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29d94b3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | (* FSOT 2.1 Symbolic Math Microscope — rebuild from seeds *)
(* Formula: S = K*(T1 + T2 + T3) — zero free params beyond seeds *)
ClearAll[FSOTSeeds, FSOTDerived, FSOTScalarSym, FSOTPrintPathway];
FSOTSeeds[] := Association[
"pi" -> Pi,
"e" -> E,
"phi" -> (1 + Sqrt[5])/2,
"gamma" -> EulerGamma,
"G_cat" -> Catalan
];
FSOTDerived[] := Module[{s = FSOTSeeds[], pi, e, phi, gamma, G},
pi = s["pi"]; e = s["e"]; phi = s["phi"]; gamma = s["gamma"]; G = s["G_cat"];
Association[
"alpha" -> Log[pi]/(e*phi^13),
"psi_con" -> 1 - 1/e,
"eta_eff" -> 1/(pi - 1),
"beta" -> Exp[-(pi^pi + (e - 1))],
"gamma_c" -> -Log[2]/phi,
"omega" -> Sin[pi/e]*Sqrt[2],
"theta_s" -> Sin[(1 - 1/e)*(1/(pi - 1))],
"poof" -> Exp[(-Log[pi]/e)/((1/(pi - 1))*Log[phi])],
"c_eff" -> (1 - Exp[(-Log[pi]/e)/((1/(pi - 1))*Log[phi])]*Sin[Sin[(1-1/e)*(1/(pi-1))]])
*(1 + 0.01*G/(pi*phi)),
"a_bleed" -> Sin[pi/e]*phi/Sqrt[2],
"p_var" -> -Cos[Sin[(1-1/e)*(1/(pi-1))] + pi],
"b_in" -> With[{ce = (1 - Exp[(-Log[pi]/e)/((1/(pi-1))*Log[phi])]*Sin[Sin[(1-1/e)*(1/(pi-1))]])*(1+0.01*G/(pi*phi)),
ts = Sin[(1-1/e)*(1/(pi-1))]}, ce*(1 - Sin[ts]/phi)],
"a_in" -> With[{ab = Sin[pi/e]*phi/Sqrt[2], ts = Sin[(1-1/e)*(1/(pi-1))]}, ab*(1 + Cos[ts]/phi)],
"suction" -> With[{pf = Exp[(-Log[pi]/e)/((1/(pi-1))*Log[phi])], ts = Sin[(1-1/e)*(1/(pi-1))]}, pf*(-Cos[ts - pi])],
"chaos" -> (-Log[2]/phi)/(Sin[pi/e]*Sqrt[2]),
"p_base" -> gamma/e,
"p_new" -> (gamma/e)*Sqrt[2],
"c_factor" -> With[{ce = (1 - Exp[(-Log[pi]/e)/((1/(pi-1))*Log[phi])]*Sin[Sin[(1-1/e)*(1/(pi-1))]])*(1+0.01*G/(pi*phi))},
ce*(gamma/e)*Sqrt[2]],
"K" -> phi*(gamma/e)*Sqrt[2]/Log[pi]*0.99
]
];
(* Numeric domain scalar: same structure as Python microscope *)
FSOTScalarSym[opts:OptionsPattern[{
N->1., P->1., DEff->12., RecentHits->0., DeltaPsi->0.8, DeltaTheta->1.,
Rho->1., Scale->1., Amplitude->1., TrendBias->0., Observed->True
}]] := Module[{
d = FSOTDerived[], s = FSOTSeeds[],
n, p, de, hits, dp, dt, rho, sc, amp, tb, obs,
growth, npSqrt, cosPsi, expD, coh, base, dScale, t1, qm, t2,
chaosMod, poofMod, valve, acoustic, phase, t3, raw, S, steps = {}
},
n = OptionValue[N]; p = OptionValue[P]; de = OptionValue[DEff];
hits = OptionValue[RecentHits]; dp = OptionValue[DeltaPsi]; dt = OptionValue[DeltaTheta];
rho = OptionValue[Rho]; sc = OptionValue[Scale]; amp = OptionValue[Amplitude];
tb = OptionValue[TrendBias]; obs = OptionValue[Observed];
growth = Exp[d["alpha"]*(1 - hits/n)*s["gamma"]/s["phi"]];
npSqrt = n*p/Sqrt[de];
cosPsi = Cos[(d["psi_con"] + dp)/d["eta_eff"]];
expD = Exp[-d["alpha"]*hits/n + rho + d["b_in"]*dp];
coh = 1 + growth*d["c_eff"];
base = npSqrt*cosPsi*expD*coh;
dScale = 1 + d["p_new"]*Log[de/25];
t1 = base*dScale; qm = 1;
If[obs, qm = Exp[d["c_factor"]*d["p_var"]]*Cos[dp + d["p_var"]]; t1 = t1*qm];
t2 = sc*amp + tb;
chaosMod = 1 + d["chaos"]*(de - 25)/25;
poofMod = 1 + d["poof"]*Cos[d["theta_s"] + Pi] + d["suction"]*Sin[d["theta_s"]];
valve = d["beta"]*Cos[dp]*npSqrt*chaosMod*poofMod;
acoustic = 1 + (d["a_bleed"]*Sin[dt]^2)/s["phi"] + (d["a_in"]*Cos[dt]^2)/s["phi"];
phase = 1 + d["b_in"]*d["p_var"];
t3 = valve*acoustic*phase;
raw = t1 + t2 + t3; S = d["K"]*raw;
Association[
"K" -> N[d["K"]], "T1" -> N[t1], "T2" -> N[t2], "T3" -> N[t3],
"raw" -> N[raw], "S" -> N[S], "quirk_mod" -> N[qm], "growth" -> N[growth]
]
];
FSOTPrintPathway[] := Module[{d = N[FSOTDerived[]], panel},
Print["=== FSOT Symbolic Microscope (numeric eval of seeds→derived) ==="];
Print["K = ", d["K"]];
Print["psi_con, eta_eff, c_eff, p_var = ", d["psi_con"], ", ", d["eta_eff"], ", ", d["c_eff"], ", ", d["p_var"]];
panel = FSOTScalarSym[DEff -> 12., DeltaPsi -> 0.8, Observed -> True];
Print["linguistic panel: ", panel];
panel
];
(* Usage:
Get["…/FSOT_Symbolic_Microscope.wl"]
FSOTPrintPathway[]
FSOTScalarSym[DEff->6., Observed->True] (* quantum-like *)
*)
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