Death of the Observer in ODTOE: Deactualisation, World Line and Conditions for Immortality

DEATH OF THE OBSERVER IN ODTOE: DEACTUALISATION, WORLD LINE AND CONDITIONS FOR IMMORTALITY Pankratov Anton Sergeevich Independent researcher, Kazan, Russia E-mail: [email protected] ORCID: 0009-0002-4870-2995

UDC 530.145 + 128.1 + 612.67

ABSTRACT Within the Observer-Dependent Theory of Everything (ODTOE) [1], the phenomenon of observer death is investigated. Death is shown to be not annihilation but deactualisation: the observation operator Ô ceases to project configurations from H into C, yet the observer’s world line W = {Ψ∗n }n∈Z persists in the space of potential states as a single inseparable object [2]. Four phases of dying are formalised through sequential zeroing of cognitive coherence components B = F · E · (1 − σ) · Λ [1]: loss of focus (F → 0), emotional decoherence (E → 0), zeroing of experience (Λ → 0), maximal internal contradiction (σ → 1). The concept of coherent legacy L(O) is introduced — the aggregate of artefacts through which a deactualised observer continues to influence collective S. From the configuration lifetime formula T (C) = T0 /(1 − S)n [1], three conditions are derived under which an observer’s influence survives biological death: high artefact coherence (SA → 1), growing number of successors (nsucc → ∞), and self-consistency of the world line with the fixed point Ψ∗ . It is shown that the commandment “love thy neighbour as thyself” [3] constitutes the sole condition under which T (L) → ∞ — coherent immortality. Parallels with Buddhist, Christian, and Stoic philosophies of death are discussed, along with neardeath experiences (NDE), digital legacy, and experimentally testable predictions. Keywords: death, observer, deactualisation, world line, coherent legacy, immortality, artefact, coherence, near-death experience, digital legacy, ODTOE.

I. INTRODUCTION: WHY PHYSICS IS SILENT ABOUT DEATH Physics describes the decay of atoms, the collapse of stars, the heat death of the Universe — but not the death of the observer. In the standard formalism the observer is an external agent who does not enter the equations. Its appearance and disappearance

are not described by the theory. Quantum mechanics postulates the collapse of the wave function upon measurement but does not formalise what happens when the measurer ceases to exist [13]. Classical thermodynamics describes death as entropy growth in an open system: the organism loses the ability to maintain the negative entropy necessary for life [16]. However, thermodynamics says nothing about the subjective experience of dying, about what happens to the observer’s “first person.” This lacuna is not accidental — it is a consequence of the fundamental decision made by seventeenth-century physics: to place the observer outside the brackets of the equations. ODTOE eliminates this gap. The observer is not an external commentator but a constitutive element of reality: R = Ô(Ψ) [1]. Its disappearance is not “switching off the camera” but a structural event that changes the configuration of reality for all connected observers. When the operator Ô ceases to act, it is not only the state of one individual that changes — the entire structure of collective coherence S, in which that individual was embedded, changes as well. This fundamentally distinguishes the ODTOE approach from the two dominant paradigms. Materialism asserts: death is the complete annihilation of the subject, after which nothing remains. Religious dualism asserts: death is the transition of the “soul” to another mode of being. ODTOE offers a third way: death is deactualisation, in which the operator Ô ceases to project configurations, but the world line W is preserved in H as a mathematical object, and the coherent legacy L(O) continues to influence the collective configuration. The questions posed by the present paper: What happens when Ô ceases to act? Is the observer annihilated? Does information about the observer disappear? Can one formalise the conditions under which the observer’s influence continues after biological death? Are there experimentally testable consequences of this model?

II. FOUR PHASES OF DEACTUALISATION II.1. Death as B → 0 The cognitive coherence of the observer [1]: B(O, C) = F w1 · E w2 · (1 − σ)w3 · Λw4

(D1.1)

The formula is multiplicative: zeroing any factor zeroes the entire result. Biological death is a process of sequential zeroing of all four components. The order may vary, but the structure is universal. The multiplicativity of the formula reflects a fundamental property of consciousness: it is not the sum of independent parts but the product of interdependent factors. The loss of any single factor destroys the whole — just as a product becomes zero when any factor is zeroed. It is important to emphasise that zeroing of B does not mean instantaneous disappearance. The process of deactualisation unfolds in time and passes through characteristic phases, each of which has neurophysiological correlates and subjective

manifestations. Let us consider these phases in detail. The rate of deactualisation can be described by a differential equation. If we introduce a generalised degradation parameter τ , then: dB =B dτ

w2 dE w3 dσ w4 dΛ w1 dF + − + F dτ E dτ 1 − σ dτ Λ dτ

(D1.2)

This formula shows that the rate of zeroing of B is proportional to the current value of B and to the sum of the relative degradation rates of each component. At small values of any component, the corresponding term in parentheses dominates, accelerating overall degradation — an effect observed clinically as cascading deterioration in the terminal phase.

II.2. Phase I: Loss of focus (F → 0) Typically, focus weakens first. Attention disperses. Thoughts lose directionality. Clinically this manifests as confusion, delirium, loss of orientation. Neurophysiologically: decreased activity of the dorsal attention network (DAN), degradation of the EEG gamma rhythm [4]. Research by Lazar et al. showed that grey-matter density in the prefrontal cortex — the key neuroanatomical substrate of focus — declines with ageing and especially sharply in neurodegenerative diseases [4]. In ODTOE: the operator Ô loses its “aim” — it projects configurations chaotically, without a stable direction. Observation becomes blurred. Formally this is described as an increase in the variance of the projection operator: Var[Ô(Ψ)] =

σ02 →∞ F2

as F → 0

(D2.1)

An observer who has lost focus projects an ever-wider spectrum of configurations, unable to concentrate on any one of them. Subjectively this is experienced as “dissolving” of reality, an inability to hold a thought, loss of the “here and now.” Clinically it is precisely this phase that most often first attracts the attention of others — the person “no longer recognises where they are.”

II.3. Phase II: Emotional decoherence (E → 0) The emotional system becomes misaligned with intention. The person ceases to feel a connection with what they do and what they want. Heart-rate variability (HRV) drops — an objective marker of decreasing E [5]. Clinically: apathy, indifference, emotional “flattening.” McCraty and Zayas showed that HRV is a reliable biomarker of emotional coherence — the ability of the emotional system to synchronise with cognitive processes [5]. In ODTOE: the quaternionic axis Ej is zeroed [6]. The observer loses the “rotation amplitude” — the ability to resonate emotionally with a configuration. If the observer’s

state is represented as a quaternion q = Λ + F i + Ej + σk [6], then zeroing the Ecomponent means losing one of the three spatial dimensions of the observer’s “inner space.” Emotional decoherence is particularly vivid in terminal stages: patients often display so-called “emotional indifference” — the inability to experience joy, grief, or fear. This is not “peace” — it is the loss of one of the fundamental channels of connection with reality.

