Copyright © 2026 by Ralf Meelker
All rights reserved
Authored by Ralf Meelker
Printed by Pumbo.nl BV
Published by Nashua BV

Precausal Substrate Theory
First Edition, released June 2026
First Edition, second print July 2026
Second Edition, released October 2026

Companion site	https://meelker.nl/pst-se
Computations	https://meelker.nl/pst-se/computations

ISBN 978-94-6567-147-5 (EU paperback version)
ISBN 978-90-9043-536-7 (US paperback version)
NUR 925

Preface

In this book I pursue a single idea as far as it will go, and Precausal Substrate Theory is where it leads: that spacetime, causality, matter, and the fundamental forces are not the bedrock of reality; they arise from logic alone. The sole primitive and first postulate is property differentiation (P1), the bare capacity for distinctions to exist at all; it carries an asymmetric vector tension (P2), and when that tension crosses a threshold, modal sublimation (P3) produces instantiated geometry.

When I started, I did not set out to write a final theory, only to see whether such a precausal substrate could carry the weight physics usually places on a presupposed spacetime. It carried more than I expected. From these three postulates, together with the established methods of noncommutative geometry, PST builds a common foundation beneath general relativity and quantum mechanics, and recovers the Standard Model gauge structure and a three-generation count of matter. It predicts a Casimir-force correction of derived form, its size below present reach. It also yields a derived Higgs self-coupling that matches the measured value at 1.4 sigma, resting on one stated premise, that the Standard Model is PST’s low-energy theory, which a renormalisation-group test in the book passes.

For transparency, the modelling choices that enter the quantitative results, and the dependence on noncommutative geometry, are set out in full in the book, with all computations on the companion website.

The subtitle says “as I see it”, but the aim is not private: my theory is set down plainly enough that another reader can see it the same way. Most striking is how much follows from how little; I hope it encourages others to research further.

The deepest implication is also the simplest: the universe exists not because something caused it, but because a reality in which no distinctions are possible is not a reality at all.

