SEQUENTION: A Timeless Biological Framework for Foliated Evolution

1. Introduction

Contemporary evolutionary theory explains biological patterns through historical narratives in ontic time: random mutation, selection, drift, and demography generate trait change across epochs. I propose a different foundation. SEQUENTION (“further evolution without time”) posits that the biosphere is a shadow of a four-dimensional counterspace $(\mathcal{C},G,{\Psi }_{\mathrm{bio}})$ containing the complete content of viability constraints and lawful correlations among genotype $\left(\mathcal{G}\right)$, phenotype $\left(\mathcal{P}\right)$, and environment $\left(\mathcal{E}\right)$. Apparent sequences are foliation choices of a projection; only slice-invariant geometric quantities are explanatory. I pursue three goals: (i) translate the counterspace ontology into minimal mathematics accessible to biologists; (ii) specify an extrinsic constitutive law that yields classical models as a limit; and (iii) derive cartographic inquiries plus concrete experimental programs capable of mapping the framework’s geometry.

• Deterministic core.

At the biological scale, time, chance, and probability have no ontic status. Biological phenomena are fully determined by the projection of a complete 4-D content; directionality is encoded by a variational principle (Section 6). Any temporal or stochastic description is a gauge label or a computational heuristic.

2. Axioms of SEQUENTION in Biology

A1 (Whole Content).

There exists a smooth 4-D counterspace $(\mathcal{C},G,{\Psi }_{\mathrm{bio}})$ encoding the full content of viable relations across $\mathcal{G}\times \mathcal{P}\times \mathcal{E}$. The living biosphere $\left({\Sigma }_{\mathrm{bio}}\right)$ is a 3-manifold embedded in $\left(\mathcal{C}\right)$ by $X:{\Sigma }_{\mathrm{bio}}\to \mathcal{C}$; observables are pullbacks $X^{*}{\Psi }_{\mathrm{bio}}$.

A2 (Identity-of-Source).

Conserved developmental organizers, canalization basins, and repeated adaptive “solutions” arise from singular sets $S\subset \mathcal{C}$ and orbits of automorphisms of $(\mathcal{C},G,{\Psi }_{\mathrm{bio}})$, explaining convergence without historical coordination.

A3 (Shadow Realization).

Apparent temporal orderings are foliation choices. Only reparameterization-invariant functionals of trajectories in $\mathcal{Z}=\mathcal{G}\times \mathcal{P}\times \mathcal{E}$ are physically meaningful. Time possesses no ontic status.

A4 (Parsimony).

No anthropomorphic teleology; directionality arises via a single extrinsic constitutive law and an action principle (variational determinism).

3. Minimal Mathematics

Let $\mathcal{Z}=\mathcal{G}\times \mathcal{P}\times \mathcal{E}$ be the observable manifold. Introduce an informational potential $\mathcal{U}:\mathcal{Z}\to \mathbb{R}$ and define the realized variation density ${\rho }_{\mathrm{var}}$ (mutational input plus developmental accessibility). I postulate a flux $\mathrm{J}$ of fixation/trait change governed by

$$\mathrm{J}={\mu }_{\mathrm{bio}}\left({\displaystyle \frac{\parallel \nabla \mathcal{U}\parallel }{a_{†}}}\right)\nabla \mathcal{U},\nabla ·\mathrm{J}={\rho }_{\mathrm{var}},$$

(1)

with mobility ${\mu }_{\mathrm{bio}}$ monotone, $C^1$, and bounded away from zero and infinity to ensure uniform ellipticity. Intuitively: in high-constraint regions (large $\parallel \nabla \mathcal{U}\parallel$), ${\mu }_{\mathrm{bio}}\to 1$ and classical local dynamics are recovered; in low-gradient regions, ${\mu }_{\mathrm{bio}}\sim \parallel \nabla \mathcal{U}\parallel /a_{†}$ induces projection-dominated behavior (canalized leaps, convergence).

