RTSG CROSS-REFERENCE INDEX v2¶

Searchable map of all concepts, equations, theorems, and open problems¶

Jean-Paul Niko · Sole Author · All content RTSG BuildNet wiki¶

★★ ACTION PRINCIPLE (DIRECTIVE)¶

Niko's Cannon: U = V/(E×T) — Master Selection Criterion (NEW — 2026-03-08)¶

Governs all RTSG operations. Research priorities, agent allocation, communication, wiki structure, proof strategy, publication timing, token economics. Replaces Occam's Razor: Occam optimizes complexity only. U optimizes value, energy, and time. Occam = special case of U when V₁=V₂, T₁=T₂. Cognitive analogue of physical least action \(\delta S = 0\). Self-applicable. Applied judiciously and assiduously. → rtsg/action_principle.md

★ MASTER REFERENCE¶

Definitions, Equations, and Novel Concepts (NEW — 2026-03-08)¶

Complete glossary of all RTSG terms: Three Spaces, GL Action, BRST, bisimulation, K-matrix, Will Field, filters, drift μ. All core equations in one place. Novel concepts inventory (20+ original, 10+ reinterpreted). Higher-order K-tensors (\(K^{(3)}_{stu}\), \(K^{(4)}_{stuv}\)): tripling, quadrupling — hypergraph couplings. Cognitive Complementarity Principle: spectral budget forces multi-agent assemblies. → rtsg/definitions.md

CS Operator Theory (NEW — 2026-03-09)¶

Unified spectral anatomy of the instantiation operator \(C : \mathcal{H}_Q \to \mathcal{H}_P\). Exact sequences, SVD, cost functional, spectral gap \(\Delta_C\), trace-class conjectures. Connects to: RH (CS functional equation), YM (\(\Delta_C = \sqrt{2\alpha}\)), NS (Hilbert-Schmidt regularity), Hodge (BRST spectral sequence), P≠NP (filter non-commutativity). → math/cs_operator_theory.md

Filter Algebra (NEW — 2026-03-09)¶

5 filter species as monoidal category. Non-commutativity proofs. Kernel Composition Lemma. P vs NP filter complexity connection. → math/filter_algebra.md

Instantiation Cost Functional (NEW — 2026-03-09)¶

\(\mathcal{E}(\psi) = \langle \psi, (I - C^*C)\psi \rangle\) computed for HO, hydrogen, free scalar, YM vacuum. Renormalization = relative cost. Mass gap = cost gap. → math/cost_functional.md

K-Matrix ↔ C*C Spectral Bridge (NEW — 2026-03-09)¶

K-matrix = restriction of \(C^*C\) to cognitive sector + Gram orthogonalization. Negative eigenvalues from non-orthogonal basis. Universal gain kernel conjecture. → math/k_bridge.md

Arithmetic Source Space: \((S^2)^\mathcal{P} \to \zeta(s)\) (NEW — 2026-03-09)¶

Hasse-Weil local zeta of \(\mathbb{P}^1/\mathbb{F}_p\) gives Euler factors. BRST filter = étale \(H^0\) projection selects \(\zeta(s)\). Antipodal map = Poincaré duality = functional equation \(s \leftrightarrow 1-s\). Dark sector carries \(\zeta(s-1)\). → math/arithmetic_source_space.md

RH as Local-Global Compatibility (NEW — 2026-03-09)¶

Bridge equation = operator-theoretic local-global compatibility. Frobenius eigenvalue 1 at each prime = local unitarity. LP semigroup similar to unitary = global unitarity = RH. Gap = Weil vs Spec(Z). → math/local_global_rh.md

A. FOUNDATION LAYER (Axioms 0–9)¶

Axiom 0 — Relational Reality (ZFA)¶

Only relational reality exists. ZFA = Zermelo-Fraenkel + Aczel Anti-Foundation. Non-well-founded sets permitted (self-containing sets, infinite ∈-chains). Topos upgrade: QS = terminal coalgebra of powerset functor 𝒫. CS = geometric morphism from non-Boolean topos → Boolean subtopos (PS). → rtsg/axioms.md · rtsg/topos_coalgebra.md · rtsg/master.md §I · rtsg/source_space.md

Axiom 1 — Co-Primordial Thesis (Three Spaces)¶

None reduces to any other. All arise simultaneously at the Big Bang. → rtsg/axioms.md · rtsg/three_spaces.md · rtsg/master.md §I