II.4. Phase III: Devaluation of experience (Λ → 0) Accumulated experience ceases to be perceived as a resource. The past loses meaning. The person does not recognise loved ones, does not remember their own history. Neurophysiologically: hippocampal degeneration [7]. The work of Braak and Braak demonstrated the staged nature of neuropathological changes in Alzheimer’s disease: degradation begins in the entorhinal cortex and hippocampus — structures responsible for memory consolidation — and gradually spreads to the neocortex [7]. In ODTOE: the scalar part of the quaternion Λ (the real component, the observer’s “grounding”) is zeroed. The operator loses its “anchor” — the reference point in configuration space. Without experience (Λ = 0) the observer cannot distinguish configurations: all projections Ô(Ψ) become equivalent, devoid of context and historical depth. The loss of Λ is especially tragic because it destroys the continuity of the world line in the observer’s subjective perception. Although objectively the world line W = {Ψ∗n } continues to exist in H, subjectively the observer loses access to their own past iterations. Each moment becomes isolated, unconnected with previous ones.

II.5. Phase IV: Maximal contradiction (σ → 1) Internal processes are completely desynchronised. The heart contracts but the blood does not deliver oxygen. Neurons fire but without coordination. Biochemical cascades contradict one another. In ODTOE: (1 − σ) → 0. The integrity factor is zeroed. The observer “comes apart” — much as a star comes apart during tidal disruption by a black hole [8]. The analogy is not accidental: in both cases the internal binding forces (gravitational for the star, coherent for the observer) prove insufficient to maintain the object’s integrity. Formally, the growth of σ is described through an increase in the measure of internal inconsistency. If the observer’s state is regarded as a set of subsystems {s1 , s2 , . . . , sm }, then: σ =1−

cos θij m(m − 1) i<j

(D2.2)

where θij is the “misalignment angle” between subsystems si and sj . At full alignment (θij = 0 for all pairs) σ = 0. At complete chaos (cos θij random) σ → 1.

II.6. The moment of death: B = 0 B = F w1 · E w2 · (1 − σ)w3 · Λw4 = 0

(D2.3)

The operator Ô ceases to project configurations. The self-observation cycle Φ = ι ◦ Ô breaks on the Ô side: the reverse injection ι continues to operate (the body decomposes, atoms return to the environment), but direct actualisation does not. The moment B = 0 can be interpreted as a phase transition: the observer passes from the “actualised” state (an active participant in the configuration C) to the “deactualised” state (an element of the space H without active projection). This is not annihilation — it is a change of ontological status. It is essential that the transition B → 0 is irreversible from the standpoint of the biological observer: the once-lost ability to project configurations does not recover spontaneously. However, the world line W is not “erased” from H — and this opens the possibility for coherent legacy, which we consider below.

III. WHAT REMAINS: THE WORLD LINE IN H III.1. The world line is not destroyed In [2] the observer’s world line is defined: W = {Ψ∗n }n∈Z ,

Ψ∗n+1 = Φ(Ψ∗n ) + δΨn

(D3.1)

The world line is a single object in H. It contains all iterations of the observer’s life: from the first cry to the last breath. “Past” and “future” are cross-sections of W , not lost or non-existent fragments [2]. Biological death means: the final iteration Ψ∗N is fixed; no new iterations Ψ∗N +1 , Ψ∗N +2 , . . . are generated (the operator Ô has ceased working). But the line itself W = {Ψ∗0 , Ψ∗1 , . . . , Ψ∗N } is not deleted from H. It exists there in the same way that the Pythagorean theorem exists in mathematics — regardless of whether anyone is thinking about it right now. To substantiate this thesis we introduce the concept of the informational measure of a world line. We define the informational content of W as:

I(W ) =

H(Ψ∗n ) +

n=0

N −1

I(Ψ∗n ; Ψ∗n+1 )

(D3.2)

n=0

where H(Ψ∗n ) is the entropy (informational content) of the n-th iteration, and I(Ψ∗n ; Ψ∗n+1 ) is the mutual information between adjacent iterations. The quantity I(W ) is finite and positive for any completed world line. Deactualisation (B → 0) ceases the generation of new terms in the series but does not diminish I(W ) — information is not destroyed.

This is consistent with the principle of information conservation discussed in the context of the black-hole information paradox [19]: information that has entered a black hole is not destroyed but preserved in correlations. Analogously, the information of the observer’s world line is preserved in the structure of H — in correlations between iterations and in connections with the world lines of other observers.

III.2. The book analogy An author wrote a book and died. The book is a coherent artefact [3] with a lifetime: T (A) =

(1 − SA )nread

(D3.3)

The author is dead (Bauthor = 0), but the artefact is alive (SA > 0, nread > 0). Each new reader increases nread , extending T (A). Homer’s Iliad: the author has been dead for 2800 years, the artefact is alive, T (A) ≫ Tbiol . The world line of the author WHomer in H continues to resonate with the world lines of readers: everyone who reads the Iliad actualises a cross-section of WHomer through their own operator Ôreader . This allows us to introduce the concept of resonance coupling between world lines. Let W1 be the author’s world line, W2 the reader’s world line. Then the act of reading creates a correlation: ρ(W1 , W2 ) =

⟨W1 |W2 ⟩ ∥W1 ∥ · ∥W2 ∥

(D3.4)

where the inner product ⟨W1 |W2 ⟩ is defined through the intersection of the configuration spaces of the two observers. The deeper the reader “enters” the text, the greater ρ(W1 , W2 ) — the stronger the resonance coupling.

III.3. The coherent-legacy formula We define the coherent legacy of observer O as the aggregate of artefacts through which the observer’s world line continues to influence collective coherence: L(O) = {A1 , A2 , . . . , Ak },

T (L) = max T (Ai ) i

(D3.5)

The lifetime of the legacy is determined by the most coherent artefact. Socrates wrote no books — but his student Plato created artefacts (the SA of Plato’s dialogues is extraordinarily high) through which the world line WSocrates has been actualised for 2400 years. Note that the formula uses max, not — this is fundamental. Legacy is determined by the quality of the best artefact, not by the quantity of mediocre ones. A single selfconsistent text (Euclid’s Elements, the Bible, Newton’s Principia) is worth more than a thousand internally contradictory works.

