Rosetta Stone — 7 CSVs ↔ Perplexity Taxonomy (12 Aug 2026)
Mapping: $N_{n+1}=aN_n-\varepsilon(N_n)$, relative constraint $q(N)=\varepsilon(N)/N$, multiplier $N_{n+1}/N_n = a-q(N_n)$ — from constraint-classes-Perplexity/
| CSV (size) — Class | $\varepsilon(N)$ form | $q(N)$ limit — Result | 81018 Meaning |
|---|---|---|---|
| I_Pure_Doubling.csv (1,343) I. No Constraint — The Ruler |
$\varepsilon\equiv0$ | $q=0$ → Theorem 1: $N_{n+1}/N_n\to a=2$, $\log N_n/n\to\log2$ | Perfect doubling. Planck to Universe baseline. 202 notations. |
| II_Sublinear_Correction.csv (3,137) II. Geometric / Packing — The Gap |
$\varepsilon=cN^p$, $0
| $q=cN^{p-1}\to0$ — asymptotically negligible, but $g(N)>N$ for large N | 7.356° openness — 5×70.5288°=352.644° leaves freedom. CDT, Causal Sets, LQG live here. $\Delta(N)$ = gap measure. |
| III_Subdoubling_Linear.csv (3,136) III. Symmetry / Conservation — HOME OF LANGLANDS ★ |
$\varepsilon\approx cN$, $0 | $q\to q_\infty$, $\lambda=a-q_\infty$, Prop.2 — reduced exponential | Symmetry holds 1-64 or gap can’t be bridged. U(1) charge, SU(2) isospin, Parity mirror at 60. Automorphic ↔ Galois. |
| IV_Logarithmic_Brake.csv (2,863) IV. Field / Force — 65-134 |
$\varepsilon=\kappa\log N$ | $\kappa\log N/N\to0$ — affects small/intermediate N, not large-N polynomial | Fields emerge. Brake $\varepsilon=\kappa\log N$. Wilczek, ‘t Hooft, Witten, Vafa, Maldacena. EM at 70, Strong/Weak at 100. |
| V_Threshold_Saturation.csv (3,006) V. Thermodynamic |
$g(N)=\alpha N$ if $N | Switching system — may give cycle, bound, or sensitive dynamics. Fixed point requires $\varepsilon(N_*)=(a-1)N_*$ and $|g'(N_*)|<1$ | Order costs. Saturation is fixed-point property, not synonym for stronger constraint. Threshold ≠ automatic equilibrium. |
| VI_Delayed_Feedback.csv (2,863) VI. Information |
$N_{n+1}=aN_n-cN_{n-d}$ | Higher-dim: $r^{d+1}-ar^d+c=0$ — growth/decay/oscillation from roots | Delay = higher-dimensional state. Decoherence, information. Not synonymous with chaos — needs Lyapunov. |
| VII_Stochastic.csv (4,033) VII. Biological + Measurement |
$N_{n+1}=N_nM_{n+1}$, $M>0$ random | $\log N_n/n\to \mathbb{E}[\log M_1]$ a.s. — relevant avg is log, not $E[M]$ | Life measures, consciousness as constraint. 90-202: atoms → life → measurement. Positivity requires multiplicative noise. |
| SUMMARY.csv (349) + chart_202_notations.json (68,197) | $\Phi(\Delta(N),N)$ | Test: Does $\Delta(N)\to0$? What is $\Phi/N$? Positivity? Fixed points? | Next decisive task: derive $\Delta(N)$ = gap, specify $\Phi$, determine which class. No cosmology from taxonomy alone. |
A. Museum label (Choice A): 7.356° openness — 5×70.5288°=352.644° leaves 7.356°. Five tetrahedra choose openness; tetra+octa choose closure. The gap is freedom.
B. Tight chart label (Choice B): 7.356° gap — 5 tetra = 352.644°, not 360°. Openness vs. tetra+octa closure. — Per Perplexity taxonomy, this is $q\to0$ with bounded-away $\Delta$, not a defect.
C. Special Note: /244837-2/ original file name