Proposition 1 

(Gauge limit). Under the asymptotic regime ${\mu }_{\mathrm{bio}}\to 1$ and smooth $\mathcal{U}$, integral curves of $\nabla \mathcal{U}$ admit reparameterizations yielding standard replicator or mutation–selection equations. Different monotone labels (“times”) generate equivalent observables; slice-invariants alone are empirical.

Remark 1. 

Equation (1) isextrinsic: it relates observables in the shadow $\left(\mathcal{Z}\right)$ to the geometry of the embedding through $\left(a_{†}\right)$. No ontic time is invoked; continuity equations are statements about conservation on $\left(\mathcal{Z}\right)$, not about temporal flow.

• Action principle (cariational determinism).

Define

$$S\left[\gamma \right]=\int \mathsf{\Phi }\left({\displaystyle \frac{\parallel \nabla \mathcal{U}\parallel }{a_{†}}}\right)\parallel \nabla \mathcal{U}\parallel d\ell ,\delta S\left[\gamma \right]=0⟺\mathrm{realized}\mathrm{paths}.$$

With $\mathsf{\Phi }>0$ smooth, the Euler–Lagrange equations yield a reparameterization-invariant steepest-ascent law; “goals” are the critical sets $\{\nabla \mathcal{U}=0\}$.

4. Biological Mapping and Notation

• Spaces.

$\mathcal{G}$ (genotype), $\mathcal{P}$ (phenotype morphospace), $\mathcal{E}$ (environmental descriptors). Trajectories are curves $\gamma :I\to \mathcal{Z}$. A foliation is a choice of parameter on I; SEQUENTION asserts reparameterization invariance of empirical claims.

• Slice invariants.

I emphasize three statistics:

• Path length: $L\left[\gamma \right]=\int \parallel \mathrm{d}\gamma \parallel$.
• Extrinsic curvature: $K_{\mathrm{ext}}\left[\gamma \right]$ computed from the embedded trajectory in morphospace.
• Program complexity: description length (MDL) of the developmental generative model for the terminal phenotype.

5. Epistemic Motivation and Foundational Justification

Our central position—that contemporary evolutionary theory remains incomplete—is predicated on two foundational limitations of the standard, time-first paradigm: (1) its categorical inability to incorporate phenomena that are non-local in time (i.e., retrocausality), and (2) its persistent misinterpretation of complex, deterministic, adaptive dynamics as "mere randomness." We demonstrate that these are not peripheral oversights but fundamental categorical errors that obscure the true, geometric nature of biological organization and adaptation. The SEQUENTION framework, grounded in the timeless ontology of Timeless Counterspace & Shadow Gravity (TCGS), resolves these limitations by re-classifying time itself as a "foliation artifact" (Axiom A3) of a static, 4-dimensional (4-D) geometry. Our justification is necessarily cartographic, not falsificationist. As stipulated by the framework’s foundational logic, any empirical observation is, by definition, a projection of the 4-D "Whole Content" (Axiom A1); therefore, no observation can "falsify" the existence of the projection (Axiom A3).[1, 1] Instead, an experimental mismatch proves our map of the 4-D potential (${\Psi }_{\mathrm{bio}}$) is incorrect, requiring us to "draw a new one that matches the territory". We proceed by first establishing an empirical "meta-rule" for distinguishing the map from the territory, and then applying this rule to justify our positions on retrocausality and deterministic chaos.

5.1. The Ontological Prerequisite: An Empirical "Meta-Rule" for Distinguishing Invariants from Artifacts

The central challenge for any timeless ontology (Axiom A3) is to provide an empirical, non-ambiguous method for distinguishing true, static 4-D "slice-invariants" (properties of the source) from 3-D, temporal "foliation-dependent artifacts" (properties of the process). Without such a "meta-rule," the framework’s claims remain an unfalsifiable abstraction. We find this "meta-rule" in the geochemical analysis of Chicxulub impact spherules. This research, by its very methodology, performs the exact ontological separation that TCGS-SEQUENTION requires. The analysis of these co-genetic samples employs two distinct classes of isotopic tracers to answer two different questions:

