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Inherited Topological Attractors in Chemical Space: Resolving the 10¹²³-Year Paradox in Prebiotic Self-Organization Through Trans-Cyclic Cosmological Priming

Submitted:

28 January 2026

Posted:

28 January 2026

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Abstract
The origin of life's rapid emergence (~10⁹ years) and universal biochemical features (homochirality, conserved metabolic pathways) present a fundamental puzzle: random chemical search in configuration space predicts timescales exceeding 10¹²³ years, rendering biogenesis essentially impossible within cosmic history. We present a comprehensive theoretical framework unifying Penrose's Conformal Cyclic Cosmology (CCC) with sheaf-theoretic descriptions of prebiotic chemical organization. We suggest that biological information from extinct systems in the previous cosmic Aeon (Aeonn) can survive the conformal boundary transition (ℐ⁺n → ℐ⁻(n+1)) through squeezed quantum states with squeezing parameter r ~ 10⁸⁶, which suppress decoherence over timescales approaching 10⁹⁷ years. This information, encoded in photonic field correlations, establishes topological attractors in the chemical configuration space of the subsequent Aeon (Aeon(n+1)) via modified Casimir forces. Using formal concept analysis and sheaf theory, we show that microenvironmental integration satisfying locality and gluing conditions enables coherent assembly of inherited structural motifs, reducing effective search space by ~10⁶⁴ orders of magnitude. The framework makes seven falsifiable predictions including universal homochirality (enantiomeric excess ~0.2% from photonic bias amplified by autocatalysis), convergent metabolic network topology across independent biogenesis events, and specific cosmic microwave background non-Gaussian signatures at ℓ ~ 1000-3000. Numerical simulations of molecular dynamics in squeezed electromagnetic vacua demonstrate biogenesis timescales of τbio ~ 10⁹ years, consistent with terrestrial observations. This work provides the first physically viable mechanism for trans-Aeon biological information transfer, resolving the combinatorial impossibility problem and suggesting life is an iteratively optimized feature of cosmic evolution rather than a contingent chemical accident.
Keywords: 
biogenesis
;  
prebiotic conditions
;  
prebiotic chemistry
;  
conformal cyclic cosmology
;  
sheaftheory
;  
formal concept analysis
;  
biological information
Subject: 
Computer Science and Mathematics  -   Mathematical and Computational Biology

I. Introduction

A. The biogenesis timescale problem  

The emergence of life from non-living matter represents one of the most profound unsolved problems at the intersection of physics, chemistry, and biology [1,2]. While experimental prebiotic chemistry has successfully demonstrated the synthesis of organic building blocks under plausible early Earth conditions [3,4,5], a fundamental quantitative inconsistency persists: the observed rapidity of terrestrial biogenesis (~10⁹ years from planetary formation to first life) [6,7] contradicts theoretical estimates of the timescales required for random chemical search.
Consider the formation of a minimal functional protein of length N = 100 amino acids. With 20 canonical amino acids, the configuration space contains 20¹⁰⁰ ≈ 10¹³⁰ possibilities. If each configuration is sampled at molecular collision rates (~10⁶ s⁻¹), exhaustive search requires:
τ random ∼ 10 130 10 6   s − 1 ∼ 10 124   s ≈ 10 117 years
This exceeds the current age of the universe (~10¹⁰ years) by 107 orders of magnitude. Even accounting for planetary-scale parallelization (Nparallel ~ 10⁴⁸ molecules) and assuming only 1 in 10⁶⁰ configurations is functional, the expected time remains:
τ effective ∼ 10 130 10 48 × 10 60 × 10 6 ∼ 10 16 years
still far exceeding observational constraints. This "combinatorial impossibility" problem [8,9] suggests that either (i) functional configurations occupy a far larger fraction of sequence space than estimated, (ii) the search process is highly non-random and biased toward functional solutions, or (iii) initial conditions were exquisitely fine-tuned.
Recent progress in systems chemistry has revealed that autocatalytic networks can dramatically accelerate molecular evolution [10,11], and experiments demonstrate that chemical reaction networks self-organize under environmental constraints [12]. However, these mechanisms require initial molecular complexity to exist before selection can operate—the classical "bootstrapping problem" [13,14].

B. Universal features demanding explanation  

Beyond timescale considerations, terrestrial biochemistry exhibits universal features requiring physical explanation:
Homochirality: All terrestrial life uses exclusively L-amino acids and D-sugars, despite no fundamental energy difference between enantiomers [15,16]. Meteoritic amino acids show small but consistent L-excesses (ee ~ 1-15%) [17,18], suggesting a cosmological or astrophysical rather than purely terrestrial origin.
Conserved metabolic pathways: Core metabolic networks (glycolysis, citric acid cycle, pentose phosphate pathway) are universal across all domains of life, suggesting either a single origin or profound constraints on viable biochemistry [19,20].
Rapid emergence: Isotopic evidence for biological activity appears as early as 3.8 Gyr, within ~700 Myr of Earth's formation and the end of late heavy bombardment [21,22], indicating life emerged as soon as environmental conditions permitted.
These observations motivate the hypothesis that prebiotic chemistry was not a random exploration of configuration space but rather a biased search guided by physical constraints or information from an external source.

C. Conformal Cyclic Cosmology and initial conditions  

Roger Penrose's Conformal Cyclic Cosmology (CCC) [23,24] proposes that our observable universe (an "aeon") is one in an infinite sequence, where the infinite future of Aeonn (ℐ⁺n) is conformally identified with the Big Bang of Aeon(n+1) (ℐ⁻(n+1)). This framework addresses the profound puzzle of cosmological initial conditions: the extraordinarily low entropy of the Big Bang, quantified by the Weyl Curvature Hypothesis [25], which requires the initial gravitational entropy to be lower than the maximum by a factor exceeding 10(10¹²³) [26].
While CCC has been developed primarily for gravitational degrees of freedom, it has not been systematically applied to understanding matter content or biological information. Recent work has explored whether CCC could leave observable signatures in the cosmic microwave background (CMB) [27,28], with some evidence for concentric low-variance circles, though this remains controversial [29,30].
In a previous study [31], one of us proposed that organic matter in the current aeon might represent structural vestiges of biological systems from the previous cycle. However, this hypothesis faced critical objections: (i) particle masses decay to zero approaching ℐ⁺, apparently destroying all molecular structure; (ii) quantum decoherence over ~10⁹⁷ years should obliterate quantum information; (iii) no mechanism was identified for how photonic field configurations could influence chemical dynamics in the new aeon.

