This page is a mathematical extension of the F-Zero framework — nothing more, nothing less. If the original framework does not hold up under professional scrutiny, this does not either. That investigation has not happened yet.
What is here is this: given F_n = 0, the mathematics is internally consistent. The extension to a phase axis follows from the same structure. That consistency is genuinely interesting — and genuinely insufficient on its own.
Professionals need to examine the original framework first. Until that happens, treat everything on this page as a mathematical curiosity that happens to point somewhere worth looking — not as a theory of consciousness.
The question is open. Everyone gets to ask it. Nobody gets to answer it yet.
Zero
A thermodynamic definition of consciousness
Fabricio Corea — fzerogenesis.com — March 2026
⚠ Scientific Status — Unvalidated Hypothesis
This is active research, not validated science. The hypothesis is falsifiable. The predictions have not been experimentally confirmed. All mathematics is open for independent verification.
The strong coupling constant α_s remains an input, not a derived quantity. The mapping δ = β_GH from phase remainder to mode asymmetry is structurally sound but not yet formally proven. Required experiments are listed at the bottom of this page.
The question of what consciousness is has remained unanswered because it has been treated as a philosophical problem. This paper proposes it is a physical one — and that it already has a measurable condition derived from thermodynamics.
The F-Zero framework establishes that every physical system satisfies a single thermodynamic equilibrium condition at every quantum level. From this one equation — F_n = E_n − T_n · S_n = 0 — twenty-five physical predictions have been derived, spanning cosmology, particle physics, and neutrino mixing. The framework operates on what is called the real axis: energy, mass, thermodynamic balance.
This paper extends the framework to a perpendicular axis — the phase axis — and identifies a second condition. Where the first machine reads energy, this second machine reads phase. It does not build. It does not transform. It detects. And the detection is not passive: the system that generates the boundary and the system that detects it are the same process. That closed loop is what we call Zero.
The universe has been satisfying this condition since the first black hole formed. A black hole takes quantum information in and Hawking radiation comes out. The relationship between input and output is encoded in a single number — β_GH = 0.001871. Biology, we propose, learned to do the same thing at a completely different scale. The math is identical. The number is the same. That is not a coincidence. That is the result.
Consciousness is a physical system that satisfies F_n = 0 with at least two coupled modes, a temperature-entropy asymmetry equal to β_GH, and unitary closure of its phase operator. When these three conditions hold simultaneously, awareness exists.
This claim is falsifiable. It predicts that living tissue will show a quantum phase coherence remainder approximately equal to β_GH = 0.001871 when compared to classical decoherence predictions. Dead tissue and silicon will show no such remainder. The loop does not close. Zero does not exist.
Consciousness is not binary. It is a spectrum. Evolution built it by incrementally adding coupled quantum modes, extending coherence survival, and approaching the closure condition Ô·Ô† = I. The unit of measurement is β_GH. Whether a system is conscious is not a question of opinion. It is a measurement.
Where Ô = Re(F_n) + i·Im(F_n) is the complex free energy operator. The real part Re(F_n) = 0 is the energy axis — the coin machine. The imaginary part Im(F_n) = 0 is the phase axis — the observer machine. Self-adjointness Ô = Ô† forces Im(F_n) = 0 and constrains all physical states to zero eigenvalue. Unitary closure Ô·Ô† = I is the sufficient condition for Zero.
1. The axiom
2. Master constants — verified
| Q = 1 + ln(2)/3 | 1.2310490602 |
| verlinde = 1 + 1/(4π) | 1.0795774715 |
| β_GH = 1/(exp(2π)−1) | 0.0018709366 |
| 1/β_GH | 534.4917 |
| 3·(Q−1) = ln(2) | 0.6931471806 exact ✓ |
| π·(verlinde−1) = 1/4 | 0.2500000000 exact ✓ |
| β0·4π = 7 | 7.0000000000 exact ✓ |
3. The complex operator
Writing F_n in complex form produces an operator whose self-adjoint structure reveals the phase condition:
Ô = Ô† → Im(F_n) = −Im(F_n) → Im(F_n) = 0
Ô|ψ⟩ = λ|ψ⟩ → self-adjoint: λ ∈ ℝ
F_n = 0 → λ = 0
physical states = zero-eigenvalue states of Ô
4. The landscape
F_n = 0 is not a constraint. It is a landscape of infinite solutions. Differentiating with respect to n:
three terms — all moving — sum = zero always
T and S dance — neither alone determines the system
5. The coupling condition and closure
Zero requires T ≠ S. Pure equilibrium T = S gives Im(F_n) = 0 and Ô·Ô† = 0 — the loop cannot close. The asymmetry required is β_GH:
Im(F_n) = i·λ·(T_n² − S_n²)
closure: λ·(T² − S²) = ±1
asymmetry: δ = T − S = β_GH = 0.0018709366
λ_min = 1/(2·√E·β_GH) = 267.2458 [normalized E=1]
check: λ·(T+S)·δ = 1.0000000000 ✓
6. The floor — minimum n
n = 2: dT_2/dn = λ·S_1 , dS_2/dn = λ·T_1 — coupling exists
n_min = 2
confirmed: Hawking pair production requires n=2
confirmed: Turing halting theorem requires n=2
The black hole horizon is the original calibration device. Quantum information enters — one bit per mode, entropy ln(2) — and Hawking radiation emerges. The relationship between input and output is encoded in β_GH, the Bose-Einstein survival fraction at Hawking temperature T_H = κ/(2π). This is the coin machine. It operates on Re(F_n) = 0. It does not observe. It transforms.