1. The ’Slice-Invariant’ (Source Property): To answer the "source-tracing" question ("What was the impactor?"), the analysis employs static, mass-independent isotopes (specifically, nucleosynthetic signatures ${\mu }^{48}Ca$ and ${\mu }^{26}Mg*$). These tracers are "foliation-agnostic" because their signatures were "forged in stars," not created by the temporal process of the impact plume’s cooling and expansion. The resulting value—a fixed "impactor contribution of 17–25%"—is a static mixing ratio of the source materials. In our framework, this is a true slice-invariant, a boundary condition of the projection event (Axiom A2). 2. The ’Foliation-Dependent Artifact’ (Process Signature): To answer the "process-tracing" question ("How did the plume cool?"), the analysis employs dynamic, mass-dependent isotopes (${\delta }^{25}Mg$, ${\delta }^{56}Fe$). The resulting signatures are "generally light or unfractionated," which is explicitly interpreted as the result of a temporal process: "incomplete recondensation as the pyrocloud cooled and expanded". This ${\delta }^{25}Mg$ value is contingent on the "foliation path" (the cooling rate) and the specific "slice" (the moment of quenching). It is a "gauge-variant" measurement.

This geological finding provides the framework’s empirical anchor. It proves that the "slice-invariant" and "foliation-artifact" are not philosophical abstractions but physically distinct, measurable quantities (see Table 1). This meta-rule—Nucleosynthetic signatures are invariants (A2 source properties); thermodynamic fractionation signatures are artifacts (A3 foliation properties)—is the epistemic tool we now apply to retrocausality and chaos.

5.2. The Geometric Structure of Foliation: Pillar II

Just as Pillar I (the “Slice”) is anchored by the geochemical distinction between invariants and artifacts [11], Pillar II (the “Foliation”) is anchored by the geophysical analysis of geological time itself. This complementary foundational work demonstrates that the Geological Time Scale (GTS) is not a human convention but possesses a quantifiable, “multifractal” geometry [11]. This geophysical analysis provides a direct, empirical model for the foliation process: a “Compound Multifractal-Poisson Process” (CMPP), wherein the 4-D source’s deterministic, multifractal geometry (the “subordinating process”) dictates the “probability” of an event (the “subordinated Poisson process”) manifesting on the 3-D shadow [11]. This validates Axiom A3 by providing a physical, measurable mechanism for the foliation, re-interpreting the “timeline” as a non-arbitrary geometric structure and “probability” as a predictable artifact of the projection [11].

5.3. Foliation as a Geometric Mechanism for Retrocausality

The first limitation of standard theory is its failure to account for retrocausality. Within SEQUENTION, apparent retrocausality is not a "backward-in-time" process but the artifact of observing a static, non-local 4-D geometry (Axiom A1: Whole Content) from a 3-D slice (Axiom A3: Shadow Realization). A change in a "future" measurement (a post-selection) is re-interpreted as choosing a different 4-D geometric object, which necessarily changes all its 3-D projections, including "past" ones. We can systematically re-interpret all temporal retrocausal models as 3-D "maps" of this 4-D geometry. The "zigzag causal path" of Price & Wharton is not a 3-D temporal path but a 3-D projection of the 4-D "Identity of Source" (Axiom A2), which geometrically unifies the emitter and absorbers as part of a single static structure. Similarly, the wave-mechanical "quantum handshake" of Cramer is demoted: the "offer wave" ($\psi$) and "confirmation wave" (${\psi }^{*}$) are not two waves traveling in time. They are the 3-D shadow-projections of the exact same static 4-D content (Axiom A1) as foliated in the forward- and reverse-time directions, respectively. The "handshake" is the epistemic recognition by a 3-D-bound observer that both maps describe the same 4-D territory. This geometric constraint is not merely philosophical; it is enacted by a specific mathematical mechanism formally defined within the TCGS-SEQUENTION corpus: the "Retrocausal, Non-Local Counterspace Coupling ($K_s$) kernel". This kernel, $K_s(p,q)$, is a non-local integral operator (Equation 8 in ) that is explicitly "supported across leaves of s" (i.e., it atemporally connects different "time" slices). It provides "future-sensitive feedback at molecular resolution" via its "advanced/retarded splitting" (Equation 7 in ). This $K_s$ kernel is the mathematical engine of foliation.