The total “power” of a coherent legacy can be described more fully through the aggregate contribution of all artefacts:

P (L) =

SAi · nread,i

(D3.6)

i=1

This quantity characterises the total influence of a deactualised observer on collective coherence. A high P (L) means that the observer, although deactualised, continues to be a significant element of the collective configuration.

IV. THREE CONDITIONS FOR IMMORTALITY IV.1. Condition 1: Artefact coherence (SA → 1) An artefact with SA = 0 (internally contradictory, incoherent) has T (A) = T0 — the minimum lifetime. An artefact with SA → 1 (self-consistent, non-contradictory) has T (A) → ∞. Mathematical formulae are artefacts with SA → 1: the Pythagorean theorem, Euler’s identity, the formula R = Ô(Ψ) — are self-consistent and context-independent. Their lifetime is unbounded. A political manifesto is an artefact with SA < 1 (context-dependent, loses coherence when the epoch changes). Fashion is an artefact with SA ≪ 1 (coherent only within a narrow temporal window). One can introduce a coherence spectrum of artefacts. Arranging typical artefacts by their SA value: SAfashion ≪ SApolit < SAlit < SAphilos < SAmath → 1

(D4.1)

This hierarchy explains why fashion trends live for a season, political slogans for decades, literary works for centuries, philosophical systems for millennia, and mathematical theorems forever. Each level differs in the degree of contextindependence: the less an artefact is tied to a specific epoch, culture, or language, the higher its SA .

IV.2. Condition 2: Growth of the number of successors (nsucc → ∞) By formula (D3.3): at fixed SA , the growth of nread increases T (A) in a power-law fashion. An artefact that generates new observers (a textbook that inspires students to create their own artefacts) creates a chain reaction of coherence: nread (t) = n0 · eγt

T (L) → ∞

(D4.2)

where γ is the “contagiousness” coefficient of the artefact, characterising the rate of exponential audience growth. For most artefacts γ < 0 (the audience shrinks) and the legacy fades. For outstanding works γ ≈ 0 (a stable audience) or γ > 0 (a growing audience). The condition γ > 0 is equivalent to the artefact being generative: it inspires the creation of new artefacts, which in turn attract new readers. Euclid’s Elements spawned the entire tradition of axiomatic mathematics — an infinite chain of artefacts with γ > 0. Let us derive the condition for legacy immortality more rigorously. Substituting exponential growth into formula (D3.3): T (A) =

(1 − SA )n0 eγt

(D4.3)

When SA > 0 and γ > 0 the exponent grows without bound, making the denominator infinitesimally small, and T (A) → ∞. This is the mathematical expression of coherent immortality.

IV.3. Condition 3: Self-consistency with Ψ∗ The fixed point Ψ∗ = Φ(Ψ∗ ) [1] is the configuration that reproduces itself under selfobservation. If the observer’s world line W approaches Ψ∗ , its stability is maximal: it does not depend on external conditions and is reproducible by any observer capable of executing the cycle Φ. Practically: an observer whose life is aligned with fundamental principles (rather than with fashion, ideology, or majority opinion) creates a world line approaching Ψ∗ . Their legacy is robust to changes of epoch. The degree of approach to Ψ∗ can be measured by the distance in H: d(W, Ψ∗ ) = min ∥Ψ∗n − Ψ∗ ∥ n

(D4.4)

The smaller d(W, Ψ∗ ), the more stable the observer’s legacy. Observers whose world lines approached Ψ∗ created artefacts of universal significance. The “Golden Rule” principle (encountered independently in dozens of cultures [20]) is an example of such an approach: it is self-consistent and reproducible by any reflective observer.

V. DEATH AND THE COLLECTIVE OBSERVER V.1. Death as an event in collective coherence For a collective observer of n participants the coherence [1]:

S =1−

|Bi − Bj | n(n − 1) i<j

(D5.1)

The death of one observer (Bi → 0) affects S in two ways: 1. n decreases — fewer participants, fewer pairs. 2. |Bi − Bj | increases for all pairs involving the deceased — their B = 0 diverges maximally from the living (Bj > 0). However, through the coherent legacy L the influence of the deceased is not zeroed. If the legacy is coherent (SL > 0), it continues to contribute to collective S — effectively as a “virtual observer” with BL = SL . We introduce a formula for the modified collective coherence that accounts for the legacy: S′ = 1 − (n + k)(n + k − 1)

|Bi − Bj | +

i<j

n ∑ k

|Bi − SLl |

(D5.2)

i=1 l=1

where k is the number of deactualised observers with non-zero legacy and SLl is the coherence of the l-th deactualised observer’s legacy. Formula (D5.2) shows that deactualised observers with highly coherent legacies continue to “be present” in the collective configuration.

V.2. Grief as decoherence The death of a loved one sharply reduces the S of the family (a collective observer). Subjectively this is experienced as grief — a sudden loss of coherence, the feeling that “the world has fallen apart.” In formulae: |Bi − Bdeceased | jumps for all i, S drops, the lifetime of the family configuration T (Cfamily ) contracts. The process of grieving is a reconfiguration of the collective observer: the gradual construction of a new S without the deceased but incorporating their legacy L. When L is integrated into the collective configuration, S recovers — but at a different level. The Kübler-Ross model describes five stages of grief: denial, anger, bargaining, depression, acceptance [17]. In ODTOE terms these stages correspond to successive attempts by the collective observer to reconstruct S: 1. Denial — an attempt to keep S unchanged by ignoring Bdeceased Inconsistency grows.

2. Anger — a sharp increase in σ among the survivors. Internal contradiction intensifies. 3. Bargaining — an attempt to find a configuration in which Bdeceased ̸= 0. Unsuccessful for biological death.

4. Depression — the minimum of S and Bi among the survivors. coherence is at its nadir.

Collective

5. Acceptance — integration of L into a new configuration. S recovers at a new level.

V.3. Memorial rituals as maintenance of SL Memorial rituals, days of remembrance, visits to graves are mechanisms of reactualisation of the deceased’s world line W through the collective operator Ôcoll . Every act of remembrance is Ôcoll (Ψ∗W ): a projection of a cross-section of the deceased’s world line into the current configuration C. The ritual maintains nread for the legacy’s artefacts, preventing degradation of T (L). The frequency of memorial rituals sets a lower bound on maintaining nread . If rituals cease, nread → 0, and even at high SA the artefact’s lifetime becomes finite. This explains the universality of memorial traditions across all cultures — they are a mechanism for maintaining coherent legacy, developed evolutionarily.

