"""Forward projection of the fleet crossover for PLRN-031. The per-turn crossover is past (the hook chain's median exceeds the measured classifier latencies). What has a date is the fleet crossover: the point where control costs the mean governed agent more time than judgment, i.e. where the mean judgment time per turn falls below the per-action control cost, Jbar(t) = (1 - f(t)) * Js + f(t) * Jf(t), control dominates when Jbar < C. Scenario (stated in section 5 of the note, conservative by construction): - f(t): fast-turn fraction rises logistically from 0.90 at the note's date (2026-10-14) to 0.99 one year later. - Jf(t): classifier latency halves annually from 50 ms (a slower cadence than the two orders of magnitude in seven months actually observed). - Js: the slow call is held at 60 s (the note's working median), so the projection does not depend on frontier calls getting faster. C: hook-chain medians from plrn031_chain_model.py (115 ms in region, 450 ms public SaaS); 12 us for an in-path decision. Running it prints the schedule as JSON and writes plrn031-projection.svg (Figure 4) next to this script. """ import json import math import os import sys MONTHS = ["", "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"] NOTE_DATE = 2026 + (9.5 + 13 / 30.0) / 12.0 # 2026-10-14 as a decimal year JS = 60_000.0 # ms, slow turn (held fixed) JF0 = 50.0 # ms, fast-turn judgment at the note's date F0, F1 = 0.90, 0.99 C_SAAS, C_REGION, C_INPATH = 450.0, 115.0, 0.012 # ms def logistic(f_start, f_year1): """Logistic parameters with f(0) = f_start and f(1) = f_year1.""" a = math.log(f_start / (1 - f_start)) return a, math.log(f_year1 / (1 - f_year1)) - a A, B = logistic(F0, F1) def f(t, a=A, b=B): return 1.0 / (1.0 + math.exp(-(a + b * t))) def jf(t): return JF0 * 2.0 ** (-t) def jbar(t, js=JS, a=A, b=B): return (1 - f(t, a, b)) * js + f(t, a, b) * jf(t) def crossing(c, js=JS, a=A, b=B): """First t (years from the note's date) where jbar < c; log-linear refine.""" prev = 0.0 for m in range(1, 4 * 12 * 10 + 1): t = m / 120.0 if jbar(t, js, a, b) < c: f0, f1v = math.log(jbar(prev, js, a, b)), math.log(jbar(t, js, a, b)) return prev + (t - prev) * (math.log(c) - f0) / (f1v - f0) prev = t return None def date_label(t): d = NOTE_DATE + t return f"{MONTHS[int((d % 1) * 12) + 1]} {int(d)}" def fstar(js, c): """Fast-turn fraction at which the mean agent becomes control-dominated.""" return (js - c) / (js - jf(0)) # --- numbers for the note ------------------------------------------------- out = { "scenario": {"f": "logistic 0.90 -> 0.99 in year 1 (leading cohort)", "Jf": "50 ms, halving annually", "Js": "60 s, fixed", "note_date": "2026-10-14"}, "jbar_ms": {d: round(jbar(t), 1) for d, t in [("note_date", 0.0), ("+1y", 1.0), ("+2y", 2.0), ("+4y", 4.0)]}, "crossings": {}, "fstar_percent": {}, "kept_percent": {}, } for name, c in [("public_saas", C_SAAS), ("in_region", C_REGION)]: tc = crossing(c) out["crossings"][name] = {"t_years": round(tc, 2), "date": date_label(tc)} # The median fleet walks the same path to the same threshold from a lower # start: 50% of turns fast at the note's date, 90% one year later (the same # nine-point cadence as the leading cohort's 90% -> 99%). A_MED, B_MED = logistic(0.50, 0.90) out["median_cohort"] = { "scenario": {"f": "logistic 0.50 -> 0.90 in year 1", "Jf": "as above", "Js": "as noted"}, "public_saas": {"date": date_label(crossing(C_SAAS, a=A_MED, b=B_MED))}, "in_region": {"date": date_label(crossing(C_REGION, a=A_MED, b=B_MED))}, "public_saas_js_10s": {"date": date_label(crossing(C_SAAS, js=10_000.0, a=A_MED, b=B_MED))}, "in_region_js_10s": {"date": date_label(crossing(C_REGION, js=10_000.0, a=A_MED, b=B_MED))}, } tc3 = crossing(C_SAAS, js=180_000.0) out["saas_crossing_if_js_triples"] = {"date": date_label(tc3), "delay_months": round((tc3 - out["crossings"]["public_saas"]["t_years"]) * 12)} # Sensitivity of the dates to the path: the same leading cohort taking two # years rather than one to go from 90% to 99%, and classifier latency frozen # at 50 ms. Only the path moves the dates by more than a quarter. out["path_sensitivity"] = { "routing_90_to_99_over_two_years": { n: date_label(crossing(c, a=A, b=B / 2.0)) for n, c in [("public_saas", C_SAAS), ("in_region", C_REGION)]}, } _jf_halving = jf jf = lambda t: JF0 # noqa: E731 out["path_sensitivity"]["jf_frozen_50ms"] = { n: date_label(crossing(c)) for n, c in [("public_saas", C_SAAS), ("in_region", C_REGION)]} jf = _jf_halving for js in [60_000, 10_000, 3_000, 1_000, 500]: out["fstar_percent"][f"Js={js / 1000:g}s"] = { "public_saas": round(100 * fstar(js, C_SAAS), 1), "in_region": round(100 * fstar(js, C_REGION), 1), } for name, c in [("in_region", C_REGION), ("public_saas", C_SAAS)]: out["kept_percent"][name] = { f"Oct {2026 + k}": round(100 * jf(k) / (jf(k) + c), 1) for k in range(4)} json.dump(out, sys.stdout, indent=2) print() # --- Figure 4 ------------------------------------------------------------- W, H = 1180, 690 X0, X1, TMAX = 230.0, 820.0, 4.0 Y0, Y1 = 40.0, 600.0 LOG_HI, DECADES = 5.0, 7 # top of axis is 100 s, bottom 10 us INK, ORANGE, BLUE, GRAY, GRID = "#16161D", "#C2410C", "#0077B6", "#787B82", "#E4E6EA" def px(t): return X0 + (t / TMAX) * (X1 - X0) def py(ms): return Y0 + (LOG_HI - math.log10(ms)) / DECADES * (Y1 - Y0) pts = [(m / 12.0, jbar(m / 12.0)) for m in range(0, 49)] curve = f"M {px(0):.1f} {py(pts[0][1]):.1f} " + " ".join( f"L {px(t):.1f} {py(v):.1f}" for t, v in pts[1:]) tc_saas, tc_reg = crossing(C_SAAS), crossing(C_REGION) wedge = (f"M {px(tc_saas):.1f} {py(C_SAAS):.1f} " + " ".join(f"L {px(t):.1f} {py(v):.1f}" for t, v in pts if t >= tc_saas) + f" L {X1:.1f} {py(C_SAAS):.1f} Z") s = [] s.append(f"" f"") s.append("The fleet crossover, projected") s.append("Log-scale projection of mean judgment time per turn from October 2026 to " "October 2030, falling from about six seconds to a few milliseconds. Two horizontal lines mark the " "modeled hook-chain control costs of 450 milliseconds (public SaaS) and 115 milliseconds (in region). " "The curve crosses the first at the end of 2027 and the second in mid-2028; below each line, control " "costs the mean agent more time than judgment. An in-path decision of 12 microseconds sits far below.") gridlines = "".join(f"" for k in range(DECADES + 1)) s.append(f"{gridlines}") labels = ["100 s", "10 s", "1 s", "100 ms", "10 ms", "1 ms", "100 µs", "10 µs"] ytext = "".join(f"{labels[k]}" for k in range(DECADES + 1)) s.append(f"{ytext}") s.append(f"MEAN JUDGMENT PER TURN · LOG SCALE · PROJECTED") ylines = "".join(f"" for y in range(5)) s.append(f"{ylines}") xtext = "".join(f"OCT {2026 + y}" for y in range(5)) s.append(f"{xtext}") s.append(f"") s.append(f"") for c, w, op in [(C_SAAS, 4, 1.0), (C_REGION, 2.5, 0.55)]: s.append(f"") for tc, dy, lab in [(tc_saas, -12, "END OF 2027"), (tc_reg, 30, "MID-2028")]: c = C_SAAS if tc == tc_saas else C_REGION s.append(f"" f"" f"{lab}") s.append(f"") s.append(f"" f"Mean judgment per turn" f"≈6 s today → 625 ms Oct 2027 → 68 ms Oct 2028" f"Public-SaaS chain" f"450 ms median · §3" f"In-region chain" f"115 ms median · §3" f"In-path decision · 12 µs" f"no crossover at any date" f"") s.append("") svg_path = os.path.join(os.path.dirname(os.path.abspath(__file__)), "plrn031-projection.svg") with open(svg_path, "w") as fh: fh.write("\n".join(s)) print(f"wrote {svg_path}", file=sys.stderr)