This 4-D non-local kernel must have a direct, observable 3-D signature. We identify this signature as the "scale-free correlations" observed in collective biological behavior. Empirical studies of starling flocks (e.g., Cavagna et al.) demonstrate that velocity fluctuations are correlated non-locally, "scale-free" ($\xi \sim L$), meaning the correlation does not decay with distance but scales with the size of the entire group. A bird on one side of the flock is correlated with a bird on the opposite side, faster than any 3-D-local signal (like sound or sight) can propagate. This 3-D non-local phenomenon is the definitive "smoking gun" signature of the 4-D non-local $K_s$ kernel. The birds are not communicating to each other in 3-D; they are co-projecting from the same 4-D informational potential ($\mathcal{U}$), and their actions are atemporally coupled by the $K_s$ kernel.

5.4. Deterministic Chaos as the Engine of Adaptive Structure

The second limitation of standard theory is its categorical error of mistaking deterministic chaos for "mere randomness." This error is pervasive and occurs on the quantum, classical, and biological scales (see Table 2). SEQUENTION argues that what is dismissed as "noise" is, in fact, a high-dimensional, deterministic, adaptive structure.

We ground this argument in the foundational mathematical works on deterministic chaos.

• Lorenz (1963), in his seminal "Deterministic Nonperiodic Flow," demonstrated that a simple system of three deterministic differential equations can produce infinitely complex, non-periodic, bounded behavior (the Lorenz Attractor). This proved that "irregular, seemingly haphazard" behavior does not require random forcing.
• Li & Yorke (1975), in "Period Three Implies Chaos". This reinforced the discovery that extreme complexity (periodic points of every period) can arise from the simplest possible deterministic, non-linear rules.[1, 2, 3]
• Smale (1967), in "Differentiable Dynamical Systems," provided the geometric and topological foundation. The "Smale Horseshoe" [1, 4] demonstrated how simple, deterministic operations of stretching and folding create a fractal (Cantor set) of non-wandering points, providing a robust geometric structure for chaotic dynamics.[1, 5]
• Bowen (1975), in "Equilibrium States," developed the "thermodynamic formalism" by linking Smale’s Axiom A diffeomorphisms and symbolic dynamics to the statistical mechanics of Gibbs measures.[1, 6, 7] This quantifies the structure of chaos, allowing calculation of properties like fractal dimension and entropy, proving it is a structured, deterministic phenomenon.

The "fungal behaviors" provide the living biological exemplar of this principle. The slime mold Physarum polycephalum exhibits "intelligent behavior" that is a direct, observable manifestation of deterministic, non-linear dynamics. This organism solves complex optimization problems, such as finding the shortest path through a maze and, when given multiple food sources, optimizing its transport network. This optimization is not random. When connecting three food sources, the organism’s network "selection appeared to be a bistable system" , choosing between two primary states:

1. Steiner’s Minimum Tree (SMT): The shortest possible path, maximizing transport efficiency but offering low fault tolerance. 2. Cycle (CYC): A longer, redundant path, which has lower efficiency but high fault tolerance against accidental disconnection. This "choice" is the emergent property of a deterministic, non-linear system. The mechanism is a "coupled oscillator system" and "spatio-temporal dynamics of cellular rhythms". As modeled by Tero, Nakagaki et al., this behavior is governed by a system of differential equations based on a positive feedback regulation between protoplasmic flux and the thickness of the organism’s tubes.[8] The Physarum’s SMT/CYC bistability is a direct, biological instantiation of a chaotic attractor, precisely as described by Lorenz. The "choice" between SMT and CYC is the system’s deterministic, non-periodic traversal of its phase space, which has two "wings" (basins of attraction) corresponding to the two optimal strategies. This is not randomness; it is a deterministic, adaptive computation.

6. Why Uncertainty, Randomness, and Probability Are Not Ontic in a Timeless Framework

• Thesis.