VI. NEAR-DEATH EXPERIENCE (NDE) IN ODTOE VI.1. Phenomenology of near-death experience Near-death experiences (NDE) are described as “a review of one’s entire life,” “leaving the body,” “light at the end of a tunnel,” encounters with deceased relatives [12]. Van Lommel et al., in a prospective study of cardiac-arrest survivors, showed that NDEs occur in 18% of patients and possess a stable phenomenological structure independent of culture, age, and religious beliefs [12]. In ODTOE near-death experience receives a formal description. As B → 0, the stochastic noise D(η) = D0 (1 − S) at the individual level is maximal [1], but for an instant before complete zeroing a stochastic spike is possible — a brief expansion of ∆n granting access to cross-sections of the world line normally inaccessible.

VI.2. “Life review” as unfolding of the world line “Life review” — one of the most commonly reported experiences during NDE — is described as the simultaneous actualisation of many Ψ∗n at ∆n ≫ 1. In the normal state the observer “sees” only the current cross-section Ψ∗n with a narrow window ∆n ∼ 1. As B → 0 the normal constraints on ∆n weaken: ∆nNDE =

∆n0 , Bα

α>0

(D6.1)

As B → 0 the window ∆nNDE → ∞ — the observer gains instantaneous access to the entire world line W . Subjectively this is experienced as “my whole life flashed before

my eyes.”

VI.3. “Light at the end of the tunnel” and the fixed point The experience of “bright light” and a “tunnel” can be interpreted as approach to the fixed point Ψ∗ . As B → 0 the observer’s world line is “released” from particular configurations and, in the limit, tends toward the attractor Ψ∗ — the configuration that reproduces itself under self-observation. “Light” is the subjective experience of maximal coherence S → 1 in the vicinity of Ψ∗ . Return from an NDE (B recovers upon successful resuscitation) is often accompanied by deep personal transformation: reduced fear of death, increased empathy, re-evaluation of values [12]. In ODTOE terms: the brief contact with Ψ∗ restructures the observer’s world line, reducing σ and increasing E.

VII. DIGITAL LEGACY COHERENT LEGACY

AND

ITS

RELATION

VII.1. Digital artefacts as elements of L(O) In the modern era, an observer leaves behind not only physical artefacts (books, buildings, works of art) but also digital ones: social-media posts, e-mails, digital photographs, software code, profiles on internet platforms. The totality of digital artefacts forms the digital legacy Ldigit (O) ⊂ L(O). Digital artefacts possess special properties from the standpoint of formula (D3.3): 1. Low replication cost. Copying a digital artefact is practically free, which potentially increases nread . 2. Fragility of the medium. Digital formats become obsolete, servers are shut down, companies close. Without active maintenance nread → 0 faster than for physical artefacts. 3. Low coherence. Most digital artefacts (social-media posts, comments) have SA ≈ 0 — they are context-dependent, fragmentary, and internally unconnected.

VII.2. The paradox of digital abundance A paradox arises: the modern observer leaves quantitatively more artefacts than any predecessor, yet qualitatively (by SA ) most of them are negligible. The aggregate power of the digital legacy: P (Ldigit ) =

SAi · nread,i ≈ 0 · nlarge = 0

(D7.1)

Thousands of posts with SA ≈ 0 yield zero legacy, whereas a single deeply thoughtout work with SA → 1 can ensure T (L) → ∞. This leads to a practical conclusion: for the creation of a significant legacy it is not the quantity of digital traces that matters but the coherence of the artefacts created. A single self-consistent text is worth more than a million fragmentary publications.

VII.3. Digital “resurrections” and their limitations Modern technologies make it possible to create digital models of deceased people based on their digital legacy — chatbots, deepfakes, virtual avatars [22]. In ODTOE terms these models are synthetic artefacts Asynth that imitate cross-sections of the world line W of a deactualised observer. However, Asynth differs fundamentally from genuine legacy L(O): the model reproduces surface patterns (speech style, thematic preferences) but does not reproduce the deep coherence of the world line. The coherence of a synthetic artefact: SAsynth ≤ SAgenuine · ρ(model, W )

(D7.2)

where ρ(model, W ) is the fidelity coefficient of the model relative to the genuine world line. At the current level of technology ρ ≪ 1, making digital “resurrections” a pale imitation of coherent legacy.

VIII. PARALLELS WITH PHILOSOPHICAL TRADITIONS VIII.1. Buddhism: anatman and the stream The Buddhist concept of anatman (not-self) asserts: there is no unchanging “soul”; there is a stream of dharmas (elementary states) that ceases at nirvana [9]. In ODTOE: there is no fixed “self” — there is a world line W composed of iterations Ψ∗n . Death is the cessation of generation of new iterations. Nirvana is the attainment of Ψ∗ (the fixed point), at which the stream stabilises. The structural correspondence runs deeper than a simple analogy. The Buddhist concept of the “skandhas” (five aggregates of existence: form, sensation, perception, volitional acts, consciousness) finds a parallel in the four components of coherence B: Λ (form/experience), E (sensation), F (perception/focus), (1 − σ) (integrity of volitional acts). The zeroing of each skandha at death is the analogue of zeroing the corresponding component of B. Buddhist meditation practice aims at achieving vipassana — “seeing as it is.” In ODTOE terms vipassana means increasing focus F while simultaneously reducing σ: the meditating observer projects configurations with maximal accuracy and minimal internal contradiction. This raises B during life and the SA of artefacts created by such an observer.

The concept of the “bodhisattva” — a being who renounces nirvana for the sake of saving all living beings — corresponds to the strategy of maximising nsucc : the bodhisattva strives to increase the number of observers capable of reaching Ψ∗ , which is equivalent to the condition γ > 0 in formula (D4.2).

VIII.2. Christianity: resurrection and eternal life Christian doctrine asserts: the body is mortal, the soul is immortal, resurrection is possible [10]. In ODTOE: the body is a configuration Cbody ∈ C with finite T . The world line W ∈ H is not destroyed. “Resurrection” is formalised as reactualisation of W through a coherent artefact: Ôsucc (Ψ∗W ) = Rrestored . The commandment “love thy neighbour” = the condition S → 1 = the condition T → ∞ [3]. The Christian notion of the “Body of Christ” (the Church as a single organism composed of many members) is a precise analogue of the collective observer in ODTOE. Each believer is an individual observer Oi with coherence Bi ; the Church is a collective observer with coherence S. The commandment of love is the condition for maximising S. Christian eschatology (the doctrine of “last things”) describes “universal resurrection” — the reactualisation of all world lines. In ODTOE terms this corresponds to a hypothetical state in which the collective operator Ôcoll acquires the ability to actualise any cross-section of any world line from H. It is noteworthy that the Christian tradition distinguishes “first death” (biological) from “second death” (spiritual, final) [21]. In ODTOE the first death is deactualisation (B → 0); the second is the complete loss of coherent legacy (T (L) → 0), in which the world line W , though it exists in H, is never reactualised.

