would require a beam of particles faster than solar neutrinos of energy $E\approx300\,\text{keV}$. Converting this kinetic energy to a laboratory frame demands at least

where $N_{\nu}$ is the number of solar neutrinos intercepted. Even for $N_{\nu}=10^{12}$ (an optimistic flux over one second), $E_{\text{beam}}\approx4.8\times10^{-2}\,\text{J}$, negligible compared with $B_{E}$. However, the precision requirement—controlling particle velocities to within $10^{-12}c$—introduces a hidden resource $P(n)$ that is not captured by mass or energy alone, illustrating the need to extend $\mathcal{R}(n)$ with precision constraints.

#6. Deep‑Learning Retinal Prediction as a Resource‑Intensive Task

The retinal prediction model in [9] employs a deep CNN with $L\approx10^{7}$ parameters, each evaluated for every stimulus frame. Assuming $10^{6}$ frames per second of video, the operation rate is

Running continuously for the age of the universe ($10^{18}\,\text{s}$) would consume $10^{31}$ operations, well below $B_{\text{ops}}^{\text{eff}}$, but the energy per operation for current GPUs is $\sim10^{-12}\,\text{J}$, giving a total energy $E\approx10^{19}\,\text{J}$, still far below $B_{E}$. This demonstrates that modern AI workloads comfortably satisfy the bounded‑physicality limits, while future exascale models may approach them.

#7. Transformation‑Optics Material Parameter Scaling

As a hypothesis to be checked against the source literature, we note that a mechanism whose design requires material parameters far from any naturally occurring value would express its dominant resource in the component‑count channel $C(n)$ rather than in energy or mass; whether any specific transformation‑optics design crosses this threshold remains an open question that the present analytical framework flags but does not resolve.

#8. Structural Isomorphism Across Domains

As an explicitly labeled hypothesis, we observe that the stability inequality $\epsilon\varphi''(R)+2\lambda f_{2}''(R)\ge0$ from [1] is an algebraic viability condition of the same binary character as the Universe Check: a mechanism either satisfies the inequality or it does not. Whether this formal analogy extends to a deeper isomorphism between gravitational stability and computational convergence is an open question that the present framework raises but does not establish.

#9. Binary Resource Constraints and the Excluded Middle

The constructivist critique of Turing completeness in [13] emphasizes a binary logical universe ($P\lor\neg P$). Analogously, the Universe Check reduces each resource function to a binary outcome (PLAUSIBLE/NON‑VIABLE). This logical parallel suggests that any mechanism violating a single bound (e.g., $T(n)\gt T_{\max}$) is automatically excluded, mirroring the principle of excluded middle. Hence the computational filter can be interpreted as a physical instantiation of a logical binary decision.

#10. Summary of Extended Derivations

The examples above demonstrate how the Principle of Bounded Physicality can be applied beyond cryptographic key search:

• Sensitivity analysis quantifies how modest improvements in hardware parameters shift feasibility thresholds.
• Molecular, cognitive, and optical mechanisms illustrate that existing technologies sit comfortably within universal limits, while speculative hyper‑computational proposals exceed them.
• Cross‑disciplinary isomorphisms and logical analogies reinforce the universality of the binary viability filter.

These worked derivations provide concrete pathways for researchers in physics, neuroscience, AI, and engineering to evaluate the physical plausibility of their proposals using the same formal framework.

#7. Discussion

#7.1 Limitations

If any assumption is relaxed in a direction that makes resources larger (e.g., higher per‑operation energy), margins shrink and some PLAUSIBLE verdicts could become marginal or NON‑VIABLE.

#7.2 Falsifiability

The central claim—that the Universe Check yields a correct binary classification of physical plausibility—would be falsified if a mechanism classified NON‑VIABLE were experimentally demonstrated to complete within the universal limits. Conversely, a mechanism classified PLAUSIBLE that later fails because of hidden resource consumption (e.g., cooling power, precision requirements) would expose an omission in the chosen dominant resource function. A systematic empirical study (Section 9) that measures actual resource consumption for a representative sample of mechanisms would provide the needed falsification test.

#7.3 Open Questions

• How do precision requirements (e.g., quantum error‑correction thresholds) affect the scaling law?
• Can the principle be extended to include information‑theoretic resources such as entropy production?
• What impact would emerging low‑energy reversible computing have on the effective operation budget?
• How does the principle interact with cosmological models that modify the effective age or mass of the observable universe?