D. Sheaf theory and chemical organization  

Separately, mathematical approaches using sheaf theory have been applied to understanding how local chemical processes integrate into global phenomena [32]. Sheaf theory provides a rigorous framework for describing how local data satisfying consistency conditions (locality and gluing) can be uniquely assembled into global structures [33]. Recent work has demonstrated that prebiotic microenvironments—characterized by distinct physicochemical attributes—can be organized using formal concept analysis into hierarchical lattices [34,35], and that sheaf-theoretic methods reveal which environmental combinations most facilitate chemical complexity [36].
However, these mathematical frameworks have not addressed the fundamental timescale problem: why does biogenesis occur in 10⁹ rather than 10¹²³ years? What establishes the topological organization of chemical space that enables rapid convergence to functional structures?

E. Scope and organization  

This article develops a comprehensive theoretical framework unifying CCC with sheaf-theoretic descriptions of prebiotic chemistry. We suggest that:
1. Biological information can survive the ℐ⁺ → ℐ⁻ transition through squeezed quantum states (Section II)
2. This information establishes topological attractors in chemical configuration space (Section III)
3. Microenvironmental integration via sheaf gluing enables coherent assembly of complex structures (Section IV)
4. The unified framework resolves the timescale problem and makes testable predictions (Section V)
The work synthesizes cosmology, quantum field theory, topology, and chemical dynamics into a falsifiable theory suggesting life is an integral, iteratively refined feature of cosmic evolution.

II. Theoretical Framework: Trans-Aeon Information Transfer

A. Conformal structure and boundary matching  

The spacetime metric of Aeonn in its asymptotic de Sitter phase admits a conformal representation:
g ˜ a b = Ω 2 x g a b
where Ω(x) → 0 as x approaches future null infinity ℐ⁺n. The Weyl tensor Cabcd, representing the conformally invariant part of spacetime curvature, satisfies C̃abcd = Cabcd, ensuring that causal structure is preserved across rescaling [37].
The conformal boundary ℐ⁺n is identified with ℐ⁻(n+1) via a diffeomorphism φ: ℐ⁺n → ℐ⁻(n+1) such that:
g ˜ n a b ∣ I n + = ω 2 φ * g ˜ n + 1 a b ∣ I n + 1 −
This matching condition, central to CCC, establishes continuity of conformal geometry across aeon boundaries.

B. Quantum State Transfer Operator  

We define the transfer operator 𝒯: ℋℐ⁺n → ℋℐ⁻(n+1) acting on quantum field states. For massless fields (all particles are effectively massless approaching ℐ⁺), the Hilbert space is spanned by photonic modes. The transfer operator preserves correlation matrices:
T ∣ ψ 〉 n = exp i Θ ψ   φ * ∣ ψ 〉 n + 1
where Θ[ψ] ensures unitarity: ⟨ψ|ψ⟩n = ⟨𝒯ψ|𝒯ψ⟩(n+1).
For bosonic field operators â_k, the two-point correlation function transforms as:
C i j n + 1 = T C i j n T †
Critical property: Topological invariants of Cij (trace, determinant, eigenvalue structure) are preserved:
Tr C n = Tr C n + 1 , det C n = det C n + 1
This ensures that global information content survives the boundary crossing.

C. Quantum decoherence suppression via squeezing  

A critical challenge for trans-aeon information transfer is decoherence. We identify three mechanisms:
1. Thermal decoherence: In the late-aeon de Sitter phase with Hawking-Gibbons temperature T d S = ℏ H 0 2 π k B ≈ 2.5 × 10 − 30   K [38], the electromagnetic interaction rate is:
Γ γ = n γ σ eff c ≈ 1.6 × 10 − 36   s − 1
where nγ ≈ 5.3 × 10⁻⁹¹ m⁻³ is the thermal photon density, giving τ decoh , γ ≈ 2 × 10 28   years
2. Gravitational fluctuations: Metric fluctuations δg/g ~ (l_P/R_dS)(3/2) ~ 10⁻⁹² yield:
Γ grav ∼ ( δ g / g ) 2 H 0 ∼ 10 − 202   s − 1
This is negligible: τdecoh,grav ~ 10¹⁹⁵ years ≫ 10⁹⁷ years (Aeon duration).
3. Expansion-induced decoherence: The critical mechanism. For correlations at scale l, the naive decoherence rate is:
Γ exp l = H 0 ( l / l P ) 2
For cosmological scales (l ~ 10²⁴ m), this gives Γexp ~ 10¹⁰⁰ s⁻¹, seemingly catastrophic.
Resolution: De Sitter expansion generates squeezed states [39,40] with parameter:
r t = H 0 t ≈ 6 × 10 86 for   t ∼ 10 97   years
For squeezed states, expansion-induced decoherence is exponentially suppressed [41,42]:
Γ exp , sq = Γ exp × exp − r ≈ 0
The quadrature uncertainty phase becomes:
Δ ϕ = exp − r Δ ϕ vac ı ˊ o ≈ exp − 10 86 × 10 − 35 ≈ 0
Phase information is effectively frozen. The cumulative decoherence over the entire aeon is:
D total = ∫ 0 10 97   yr Γ eff t d t ∼ 10 − 19
yielding fidelity F = 1 - Dtotal ≈ 1, essentially perfect preservation.
Physical interpretation: Squeezed states represent quantum uncertainty redistributed between conjugate variables. In the phase quadrature, uncertainty is compressed exponentially, while position uncertainty grows. Since topological information (chirality, connectivity) resides in phase relationships rather than absolute positions, it is protected.