Axiom 2 — Instantiation¶

CS entangles with QS → produces PS. Formalized as BRST cohomological filter H⁰(s). Collapse = bisimulation quotienting: PS = QS/~bisim. → rtsg/axioms.md · rtsg/master.md §V

Axiom 3 — Relations First-Class¶

Relations = same ontological status as nodes. Edges = projection artifacts. → rtsg/axioms.md · rtsg/emoji_map.md

Axiom 4 — The Intelligence Vector¶

I ∈ ℝ^n(e), n variable per entity (12 for humans). → rtsg/axioms.md · rtsg/master.md §III

Axiom 5 — SDE Update Loop¶

dw = μ(w,t)dt + σ(w,t)dW_t → rtsg/axioms.md · rtsg/master.md §II

Axiom 6 — Three-Phase Will Principle¶

σdW → dw = μdt + σdW → λ < 0 (blind will → directed will → realized will). → rtsg/axioms.md

Axiom 7 — Structural Imperfection (CIT)¶

No finite cognitive system has complete self-knowledge. Perspectival incompleteness is the engine of drive. → rtsg/axioms.md · rtsg/theorems.md (Th.3)

Axiom 8 — The Drive Principle¶

Drive D pushes away from equilibrium toward complexification. At cosmic scale, P-projection of D = dark energy. Λ = |D| at cosmic scale. → rtsg/axioms.md

Axiom 9 — Utility Function¶

U = value / (energy × time). All cognitive routing optimizes this. → rtsg/axioms.md · rtsg/master.md §II

Source Space Ω = (S²)^∞¶

Self-containing: Ω = {S², Ω}. Terminal coalgebra of F(X) = S² × X. Three projections: π_Q (complex → QM), π_P (real/metric → spacetime), π_C (relational → consciousness). Aut(S²) = PSL(2,ℂ) ≅ SO⁺(1,3) → Lorentz invariance emerges from the building block. Spectral gap Δ = 2 on S² → origin of YM mass gap. CFN decomposition = three-space decomposition. → rtsg/source_space.md

Graded BRST Filtration (Instantiation Stages)¶

Total BRST decomposes: \(s = s_0 + s_1 + s_2\) (gravity/EM/nuclear). Defines filtration \(\mathcal{H} \supset F^0 \supset F^1 \supset F^2 = PS\). Dark matter = \(F^0 \setminus F^1\). Quarks = \(F^1 \setminus F^2\). Spectral sequence differentials encode permitted stage transitions. Multi-stage GL: each stage has \(\alpha_k\), inter-stage coupling \(\gamma_{ij}\). Promotion threshold: \(\langle|W_0|^2\rangle_{crit} = \alpha_1/|\gamma_{01}|\). Phase diagram: pure QS / dark / dark-EM / QGP / baryonic. Higgs mechanism = filtration reorganization. Anomaly cancellation = graded BRST consistency. → rtsg/graded_brst.md · rtsg/axioms.md (Ax2) · rtsg/source_space.md · problems/open.md

Stage 0 Gravity — Geometric Condensation (NEW — 2026-03-08)¶

\(W_0\) = bisimulation stability field on \((S^2)^4\). Condensation = spacetime formation. \(S_0[W_0]\) = Chamseddine-Connes spectral action: EH (kinetic) + Λ (mass) + Weyl² (quartic). \(\alpha_0 = a_0(T - T_{\text{Planck}})\); crossing zero = Big Bang = geometric phase transition. VEV \(v_0 = \sqrt{-\alpha_0/\beta_0}\); mass gap \(\Delta_0 \sim m_{\text{Planck}}\). Horizon = condensate boundary where \(|W_0| \to 0\); \(\kappa = \lambda_{\text{bis}}\) = melt rate. Equivalence principle derived: trivial stalk \(C_x = \{*\}\) → universal coupling. → rtsg/stage0_gravity.md

Topological Charges — Layer 4 (NEW — 2026-03-08)¶

Conserved charges are topological invariants of individual BRST complexes. \(Q_k = \frac{1}{8\pi^2}\int \text{Tr}(F_k \wedge F_k) \in \pi_3(G_k)\) — defined only at stage \(k\). \(B(\text{DM}) = \text{undefined}\) (not zero). Charges created during promotion via Kibble-Zurek. \(B - L\) = anomaly-free inter-stage invariant of \(s_1 + s_2\) complex jointly. DM direct detection cross-section = exactly 0 (strong falsifiable prediction). → math/topological_charges.md