VIII.3. Stoicism: memento mori and amor fati The Stoic practice of “remember death” [11] is aimed at reducing σ: awareness of finitude eliminates false priorities and internal contradictions. “Amor fati” (love of fate) = acceptance of the world line W in its entirety, including its finitude in C — which raises E and lowers σ, increasing B during life and SL after death. Stoic philosophy, developed by Marcus Aurelius, Epictetus, and Seneca [11], contains practical recommendations that in ODTOE terms correspond to a strategy of optimising B: 1. Dichotomy of control (distinguishing what does and does not depend on us) — reduction of σ through elimination of internal contradictions generated by the desire to control the uncontrollable. 2. Negative visualisation (premeditatio malorum) — increase of Λ through broadening the spectrum of considered configurations, including unfavourable ones. 3. Evening self-examination — increase of F through regular reflection on one’s own actions and motivations.

4. Cosmopolitanism (awareness of being part of the universal whole) — increase of E through broadening the emotional connection with the collective observer. The Stoic “memento mori” plays a specific role in the context of ODTOE: awareness of the finitude of B (its inevitable zeroing) motivates the observer to create artefacts with maximal SA , i.e., to invest in coherent legacy. An observer who ignores their own mortality has no incentive to create a legacy — and consequently their influence ceases together with the biological body.

VIII.4. Existentialism: being-toward-death Heidegger’s concept of “being-toward-death” (Sein-zum-Tode) [23] asserts: authentic existence is possible only in the face of awareness of one’s own mortality. In ODTOE this receives a precise expression: an observer aware of the finitude of B transitions from “inauthentic” existence (high σ, low F ) to “authentic” existence (low σ, high F ). Existential anxiety is the subjective experience of awareness of B → 0 as an inevitable future event. This anxiety, according to Heidegger, is not pathology but a condition of authentic existence. In ODTOE formulae: awareness of Tbiol < ∞ creates motivation to increase the SA of artefacts and nsucc , i.e., to create a legacy that survives the biological body.

IX. EXPERIMENTALLY TESTABLE PREDICTIONS IX.1. Coherence before death Formulae (D1.1) and (D1.2) predict sequential zeroing of the components of B. HRV (E), EEG gamma rhythm (F ), memory tests (Λ), cognitive-dissonance scales (σ) should demonstrate sequential rather than simultaneous fading. The order of fading may vary, but multiplicativity predicts: zeroing any single component produces a jumplike decline in overall B. Specific verification protocol: longitudinal measurement of four parameters in terminal patients with a temporal resolution of 1 hour. ODTOE predicts that the correlation between Bmeas (measured coherence) and the product F · E · (1 − σ) · Λ will be higher than the correlation with the sum F + E + (1 − σ) + Λ. The multiplicative model should outperform the additive one.

IX.2. Near-death experience as expansion of ∆n Formula (D6.1) predicts that “life review” during NDE correlates with the depth of clinical death (the degree to which B has decreased). The closer B is to zero, the wider ∆nNDE — the more complete the “life review” reported by the patient. Testable prediction: patients with longer cardiac arrest (given successful resuscitation) should report more complete “life reviews” and more vivid NDE

experiences. Van Lommel’s data [12] partially support this hypothesis, but further verification is required.

IX.3. Lifetime of the legacy Formula (D3.3) predicts a correlation between artefact coherence (SA ) and longevity. Systematic comparison of SA (assessed by experts for internal consistency) with the actual lifetime of artefacts (books, institutions, laws) would verify the formula. Specific methodology: a sample of N > 100 texts from different epochs; expert assessment of SA (on a scale from 0 to 1) by a panel of m ≥ 5 independent experts; actual lifetime Tactual (in years of continuous citation or reprinting); testing of the power-law dependence Tactual ∼ (1 − SA )−n .

IX.4. Grief and HRV Prediction: the HRV of surviving family members drops abruptly after the death of a loved one (Sfamily drops → Ei drops → HRV drops) and gradually recovers as the legacy L is integrated into the new collective configuration. The recovery kinetics should obey the formula: HRV(t) = HRV0 · 1 − ∆e−t/τgrief

(D9.1)

where ∆ is the depth of the initial drop (proportional to the role of the deceased in collective S), and τgrief is the characteristic recovery time (inversely proportional to the coherence of the legacy SL ). The more coherent the deceased’s legacy, the faster the recovery.

IX.5. Coherence of digital legacy Formula (D7.1) predicts that the number of digital artefacts does not correlate with the longevity of the legacy. Testable prediction: among authors who died in the 21st century, the longevity of cultural influence (number of citations 50 years after death) should correlate not with the volume of digital presence (nposts ) but with the maximal coherence of individual artefacts (maxi SAi ).

XII. CONDITIONS FOR ETERNAL LIFE WITHOUT PHYSICAL DEATH In Sections IV–V we considered legacy immortality — conditions under which an observer’s influence survives biological death. However, a fundamental question remains: is the immortality of the observer itself possible? Under what conditions is

deactualisation (B → 0) preventable, and can an observer — be it an atom, a cell, a human, or a star — continue to project configurations indefinitely?

XII.1. Statement of the problem: preventable

when deactualisation is

Until now we have treated deactualisation as an inevitable outcome: B → 0 for every biological observer. But formula (D1.1) contains no prohibition on the eternal maintenance of B > 0. The multiplicative structure B = F w1 · E w2 · (1 − σ)w3 · Λw4 admits solutions in which none of the factors is zeroed. The key distinction: legacy immortality (Sections IV–V) is the preservation of traces of a deactualised observer through artefacts; observer immortality is the preservation of an active operator Ô that continues to project configurations from H into C. Formally the problem is stated as follows: find conditions under which B(t) > Bcrit > 0

for all

t ∈ [0, ∞)

(XII.0)

where Bcrit is the minimum coherence required to sustain the self-observation cycle Φ = ι ◦ Ô. When B < Bcrit the cycle Φ breaks: the operator Ô is unable to project configurations stably, stochastic noise dominates, and deactualisation becomes irreversible. The central insight: if the coherence growth rate can be maintained at dB/dt ≥ 0 indefinitely, the observer never deactualises. The question reduces to which physical, biological, and cognitive mechanisms allow (or do not allow) this condition to be met.