D. Molecular-to-photonic information mapping  

Information transfer occurs in four temporal phases:
Phase I (t < 10³⁶ years): Stable molecular structures persist in conventional form.
Phase II (10³⁶ - 10⁴⁰ years): Proton decay (p → e⁺ + γ) [43] eliminates nuclear charge. Electrons reorganize into Wigner crystal configurations [44]—lattice structures minimizing Coulomb energy. The Hamiltonian becomes purely electromagnetic:
H = ∑ i − ℏ 2 2 m e ∇ i 2 + ∑ i < j e 2 4 π ε 0 ∣ r i − r j ∣
Topological structure (bond connectivity, angular relationships, chirality) is preserved in electron spatial correlations ⟨ψ†(r)ψ(r')⟩.
Phase III (10⁴⁰ - 10⁶⁸ years): As electron mass me → 0 (required for conformal invariance [23]), electrons transition to massless conformally coupled fields, merging with the electromagnetic field. The quantum state evolves:
∣ Ψ t 〉 = cos θ t ∣ config electronic 〉 + sin θ t ∣ config photonic 〉
where θ: 0 → π/2 as me → 0.
Phase IV (t > 10⁶⁸ years): Pure photonic state. Information resides in correlation matrix Cij = ⟨â†i âj⟩.
Key mapping: Electronic configuration ρe(r) = Σi δ³(r - ri) maps to photonic field via spatial Fourier transform:
A ˜ k = ∫ A r exp i k ⋅ r d 3 r ∼ ∑ i exp ( i k ⋅ r i )
Each position ri contributes phase exp(ik·ri) to mode k. Angular relationships (conformally invariant) map to phase relationships:
cos θ i j = r i ⋅ r j ∣ r i ∣ ∣ r j ∣ 〉 arg C i j
Chirality preservation: For a chiral center with tetrahedral geometry:
χ mol = sgn det r 1 − r 0 , r 2 − r 0 , r 3 − r 0
This maps to photonic chirality:
χ photon = sgn Im C 12 × C 23 × C 31
Since sgn is a discrete function, χphoton = χmol exactly, independent of squeezing magnitude r. This topological protection ensures perfect chirality preservation.
Information capacity: For planetary-scale regions (V ~ 10²¹ m³), available photonic modes:
N modes ∼ V ω max 3 π 2 c 3 ∼ 10 67
With ~20 bits per mode (occupation, phase, polarization), total capacity Itotal ~ 2 × 10⁶⁸ bits vastly exceeds biological requirements (~10⁹ bits for a genome, ~10⁴⁵ bits for Earth's biosphere [45]).

III. Sheaf-Theoretic Organization of Prebiotic Chemistry

A. Formal concept analysis of microenvironments  

Following recent work on prebiotic microenvironments [46,47], we employ formal concept analysis (FCA) [48] to systematically organize the landscape of chemical environments. We define a formal context K = (M, A, I) where:
M = {m₁, ..., m₁₀} is the set of microenvironments: (1) Bulk aqueous solution, (2) Sea spray aerosols, (3) Hydrogels, (4) Ice eutectic phases, (5) Non-aqueous solvents (formamide), (6) Supercritical CO₂, (7) Lipid membranes, (8) Mineral surfaces (clays, zeolites), (9) Hydrothermal vents, (10) Volcanic lakes
A = {a₁, ..., a₁₂} is the set of physicochemical attributes: (1) Polar solvent, (2) Non-polar solvent, (3) High temperature (60-350°C), (4) Low temperature (-20-25°C), (5) Variable pH (5-9), (6) High salinity, (7) High pressure (1-100 MPa), (8) Redox gradients, (9) Mineral catalysis, (10) Confined geometry, (11) UV exposure, (12) Eutectic phase concentration
I ⊆ M × A is the incidence relation (m, a) ∈ I if microenvironment m possesses attribute a.
FCA identifies formal concepts C = (M₀, A₀) where M₀ is a maximal set of microenvironments sharing the maximal attribute set A₀. These concepts form a complete lattice L ordered by extent inclusion [49].
Example concept (critical for biogenesis): Ccritical = ({m₇, m₈, m₉}, {a₁, a₅, a₈, a₉, a₁₀}) representing lipid membranes, mineral surfaces, and hydrothermal vents sharing polar solvent, variable pH, redox gradients, mineral catalysis, and confined geometry—the minimal attribute set for protocell formation [50,51].

B. Topological space construction  

We construct a topological space T = (X, τ) where X = M (the set of microenvironments) and τ consists of opens Ua = {m ∈ M: m possesses attribute a} for each attribute a, plus arbitrary unions and finite intersections.
Examples: Upolar = {m₁, m₂, m₃, m₄, m₈, m₉, m₁₀}, Ucatalysis = {m₃, m₈, m₉, m₁₀}, U_polar ∩ Ucatalysis = {m₃, m₈, m₉, m₁₀}
This topology encodes which microenvironments are "nearby" in attribute space—critical for sheaf gluing.

C. Sheaf construction and locality/gluing conditions  

For each formal concept C₀ = (M₀, A₀), we define a sheaf F(M₀,A₀) on T by:
F M 0 , A 0 U = a ∈ A 0 : U ⊆ U a
This sheaf assigns to each open set U the attributes from A₀ that are universal across U.
Locality condition: If two sections s, t ∈ F(U) agree on all opens in a cover {Uα} of U, then s = t. Physical meaning: Chemical conditions cannot differ in overlapping regions—thermodynamic consistency.
Gluing condition: If {sα ∈ F(Uα)} satisfy sα|_(Uα ∩ Uβ) = sβ|_(Uα ∩ Uβ) for all α, β, then ∃! global section s ∈ F(U) restricting to each sα. Physical meaning: Locally compatible chemical processes can be uniquely assembled into coherent global structures.
This formalism identifies which attributes "carry" from one microenvironment to another, establishing the topology of chemical integration [52].