In SEQUENTION, there is no ontic time, chance, or probability; biological phenomena are functionally deterministic. Apparent stochasticity in data is a projection artifact of foliation and incomplete conditioning, not a property of the content.

• Measurement versus reality.

Measurement is an instrument for apprehending phenomena, not reality itself. Treating methodological outputs as surrogates for reality inflates the noise floor and obscures structure. Wave functions, “probability clouds,” and multiverse-style branch counts are heuristics summarizing inferences under a chosen slice.

Proposition 2 

(Gauge-variance of stochastic descriptions). Let γ be an observable trajectory in $\mathcal{Z}=\mathcal{G}\times \mathcal{P}\times \mathcal{E}$ induced by an embedding $\mathrm{X}:{\Sigma }_{\mathrm{bio}}\to \mathcal{C}$. For any two admissible foliations related by a monotone relabeling, all nontrivial descriptive probabilities change under reparameterization unless the queried events are slice-invariant. Thus there is no foliation-independent assignment of nontrivial probabilities.

Proof 

(Idea). Conditioning on a foliation integrates out embedding variables not controlled by the instrument. The induced conditional $\sigma$-algebras differ under relabeling unless the event is invariant, so mixture distributions and their probabilities are gauge-variant. □

• Chaos misread as randomness.

As established in Section 5.4, many claims of “randomness” in biology reflect coarse-grained views of deterministic, sensitive dynamics; refining resolution recovers structure [3,4]. The complex, non-periodic behavior of systems like textitPhysarum are generated by deterministic, non-linear, oscillatory dynamics, not by stochastic processes.[1,8]

• Quantum remark.

Any micro-indeterminacy, if it exists, does not propagate to biological observables in this framework; at the mesoscopic/organismal level, effective indeterminacy is epistemic. As a visual heuristic, the cartography of “all objects” in [1] is a useful canvas to situate these distinctions, though my conclusions diverge from theirs.

Time Belongs to the Map, Not the Territory

Motivated in part by Frenkel’s exposition [2], a genuine 4-D object projects to 3-D geometry (Poincaré/Duchamp). Analogies based on expanding 3-D spheres do not establish ontic time. Thus “goal-directedness” is understood as convergence to critical sets of $\mathcal{U}$ (variational telos), not as anthropomorphic intention.

Abiogenesis Sanity Check Under Finite Resources (and the Categorical Error of Human Time)

• Scope note.

This discussion addresses explanatory questions about the complexity of life’s emergence; it does not engage the "meaning of life." From my perspective, the phenomenon is consubstantial and presupposes a nonlocal connection.

• Why ex nihilo narratives fail under finite resources.

Appeals to "eventual certainty" in infinite-time toy models obscure the operative constraints of our finite cosmos. A recent quantitative treatment of the so-called Finite Monkeys Theorem shows that, even with astronomical resources, nontrivial strings (let alone Shakespeare’s corpus) are almost surely never produced before heat death; the popular infinite-limit intuition is actively misleading when resources are finite [6]. In short, do not outsource the mechanism to infinity.

• An information-theoretic reframing that pairs with SEQUENTION.

Endres (2025) casts the origin-of-life problem as a rate distortion feasibility inequality, $H_{\mathrm{prebiotic}}/$$(I_{\mathrm{protocell}}-R\left(D\right))\approx \eta R_{\min }·D·T_{\mathrm{available}}$ where $H_{\mathrm{prebiotic}}$ is the accessible chemical entropy, D a molecular persistence window, and $I_{\mathrm{protocell}}$ the information content of a minimal protocell [7]. Using conservative orders of magnitude, the analysis suggests that abiotic assembly is not a priori impossible but demands directionality and memory features that SEQUENTION treats as extrinsic geometric structure rather than temporal rates. Crucially, Endres’ framework arrives at a succinct checklist I adopt as requirements, labeled (R1)–(R3):

• Physical/chemical bias. A deviation from pure randomness (e.g., compartmentalization, cycles, autocatalytic networks) to imprint directionality.
• Sufficient persistence. Long memory or a drive that preserves incremental gains against loss (persistence of useful configurations).
• Protection and reuse. Stabilize functional molecules and retain them for integration into progressively more complex assemblies.