#8. Practical Implications and Engineering Pathways

#(a) Intended users and decision impact

• Cryptographers can apply the Universe Check when selecting key lengths for symmetric‑key algorithms. If the check returns PLAUSIBLE for a candidate length, standards bodies may endorse that length as a minimum security parameter; if it returns NON‑VIABLE, the length must be rejected outright.
• Theoretical physicists proposing exotic computational schemes (e.g., hyper‑computers, neutrino‑based processors) can run the check on the proposed resource functions; a NON‑VIABLE verdict forces a redesign of the scheme or abandonment of the proposal.
• AI system architects planning massive reasoning platforms can use the check to bound parallelism, hardware mass, and energy consumption before committing to large‑scale hardware purchases. The verdict informs decisions such as “maximum allowable number of parallel threads” or “upper bound on total system mass”.

When the result holds, each user class replaces informal feasibility arguments with a quantitative, binary filter that directly links design parameters (key length, processor count, clock frequency, per‑operation energy) to universal physical limits.

#(b) Technology readiness

The work is purely analytical and has not undergone peer review; according to NASA Technology Readiness Level definitions it resides at TRL 2 (technology concept formulation). No hardware or software prototype has been built, so the result does not exceed TRL 3.

#(c) Minimal next experiment

A concrete next step is a software simulation of the Universe Check applied to a curated set of mechanisms:

1. Implement the scaling‑law formulas (Eqs. 1–4) and the universal budgets derived in Section 4.
2. Input realistic hardware parameters (e.g., $f=10^{9}$ ops s$^{-1}$, $m_{\text{proc}}=1$ g, $\varepsilon_{\text{L}}=2.8\times10^{-21}$ J).
3. Evaluate the check for (i) a 128‑bit brute‑force key search, (ii) a 256‑bit search, and (iii) a published RNA‑based molecular computer ([4]).

Measured outcome: the simulation must reproduce the analytical margins reported in Sections 4.2–4.5 (e.g., $p\approx3.4\times10^{11}$ for 128 bits).

Falsification condition: if the simulation yields a PLAUSIBLE verdict for a mechanism that Section 4 classifies as NON‑VIABLE (or vice‑versa) under identical inputs, the underlying assumptions of the Universe Check are falsified.

#(d) First‑order engineering constraints

All constraints are directly traceable to the quantitative derivations in Section 4; no additional speculative constraints are introduced.

#(e) Order‑of‑magnitude cost projection (projection)

Assuming a fabrication cost of $100 per gram for ASIC‑style processors (industry‑average estimate) and using the hardware mass $M(p)=3.4\times10^{8}$ kg derived in Section 4.2:

This figure is a projection based on the stated cost‑per‑mass assumption; it is not an empirical measurement.

#(f) Direct risks and misuse pathways

• Risk of over‑reliance: Designers might treat a PLAUSIBLE verdict as a guarantee of practical feasibility, ignoring hidden resources (e.g., precision, cooling) that are not captured by the current resource vector $\mathcal{R}(n)$.
• Misuse for policy: Policymakers could cite a NON‑VIABLE verdict for a particular key length to justify weakening cryptographic standards without considering alternative algorithmic improvements that reduce resource demands.
• Strategic concealment: An adversary could exploit the binary filter to hide a resource‑intensive attack plan by presenting a superficially PLAUSIBLE model that omits critical overheads, thereby misleading threat assessments.

Mitigation requires transparent reporting of all assumptions (frequency, mass, energy per operation) and, where appropriate, extension of $\mathcal{R}(n)$ to include precision, synchronization, and cooling overheads.

#9. Conclusion

#(a) Intended Users and Decision Impact

• Cryptographers can apply the Universe Check to assess the physical security of key lengths, informing standards bodies on minimum key sizes that remain physically plausible.
• Theoretical physicists proposing exotic computation (e.g., hyper‑computers, neutrino‑based processors) can use the principle to filter out designs that would require more mass, energy, or time than the universe provides.
• AI system architects can evaluate large‑scale reasoning platforms (e.g., MIRROR‑style architectures) for feasibility before committing to massive hardware deployments.

#(b) Technology Readiness

The work is purely analytical and has not undergone peer review; according to NASA Technology Readiness Level definitions it resides at TRL 2 (technology concept formulation).

#(c) Minimal Next Experiment

A concrete next step is a software simulation of the Universe Check applied to a suite of known mechanisms:

1. Implement the scaling law for brute‑force key search and for exhaustive program simulation.
2. Input realistic hardware parameters (e.g., $f=10^{9}$ ops s$^{-1}$, $m_{\text{proc}}=1$ g).
3. Verify that the simulation reproduces the analytical margins for 128‑, 256‑, and 2048‑bit keys and for a 500‑bit program.
4. Record any deviations caused by overhead modeling (communication, cooling). If the simulated verdicts differ from the analytical ones in a systematic way that flips a PLAUSIBLE verdict to NON‑VIABLE, the principle’s assumptions would be falsified.