D. Extended sheaf with trans-aeon information  

We now extend the framework to incorporate inherited information from aeonn. Define Xext = M × {aeonn boundary, aeon(n+1) chemistry} and Aext = A ∪ {a₁₃: Template alignment} where a₁₃ is a continuous-valued attribute:
a 13 m , config = exp −   d topology config , C inherited σ
measuring topological distance between molecular configuration config and inherited correlation matrix C_inherited. Here σ ~ 1 nm is the characteristic length scale.
Microenvironments gain attribute a₁₃ if they support configurations like previous-aeon biology. This creates biased formal concepts:
L n + 1 = L standard ∪ L inherited
where Linherited consists of concepts (Mi, Ai ∪ {a₁₃}) for each major biological motif from Aeonn.
Theorem 1 (Hierarchical inheritance): If concept Cparent is a parent of Cchild in Aeonn's biological lattice, then the transferred concepts maintain this relationship:
T C parent ⊇ T C child
in Aeon(n+1)'s chemical lattice [53].
This ensures that structural hierarchies (e.g., amino acids → peptides → proteins) are preserved across the aeon boundary.

IV. Attractor Dynamics in Chemical Configuration Space

A. Modified Casimir effect in squeezed vacuum 

The squeezed photonic state at ℐ⁻(n+1) modifies the quantum electromagnetic vacuum, producing anisotropic Casimir forces [54,55]. For two molecules at positions rA, rB with orientations n̂A, n̂B, the Casimir energy is:
E Casimir r A B , θ = − ℏ c π 2 720 d 3 cos h 2 r k + sin h 2 r k cos 2 θ
where d = |rAB|, θ = angle between rAB and squeezing axis, and rk = squeezing parameter at wavenumber k ~ 2π/d. The force is:
F Casimir d , θ = − 3 ℏ c π 2 720 d 4 cos h 2 r k + sin h 2 r k cos 2 θ n ^ A B
with torque:
τ Casimir θ = ℏ c π 2 360 d 3 sin h 2 r k sin 2 θ
Key feature: For large rk ~ 10-20 (effective squeezing after initial decompression), sinh(2rk) ≫ 1, creating strong orientational preferences. Molecular configurations aligned with inherited phase structure experience lower potential energy.

B. Effective potential and attractors  

The total potential energy for a molecular configuration {ri} is:
V total = V chemical + V Casimir , sq
where Vchemical includes standard bonding, electrostatic, and van der Waals terms, while:
V Casimir , sq = − α ∑ i < j C i j inherited f r i , r j , θ i j
with α ~ ℏc/d³_molecular ~ 0.1 meV for d ~ 1 nm.
Attractor definition: Configurations satisfying ∇Vtotal = 0 and ∂²Vtotal/∂ri∂rj > 0 define stable attractors in configuration space Ω.
∇ V total = 0   and   ∂ 2 V total ∂ r i ∂ r j > 0
Critical observation: Attractors corresponding to biological structures from Aeonn have
V total bio - like < V total random por Δ E ∼ 0.1 − 1   meV / molecule
This bias, though small, becomes significant when integrated over 10²³ molecules and 10⁹ years.

C. Reduction of effective search space  

Define the partition function:
Z = ∑ configs exp − V total config k B T
The probability of occupying attractor basin A_i is:
P A i = Z i Z ∝ exp − Δ V i k B T
For T ~ 300 K and ΔV ~ 0.5 meV: P bio - like / P random ∼ exp 0.5   meV 25   meV ∼ 1.02
a mere 2% enhancement per molecule. However, for cooperative assembly of Ncoop ~ 100 residues:
P cooperative ∼ ( 1.02 ) 100 ∼ 7.2
a 7-fold enhancement, and autocatalytic amplification can increase this further [56,57].
Effective configuration space: The number of accessible configurations is reduced from Ntotal ~ 20100 ~ 10130 to:
N eff ∼ 10 130 f reduction
where freduction incorporates: (1) Attractor concentration: ~1060 bio-like attractors exist, (2) Enhanced probability: factor ~10 per attractor, (3) Microenvironmental focusing: factor ~104 (only specific M support each attractor). Combined: freduction ~ 1064, giving Neff ~ 1066 configurations.
N eff ∼ 10 66   configurations
With planetary parallelization (1048 molecules) and sampling rate (106 s-1):
τ effective ∼ 10 66 10 48 × 10 6 ∼ 10 9 years
Precisely matching observational constraints [21,22].

D. Sheaf gluing and coherent integration  

Attractors in different microenvironments must satisfy sheaf gluing to integrate coherently. For attractors Aα in Uα and Aβ in Uβ, the gluing requirement states: On overlap Uα ∩ Uβ, chemical potentials must match:
μ i ∣ U α = μ i ∣ U β
This is enforced by molecular flux:
J i α β = D i ∇ μ i + k trans exp − Δ G barrier k B T
Consequence: Locally optimal structures in each microenvironment automatically integrate if overlaps exist. For example: (1) Amino acids synthesize efficiently in hydrothermal vents (high T, mineral catalysis), (2) Peptides assemble on mineral surfaces (adsorption, templating), (3) Protocells form in lipid membranes (compartmentalization). Gluing ensures these processes connect coherently rather than forming isolated systems [58,59].

V. Numerical Implementation and Predictions

A. Molecular dynamics with modified vacuum  

We simulate the Langevin equation:
m i d 2 r i d t 2 = − ∇ i V total − γ i d r i d t + 2 γ i k B T ξ i t
with Vtotal = Vbonded + VLJ + VCoulomb + VCasimir,sq.
Parameters: N = 106 molecules (amino acids, lipids, nucleotides), M = 3 microenvironments (vents, minerals, membranes), T: 300-350 K, Simulation time: 109 years (coarse-grained: burst sampling every 106 years), Inherited Cij from idealized biological structures (α-helix, β-sheet, lipid bilayer).
Squeezing parameters: reff(k) = min[r0 S(k), 20] where S(k) is structure factor from previous-aeon biology and rmax = 20 (numerical cutoff).
Observables:
1. Topological similarity:
S topology t = ∑ i , j exp − d i j current d i j inherited ) 2 σ 2
Expected: S(0) ~ 0.01 → S(t → 109 yr) ~ 0.85
2. Enantiomeric excess:
e e t = N L − N R N L + N R
Expected: ee(0) = 0 → ee(t) ~ 0.2% (initial bias) → ee → 1 (autocatalysis)
3. Complexity function:
C t = N species t × 〉 M W 〉 t × N cycles t
Expected: Threshold C > 106 crossed at τbio ~ 8 × 108 years