Ralf Meelker, June 2026

Contents

1. Preface
2. Summary
3. 1 Introduction
   1. 1.1 The incompatibility of quantum mechanics and relativity
   2. 1.2 Assumed backgrounds and the missing question
   3. 1.3 The precausal starting point
   4. 1.4 The case for ontological minimality
   5. 1.5 The foundational object: the KO-dimension-ten triple
      1. 1.5.1 The substrate–Higgs identification
   6. 1.6 Principal consequences
   7. 1.7 The foundational postulates of PST
      1. 1.7.1 Derived statement: the Laplace-type projection
   8. 1.8 Structure of this book
   9. 1.9 Summary
4. 2 Property Differentiation: The Sole Primitive
   1. 2.1 Differentiation by non-identity alone
   2. 2.2 The substrate triple $(D,\delta,v)$
   3. 2.3 The direction algebra $V_{7}$
   4. 2.4 Configurations and configuration space
   5. 2.5 The canonical measure on configurations
      1. 2.5.1 Theorem (Canonical Measure)
   6. 2.6 Summary
5. 3 Asymmetric Vector Tension: The Preferred Direction
   1. 3.1 The structural origin of asymmetric tension
   2. 3.2 The tension functional and the direction algebra $V_{7}$
   3. 3.3 Epistemological status of the formalism
   4. 3.4 Complement asymmetry and the substrate’s directional bias $\hat{\tau}$
   5. 3.5 The modal and ontological status of $T(C)$
   6. 3.6 Philosophical lineage: Leibniz, Spencer-Brown, Hegel
   7. 3.7 Summary
6. 4 Modal Sublimation: How the Possible Becomes Real
   1. 4.1 Why a modal threshold must exist
   2. 4.2 The boundary condition on $|T(C)|$
   3. 4.3 The order parameter and its ontological status
   4. 4.4 Variational formulation of $\tau$
   5. 4.5 Stability analysis and the two regimes
      1. 4.5.1 Structural versus spontaneous asymmetry
   6. 4.6 The bifurcation point and the derivation of $\tau$
      1. 4.6.1 Notation: which threshold $\tau$ names
   7. 4.7 Summary of the threshold half
   8. 4.8 The character of the threshold
   9. 4.9 Categorical formulation: the sublimation functor
   10. 4.10 Explicit construction of $\Phi$
   11. 4.11 Uniqueness of $\Phi$ and the origin of diffeomorphism invariance
   12. 4.12 Lorentzian signature from Goldstone hyperbolic well-posedness
   13. 4.13 Summary
7. 5 Coinstantiation of Spacetime and Causality
   1. 5.1 Causality as coinstantiated structure
   2. 5.2 Mathematical formulation of coinstantiation
   3. 5.3 The direction of time as a structural consequence
   4. 5.4 The causal order and the degenerate vacuum
   5. 5.5 Category error and the dissolution of first-cause questions
   6. 5.6 Contrast with competing approaches
   7. 5.7 Summary
8. 6 The Emergence Chain: Eight Steps to a Universe
   1. 6.1 Overview and the eight-step summary table
   2. 6.2 The character of the chain
   3. 6.3 Step 1 to Step 2: from differentiation to tension
   4. 6.4 Step 2 to Step 3: from tension to threshold
   5. 6.5 Step 3 to Step 4: from threshold to sublimation
   6. 6.6 Step 4 to Steps 5 & 6: sublimation to spacetime & causality
   7. 6.7 Steps 6 and 7: from causality and geometry to matter
   8. 6.8 Step 8: from geometry and the vacuum to angular momentum
   9. 6.9 The chain as a closed logical structure
   10. 6.10 Summary
9. 7 Energy and Matter as Projected Tension
   1. 7.1 Results imported from the technical core
   2. 7.2 The source problem in General Relativity
   3. 7.3 The stress-energy tensor as projected tension
   4. 7.4 The tensor projection $\Pi_{\mu\nu}$
      1. 7.4.1 Why the obvious completion fails
      2. 7.4.2 The separation dyad and its trace
      3. 7.4.3 What fixes the equation of state
      4. 7.4.4 The weight is not free either
      5. 7.4.5 What is not derived
      6. 7.4.6 What the matter sector can and cannot be
   5. 7.5 The field equations as a conservation statement
      1. 7.5.1 Why both routes are kept
   6. 7.6 The F–S dichotomy: free energy versus action
   7. 7.7 The projected action and the Einstein–Hilbert term
   8. 7.8 Seeley–DeWitt argument for the projected action
   9. 7.9 Summary
10. 8 Gravity from the Projected Geometry
    1. 8.1 Spacetime curvature
    2. 8.2 The weak-field limit and the recovery of Newtonian gravity
       1. 8.2.1 Post-Newtonian parameters and scalar-mode decoupling
    3. 8.3 The strong-field limit: horizons, and why light cannot leave
