"""Original CC0 diagram for 11R.1--11R.4. Run with --output-dir PATH. Uses only the exact one-dimensional cone slice named in the proof. This generator does not construct a kernel or a Kasparov factor. Font/software notices are retained beside the source. """ from pathlib import Path import argparse import json import xml.etree.ElementTree as ET import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from matplotlib.font_manager import FontProperties from matplotlib.patches import FancyBboxPatch import numpy as np HERE = Path(__file__).resolve().parent REGULAR = FontProperties(fname=str(HERE / "fonts" / "DejaVuSans.ttf")) BOLD = FontProperties(fname=str(HERE / "fonts" / "DejaVuSans-Bold.ttf")) BLUE = "#155e94" GREEN = "#087858" ORANGE = "#b65d16" INK = "#19334a" def label(ax, x, y, s, size=14, bold=False, **kwargs): return ax.text(x, y, s, fontsize=size, fontproperties=BOLD if bold else REGULAR, color=INK, **kwargs) def box(ax, xy, width, height, color="#edf4f9"): ax.add_patch(FancyBboxPatch(xy, width, height, boxstyle="round,pad=0.018", linewidth=1.2, edgecolor=BLUE, facecolor=color)) def arrow(ax, p, q, color=BLUE): ax.annotate("", xy=q, xytext=p, arrowprops={"arrowstyle": "->", "color": color, "lw": 2.0, "shrinkA": 2, "shrinkB": 2}) def render(output_dir): output_dir.mkdir(parents=True, exist_ok=True) matplotlib.rcParams.update({"svg.hashsalt": "coherent-groupoid-auxiliary-CA-v1", "svg.fonttype": "path", "axes.unicode_minus": True}) fig = plt.figure(figsize=(15, 11), facecolor="white") gs = fig.add_gridspec(2, 2, height_ratios=[1.02, 1.23], width_ratios=[1.06, 1.0], hspace=.18, wspace=.17, left=.055, right=.97, top=.92, bottom=.075) a = fig.add_subplot(gs[0, :]); a.set_xlim(0, 1); a.set_ylim(0, 1); a.axis("off") label(a, .0, .97, "A The typed transfer and its exact unit restriction", 18, True) label(a, .0, .88, "G ⇒ T is an actual étale groupoid; C = C₀(T). All coefficients remain present.", 13) xs = [.07, .28, .49, .70, .93] nodes = ["Aᵣ", "Pᵣ", "Pₘ", "Aₘ", "ℂ"] for x, n in zip(xs, nodes): box(a, (x-.042, .64), .084, .105) label(a, x, .692, n, 22, True, ha="center", va="center") labels = [("jᵣ(η)", "degree k"), ("v", "degree 0"), ("jₘ(d)", "degree k"), ("dₘ", "degree q")] for i, (top, bottom) in enumerate(labels): arrow(a, (xs[i]+.05, .693), (xs[i+1]-.05, .693)) label(a, (xs[i]+xs[i+1])/2, .79, top, 16, ha="center") label(a, (xs[i]+xs[i+1])/2, .60, bottom, 11, ha="center") label(a, .0, .47, "SUPPLIED: proper P, factors η and d, coefficient inverse v, descent identities, normal dₘ.", 12, True) box(a, (.01, .15), .97, .245, "#eff8f3") label(a, .03, .345, "iᵣ ⊗ dᵣ = γ₀ ⊗ dN with γ₀ = For(η ⊗ d), dN = iₘ ⊗ dₘ", 17, True) label(a, .03, .26, "Whole normal restriction: γ₀ = 1C suffices. Original local test: bU ⊗ γ₀ = bU suffices.", 12) label(a, .03, .185, "Then (bU ⊗ iᵣ) ⊗ dᵣ = +1. No inverse of qA or equivariant-unit identity was inserted.", 12) label(a, .0, .035, "11R.1–11R.2: the unit restriction is proved by Φ(e ⊗ k)(g) = e(rg)k(g), not by choosing one fibre.", 12) b = fig.add_subplot(gs[1, 0]); b.set_xlim(0, 1); b.set_ylim(0, 1); b.axis("off") label(b, .0, .98, "B What a proper coefficient must supply", 17, True) label(b, .0, .90, "11R.3: Q = K(E), E a full nonzero Hilbert field over Y.", 12) box(b, (.025, .65), .94, .15) label(b, .055, .755, "ZM(Q) = Cb(Y)", 