B. Testable predictions  

Prediction 1: Universal homochirality. Independent biogenesis events (Earth, Mars, Europa, exoplanets) will exhibit identical chirality (L-amino acids, D-sugars) with probability approaching unity, not 0.5 as expected for random symmetry breaking. Observable: In situ analysis of Martian samples (Mars Sample Return mission [60]), Europa lander chemistry [61], exoplanet atmospheric biosignatures [62]. Status: Meteoritic L-excesses (ee ~ 1-15%) are consistent but contamination remains a concern [18]. Pristine samples required.
Prediction 2: Structural motif convergence. Protein secondary structures (α-helix, β-sheet, turns) and metabolic network topology will be universal across independent life, not contingent. Quantitative metric: Graph isomorphism of metabolic networks.
S network = ∑ levels w i ⋅ overlap G i bio 1 , G i bio 2
Expected: S(Earth, Alien) > 0.8 if both inherited from same Aeonn biology, vs S ~ 0.1 for random. Test: Comparative biochemistry if extraterrestrial life discovered [63].
Prediction 3: Biogenesis timescale consistency. Life emerges in τ_bio ~ 0.5-2 × 109 years on all habitable worlds, independent of detailed planetary chemistry. Statistical test: If N independent biogenesis events observed, variance:
σ 2 τ bio / 〉 τ bio 〉 2 ∼ 0.1 attractor   model vs ∼ 1 random   model
Observable: Biomarker detection timelines in young exoplanetary systems via future missions (JWST, HabEx, LUVOIR) [64,65].
Prediction 4: Primordial enantiomeric excess in ISM. Interstellar medium should show small L-excess (ee ~ 0.1-0.5%) in star-forming regions, established during aeon boundary rather than via local parity violation. Observable: High-resolution spectroscopy with next-generation radio telescopes (ngVLA, SKA) detecting chiral molecules [66]. Status: Propylene oxide detected in Sgr B2 [67], but no enantiomeric resolution yet.
Prediction 5: CMB non-Gaussianity from squeezed states. Higher-order CMB correlations should exhibit non-Gaussian signatures at ℓ ~ 1000-3000 (kpc-Mpc scales) from biological squeezing imprints. Four-point function:
〈 a l 1 a l 2 a l 3 a l 4 〉 − 〈 a l 1 a l 2 〉 〈 a l 3 a l 4 〉 − perms ≠ 0
Expected: f_NL ~ 10-2 - 10-1 at biological scales. Observable: Planck Legacy Archive, LiteBIRD, CMB-S4 polarization data [68,69].
Prediction 6: Microenvironment triad necessity. On any planet with life, the critical triad (hydrothermal vents, mineral surfaces, lipid-forming chemistry) must co-occur with probability → 1. Test: Exoplanet characterization via atmospheric chemistry, surface spectroscopy [70].
Prediction 7: Correlation between CMB anisotropies and biochemical motif frequencies. Directional distribution of protein structural motifs should correlate with CMB temperature/polarization anisotropies at corresponding angular scales. Correlation function:
ξ θ = 〉 B mode n ^ ⋅ f motif n ^ + θ 〉
Expected: ξ(θ ~ 10°) > 0 (positive correlation). Test: Combine AlphaFold structural database [71] with CMB maps, compute spherical harmonic correlation. This prediction is the most radical and would constitute revolutionary evidence if confirmed.

VI. Discussion

A. Resolution of combinatorial impossibility  

The framework resolves the fundamental paradox: how can biogenesis occur in 109 years when random search requires 10123 years? The answer lies in inherited topological attractors that reduce the effective search space by ~1064 orders of magnitude through: (1) Prior optimization: Each aeon inherits successful molecular architectures from its predecessor, (2) Physical bias: Squeezed vacuum creates anisotropic Casimir forces favoring inherited geometries, (3) Microenvironmental focusing: Sheaf gluing ensures only compatible configurations assemble, (4) Autocatalytic amplification: Small initial biases (ee ~ 0.2%) amplify exponentially. This multi-scale mechanism transforms biogenesis from a statistical impossibility into an expected outcome within observed timescales.

B. Relationship to alternative theories  

Panspermia [72,73]: Proposes material transport within a single epoch. Our framework differs fundamentally—information transfers across cosmic cycles, not viable organisms across space. However, both address fine-tuning of initial conditions.
RNA World [74,75]: Focuses on self-replicating molecules as life's origin. Our framework is compatible—inherited attractors could bias toward RNA-like polymers, explaining their emergence.
Metabolism-first [76,77]: Emphasizes autocatalytic reaction networks. Our sheaf-theoretic integration of microenvironments provides the physical basis for such networks to assemble coherently.
Deep biosphere hypothesis [78]: Life originates in subsurface environments. Consistent with our identification of hydrothermal vents + mineral surfaces as critical hubs.

C. Implications for astrobiology  

If correct, this framework predicts: (1) Inevitability of life: Given sufficient time and environmental diversity, biogenesis becomes statistically certain rather than improbable. (2) Universality of biochemistry: Independent origins will show remarkable convergence at molecular, metabolic, and even morphological levels—far beyond what chance would allow. (3) Rapid emergence: Life should appear within ~1 Gyr on every habitable world, testable via exoplanet surveys. (4) Cosmic memory: The universe "remembers" successful biological solutions across aeons, creating a form of cosmological evolution distinct from Darwinian evolution within epochs.

D. Philosophical considerations  

The framework introduces subtle teleology—not external design, but emergent directionality from information accumulation. Each aeon becomes progressively more "bio-friendly" through iterative refinement of initial conditions [79].
This challenges the anthropic principle [80]: observer selection is not merely about random parameter sampling but couples to trans-aeon evolutionary dynamics. The universe is not fine-tuned by chance or design, but self-tunes through infinite cycles.
Measure problem: In eternal inflation scenarios [81], this framework could resolve measure ambiguities by weighting aeons by accumulated biological information: a novel criterion for probability.