       1. 8.3.1 A horizon is a threshold surface, not a trap
       2. 8.3.2 Why light cannot leave, when nothing is pulling on it
       3. 8.3.3 Where the projected field equations stop
       4. 8.3.4 What the null threshold fixes about light
       5. 8.3.5 The Planck spectrum, assembled
       6. 8.3.6 What the ladder already settles about the photoelectric effect
       7. 8.3.7 The Hawking temperature, and four things not claimed
    4. 8.4 Stress-energy as projected tension
    5. 8.5 Newton’s constant as a consistency relation
    6. 8.6 Uniqueness of $G_{\mu\nu}$: Lovelock’s theorem
    7. 8.7 The equivalence principle from single-source projection
    8. 8.8 The gravitational constant as a unit conversion
    9. 8.9 $G$ from the projection scale: form and magnitude
    10. 8.10 Kernel normalisation: the finite-internal-factor trace
    11. 8.11 Summary
11. 9 Vacuum Structure and Angular Momentum
    1. 9.1 The cosmological constant: substrate vs emergent energy
       1. 9.1.1 What $\mathcal{F}\big{|}_{\mathcal{V}}$ is, and is not
       2. 9.1.2 Mechanism A: bare Goldstone zero-point on the slice $\mathcal{V}_{\hat{\eta}}\cong S^{1}$
       3. 9.1.3 Mechanism B: the ongoing-sublimation source
    2. 9.2 The degenerate vacuum manifold and angular momentum
    3. 9.3 The incomplete vacuum of standard physics
    4. 9.4 Angular momentum as Noether charge
    5. 9.5 Angular momentum and the Goldstone–geodesic connection
    6. 9.6 Summary
12. 10 Recovering Quantum Mechanics
    1. 10.1 Structural and specific predictions
    2. 10.2 The Born rule from the Bernoulli measure
       1. 10.2.1 Two non-contextualities, and which one is assumed
    3. 10.3 The full measurement postulate from threshold-crossing
       1. 10.3.1 The threshold-crossing event as collapse
       2. 10.3.2 Probability of selection
          1. 10.3.2.1 Closure (1): Explicit measurement-coupling Hamiltonian
          2. 10.3.2.2 Closure (2): Decoherence inheritance
          3. 10.3.2.3 Closure (3): threshold-crossing uniqueness
          4. 10.3.2.4 Theorem (threshold-crossing uniqueness)
          5. 10.3.2.5 Closure (4): agreement with the Born rule
       3. 10.3.3 Why this is not the many-worlds picture
       4. 10.3.4 Why this is not an objective-collapse theory
    4. 10.4 The canonical experiments
       1. 10.4.1 The double slit and which-path information
       2. 10.4.2 Delayed choice and the quantum eraser
       3. 10.4.3 Stern–Gerlach and the definite eigenvalue
    5. 10.5 Composite systems, the reduced state and no-signalling
       1. 10.5.1 The bipartition is of the property domain, not of space
       2. 10.5.2 Theorem (tensor factorisation over a bipartition)
       3. 10.5.3 The reduced state and local observables
       4. 10.5.4 No-signalling across the bipartition
       5. 10.5.5 Bell correlations and emergent spatiality
    6. 10.6 Canonical commutation relations from the Boolean gradient
    7. 10.7 Quantum fluctuations
    8. 10.8 Summary
13. 11 Spin and Statistics from Boolean Exclusion
    1. 11.1 The fermionic sector: structure and the open problem
    2. 11.2 Fermionic excitations: the CAR algebra identification
    3. 11.3 Spin-statistics from Boolean exclusion (structural theorem)
       1. 11.3.1 Structural theorem (Boolean spin-statistics)
       2. 11.3.2 Consequence: half-integer excitations are fermionic
       3. 11.3.3 Relation to the standard QFT spin-statistics theorem
       4. 11.3.4 Closure (1): CAR convergence
       5. 11.3.5 Theorem (CAR Mosco convergence)
       6. 11.3.6 Closure (2): Wightman axioms
       7. 11.3.7 Closure (3): the Dirac equation
    4. 11.4 Summary
14. 12 Quantum Fields and the Higgs Quartic
    1. 12.1 The projected field theory: emergence of quantum fields
    2. 12.2 Interacting vacuum and $M_{*}$-regulated renormalisation
       1. 12.2.1 Scope of the cancellation argument
       2. 12.2.2 Candidate substrate-side identification of $Z^{2}$
    3. 12.3 Closure via the binary-gap-tempered partition function
       1. 12.3.1 An independent substrate-side derivation of $\mathrm{e}^{-1}$
       2. 12.3.2 The substrate Higgs Hamiltonian
       3. 12.3.3 What the identification carries, and what it does not
          1. 12.3.3.1 Notation: the KO subscript