17, True) label(b, .055, .687, "central, nondegenerate C₀(Z) action", 12) arrow(b, (.49, .64), (.49, .54)) box(b, (.025, .38), .94, .15, "#eff8f3") label(b, .055, .483, "y ↦ zy : Y → Z", 17, True) label(b, .055, .414, "continuous, anchored and equivariant", 12) arrow(b, (.49, .37), (.49, .27)) box(b, (.025, .08), .94, .18, "#fff4e7") label(b, .055, .206, "Z proper ⇒ Y proper", 18, True) label(b, .055, .143, "compact transporters pull back", 12) label(b, .055, .096, "A different proper Bott algebra is still possible.", 11) c = fig.add_subplot(gs[1, 1]) c.set_xlim(-1.35, 1.35); c.set_ylim(-.08, 2.05) c.spines[["top", "right"]].set_visible(False) v = np.linspace(-1.35, 1.35, 500) c.fill_between(v, v*v, 2.05, color="#eff8f3") c.plot(v, v*v, color=GREEN, lw=2) c.axhline(.75, color="#526477", lw=1.2, linestyle=(0, (4, 3))) c.plot([-.5, -.5], [.25, .75], color=BLUE, lw=2) c.plot([.5, .5], [.25, .75], color=ORANGE, lw=2) c.scatter([-.5, .5], [.75, .75], s=74, color=[BLUE, ORANGE], zorder=5) arrow(c, (-.44, .75), (.44, .75), GREEN) label(c, -.5, .90, "(−½, ¾)", 13, ha="center") label(c, .5, .90, "(½, ¾)", 13, ha="center") label(c, -.63, .45, "½", 12, ha="right") label(c, .63, .45, "½", 12, ha="left") label(c, .0, .64, "b = 1", 12, ha="center") label(c, -1.30, 1.95, "C Exact one-dimensional cone slice", 16, True) label(c, -1.28, 1.72, "Z: t ≥ v²; L = 1; ψ(g) = b² = 1", 12) label(c, -1.28, 1.50, "t′ = t + 2vb + b² = ¾ − 1 + 1 = ¾", 12, True) label(c, -1.28, 1.28, "Excess t − v² = ½ is preserved.", 12) c.set_xlabel("real fibre coordinate v", fontproperties=REGULAR, fontsize=12) c.set_ylabel("height t", fontproperties=REGULAR, fontsize=12) for tick in c.get_xticklabels()+c.get_yticklabels(): tick.set_fontproperties(REGULAR) fig.text(.055, .975, "Coherent groupoid auxiliaries: restriction, proper coefficient and cone", fontsize=21, fontproperties=BOLD, color=INK) fig.text(.055, .021, "11R.1–11R.4. Cone slice is exact; the general topology is weak. Compatible kernels and proper Bott/Dirac factors are separate inputs.", fontsize=11, fontproperties=REGULAR, color=INK) notice = (HERE / "FONT-NOTICE.txt").read_text(encoding="utf-8") png = output_dir / "groupoid-compatible-auxiliary.png" svg = output_dir / "groupoid-compatible-auxiliary.svg" fig.savefig(png, dpi=200, metadata={"Software": "Matplotlib; original diagram CC0 1.0", "Description": notice}) fig.savefig(svg, metadata={"Date": None, "Creator": "Original CC0 mathematical diagram", "Description": notice}) plt.close(fig) svg.write_text(svg.read_text(encoding="utf-8"),encoding="utf-8",newline="\n") ET.parse(svg) data = {"figure_scope": "typed conditional transfer; full compact-field centre criterion; exact real cone slice", "slice": {"L": 1, "b": 1, "v": -.5, "t": .75, "v_prime": .5, "t_prime": .75, "excess": .5, "psi": 1, "proper_bound": 3}, "proved_locators": ["11R.1", "11R.2", "11R.3", "11R.4"], "not_claimed": ["existence of a general holonomy kernel", "proper Bott/Dirac factorization", "full target 55"]} (output_dir / "figure-data.json").write_text(json.dumps(data, indent=2)+"\n", encoding="utf-8", newline="\n") if __name__ == "__main__": parser = argparse.ArgumentParser() parser.add_argument("--output-dir", type=Path, default=HERE / "figures") render(parser.parse_args().output_dir.resolve())