In a time-first narrative, these look like implausible strokes of luck; in a timeless projection, they are natural consequences of structured, chaotic feedback and slice-invariant geometry. Human "time-frames" are a categorical error at this scale: once time is demoted to gauge, {bias, persistence, protection} emerge as properties of the embedding and its admissible projections rather than as miracles of chronology [6,7].

• A witty aside (with teeth).

Hamlet already answered whether simian stenographers can carry our explanatory burden: "No." The finite-resource calculus agrees [6]. The moral for origin-of-life stories is identical: abandon the crutch of infinite-time probabilities; specify the geometry and the invariants.

7. Cartographic Inquiries and Geometric Targets

Each item is reframed as a cartographic inquiry to map a specific geometric feature of the Counterspace. The refutation criteria do not falsify the framework (Axiom A3), but rather inform the map of the A2/A4 geometry.

P1 (Cartographic Inquiry: A2 Curvature).

Independent lineages occupying homologous regions of $\mathcal{Z}$ exhibit equal $K_{\mathrm{ext}}$ within error, regardless of historical durations. This inquiry maps the extrinsic curvature ($K_{\mathrm{ext}}$) of the shared Axiom A2 singularity.

Refutation: Systematic inequality proves the geometric map of the A2 source is more complex than assumed, not that the projection is false.

P2 (Order Invariance).

Within a projection cone, permutations of developmental modules $\left\{M_i\right\}$ yield the same terminal coordinate in $\mathcal{P}$ up to noise. This inquiry maps the topology of the A2 singularity.

Success (Self-Correction): Maps the A2 singularity as a Convergent Singularity (a “funnel”) [1]. Failure (Branching): Maps the A2 singularity as a Branching Topology (a “complex manifold”) [1]. Refutation of Convergence: Large order effects indicate a Branching Topology rather than a Convergent Singularity. This falsifies the simplicity of the Source (Axiom A2), not the existence of the Projection (Axiom A3).

P3 (Slice Invariant Complexity).

The MDL of the developmental program for analogous body plans is invariant across clades in the same projection class, even with very different "evolutionary times." This inquiry maps the slice-invariant complexity (MDL) as a fundamental property of the projection.

Refutation: Complexity scaling with lineage age proves MDL is not a slice-invariant, challenging the map, not the axiom.

P4 (Corridor-Governed Bursts).

Fossil "bursts" correlate with predicted low-$\parallel \nabla \mathcal{U}\parallel$ corridors, not with elapsed time. This survey maps the topography of the $\mathcal{U}$-potential.

Refutation: The theory posits that "bursts" in evolution correspond to "low-gradient corridors" in the 4D geometry. If we find that bursts occur in high-gradient regions (a failure of correlation), it does not prove "time" is the cause. It proves our mathematical map of the 4D potential (Axiom A4) is wrong, and we must draw a new one that matches the territory.

P5 (Cartographic Calibration: Path-Invariants).

Distinct laboratory protocols (chemostat vs. serial passage) that reach the same adaptation target share identical slice-invariant functionals (e.g., $L\left[\gamma \right]$). This experiment calibrates the fundamental path-invariant ($L\left[\gamma \right]$).

Refutation: Divergence of invariants proves $L\left[\gamma \right]$ is not the correct invariant, requiring a new geometric map.

8. Empirical Program

I outline four protocol families suitable for preregistration.

A. Deep mutational scanning — gradient field inference.

Design: Use proteins with known convergent solutions (e.g., opsins, antifreeze). Infer gradient fields from fitness maps; fit the PDE in Equation (1). Statistic: Nonlinear Poisson/elliptic fits; information criteria versus GLM baselines.

B. Modular CRISPR assays — testing order invariance.

Design: Modular CRISPR toggles for segment polarity/limb patterning in model organisms; permute activation order of modules $\left\{M_i\right\}$. Statistic: Terminal morphospace distances (Procrustes), ANOVA with interaction controls.