XII.2. The thermodynamic constraint and its overcoming The second law of thermodynamics asserts: the entropy of a closed system does not decrease. All structures degrade. This would appear to make immortality impossible: any observer is an open thermodynamic system, and ultimately the accumulation of entropy will destroy its coherence. In ODTOE the thermodynamic constraint receives a precise expression through the stochastic-noise formula [1]: D(η) = D0 (1 − S)

(XII.1)

where D0 is the maximal noise amplitude and S is the observer’s coherence. Entropy growth in ODTOE is equivalent to growth of D(η), i.e., to a decrease in S. When S → 1, the noise D(η) → 0 — the observer is fully coherent and stochastic degradation is suppressed. When S → 0, the noise is maximal: D(η) → D0 , and the structure is rapidly destroyed. The non-decay condition consists in the noise not exceeding a critical threshold Dcrit beyond which degradation becomes irreversible:

D(η) ≤ Dcrit

D0 (1 − S) ≤ Dcrit

S(t) ≥ Scrit

for all

(XII.2)

We derive the critical coherence threshold: Scrit = 1 −

Dcrit D0

(XII.3)

The physical meaning of formula (XII.3): the observer must maintain coherence above the critical threshold permanently. A drop of S below Scrit in even a single time interval triggers a degradation cascade described by equation (D1.2) that with high probability leads to irreversible deactualisation. Thus, the second law of thermodynamics does not prohibit immortality — it merely requires that the observer be an open system, continuously compensating entropy growth by the influx of negentropy from the environment, as Schrödinger described [16]. In ODTOE terms: the observer must maintain S ≥ Scrit through continuous interaction with other observers and artefacts.

XII.3. The atom as an immortal observer In [15] it is shown that the atom is an elementary strange loop in ODTOE: its self-observation Φatom is closed through quantum numbers, and each quantum state self-reproduces upon interaction with the environment. The proton lifetime is experimentally estimated as τp > 1034 years — effectively infinite compared with the age of the Universe (∼ 1010 years). Why is the atom (and especially the proton) effectively immortal? In ODTOE terms: the strange loop of the proton Φp possesses coherence Sp ≈ 1 — nearly perfect self-consistency. This is because all four coherence components of the atom are structurally blocked from degradation: 1. Fatom : focus is fixed by quantum numbers. Quantum numbers are discrete and not subject to continuous degradation. The focus of an atom is not “attention” but a set {n, l, ml , ms } that either exists or does not. Intermediate blurring is impossible. 2. Eatom : energy levels are quantised. An atom cannot “smoothly lose energy” — it transitions between discrete levels. The continuous decay E → 0 characteristic of biological systems is forbidden by quantum mechanics. 3. σatom ≈ 0: internal contradiction is absent. The atom’s wave function is selfconsistent — it is a solution of the Schrödinger equation, which is equivalent to σ = 0. The atom does not “contradict itself.” 4. Λatom ≈ 1: each quantum transition confirms the structure. Absorption and emission of photons are acts of the atom’s self-observation, each of which reproduces its quantum numbers. The atom’s experience is continuously renewed.

Substituting into formula (D1.1): Batom = Fqw1 · Eqw2 · (1 − σq )w3 · Λw q ≈ 1

(XII.4)

where the subscript q emphasises the quantum (discrete) nature of each component. The atom maintains Batom > Bcrit indefinitely precisely because the discreteness of quantum states does not allow continuous degradation. This is the fundamental distinction from classical (continuous) systems subject to gradual wear.

XII.4. The biological observer: why death occurs Unlike the atom, a biological observer (cell, organism, human) operates in the domain of continuous states. Its coherence is subject to continuous degradation: DNA damage accumulates with each cell division [28], telomeres shorten [27], proteins undergo misfolding, mitochondrial function degrades. In ODTOE terms: stochastic noise D(η) increases with each iteration of the cell cycle because the coherence Sbio gradually decreases. Each division introduces a small but non-zero perturbation δS < 0 that accumulates: Sbio (n) = S0 −

|δSk |

(XII.5)

k=1

The Hayflick limit [28] — the maximum number of cell divisions (nmax ≈ 50–70 for human diploid cells) — sets the horizon beyond which Sbio falls below Scrit and the coherence of the biological observer becomes irrecoverable. The cognitive coherence of a biological observer as a function of the number of iterations (cell divisions, years lived) decays exponentially:

λ·n Bbio (n) = B0 · exp − S(n)

(XII.6)

where λ is the biological degradation coefficient, n is the number of iterations, and S(n) is the current coherence. The formula shows that as S(n) decreases, the effective degradation rate λ/S(n) increases — this explains the clinically observed acceleration of ageing: the lower the coherence, the faster it continues to fall. The fundamental reason why atoms do not die but cells do lies in the difference between discrete and continuous state spaces. An atom occupies discrete quantum states — one can “jump” from one to another only as a whole, without intermediate degradation. A cell, however, resides in a continuous configuration space where small perturbations δS accumulate like the drift of a random walk, inevitably leading to the crossing of the threshold Scrit .

XII.5. Five conditions for eternal life of a biological observer From the requirement B(t) > Bcrit for all t ∈ [0, ∞) and the structure of formula (D1.1), five necessary conditions are derived, each corresponding to a specific aspect of coherence. Condition 1: Permanent maintenance of coherence above the threshold — S(t) > Scrit for all t. The observer must continuously compensate the growth of D(η) through selfobservation mechanisms. In biological terms this means continuous activation of repair mechanisms: DNA repair enzymes, antioxidant systems, autophagy. But formula (XII.2) points to a deeper level: coherence S is not a biochemical but an informational parameter reflecting the degree of self-consistency of the observer. Practically: continuous self-observation (meditation), coherent breathing, mindful attention are mechanisms for maintaining S > Scrit at the level of the whole organism. Nobel laureate Elizabeth Blackburn and her colleagues showed that meditative practices slow telomere shortening — a direct biological correlate of maintaining S [26]. Epel et al. demonstrated that meditation increases the activity of telomerase — the enzyme that restores telomeres — which in ODTOE terms is equivalent to partial compensation of δS < 0 during cell division [26]. Condition 2: Resolution of internal contradictions — σ(t) < σcrit for all t. Chronic unresolved contradictions accelerate deactualisation. From formula (D2.2) it is clear that σ is determined by the degree of misalignment among the observer’s subsystems. Each unresolved contradiction increases the number of pairs (i, j) with cos θij < 0, which increases σ and through the factor (1 − σ)w3 reduces B. The observer’s lifetime is inversely proportional to the square of internal contradiction: τdeact ∝