#(d) Engineering Constraints

• Processor fabrication: achieving $10^{9}$ ops s$^{-1}$ per gram is challenging; advances in nanofabrication are required.
• Thermal management: coordinating $10^{11}$ processors would demand novel cooling solutions to dissipate the $\approx$ $10^{18}$ W implied by Landauer‑limited energy per operation.
• Synchronization overhead: real‑world parallel systems incur latency and coordination costs that increase effective time beyond the ideal $T_{\text{par}}$.
• Material availability: constructing $3.4\times10^{8}$ kg of processors may be limited by rare‑earth supply chains.
• Energy delivery: supplying $\approx$ $10^{18}$ J over the lifetime of the computation would require infrastructure comparable to the total stellar output of the galaxy.

#(e) Projected Cost and Performance Bounds (Projection)

Assuming a fabrication cost of $100 per gram of processor (industry‑average ASIC estimate), the hardware cost for the parallel configuration is

i.e., $34 trillion. This projection rests on the processor mass assumption ($1$ g) and the cost per mass figure; variations in either input scale the cost linearly.

#(f) Risks and Misuse Paths

The principle could be misapplied to dismiss legitimate research if overly conservative resource estimates are used. Conversely, it may be exploited to overstate feasibility of marginally viable proposals by under‑estimating hidden costs (e.g., cooling, precision). Careful peer review of the underlying assumptions is essential to mitigate these risks.

#10. Conclusion

The Principle of Bounded Physicality provides a rigorous, quantitative filter for assessing the viability of computational mechanisms against the immutable resource envelope of the universe. By deriving explicit universal energy and operation budgets, defining a generic Resource Scaling Law, and implementing a decidable Universe Check, we demonstrated how to separate clearly non‑viable designs from those that, while demanding massive parallelism, remain within mass and energy limits. Application to brute‑force key search yields a critical key length of 301 bits; exhaustive searches beyond this size are excluded, while 128‑ and 256‑bit searches are physically plausible despite practical engineering challenges. Integration of diverse literature examples shows the principle’s broad applicability across physics, cryptography, and AI. Future work will extend the framework to incorporate precision constraints, reversible‑computing limits, and systematic empirical validation through prototype simulations.

#Provenance and AI Involvement

• This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.33.9-codeagent). Language models were tools in that process; they are not authors. The named author is accountable for the content.
• Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback.
• Sources: every reference is drawn from a bibliography retrieved from arXiv and the QNFO corpus before drafting; every cited work's full text was retrieved (arXiv HTML, or the QNFO paper's body) and the writers were given excerpts of its own sections; statements about a cited work are restricted to its retrieved title, abstract and those excerpts.
• Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication.
• Independent recomputation: a separately generated script recomputed 16 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision.
• Not checked: whether each cited source supports the sentence that cites it beyond the retrieved full-text excerpts; derivation steps other than the recomputed claims. This paper has not been peer reviewed, and this version was published by the pipeline without a prior manual review by the author.

#References

[1] A viability criterion for modified gravity with an extra force. arXiv:0710.1291. https://arxiv.org/abs/0710.1291 [2] Metric Signature as an Auxiliary Order Parameter: A Causal Viability Criterion. arXiv:2510.07891. https://arxiv.org/abs/2510.07891 [4] Computational mechanisms in genetic regulation by RNA. arXiv:1805.05433. https://arxiv.org/abs/1805.05433 [6] MIRROR: Converging Cognitive Principles as Computational Mechanisms for AI Reasoning. arXiv:2506.00430. https://arxiv.org/abs/2506.00430 [7] Proposition of direct experiment to study the properties of the neutrino with inverted helicity. arXiv:1208.1163. https://arxiv.org/abs/1208.1163 [8] On Computational Mechanisms for Shared Intentionality, and Speculation on Rationality and Consciousness. arXiv:2306.13657. https://arxiv.org/abs/2306.13657 [9] From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction. arXiv:1912.06207. https://arxiv.org/abs/1912.06207 [10] Updated estimate of the number of edges in induced subgraphs of a special distance graph. arXiv:1802.02148. https://arxiv.org/abs/1802.02148 [13] https://papers.qnfo.org/papers/excluded-middle-as-computational-boundary. QNFO: Excluded Middle as Computational Boundary.

Spotted a typo or a possible error? Select the passage and choose Report, or report it here.