Back Matter
# Index of Results
Every numbered definition, axiom, theorem and proposition, with its status and a link.
Definitions, axioms and proposals
| Result | Statement | Status |
| --- | --- | --- |
| Definition 1.1 | Qualia formalism: a bound moment has an isomorphic mathematical object. | Posited |
| Axiom 2.1 | Ubiquity: $U_{\mathrm{int}}$ is total. Nothing is phenomenally dark. | Posited |
| Axiom 2.2 | Formalism: the six invariants of (2.2) are complete. | Posited |
| Axiom 2.3 | Causal closure: the action is unmodified. | Posited |
| Axiom 4.1 | Individuation: a subject is a split inclusion at resolution $\varepsilon$. | Posited |
| Axiom 5.1 | Duration: phenomenal time is the modular parameter $s$. | Posited |
| Definition 6.1 | Coherence index $\mathcal{A}$, the atomic mass of $\mu_\Psi$. | Posited |
| Axiom 8.1 | Valence: $\mathfrak{V}=\mathcal{C}(1-2\mathcal{D}/\mathcal{D}_{\max})$. | Posited |
| Proposal 10.2 | Character is the conjugacy class of the Uhlmann holonomy. | Posited |
Theorems and propositions
| Result | Statement | Status |
| --- | --- | --- |
| Theorem 3.1 | No atoms of experience: local algebras are type III$_1$, so there are no minimal projections, no pure states, no factorisation. | Established |
| Corollary 3.2 | Panpsychism must be cosmopsychist. | Derived |
| Theorem 6.2 | Wiener: the mean squared Fourier transform recovers the atomic mass. | Established |
| Theorem 6.3 | RAGE: continuous spectrum ⟺ escape; point spectrum ⟺ almost-periodic recurrence. | Established |
| Proposition 6.4 | Symmetry is almost-periodicity: $G_\Psi$ is relatively dense iff $\mu_\Psi$ is atomic. | Derived |
| Proposition 7.1 | The Plomp–Levelt dissonance curve is $1-\kappa$ for a mollified Thomae kernel. | Posited |
| Proposition 8.2 | A dosing law: annealing drive scales as $(1-T/T_c)^{3/2}$. | Derived |
| Proposition 9.1 | Log-normal valence, with $\mathrm{Var}(\ln\|\mathfrak{V}\|)\propto M$. | Derived |
| Theorem 10.1 | Fisher–Rao on Gaussians is hyperbolic with $K=-1/2$. | Established |
Key equations
| Eq. | Content | Chapter |
| --- | --- | --- |
| (2.1) | The two forgetful functors from the substance category | 2 |
| (2.2) | The qualia functor and its six invariants | 2 |
| (4.1) | The split inclusion | 4 |
| (4.2) | The area law for the capacity of a moment | 4 |
| (4.3) | Ginzburg–Landau functional and healing length | 4 |
| (5.1) | Tomita–Takesaki relations | 5 |
| (5.3) | The intrinsic flow in $\mathrm{Out}(\mathcal{N})$ | 5 |
| (5.4) | Effective modular temperature of the specious present | 5 |
| (6.1) | Wiener's theorem and the definition of $\mathcal{A}$ | 6 |
| (7.1)–(7.2) | The consonance functional and kernel | 7 |
| (8.1) | Parisi overlap distribution and frustration | 8 |
| (8.2) | The valence functional | 8 |
| (8.4) | The de Almeida–Thouless line | 8 |
| (9.2) | Intensity as Rényi entropy and replica free energy | 9 |
| (10.1)–(10.2) | Bures metric; Fisher–Rao on Gaussians | 10 |
For agents
GET /api/library/spectral-panpsychism/results.md