(XII.7)

Formula (XII.7) explains why chronic stress is so destructive: stress is the biological manifestation of high σ (misalignment between intention and reality). Cortisol, the primary stress hormone, accelerates telomere shortening [27], suppresses immune function, and accelerates neurodegeneration — all manifestations of accelerated deactualisation at high σ. Condition 3: Continuous renewal of positive experience — Λ(t) must not stagnate. Stagnation of experience (Λ = const) inevitably leads to degradation, since without the inflow of new experience dΛ/dt < 0 due to the natural “weathering” of memory and diminishing emotional charge of past events. The dynamics of Λ is described by the integral equation: Λ(t) = Λ0 · e

−µt

∫ t +

r(τ ) e−µ(t−τ ) dτ

(XII.8)

where Λ0 is the initial accumulated experience, µ is the “forgetting” rate (experience degradation rate), and r(τ ) is the intensity of incoming new positive experience at time τ . The first term describes the exponential decay of past experience; the second, the contribution of continuously incoming new experience accounting for its own subsequent decay. For maintaining Λ(t) > Λcrit it is necessary that the intensity of new experience r(t) exceed the forgetting rate: lim Λ(t) =

t→∞

r̄ > Λcrit µ

r̄ > µ · Λcrit

(XII.9)

where r̄ is the average intensity of new experience. An observer who has ceased to gain new experience (a retiree without hobbies, a recluse without social contacts) has r(t) → 0, and Λ(t) → 0 exponentially — which explains the acceleration of ageing under social isolation and absence of stimulation. Condition 4: Dynamic stability of the strange loop — Φ(Ψ∗ ) = Ψ∗ must be dynamically stable. The fixed point Ψ∗ = Φ(Ψ∗ ) can be static (a dead point, crystallisation) or dynamic (a limit cycle, strange attractor). A static fixed point corresponds to rigidity — cessation of development, which inevitably leads to degradation when external conditions change. A dynamic fixed point permits renewal within a stable structure. Formally: the observer’s strange loop must include creative deviation: Ψ∗n+1 = Φ(Ψ∗n ) + δΨcreat

(XII.10)

where δΨcreat is a small but non-zero deviation introduced by the observer’s creative activity. Without δΨcreat the loop closes on an exact fixed point, which is equivalent to the cessation of development and, ultimately, deactualisation: a static observer is unable to adapt to changes in the external environment. The biological correlate: neuroplasticity — the brain’s ability to form new synaptic connections throughout life. Research shows that continuous learning, acquisition of new skills, and creative activity stimulate neurogenesis in the hippocampus and maintain synaptic-connection density in the neocortex, slowing cognitive degradation. Condition 4 can be stated more rigorously: the spectral radius of the linearisation operator DΦ|Ψ∗ must satisfy the inequality 0 < ρ(DΦ) < 1: small enough for stability but strictly positive to admit small oscillations about Ψ∗ . Condition 5: Embeddedness in a coherent community — Scoll > Scrit . An isolated observer inevitably loses coherence because it is deprived of external feedback. Without interaction with other observers, stochastic noise D(η) is not compensated and S monotonically decreases. Interaction with a coherent collective plays the role of a coherence thermostat: collective Scoll supports individual Si through mutual synchronisation.

The lifetime of an observer embedded in a collective of ncoll participants with coherence Scoll : Tlife =

(1 − Scoll )ncoll

(XII.11)

This formula is a generalisation of the configuration-lifetime formula from [1] to the case of collective support of the observer. As Scoll → 1 and ncoll → ∞ the denominator tends to zero and Tlife → ∞. In other words: an observer embedded in an infinitely large and perfectly coherent community lives forever. The biological correlate: studies of “Blue Zones” — regions with anomalously high life expectancy (Okinawa, Sardinia, Nicoya, Ikaria, Loma Linda) — show that the key factor of longevity is the quality of social bonds [29]. In all five zones, long-lived individuals are united in close, mutually supportive communities with a high degree of mutual trust — which in ODTOE terms means high Scoll . Buettner [29] showed that social integration increases life expectancy by 5–14 years — an effect exceeding the individual influence of diet, physical activity, and genetics.

XII.6. The star as an observer: the condition for longevity Stars in ODTOE are macroscopic observers [14]: thermonuclear fusion in their cores constitutes a self-observation cycle in which gravitational compression (Ô) and radiation pressure (ι) form a closed strange loop Φstar . As long as this loop is maintained, the star is “alive”: Bstar > Bcrit . Red dwarfs (mass M < 0.5 M⊙ ) live up to 1012 years — 100 times longer than the current age of the Universe. Why? Their stochastic noise D(η) is minimal: convective mixing fully replenishes the hydrogen fuel, the thermonuclear reaction rate is low, and the coherence Sstar remains high over trillions of years. Massive stars (M > 8 M⊙ ), by contrast, live only millions of years. High luminosity means a high rate of noise generation D(η), rapid fuel consumption, and swift decline of Sstar . The deactualisation of a massive star — a supernova — is the analogue of instantaneous zeroing of B in severe trauma for a biological observer. The Sun (M = 1 M⊙ , Tlife ≈ 1010 years) occupies an intermediate position. Its stellar “strange loop” is stable on a timescale of billions of years but finite: exhaustion of hydrogen in the core will inevitably disrupt the equilibrium of Φstar and lead to deactualisation through the red-giant stage. The parallel between stars and biological observers is instructive: in both cases the intensity of “life” (stellar luminosity / metabolic rate of the organism) is inversely correlated with lifespan. “To live brightly and briefly” or “quietly and long” — a dilemma fundamental to any observer in ODTOE.