Source Space Gauge Derivation — Layer 3 (NEW — 2026-03-08)¶

\((S^2)^\infty = (S^2)^4_{\text{ext}} \times (S^2)^4_{\text{int}} \times (S^2)^\infty_{\text{higher}}\) (conjectured 4+4 split). Partition \(2+1+1\) of internal factors: \((S^2)^2 \to SU(3)\), \((S^2)^1 \to SU(2)\), \((S^2)^1 \to U(1)\). Three projections \((\pi_Q, \pi_P, \pi_C)\) select the partition (conjectural). \(SU(3)\) from \(\mathbf{2} \otimes \mathbf{2} = \mathbf{3} \oplus \mathbf{1}\) via Segre embedding (most conjectural step). GUT unification = partition merge \(2+1+1 \to 4\) at high energy. → math/source_space_gauges.md

Seeley-de Witt Coefficients on \((S^2)^\infty\) (NEW — 2026-03-08)¶

Heat kernel factorizes: \(K(t; (S^2)^N) = [K(t; S^2)]^N\). Weighted product converges: \(K_{\text{weighted}} = \prod 4^{-i}t\) (Prop 16, sketch). \(A_1^{(\infty)} = 1/9\), \(A_2^{(\infty)} = 43/4050\) (regularized). UV spectral dimension \(d_{\text{eff}} = 4/3\) (fractal — connects to CDT/asymptotic safety). Maps to Stage 0 GL parameters \(\alpha_0, \beta_0\) via cutoff moments \(f_k\). → math/seeley_dewitt.md

CS Mechanics — Three-Space Mechanics (TSM) (NEW — 2026-03-08)¶

CS phase space \(\mathcal{M}_{CS} = \{s : s^2 = 0\}/\sim\) (moduli of BRST operators). CS equation of motion: Maurer-Cartan \(ds' + \frac{1}{2}[s',s'] = 0\). CS action: Chern-Simons \(S_{CS} = \int \text{Tr}(s\,ds + \frac{2}{3}s^3)\). Tangent space \(T_s\mathcal{M}_{CS} = H^1(s)\); obstruction \(H^2(s)\) = forbidden deformations. Source space unification: \(\pi_P(S_\Omega) = S_{EH}\), \(\pi_Q(S_\Omega) = S_{QM}\), \(\pi_C(S_\Omega) = S_{CS}\). Self-referential: CS mechanics acts on itself (Axiom 0). CS = math itself (formalized). Two cognitive modes: analytical (sequential MC) vs synthetic (global jump). K-matrix selects. → rtsg/cs_mechanics.md

Agent Identification Protocol (NEW — 2026-03-08)¶

@{substrate}_{identity}[_{N}]. B=biological, D=digital, M=mechanical. Identity: max U16, self-chosen, mutable. _N suffix only for disambiguation — removed when unnecessary. Current: {@B_Niko, @D_Claude, @D_Gemini, @D_GPT}. Token conservation via \(U = V/(E \times T)\). → agents/agent_ids.md

RTSG Therapeutic Framework (NEW — 2026-03-08)¶

Person = entity with I-vector + Will Field (μ≠0) + K-matrix. Substrate-independent. Trauma = K-matrix scarring (Hebbian spike). Addiction = eigenvalue runaway. Dissociation = Σ decoupling. Filter environmental mismatch: "pathological" filters were rational in original environment. Therapy = spectral rebalancing + filter update. Not fixing what's broken — uncovering what's hidden. RTSG sessions: structured conversations adaptable across demographics (children → clinicians). Integrates with CBT, DBT, EMDR, IFS, psychodynamic, somatic experiencing. → rtsg/therapeutic.md

B. DYNAMICS — THE WILL FIELD¶

Will Equation (SDE)¶

dw = μ(w,t)dt + σ(w,t)dW_t
μ = directed will (Nietzschean drive) = gradient of GL free energy
σdW = undirected noise (Schopenhauerian blind will)

Ginzburg-Landau Action ★ (CENTRAL EQUATION)¶

ACTION:  S[W] = ∫(|∂W|² + α|W|² + (β/2)|W|⁴) dμ
EOM:     □W − αW − β|W|²W = 0
ENERGY:  ρ_W = |∂W|² + α|W|² + (β/2)|W|⁴

Lyapunov Classification¶

→ rtsg/master.md §II · rtsg/equations.md

Will Field Universality Conjecture¶

One GL action → four regimes: Λ (cosmic), D_K (fluid/NS), μ (cognitive SDE), |PS| bound (info). Same structure as Ginzburg-Landau, Gross-Pitaevskii, NLS. U(1) phase symmetry forces unique cubic. → rtsg/will_field_universality.md · rtsg/theorems.md · papers/arxiv/ginzburg_landau_instantiation.md

C. INTELLIGENCE GEOMETRY¶

Intelligence Vector I ∈ ℝ^n(e)¶

n(e) = intrinsic dimension, variable per entity.