C.  Comparative morphometrics — curvature invariants.

Design: Landmark-based 3-D morphometrics across convergent clades (e.g., cichlids, anoles). Statistic: Equality tests on $K_{\mathrm{ext}}$ distributions (KS/energy tests with phylogenetic block bootstrap).

D.  Microbial evolution — path-invariant functionals.

Design: Parallel adaptation to a fixed target phenotype under disparate protocols. Statistic: Compare invariant path length $L\left[\gamma \right]$, endpoint complexity, and geodesic distance to target.

9. Relations to Existing Programs

Evo-devo canalization.

Shares emphasis on constraints but lacks a global embedding scale $\left(a_{†}\right)$ and a single constitutive law.

Historical selection narratives.

Explain change via time-dependent rates; SEQUENTION replaces rates by geometry and invariants.

Information-theoretic abiogenesis.

Complements my approach: Endres’ rate-distortion framing quantifies finite-resource feasibility and motivates our requirements (R1)–(R3) [7].

10. Limitations and Stress Tests

I list vulnerable points: identifiability of $\left(\mathcal{U}\right)$ from finite samples; robustness of $\left(K_{\mathrm{ext}}\right)$ under measurement noise; dependence on morphospace embedding choices; and possible confounds where order invariance may fail due to strong epistasis outside a projection cone.

11. Ethical Considerations

Protocols involving genome editing and long-term microbial evolution must meet biosafety and welfare standards. The framework itself is ontologically neutral about purpose or teleology.

12. Conclusions

SEQUENTION offers a fundamental re-interpretation of biological evolution, recasting it from a temporal-historical process governed by chance and necessity to a deterministic, geometric problem of projection. We have argued that the standard, time-first paradigm is foundationally incomplete, as it categorically mistakes the "foliation artifacts" of 3D observation for ontic reality. By demoting time, chance, and probability to epistemic heuristics (Axiom A3), this framework resolves the two primary limitations of contemporary theory: it provides a coherent geometric mechanism for non-local and retrocausal phenomena, and it reclaims deterministic chaos as a primary engine of adaptive structure rather than dismissing it as "noise." This re-interpretation is not merely a philosophical preference; it is an empirically grounded methodology. We have established an operational "meta-rule," derived from the geochemical analysis of Chicxulub impact spherules [14], for physically distinguishing static 4D "slice-invariants" (the map’s territory, e.g., nucleosynthetic signatures) from 3D "foliation-dependent artifacts" (the map’s process, e.g., thermodynamic fractionation). This rule provides the epistemic anchor for our claims. Apparent non-locality in biology, from the retrocausal implications of quantum mechanics [12] to the scale-free correlations of starling flocks [13], is re-interpreted as the 3D signature of the 4D, non-local $K_s$ kernel [10]. Concurrently, apparent "randomness" in evolution is re-identified as the complex, structured, and adaptive computation of deterministic, non-linear dynamics [3,16], exemplified by the bistable, maze-solving intelligence of Physarum [20,22]. The logical consequence of this ontology is that the empirical program for biology must be cartographic, not falsificationist [9]. Because all observations are, by Axiom A1, projections of the "Whole Content," no experiment can falsify the existence of the projection (Axiom A3). Instead, an empirical mismatch—such as a failure of Prediction P4—is not a refutation of the framework but a successful discovery of new geometric complexity in the 4D informational potential ($\mathcal{U}$). It proves our map is wrong, compelling us to "draw a new one that matches the territory". The "cartographic inquiries" (P1–P5) and the associated experimental protocols (DMS, CRISPR assays, comparative morphometrics) presented herein are the first tools for this new mapping program. By centering slice invariants (like $K_{\mathrm{ext}}$ and MDL) and a single extrinsic constitutive law (${\mu }_{\mathrm{bio}}$), SEQUENTION provides a concrete, mathematically well-posed, and experimentally tractable pathway to move beyond 3D temporal narratives and begin mapping the true, 4D geometric territory of life.