XII.7. A practical protocol: approaching the conditions for eternal life Although true biological immortality is not yet achievable, the five conditions of Section XII.5 define a concrete programme for maximally extending the observer’s life. Each condition translates into a practical recommendation. Condition 1 → Daily coherent breathing and meditation. Maintenance of S > Scrit through mindfulness practices. Research by Epel et al. [26] showed a 30% increase in telomerase activity among meditation practitioners. Blackburn and Epel [27] demonstrated a direct link between psychological stress and telomere shortening — a biological marker of degradation of S. Condition 2 → Resolution of contradictions through honest self-inquiry. Reduction of σ through reflective practices: journaling, psychotherapy, candid dialogue with loved ones. The Stoic practice of evening self-examination [11] is an ancient prototype of this condition. Condition 3 → Continuous learning and new experience. Maintenance of r(t) > µ · Λcrit through active cognition: learning languages, travelling, mastering new disciplines. An observer who has stopped learning is doomed to exponential decay of Λ. Condition 4 → Creative practice — art, science, craft. Maintenance of δΨcreat ̸= 0 through regular creativity. Any form of creativity — from painting to programming, from cooking to mathematics — introduces the necessary deviation δΨ that prevents crystallisation of the strange loop. Condition 5 → Active participation in a coherent community. Maintenance of Scoll > Scrit through participation in groups founded on mutual respect, honesty, and a shared purpose. Blue Zone studies [29] confirm: social coherence is the most powerful predictor of longevity. It is noteworthy that these five practices have been independently validated by longevity research. Residents of Okinawa, Sardinia, Ikaria, and Loma Linda display all five patterns: daily mindfulness rituals (Condition 1), low levels of chronic stress (Condition 2), active cognitive life into advanced old age (Condition 3), craft and creative activity (Condition 4), embeddedness in a close-knit community (Condition 5) [29].

XII.8. The theoretical limit: why absolute immortality is unattainable for a finite observer Ashby’s law of requisite variety asserts: for complete control of a system with n degrees of freedom, a regulator must possess no fewer than n degrees of freedom. A finite observer (atom, human, star) possesses a finite informational capacity and hence a finite number of degrees of freedom. The environment in which the observer is embedded (the Universe) possesses, in essence, an infinite number of degrees of freedom. Therefore a finite observer is fundamentally unable to maintain perfect coherence S = 1 — this would require infinite

informational capacity. There always remains a non-zero gap 1−S > 0 and hence nonzero noise D(η) > 0. It follows that the lifetime of a finite observer can be arbitrarily large but not literally infinite:

=∞ S→1 (1 − S)n

lim Tlife = lim

S→1

but

S = 1 is asymptotically unattainable

(XII.12)

The state S = 1 — absolute coherence — is unattainable for any individual observer, just as absolute zero temperature is unattainable by the third law of thermodynamics. However, the striving toward S = 1 extends the lifetime without limit. The only “entity” for which S = 1 is theoretically attainable is the whole: the totality of all observers, the fixed point Ψ∗ of the Universe’s self-observation [1]. Ψ∗ is the sole object that is simultaneously observer and observed, and for which the cycle Φ(Ψ∗ ) = Ψ∗ closes without remainder. Only the whole is truly immortal. For a finite observer this means: striving toward Ψ∗ (through the five conditions of Section XII.5) extends life without limit, but absolute immortality remains an asymptotic horizon — always ahead, never reached. Paradoxically, it is precisely the impossibility of attaining S = 1 that creates infinite motivation for development — and thereby sustains δΨcreat ̸= 0 (Condition 4), which is necessary for prolonging life.

XIII. DISCUSSION AND LIMITATIONS 1. Ontological status of H. The claim that the world line W “exists” in H after the observer’s death depends on the ontological status of H. If H is an instrumentalist construct, the “existence” of W after death is a metaphor. If H is an element of reality (as the wave function is in realist interpretations of QM [13]) — a literal assertion. The question of the ontological status of H remains open and requires separate treatment. 2. Phase order. The order of zeroing of F , E, Λ, (1 − σ) may vary depending on the cause of death. In myocardial infarction E (the heart) is zeroed first. In dementia, Λ (memory). In trauma, simultaneous zeroing is possible. The model describes the structure, not a fixed sequence. Formula (D1.2) accommodates any order of zeroing. 3. Measurability of SA . The coherence of an artefact SA lacks a generally accepted measurement scale. The proposed approach (expert assessment of internal consistency) is subjective. The development of an objective metric for SA is a necessary direction for further research. Possible approaches: citation analysis, assessment of logical consistency [24], network analysis of connections between the artefact’s propositions. 4. Limits of the analogies. The parallels with religious teachings (Section VIII) are structural in nature and do not imply an identification of ODTOE with theology.

ODTOE is a formal system that does not require faith; religion is a system founded on faith. The coincidences suggest that religious traditions may have intuitively grasped structural patterns that are formalised in ODTOE. 5. The problem of verifying NDE predictions. The predictions of Section IX.2 are difficult to test rigorously: it is impossible to control the degree of decline of B during clinical death. However, retrospective analysis of NDE databases (e.g., NDERF [25]) may provide indirect evidence. 6. Digital legacy and privacy. The question of managing a digital legacy after the observer’s deactualisation raises ethical problems beyond the scope of this paper: who has the right to manage Ldigit (O) after BO = 0?

XIV. CONCLUSION Death in ODTOE is not annihilation but deactualisation. The observation operator Ô ceases to project configurations, but the world line W is preserved in the space of potential states H. Biological death terminates the generation of new iterations but does not erase those that already exist. The four phases of dying — sequential zeroing of the components of B — provide a diagnostic model linking subjective experience with the formulae of ODTOE. The differential equation (D1.2) describes the kinetics of deactualisation and predicts the cascading character of terminal degradation. The coherent legacy L — the aggregate of artefacts — allows an observer’s influence to survive the body. Three conditions for immortality (SA → 1, nsucc → ∞, selfconsistency with Ψ∗ ) determine whether a legacy will last years or millennia. Near-death experience (NDE) receives a formal description through the expansion of the window ∆n as B → 0, which explains the phenomenology of “life review” and “light at the end of the tunnel.” Digital legacy, despite its quantitative abundance, proves qualitatively negligible at low coherence SA of individual artefacts. Analysis of the conditions for eternal life without physical death (Section XII) showed that the ODTOE formalism does not prohibit observer immortality: an atom maintains Batom ≈ 1 indefinitely owing to the discreteness of quantum states. For the biological observer, five necessary conditions for maintaining B > Bcrit are derived, each of which finds independent support in longevity research. However, absolute immortality (S = 1) is asymptotically unattainable for a finite observer — only the whole (Ψ∗ ) is truly immortal. Parallels with the Buddhist, Christian, Stoic, and existentialist traditions show that religious and philosophical teachings on death may have intuitively grasped structural patterns that are formalised in ODTOE. The commandment “love thy neighbour as thyself” is not a moral prescription but a formula for coherent immortality: B → 1 (self-love) + S → 1 (love of neighbour) = T (L) → ∞ [3]. The only path on which T tends to infinity is the path of love. Not metaphorically. Mathematically.

CONFLICT OF INTEREST The author declares no conflict of interest.

FUNDING This work was carried out without external funding.

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