       4. 12.3.4 The bridge identification: seven-step proof sketch
          1. 12.3.4.1 Theorem sketch ($Z^{2}\approx\mathrm{e}^{-1}$ bridge)
    4. 12.4 The spectral-action route to the Higgs quartic
       1. 12.4.1 Conjecture (spectral-action Higgs-quartic identity)
       2. 12.4.2 The Yukawa as a fourth root of the measure
       3. 12.4.3 First-cut inner-fluctuation calculation
    5. 12.5 Partition-function Chamseddine–Connes framework
       1. 12.5.1 The eleven statements of the framework (F1–F11)
       2. 12.5.2 The bridge premise and its reduction
          1. 12.5.2.1 Reduction of (B): the substrate side closed
       3. 12.5.3 What the four steps establish, and what remains
       4. 12.5.4 Substrate-side closure; the open matching step
    6. 12.6 The framework in full: F1–F11
       1. 12.6.1 Definitions (F1–F3)
          1. 12.6.1.1 Definition F1 (PST partition-function spectral triple)
          2. 12.6.1.2 Definition F2 (partition function of an observable)
          3. 12.6.1.3 Definition F3 (Matched-scaling exponent)
       2. 12.6.2 Propositions (F4–F7)
          1. 12.6.2.1 Proposition F4 (PST EFT below $M_{*}$)
          2. 12.6.2.2 Proposition F5 (Wilsonian matching at $M_{*}$)
          3. 12.6.2.3 Proposition F6 (PST UV Higgs quartic)
          4. 12.6.2.4 Proposition F7 (Substrate UV-IR scale separation)
       3. 12.6.3 Theorems (F8–F11)
          1. 12.6.3.1 Theorem F8 (substrate Higgs Hamiltonian)
          2. 12.6.3.2 Theorem F9 (tempered Bernoulli partition function)
          3. 12.6.3.3 Theorem F10 (unique soft mode; total reduction)
          4. 12.6.3.4 Main theorem of the framework
          5. 12.6.3.5 Theorem F11 ($Z^{2}\to\mathrm{e}^{-1}$ in the substrate)
       4. 12.6.4 Remark on what the framework achieves
    7. 12.7 Status of the derivations
    8. 12.8 Summary
15. 13 Gauge Structure, Quantisation, and the Standard Model
    1. 13.1 From $\mathrm{U}(1)$ to the full Standard Model gauge group
    2. 13.2 Path-integral quantisation of the projected theory
    3. 13.3 Local gauge symmetry: the photon as a connection
       1. 13.3.1 Minimal coupling is forced, and this is the algebra
    4. 13.4 $\mathrm{SU}(2)_{L}$ from threshold topology: the electroweak doublet
       1. 13.4.1 Two descriptions of one would-be Goldstone phase
       2. 13.4.2 Relation to existing electroweak approaches
       3. 13.4.3 The doublet does not fix chirality
    5. 13.5 Colour $\mathrm{SU}(3)_{c}$: octonionic origin and Casimir decomposition
       1. 13.5.1 Octonionic origin: the $G_{2}$ stabiliser of a $V_{7}$ direction
       2. 13.5.2 Rigorous Casimir decomposition
       3. 13.5.3 What the decomposition does and does not settle
       4. 13.5.4 The strong sector: what is derived and what is inherited
    6. 13.6 Consistency of the octonionic interpretation
       1. 13.6.1 Embedding-independence of the structural results
       2. 13.6.2 Unitary covariance of the order-one selection
       3. 13.6.3 Structural scope under the octonionic embedding
    7. 13.7 The internal algebra $A_{F}$ derived from P1–P3
       1. 13.7.1 Piece 1: the chirality grading
       2. 13.7.2 Piece 2: $f$ as the canonical idempotent
       3. 13.7.3 Piece 3: $\mathrm{SU}(3)_{c}\times\mathrm{U}(1)$ from the chain algebra
       4. 13.7.4 Piece 4: $\mathrm{SU}(2)$ from the Lorentzian Dirac sector
       5. 13.7.5 Piece 5: Dixon hyperspinor synthesis
       6. 13.7.6 Conjecture 1, closed (within the Dixon synthesis)
       7. 13.7.7 $\mathrm{Cl}(0,6)$ representation theory
       8. 13.7.8 The minimal left ideal
       9. 13.7.9 Furey’s chain-algebra action and the commutant
       10. 13.7.10 $\mathrm{Cl}(1,3)\cong M_{2}(\mathbb{H})$ and the internal $\mathrm{SU}(2)$
       11. 13.7.11 Dixon synthesis: $T=\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$
       12. 13.7.12 The algebra identity $A_{F}=\mathbb{C}\oplus\mathbb{H}\oplus M_{3}(\mathbb{C})$
       13. 13.7.13 Three generations from six $\mathrm{SU}(3)$ triplets
       14. 13.7.14 The gauge group as substrate automorphisms
    8. 13.8 Gauge anomaly cancellation as a structural check
    9. 13.9 $\mathrm{U}(1)_{Y}$ hypercharges compatible with PST structure
    10. 13.10 The Standard Model Lagrangian as leading-order projection
    11. 13.11 Summary