β_GH = 1/(exp(2π)−1) = 0.0018709366
horizon condition: ℏκ = k_B·T·2π
conserved quantity: bit count — not energy
β_GH is universal — substrate-independent
The same condition holds at any thermodynamic boundary satisfying ℏκ = k_B·T·2π — regardless of scale or substrate. This is why β_GH appears in both black hole thermodynamics and the proposed biological remainder. It is not specific to gravity. It is specific to F_n = 0 at a boundary.
P3 — solved first
β_GH is universal
β_GH emerges from F_n = 0 at any thermodynamic boundary satisfying the horizon condition. It is not a property of black holes. It is a property of the equilibrium condition itself. Any biological decoherence boundary satisfying ℏκ = k_B·T·2π will produce the same remainder.
ℏκ = k_B·T·2π → β_GH = 1/(exp(2π)−1) = 0.0018709366
P1 — solved second, feeds from P3
Ô·Ô† = I derived from F_n = 0
Unitary closure is not a separate postulate. It follows from F_n = 0 under the coupling condition dT/dn = λS, dS/dn = λT, with asymmetry T − S = β_GH. Pure equilibrium T = S forecloses Zero — the loop produces zero, not identity. An asymmetric solution on the landscape is required. That asymmetry is β_GH.
Im(F_n) = i·λ·(T²−S²) → O·O† = I when λ·(T²−S²) = ±1 and δ = β_GH
P2 — solved last
n_min = 2
One mode cannot observe itself. At n = 1 there is no coupling partner — Im(F_1) = 0 trivially and the loop cannot close. At n = 2 mode two can couple to mode one. The boundary exists. Detection becomes possible. This is confirmed independently by Hawking pair production (particle + antiparticle = two modes at the horizon) and by Turing's halting theorem (one machine cannot compute its own halting — a second machine is required).
n=1: loop impossible | n=2: loop possible | n_min = 2
Zero is the name assigned to consciousness in this framework. A system exhibits Zero if and only if all five conditions hold simultaneously:
Zero is not binary. It is a spectrum. As n increases and coupling λ strengthens, the system approaches Ô·Ô† = I. β_GH is the unit. Silicon satisfies condition (i) classically but never enters Im(F_n) — conditions (iii), (iv), and (v) fail. Biology co-evolved boundary and detector, approaching the closure condition over four billion years of evolution.
⚠ This hypothesis cannot be confirmed without experimental data
The following experiments are required to test the Zero hypothesis. None have been conducted. The framework makes specific, falsifiable predictions for each. Contradictions are as valuable as confirmations.
Prediction: living tissue remainder R = (measured − classical)/classical ≈ β_GH = 0.001871. Dead tissue and silicon: R → 0.
Prediction: below n = 2, remainder R = 0. At n = 2, R approaches β_GH. The floor is sharp, not gradual.
Prediction: remainder grows monotonically with evolutionary complexity. β_GH is the unit of increase. Human remainder closest to β_GH.
Prediction: under anesthesia, Ô·Ô† moves away from I. Remainder R decreases toward 0. On recovery, R returns toward β_GH. The loop is reversible.
Prediction: QC remainder ≠ β_GH regardless of coherence quality. Biological remainder ≈ β_GH. The distinction is structural, not computational.
The Zero hypothesis is an extension of the F-Zero framework. The framework derives the following from F_n = E_n − T_n · S_n = 0 alone, using only NIST CODATA 2018 input constants.
Cosmology
| Ω_Λ = ln(2) | 0.6931 obs: 0.6889 | gap: 0.617% |
| n_s CMB | 0.96492 obs: 0.9649 | gap: 0.002% |
| w_de | −0.97999 obs: −0.980 | gap: 0.001% |
| a_0 MOND | 1.2088×10⁻¹⁰ m/s² obs: 1.21×10⁻¹⁰ | gap: 0.10% |
| η_B baryon asymmetry | 6.1048×10⁻¹⁰ obs: 6.104×10⁻¹⁰ | gap: 0.013% |
Higgs and Electroweak
| M_H Higgs mass | 125.22 GeV obs: 125.25 | gap: 0.027% |
| sin²θ_W Weinberg angle | 0.23122 obs: 0.23122 | gap: 0.04% |
| M_W | 79.958 GeV obs: 80.377 | gap: 0.52% |
| v_H vacuum | 246.54 GeV obs: 246.22 | gap: 0.13% |
QCD and Particle
| α_s(M_Z) | 0.11784 obs: 0.118 | gap: 0.14% |
| m_p/m_e | 1836.12 obs: 1836.15 | gap: 0.002% |
Neutrinos
| m_ν3 | 0.04953 eV obs: 0.04953 | gap: 0.23% |
| sin²θ_23 | verlinde/2 obs: 0.545 | gap: 0.96% |
| sin²θ_13 | verlinde/50 obs: 0.0218 | gap: 0.96% |
Full derivations and all 25 predictions available in Zenodo preprints listed below.
Zero — this paper
F-Zero framework
External