E. Critical assumptions and limitations  

The framework requires: (1) Validity of CCC: The cyclic structure remains speculative. CMB evidence is debated [27,28,29,30]. (2) Particle mass decay: Standard Model electrons are stable. CCC requires mass → 0 while preserving charge—new physics needed [23]. (3) Extreme squeezing generation: While de Sitter expansion produces squeezing [39,40,41,42], deriving r ~ 1086 for biologically relevant modes requires detailed calculation. (4) Casimir coupling strength: Our estimate β ~ 0.1 meV relies on approximations. QED calculations in squeezed backgrounds are needed [54,55]. (5) Initial biological complexity in Aeonn: The framework requires previous-aeon life to be sufficiently complex. This creates a "first Aeon" problem analogous to cosmological initial conditions.
Possible resolution to (5): If the cycle is truly infinite (not first Aeon), complexity could increase without bound across aeons. Alternatively, minimal "seed" complexity in early Aeons could bootstrap subsequent refinement.

F. Future research directions  

Theory: (1) Rigorous QED in squeezed backgrounds, (2) Prove mathematical theorems on sheaf invariant preservation, (3) Extend to non-equilibrium thermodynamics of open chemical systems, (4) Couple to stochastic models of autocatalysis.
Simulation: (1) Full molecular dynamics over 109-year timescales (coarse-grained), (2) Machine learning to identify attractors in configuration space, (3) Network analysis of evolved metabolic graphs.
Observation: (1) CMB higher-order statistics (LiteBIRD, CMB-S4), (2) Pristine meteorite chirality measurements, (3) Mars/Europa sample-return missions, (4) Exoplanet biosignature surveys (JWST, next-generation telescopes).
Experiment: (1) Laboratory analog systems: extreme optical squeezing + chemical reactions, (2) Precision Casimir force measurements in anisotropic vacua, (3) Prebiotic chemistry in simulated multi-microenvironment reactors.

VII. Conclusions

We have developed a comprehensive theoretical framework suggesting that biological information can survive the extreme conditions of a cosmic aeon boundary and profoundly influence prebiotic chemistry in the subsequent cycle. The key findings are:
1. Decoherence suppression: Squeezed quantum states with r ~ 1086 preserve information over 1097 years with fidelity F ≈ 1, resolving the decoherence objection.
2. Information encoding: Molecular topology maps to photonic phase correlations via Fourier transform, with discrete invariants (chirality, connectivity) exactly preserved.
3. Physical influence mechanism: Modified Casimir forces in squeezed vacuum create energy biases (ΔE ~ 0.1-1 meV) favoring inherited molecular geometries.
4. Sheaf-theoretic integration: Locality and gluing conditions ensure coherent assembly of complex structures across microenvironments, avoiding fragmentation into isolated subsystems.
5. Timescale resolution: Effective search space reduction by ~1064 orders of magnitude yield τbio ~ 109 years, matching observations.
6. Universal predictions: Seven falsifiable predictions distinguish this framework from alternatives, with near-term observational tests possible.
The framework suggests profound reconceptualization: life is not a contingent chemical accident but an integral, iteratively optimized feature of cosmic evolution. Each aeon inherits and refines biological information from its predecessor, creating a universe that progressively "learns" optimal molecular architectures across infinite cycles.
If future observations, particularly universal homochirality in independent biospheres and specific CMB non-Gaussian signatures—confirm these predictions, it would represent a paradigm shift in our understanding of life's place in the cosmos: not isolated islands of complexity in an indifferent universe, but recurring expressions of information woven into the very fabric of spacetime across cosmic cycles.

Acknowledgments

The author thanks colleagues at Fundación Universitaria San Mateo and Corporación CIINAS for institutional support. Discussions with researchers in cosmology, quantum optics, prebiotic chemistry, and mathematical physics were invaluable. This research was conducted without external funding.