16. 14 Fermion Content: Generations, Yukawa and Chirality
    1. 14.1 Fermionic representation content under $\Pi$
    2. 14.2 The three-generation count from the $V_{7}$ directional content
       1. 14.2.1 The structural chain
       2. 14.2.2 Three disjoint generation sectors
       3. 14.2.3 Colour and generation: two guises of one three
    3. 14.3 Yukawa and CKM: the structural-scope theorem
    4. 14.4 Chirality of $\mathrm{SU}(2)_{L}$ as a structural consequence
    5. 14.5 Summary
17. 15 Grounding $d_{0}$ and the Casimir Prediction
    1. 15.1 Modal sublimation and the substrate scales
    2. 15.2 The modal scale and the electroweak identification
       1. 15.2.1 Relation to other approaches to the Higgs mechanism
    3. 15.3 Grounding the scale $d_{0}$: the coherence length
       1. 15.3.1 Two distinct scales: grain versus coherence length
    4. 15.4 Vacuum phenomena and the Casimir effect
    5. 15.5 Casimir detectability at each separation regime
    6. 15.6 The parameter-free exponent and falsifiability
       1. 15.6.1 Kernel-shape sensitivity and the $d_{0}$ bound
       2. 15.6.2 The Gaussian as the substrate’s kernel
    7. 15.7 Falsifiability and the experimental programme
    8. 15.8 Observational constraint on $d_{0}$ from Casimir data
    9. 15.9 Correction budget for the Casimir measurement
       1. 15.9.1 Predicted deviation across separations
    10. 15.10 Experimental status of $M_{*}$ and the ADD comparison
    11. 15.11 Wilson coefficients: tree-level custodial $\Delta T$ protection
    12. 15.12 Summary
18. 16 Cosmology: Acceleration from Ongoing Sublimation
    1. 16.1 PST’s reframing of the standard cosmological picture
    2. 16.2 The Cosmological Principle from the Bernoulli measure
    3. 16.3 Horizon and flatness problems dissolved
    4. 16.4 Ongoing instantiation: why it does not dilute
    5. 16.5 Equation of state and the sign of the cosmological constant
    6. 16.6 Friedmann equations and cosmic acceleration
    7. 16.7 The rate problem
    8. 16.8 Observational commitments
    9. 16.9 What would refute the constancy, and what would not
       1. 16.9.1 The falsifier, stated sharply
       2. 16.9.2 Where the measurements currently stand
       3. 16.9.3 Why PST cannot retreat, and what that costs
    10. 16.10 Comparison with steady-state cosmology
    11. 16.11 Summary
19. 17 Standing Among Existing Frameworks
    1. 17.1 PST as foundation, not competitor
    2. 17.2 Comparison with established physics frameworks
    3. 17.3 String theory: the scope contrast
    4. 17.4 Non-Commutative Geometry
    5. 17.5 Other approaches to the Higgs mechanism
    6. 17.6 Inflationary Cosmology and the Multiverse
    7. 17.7 Spencer-Brown and Distinction-Based Ontologies
    8. 17.8 Wheeler’s “It from Bit” and the Mathematical Universe
    9. 17.9 Structural Realism and Bohm’s Implicate Order
    10. 17.10 How the claims in this book are meant to be checked
    11. 17.11 Summary
20. 18 Convergence of the Projected Geometry
    1. 18.1 Mosco convergence: theorem and assumptions
       1. 18.1.1 Setup: the substrate sequence and matched scaling
       2. 18.1.2 The seven assumptions A1–A7
       3. 18.1.3 The Mosco-convergence theorem
          1. 18.1.3.1 Theorem (Mosco convergence, under A1–A7)
          2. 18.1.3.2 Proof sketch of the Mosco theorem
       4. 18.1.4 Numerical verification on finite models
       5. 18.1.5 What the theorem establishes
       6. 18.1.6 Sharpening A7: a uniform-rate inequality
          1. 18.1.6.1 Lemma (A7 reduction)
       7. 18.1.7 The physical content of the bound
       8. 18.1.8 $K$-uniformity of the constant
       9. 18.1.9 The analytic content of the rate hypothesis
       10. 18.1.10 Numerical verification of the rate
    2. 18.2 The $K$-uniform rate: proof and three closures
       1. 18.2.1 Setup: the domain $K$ and the empirical aggregate
       2. 18.2.2 Step 1: Taylor expansion
       3. 18.2.3 Step 2: Expectation under $\xi$
       4. 18.2.4 Step 3: Empirical average over the realisation map
       5. 18.2.5 Step 4: $K$-uniform bounds
       6. 18.2.6 Step 5: $K$-uniform rate
       7. 18.2.7 Caveats and what remains
       8. 18.2.8 Closure (a): Explicit $\Pi_{n}^{\dagger}$ construction
       9. 18.2.9 Closure (b): Thin-support $d_{0}$-corrections