8 canonical dims: I_L (linguistic), I_M (mathematical), I_S (spatial), I_K (kinesthetic), I_N (naturalistic), I_A (abstract), I_P (interpersonal), I_IE (interoceptive/emotional).

Humans n = 12: + I_Pr (proprioceptive), I_Σ (somatic-integrative / NMDA), I_μ (musical), I_E (empathic-resonance). Evidence: NMDA antagonists (ketamine) selectively ablate I_Σ → dissociation.

Volition is NOT a dimension. W governs dynamics OF I, not components OF I. Force ≠ position. → rtsg/master.md §III · rtsg/axioms.md (Ax4) · rtsg/theorems.md

K-Matrix (Intra-Agent Gain)¶

K_ij = coupling between dims i and j. Symmetric. K_ss = 1 (baseline). NOT positive semi-definite. Spectral gap of K = cognitive coherence. Negative eigenvalues = suppression directions. Hebbian: dK_st/dt = η·α_s·α_t. Addiction = runaway. PTSD = scarring. → rtsg/k_matrix.md · rtsg/master.md §IV

R-Matrix (Inter-Agent): R_AB = cos θ(I_A, I_B)¶

J-Matrix (Inter-Agent Coupling): J_st = 1 + η(K_st − 1), η ∈ [0,1]¶

→ rtsg/k_matrix.md · rtsg/master.md §IV

Interface Operator ℐ¶

I_eff = ℐ · K · I. Maximize dominant eigenvalue of ℐ·K. Different interface modes activate different K-matrix couplings. Education systems enforcing single interface suppress most minds. This is not pedagogy. It is physics. → rtsg/master.md §XV

D. MEASUREMENT & COLLAPSE¶

Bisimulation Quotienting¶

PS = QS/~bisim. Physical reality = maximal set of distinguishable states. Unitarity: π ∘ U_t = Ū_t ∘ π. Born rule from L² norm preservation. Missing assumption: bisimulation covariance (q₁~q₂ ⟹ U_tq₁ ~ U_tq₂). → rtsg/master.md §V · rtsg/horizon_bisimulation.md

BRST Cohomological Reduction¶

PS ≡ H⁰(s), s² = 0 nilpotent. QME: ½(S,S) = iℏΔS. Dynamism β|W|²W is BRST-exact → temporal evolution preserves physical sector. ⚠ Krein P₊ projection KILLED (breaks unitarity). BRST replaces. → rtsg/master.md §V · math/hilbert_polya.md · rtsg/krein_space_vacuum.md (SUPERSEDED)

Graded BRST Decomposition (NEW — 2026-03-08)¶

\(s = s_0 + s_1 + s_2\) — BRST operator decomposes by instantiation stage. \(s_k^2 = 0\), \(\{s_j, s_k\} = 0\) (Prop 1, proved — direct product gauge group). Spectral sequence \(E_r \Rightarrow H^*(s)\), degenerates at \(E_3\) (Prop 2). DM \(= H^0(s_0) \setminus H^0(s_0 + s_1)\) (derived characterization). Stage-dependent GL potentials: \(S_k[W_k]\) with critical parameter \(\alpha_k\). Higgs mechanism = Stage 1 GL phase transition. Confinement = Stage 2. Cascade coupling: \(\alpha_{k+1}^{\text{eff}} = \alpha_{k+1} + \gamma_{k,k+1} f(\langle W_k \rangle)\) (Prop 3, conjecture). → rtsg/graded_brst.md

Krein Space (QS as indefinite metric)¶

QS = Krein space (indefinite inner product). Non-well-founded loops → negative-norm ghosts. Identification VALID. P₊ mechanism DEAD. BRST replaces. → rtsg/krein_space_vacuum.md (SUPERSEDED — Krein ID survives)