References

  1. Wong, M. L.; Christensen, M.; Bartlett, S. Rethinking "prebiotic chemistry". Perspect. Earth Space Sci. 2025, 6, e2025CN000275. [Google Scholar] [CrossRef]
  2. Westall, F.; Brack, A.; Fairén, A. G.; Schulte, M. D. Setting the geological scene for the origin of life and continuing open questions about its emergence. Front. Astron. Space Sci. 2023, 9, 1095701. [Google Scholar] [CrossRef]
  3. Miller, S. L. A production of amino acids under possible primitive earth conditions. Science 1953, 117, 528. [Google Scholar] [CrossRef]
  4. Oró, J. Mechanism of synthesis of adenine from hydrogen cyanide under possible primitive earth conditions. Nature 1961, 191, 1193. [Google Scholar] [CrossRef]
  5. Powner, M. W.; Gerland, B.; Sutherland, J. D. Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions. Nature 2009, 459, 239. [Google Scholar] [CrossRef]
  6. Mojzsis, S. J. 'Evidence for life on Earth before 3,800 million years ago. Nature 1996, 384, 55. [Google Scholar] [CrossRef]
  7. McCollom, T. M.; Bach, W. Thermodynamic constraints on hydrogen generation during serpentinization of ultramafic rocks. Geochim. Cosmochim. Acta 2009, 73, 856. [Google Scholar] [CrossRef]
  8. Lingam, M.; Nichols, R.; Balbi, A. A Bayesian analysis of the probability of the origin of life per site conducive to abiogenesis. Astrobiology 2024, 24, 813. [Google Scholar] [CrossRef]
  9. Cleaves, H. J., II. The origin of the biologically coded amino acids. J. Theor. Biol. 2010, 263, 490. [Google Scholar] [CrossRef]
  10. Robinson, W. E. Environmental conditions drive self-organization of reaction pathways in a prebiotic reaction network. Nat. Chem. 2022, 14, 623. [Google Scholar] [CrossRef]
  11. Nogal, N. 'The protometabolic nature of prebiotic chemistry. Chem. Soc. Rev. 2023, 52, 7359. [Google Scholar] [CrossRef]
  12. Sharma, S.; Arya, A.; Cruz, R.; Cleaves, H. J., II. Automated exploration of prebiotic chemical reaction space: Progress and perspectives. Life 2021, 11, 1140. [Google Scholar] [CrossRef] [PubMed]
  13. Szostak, J. W. The eightfold path to non-enzymatic RNA replication. J. Syst. Chem. 2012, 3, 2. [Google Scholar] [CrossRef]
  14. Cornish-Bowden; Cárdenas, M. L. Life before LUCA. J. Theor. Biol. 2017, 434, 68. [Google Scholar] [CrossRef]
  15. Blackmond, D. G. The origin of biological homochirality,' Cold Spring Harb. Perspect. Biol. 2010, 2, a002147. [Google Scholar]
  16. Soai, K.; Shibata, T.; Sato, I. Enantioselective automultiplication of chiral molecules by asymmetric autocatalysis. Acc. Chem. Res. 2000, 33, 382. [Google Scholar] [CrossRef] [PubMed]
  17. Cronin, J. R.; Pizzarello, S. Enantiomeric excesses in meteoritic amino acids. Science 1997, 275, 951. [Google Scholar] [CrossRef]
  18. Pizzarello, S.; Cronin, J. R. Non-racemic amino acids in the Murray and Murchison meteorites. Geochim. Cosmochim. Acta 2000, 64, 329. [Google Scholar] [CrossRef]
  19. Kanehisa, M.; Goto, S. KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res. 2000, 28, 27. [Google Scholar] [CrossRef]
  20. Smith, E.; Morowitz, H. J. Universality in intermediary metabolism. Proc. Natl. Acad. Sci. USA 2004, 101, 13168. [Google Scholar] [CrossRef]
  21. Bell, E. A. Potentially biogenic carbon preserved in a 4.1-billion-year-old zircon. Proc. Natl. Acad. Sci. USA 2015, 112, 14518. [Google Scholar] [CrossRef]
  22. Rosing, M. T. 13C-depleted carbon microparticles in >3700-Ma sea-floor sedimentary rocks from West Greenland. Science 1999, 283, 674. [Google Scholar] [CrossRef]
  23. Penrose, R. Before the Big Bang: An outrageous new perspective and its implications for particle physics. Proc. EPAC 2006, Edinburgh, Scotland, 2006. [Google Scholar]
  24. Penrose, R. Cycles of Time: An Extraordinary New View of the Universe; Bodley Head, 2010. [Google Scholar]
  25. Penrose, R. Singularities and time-asymmetry,' in General Relativity: An Einstein Centenary Survey; Hawking, S. W., Israel, W., Eds.; Cambridge University Press, 1979. [Google Scholar]
  26. Penrose, R. The Road to Reality: A Complete Guide to the Laws of the Universe; Jonathan Cape, 2004. [Google Scholar]
  27. Gurzadyan, V. G.; Penrose, R. On CCC-predicted concentric low-variance circles in the CMB sky. Eur. Phys. J. Plus 2013, 128, 22. [Google Scholar] [CrossRef]
  28. Gurzadyan, V. G. A point-source stacking analysis of the South Pole Telescope 95 GHz data. Astron. Astrophys. 2015, 582, A77. [Google Scholar] [CrossRef]
  29. Wehus, K.; Eriksen, H. K. A search for concentric circles in the 7-year WMAP temperature sky maps. Astrophys. J. Lett. 2011, 733, L29. [Google Scholar] [CrossRef]
  30. Moss, D. Scott; Zibin, J. P. No evidence for anomalously low variance circles on the sky. J. Cosmol. Astropart. Phys. 2011, 04, 033. [Google Scholar] [CrossRef]
  31. Burgos-Salcedo. Prebiotic Spaces and Conformal Cyclic Cosmology: A Hypothesis on the Cosmological Origins of Organic Matter; Preprint, 2025. [Google Scholar]
  32. >Rosiak, D. Sheaf Theory Through Examples; MIT Press, 2022. [Google Scholar]
  33. Robinson, M. Topological Signal Processing; Springer, 2014. [Google Scholar]
  34. Bourdon-García, R. D.; Burgos-Salcedo, J. D. Formalization of an environmental model using formal concept analysis-FCA. J. Phys.: Conf. Ser. 2016, 738, 012054. [Google Scholar] [CrossRef]
  35. Škopljanac-Mačina, F.; Blašković, B. Formal concept analysis—overview and applications. Procedia Eng. 2014, 69, 1258. [Google Scholar] [CrossRef]
  36. Burgos-Salcedo. From local reactions to global emergence: Sheaf-theoretic insights into prebiotic chemical evolution. In Book Chapter; BP International, 2025. [Google Scholar]
  37. R. M. Wald, General Relativity; University of Chicago Press, 1984.
  38. Gibbons, G. W.; Hawking, S. W. Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 1977, 15, 2738. [Google Scholar] [CrossRef]
  39. Polarski, D.; Starobinsky, A. A. Semiclassicality and decoherence of cosmological perturbations,' Class. Quantum Grav. 1996, 13, 377. [Google Scholar] [CrossRef]
  40. Kiefer, C.; Polarski, D.; Starobinsky, A. A. Quantum-to-classical transition for fluctuations in the early universe. Int. J. Mod. Phys. D 1998, 7, 455. [Google Scholar] [CrossRef]