       10. 18.2.10 Closure (c): Riemannian extension on $M=\mathbb{R}\times S^{3}$
       11. 18.2.11 Explicit constants: Berry–Esseen and finite elements
    3. 18.3 Dirac-operator convergence: a single analytic estimate
       1. 18.3.1 The three ingredients of the Dirac estimate
       2. 18.3.2 Ingredient 3, what is exact at finite substrate size: the Clifford algebra, the multiplicities and the bridge map
       3. 18.3.3 Ingredient 3, what remains: the commutator residual as a Sobolev-tail estimate
       4. 18.3.4 Step 5, the discrete-derivation defect: why no citation closes it, and what does
          1. 18.3.4.1 Section round-trip in Gromov–Hausdorff distance
       5. 18.3.5 Dirac-aware lift to substrate-to-continuum metric
       6. 18.3.6 Why the relaxed criterion suffices for PST
          1. 18.3.6.1 Caveat on the rate
       7. 18.3.7 Refined bridge: the Lemma 5–8 closure of L_comm
    4. 18.4 Dirac convergence: the L_round and L_comm lemma chain
       1. 18.4.1 The L_round side: the Gromov–Hausdorff round-trip
       2. 18.4.2 The L_comm side: the refined-bridge lemma chain
          1. 18.4.2.1 Refined bridge, symmetric-monomial construction
          2. 18.4.2.2 Refined bridge: the ratio match (Lemma 5)
          3. 18.4.2.3 Refined bridge, Berezin compatibility (Lemma 6)
          4. 18.4.2.4 Refined bridge: finite-$N$ closure rate (Lemma 7)
          5. 18.4.2.5 Refined bridge: spectral-action invariance (Lemma 8)
    5. 18.5 Summary
21. 19 Resolved Problems and the Open Frontier
    1. 19.1 The resolved sectors
       1. 19.1.1 The foundational object
       2. 19.1.2 Emergent geometry and the Lorentzian signature
       3. 19.1.3 Gravity
       4. 19.1.4 Cosmology
       5. 19.1.5 Quantum mechanics
       6. 19.1.6 The Standard Model
    2. 19.2 The Dirac-convergence step
       1. 19.2.1 Reducing the bound to ladder commutators
       2. 19.2.2 Asymptotic Toeplitz-symbol closed form for $c_{1}(k)$
       3. 19.2.3 Analytical uniform-in-$(k,N)$ bound
    3. 19.3 Octonionic-$\mathrm{SU}(3)$ structure inside $\mathrm{Cl}(0,6)$
    4. 19.4 Matter, and the theory’s empirical exposure
       1. 19.4.1 Boolean occupation makes spin-statistics structural
       2. 19.4.2 A 6-sphere vacuum quantises angular momentum
       3. 19.4.3 The three places the theory can be measured
       4. 19.4.4 Where PST matches general relativity, on purpose
       5. 19.4.5 What the theory does not predict: the fermion masses and mixings, and why that is a theorem
    5. 19.5 The $A_{F}$ algebra identity
    6. 19.6 Robustness of the structural-scope theorem
    7. 19.7 The substrate-side identification of Z²
       1. 19.7.1 The CC inner-fluctuation bridge is obstructed
       2. 19.7.2 An alternative substrate-to-SM bridge
       3. 19.7.3 The substrate side of the bridge, closed
       4. 19.7.4 The matching, by wave-function renormalisation
       5. 19.7.5 Empirical-precision test
       6. 19.7.6 The bridge proof sketch
    8. 19.8 Standing among substrate theories
    9. 19.9 The remaining open frontier
       1. 19.9.1 The structural front
       2. 19.9.2 Localising an apparatus in the property domain
       3. 19.9.3 The black-hole interior
       4. 19.9.4 Beyond the two quantitative bounds
       5. 19.9.5 Bridge Premise (B), reduced
       6. 19.9.6 The full-SM extension, settled in the negative
    10. 19.10 Summary
22. 20 Conclusion
    1. 20.1 The shape of the argument
    2. 20.2 The central claim, stated precisely
       1. 20.2.1 Standing among substrate theories
       2. 20.2.2 The Dirac-convergence constant
    3. 20.3 What the emergence chain establishes
    4. 20.4 The open questions PST closes
    5. 20.5 The unification of quantum mechanics and general relativity
    6. 20.6 The quantitative standing of the theory
    7. 20.7 The scope and limits of the theory
       1. 20.7.1 What is foundational, and what is inherited
       2. 20.7.2 Structurally contingent versus derived
    8. 20.8 Open questions and the next research
    9. 20.9 On intelligibility and necessity
    10. 20.10 Summary
23. Appendix A: Notation Conventions
24. Appendix B: Computation Scripts
25. Appendix C: Claims Status
26. Appendix D: Comparison to Other Theories
27. Appendix E: Bibliographic References