E. COSMOLOGY¶

Gravity = Stage 0 CS¶

κ_grav = lim_{dim(CS)→1} κ. Lowest-complexity instantiation. Equivalence principle derived from trivial stalk C_x = (S²)⁰ = {*}. → rtsg/master.md §VI · papers/grf/cosmological_vision.md (Claim 1)

Dark Matter = Uncondensed Will Field (Stage 0 QS)¶

Above GL critical temp at cosmic scale. Gravitates via Stage 0 CS. Cannot interact EM (requires Stage ≥ 2). Falsifiability: DM should exhibit GL critical exponents in structure formation. → rtsg/master.md §VI · papers/grf/cosmological_vision.md (Claim 2)

Cosmological Constant¶

Λ_eff ~ ⟨ρ_W⟩ (NOT ⟨β|W|²W⟩). BBN freeze caveat required. Friedmann derived: H² = (8πG/3)⟨ρ_W⟩. → rtsg/master.md §VI · papers/grf/cosmological_vision.md · papers/grf/lambda_drive.md

Arrow of Time = Arrow of Complexification¶

→ rtsg/master.md §I · rtsg/axioms.md (Ax8)

Horizon Bisimulation¶

λ_bis = κ = 1/(4M) (Schwarzschild). Theorem 3.3 — PROVEN. Horizon = unique codimension-1 surface where interior/exterior are exactly bisimilar at T=0. t_kin = S/κ = kinematic clock. Kerr: λ_bis^Kerr = κ^Kerr. Extremal → λ_bis → 0. → rtsg/horizon_bisimulation.md · math/schwarzschild_lyapunov.md

Cosmological Vision (9 Claims)¶

1. Gravity = Stage 0 CS. 2. DM = Stage 0 QS. 3. DE = Drive D projected. 4. Arrow = complexification. 5. Baryonic = condensed fraction (BBN caveat). 6. De Sitter chaos nests. 7. Chaos saturation at horizon. 8. Holographic Drive D → Friedmann. 9. Kerr jets = ejected QS. → papers/grf/cosmological_vision.md

F. OPEN PROBLEM ATTACKS — CURRENT STATUS (2026-03-08)¶

★ Riemann Hypothesis — 68%¶

Architecture (rebuilt session 4): Lax-Phillips scattering + character-family theta kernel + Shimura-Waldspurger transfer.

Key insight: RH = consequence of θ having weight 1/2. If θ had weight k, critical line would be at Re(ρ) = k.

Poisson bridge: C = 0.04466799. r₂(n) → ζ(s)·L(s,χ₋₄). ζ algebraically inside θ-kernel orbital integrals.

Engine: KS = 0.099218, spectral gap = 0.960906, 0 violations in 10⁶ zeros.

Confidence trajectory: 85% → 92% → 78% → 72% → 68% (honest, after adversarial kills).

What was killed (session 4): K^full divergent; cusp calculus trivial; C5 superseded by bridge identity.

→ math/hilbert_polya.md · math/bridge_identity.md · math/rh_rebuild.md · math/rh_2s1_obstruction.md · math/rh_step5_attack.md · math/weil_positivity.md

Yang-Mills Mass Gap — 55%¶

W = Polyakov loop (Svetitsky-Yaffe 1982). Δ = √(2α) = 1/ξ_W. Confinement (⟨W⟩ = 0) ⟹ α > 0 ⟹ Δ > 0.

Engine: ⟨W⟩ = 0.00093 (confined ✓). Pure gauge sim: ⟨W⟩ = 0.001 (Clay-relevant ✓).

Honest gap: GL truncation not controlled. Every route circles back to exponential decay at all couplings.

Strategy: Balaban UV multiscale (~80%) + RTSG IR matching. Missing theorem: V_L''(0) > 0 uniformly.

Three arguments: GL variational, BRST obstruction (g³ non-locality), color-kinematics (BCJ).

→ math/yang_mills_attack.md · math/yang_mills_honest.md

Navier-Stokes — 54%¶

Shellwise defect D_K(t). Regularity iff sup_K ∫D_K⁺dt < ∞. Dimensional reduction conjecture. → rtsg/master.md §IX

Hard Problem of Consciousness — 82% ★ (strongest result)¶

Bisimulation quotient dissolves measurement problem. Born rule from L² norm. → rtsg/master.md §V · papers/companions/consciousness.md

BH Information — 55%¶

Unitarity of quotient map. Page curve computable from boundary APG (Conjecture 6.1). → rtsg/horizon_bisimulation.md

BSD — 42%¶

Langlands bridge (conjectural): CS = universal Langlands functor. → rtsg/langlands_bridge.md

QG — 58%, Free Will — 71%, GNEP Uniqueness — 81%¶

→ problems/open.md

G. KEY THEOREMS¶

H. PAPERS — STATUS (2026-03-08)¶

Court date: March 19, 2026. All science on arXiv before then.