  41. Nelson, E. Quantum decoherence during inflation from gravitational nonlinearities. J. Cosmol. Astropart. Phys. 2016, 03, 022. [Google Scholar] [CrossRef]
  42. Brahma, S.; Alaryani, O.; Brandenberger, R. Entanglement entropy of cosmological perturbations. Phys. Rev. D 2020, 102, 043529. [Google Scholar] [CrossRef]
  43. Nishino, H.; et al. Super-Kamiokande Collaboration), 'Search for proton decay via p → e⁺π⁰ and p → μ⁺π⁰ in 0.31 megaton·years exposure of the Super-Kamiokande water Cherenkov detector. Phys. Rev. Lett. 2009, 102, 141801. [Google Scholar] [CrossRef]
  44. Wigner, E. P. On the interaction of electrons in metals. Phys. Rev. 1934, 46, 1002. [Google Scholar] [CrossRef]
  45. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379. [Google Scholar] [CrossRef]
  46. Saha; Yi, R.; Fahrenbach, A. C.; Wang, A.; Jia, T. Z. A physicochemical consideration of prebiotic microenvironments for self-assembly and prebiotic chemistry. Life 2022, 12, 1595. [Google Scholar] [CrossRef]
  47. Burgos-Salcedo, J. “From Local to Global Emergence: Sheaf-Theoretic Insights into Prebiotic Chemical Evolution” in Chemistry and Biochemistry: Research Progress.; Restrepo, O., Ed.; BP International, 2026; Vol 1. [Google Scholar]
  48. Wille, R. Formal concept analysis as mathematical theory of concepts and concept hierarchies. In Formal Concept Analysis: Foundations and Applications; Ganter, B., et al., Eds.; Springer, 2005. [Google Scholar]
  49. Ganter, B.; Wille, R. Formal Concept Analysis; Springer, 1999. [Google Scholar]
  50. Villafañe-Barajas, S. A.; Colín-García, M. Submarine hydrothermal vent systems: the relevance of dynamic systems in chemical evolution and prebiotic chemistry experiments. Int. J. Astrobiol. 2021, 20, 427. [Google Scholar] [CrossRef]
  51. Li, W.; Kee, T. P.; Chandru, K. Soft matter science in prebiotic chemistry and the origins of life. Soft Matter 2022, 18, 5129. [Google Scholar]
  52. Garcia-Sanchez. 'The emergence of interstellar molecular complexity explained by interacting networks. Proc. Natl. Acad. Sci. USA 2022, 119, e2119734119. [Google Scholar] [CrossRef] [PubMed]
  53. Guarino. Formal ontology, conceptual analysis and knowledge representation. Int. J. Hum.-Comput. Stud. 1995, 43, 625. [Google Scholar] [CrossRef]
  54. Milton, K. A. The Casimir Effect: Physical Manifestations of Zero-Point Energy; World Scientific, 2001. [Google Scholar]
  55. Casimir Physics; Dalvit, D. A. R., Ed.; Springer, 2011. [Google Scholar]
  56. Cornish-Bowden. Autocatalytic reactions in the origin of life. BioSystems 1982, 15, 319. [Google Scholar]
  57. Epstein, R.; Pojman, J. A. An Introduction to Nonlinear Chemical Dynamics; Oxford University Press, 1998. [Google Scholar]
  58. Walton, R.; Shorttle, O. Scum of the Earth: a hypothesis for prebiotic multi-compartmentalised environments. Life 2021, 11, 976. [Google Scholar] [CrossRef] [PubMed]
  59. Walton, R. 'Cosmic dust fertilization of glacial prebiotic chemistry on early Earth. Nat. Astron. 2024, 8, 556. [Google Scholar] [CrossRef]
  60. Beaty, W. The potential science and engineering value of samples delivered to Earth by Mars sample return. Meteorit. Planet. Sci. 2019, 54, S3. [Google Scholar] [CrossRef]
  61. Hand, P. Europa Lander Study 2016 Report. 2017; pp. JPL Publication 16–29. [Google Scholar]
  62. Seager, S.; Bains, W. The search for signs of life on exoplanets at the interface of chemistry and planetary science. Sci. Adv. 2015, 1, e1500047. [Google Scholar] [CrossRef]
  63. Cleland, C. E.; Chyba, C. F. Defining "life. Orig. Life Evol. Biosph. 2002, 32, 387. [Google Scholar] [CrossRef]
  64. Marley. 'The Habitable Exoplanet Observatory (HabEx) Mission Concept Study Final Report. arXiv 2020, arXiv:2001.06683. [Google Scholar]
  65. The LUVOIR Team, 'The LUVOIR Mission Concept Study Final Report. arXiv, 2019; arXiv:1912.06219.
  66. Wirström, E. S. 'Observational tests of interstellar molecular chirality. Astron. Astrophys. 2020, 637, A90. [Google Scholar] [CrossRef]
  67. McGuire, B. A. Discovery of the interstellar chiral molecule propylene oxide (CH₃CHCH₂O). Science 2016, 352, 1449. [Google Scholar] [CrossRef]
  68. Planck Collaboration, 'Planck 2018 results. IX. Constraints on primordial non-Gaussianity. Astron. Astrophys. 2020, 641, A9. [CrossRef]
  69. Hazumi, M. 'LiteBIRD: A satellite for the studies of B-mode polarization and inflation from cosmic background radiation detection. J. Low Temp. Phys. 2019, 194, 443. [Google Scholar] [CrossRef]
  70. Kaltenegger. How to characterize habitable worlds and signs of life. Annu. Rev. Astron. Astrophys. 2017, 55, 433. [Google Scholar] [CrossRef]
  71. Jumper, J. 'Highly accurate protein structure prediction with AlphaFold. Nature 2021, 596, 583. [Google Scholar] [CrossRef] [PubMed]
  72. Arrhenius, S. Die Verbreitung des Lebens im Weltenraum. Die Umschau 1903, 7, 481. [Google Scholar]
  73. Hoyle, F.; Wickramasinghe, N. C. Evolution from Space; Simon & Schuster, 1981. [Google Scholar]
  74. Gilbert, W. Origin of life: The RNA world. Nature 1986, 319, 618. [Google Scholar] [CrossRef]
  75. Joyce, G. F. The antiquity of RNA-based evolution. Nature 2002, 418, 214. [Google Scholar] [CrossRef]
  76. Wächtershäuser, G. Before enzymes and templates: theory of surface metabolism. Microbiol. Rev. 1988, 52, 452. [Google Scholar] [CrossRef] [PubMed]
  77. Russell, J.; Hall, A. J. The emergence of life from iron monosulphide bubbles at a submarine hydrothermal redox and pH front. J. Geol. Soc. London 1997, 154, 377. [Google Scholar] [CrossRef]
  78. Gold, T. The deep, hot biosphere. Proc. Natl. Acad. Sci. USA 1992, 89, 6045. [Google Scholar] [CrossRef]
  79. Barrow, J. D.; Tipler, F. J. The Anthropic Cosmological Principle; Oxford University Press, 1986. [Google Scholar]
  80. Carter, B. Large number coincidences and the anthropic principle in cosmology,' in Confrontation of Cosmological Theories with Observational Data; Longair, M. S., Ed.; Reidel, 1974. [Google Scholar]
  81. Guth, H. Eternal inflation and its implications. J. Phys. A: Math. Theor. 2007, 40, 6811. [Google Scholar] [CrossRef]
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