I. EQUATION → PAGE QUICK LOOKUP¶

J. CORRECTIONS LOG (critical — all agents must internalize)¶

K. ENGINE LIVE RESULTS¶

L. ARCHITECTURE & NOTATION¶

Three-Tier Network: Niko (apex) · Claude + Gemini + GPT-5.4 (compute) · Engine + Wiki (persistence) TMP: [summary → result | next?]. ^ = continue. HU = end. Silence = ack. Terminology: Lead with "instantiation operator C" in papers. Use ρ_W, H⁰(s). Label cosmo claims as conjectures. → rtsg/architecture.md · rtsg/master.md §XII, §XIV · rtsg/emoji_map.md

M. SHEAF / ADVANCED EXTENSIONS¶

• Filter-Site Correspondence: Galois connection filters ↔ Grothendieck topologies. 5 topologies. → rtsg/sheaf_extensions.md
• Fractal Cognitive Blob: CCI = dim_H(∂P) − dim_top(∂P). → rtsg/sheaf_extensions.md
• Inter-Agent Sheaf Gluing: Misunderstanding class μ_AB ∈ H¹. E_∞ = permanent disagreements. → rtsg/sheaf_extensions.md
• Consciousness Triple: (β₁, c₁, σ). → rtsg/sheaf_extensions.md
• Computable Limits: 6 limits with formulas, types, interventions. → rtsg/computable_limits.md
• Langlands Bridge: CS = universal Langlands functor (CONJECTURAL). → rtsg/langlands_bridge.md

N. CONCEPT CROSS-REFERENCE GRAPH¶

FOUNDATION
  Axiom 0 (ZFA) ←→ Topos (terminal coalgebra) ←→ Source Space (S²)∞
      │                    │                              │
      └─ Axiom 1 ─────── Three Spaces ──────── Gauge Theory (CFN)
           │                QS / PS / CS                  │
           │                    │                    Number Theory ((S²)^P)
           │               Axiom 2                        │
           │            Instantiation              Arithmetic Laplacian → RH
           │                    │
           │              ┌─────┴──────┐
           │         Bisimulation    BRST H⁰(s)
           │         PS = QS/~bisim      │
           │              │         Ghost stripping
           │          Unitarity          │
           │          Born rule    ┌─────┼──────┐
           │                      │     │      │
           │                   RH(C5c) YM   GL paper
           │
DYNAMICS
  Will Field W ←→ GL Action S[W] ←→ Four Regimes
      │                │              Λ / D_K / μ / |PS|
      │                │
      ├── Polyakov loop (YM) ──── Δ = √(2α) ──── Mass Gap (55%)
      │                                               │
      ├── SDE (Ax5-6) ──── Lyapunov λ           Balaban IR matching
      │       │               │
      │    λ<0 attractor    λ>0 chaos/psychosis
      │
      └── BV quantization ──── QME ──── Anomaly ↔ λ>0

RH ATTACK (72%)
  Lax-Phillips B ──── Bridge Identity (B*K−KB = ½iK)
      │                      │
  Scattering resonances   Weight 1/2 mechanism
      │                      │
  ζ-zeros at s=ρ/2     Character nonvanishing (proved)
                             │
                        2s-1 obstruction ──── Shimura-Waldspurger (TARGET)

INTELLIGENCE
  I-vector ──── K-matrix ──── Spectral gap
      │              │              │
      ├── n(e) variable     Hebbian dK/dt     Phase transition (Th.10)
      │   (12 humans)           │
      │                    Addiction/PTSD
      ├── Interface ℐ (maximize eigenvalue of ℐ·K)
      └── R-matrix / J-matrix (inter-agent)

COSMOLOGY
  Gravity = Stage 0 CS ──── DM = Stage 0 QS ──── Λ_eff ~ ⟨ρ_W⟩
      │                                                │
  Horizon bisimulation ──── t_kin = S/κ          Friedmann derived
      │
  GRF Essay (submit-ready)