"""Render the exact induced-corner diagram, using only its local data and fonts. Run: python render.py Outputs: induced-corners.svg and induced-corners.png in this directory. All geometry is independently specified here; no source-page image is loaded. """ from pathlib import Path import json import argparse import hashlib import matplotlib matplotlib.use("Agg") from matplotlib import pyplot as plt from matplotlib import font_manager as fm from matplotlib.patches import Rectangle, FancyArrowPatch ROOT = Path(__file__).resolve().parent parser = argparse.ArgumentParser() parser.add_argument('--shared-font-dir', type=Path, default=ROOT.parent / 'typeiii-zero-decomposition') args = parser.parse_args() DATA = json.loads((ROOT / "data.json").read_text(encoding="utf-8")) for name in ("DejaVuSans.ttf", "DejaVuSans-Bold.ttf", "DejaVuSans-Oblique.ttf", "DejaVuSansDisplay.ttf", "STIXNonUniIta.ttf", "cmsy10.ttf"): fm.fontManager.addfont(str((args.shared_font_dir if name in {'DejaVuSans.ttf', 'DejaVuSans-Bold.ttf'} else ROOT) / name)) plt.rcParams.update({ "font.family": "DejaVu Sans", "font.size": 11, "mathtext.fontset": "dejavusans", "axes.unicode_minus": True, "svg.fonttype": "path", "svg.hashsalt": "induced-central-corners-20261007", "figure.facecolor": "#f6f8fb", "savefig.facecolor": "#f6f8fb", }) NAVY = "#203348" BLUE = "#2466a5" ORANGE = "#bb5b14" TEAL = "#167a67" MUTED = "#617082" PALE = "#e6eef7" LINE = "#bccbdc" h = DATA["hit_sample"] assert h["R2"] == h["R1"] - h["a"] + h["a_next"] assert h["R2"] == h["next_pair"][1] - h["first_pair"][1] for x, y in h["displayed_pairs"]: right = min(t for t in h["first_section"] if t > x) assert x <= y < right assert y == min(t for t in h["second_section"] if x <= t < right) assert DATA["coincident_sample"]["a"] == DATA["coincident_sample"]["b"] == 0 d = DATA["deck_square"] assert d["source_top"][0] - d["top_displacement"] == d["target_top"][0] assert d["source_top"][0] - d["left_roof"] == d["source_bottom"][0] assert d["target_top"][0] - d["right_roof"] == d["target_bottom"][0] assert d["source_bottom"][0] - d["bottom_displacement"] == d["target_bottom"][0] for a in [0, h["a"], h["a_next"], -2, 17]: for s in [-5, 0, 9]: assert (s - a) + a == s fig = plt.figure(figsize=(15.2, 12.2), dpi=180) fig.text(.055, .965, "Return corners and the exact section-pairing maps", fontsize=23, weight="bold", color=NAVY, va="top") fig.text(.055, .925, "Two partitions make the return unitary; paired hits determine the roof difference.", fontsize=13, color=MUTED, va="top") def arrow(ax, start, end, color=BLUE, style="-|>", scale=15, width=1.7, connection="arc3,rad=0", **kw): a = FancyArrowPatch(start, end, arrowstyle=style, mutation_scale=scale, linewidth=width, color=color, connectionstyle=connection, shrinkA=0, shrinkB=0, **kw) ax.add_patch(a) return a # A: symbolic central bands. Their drawing widths are deliberately not weights. ax = fig.add_axes([.055, .605, .41, .26]) ax.set_xlim(-.45, 6.8); ax.set_ylim(-.85, 3.45); ax.axis("off") ax.text(0, 3.27, "A Two orthogonal central partitions", fontsize=14, weight="bold", color=NAVY) xs = [0, 1.7, 3.4, 5.1] src = [r"$e_1$", r"$e_2$", r"$e_3$", r"$\cdots$"] dst = [r"$\alpha(e_1)$", r"$\alpha^2(e_2)$", r"$\alpha^3(e_3)$", r"$\cdots$"] maps = [r"$u e_1$", r"$u^2 e_2$", r"$u^3 e_3$", r"$u^n e_n$"] for x, a, b, m in zip(xs, src, dst, maps): for y, label in [(2.1, a), (.1, b)]: ax.add_patch(Rectangle((x, y), 1.27, .60, facecolor=PALE, edgecolor=BLUE, linewidth=1.3)) ax.text(x+.635, y+.30, label, ha="center", va="center", color=NAVY, fontsize=13) arrow(ax, (x+.635, 2.03), (x+.635, .78), color=ORANGE) ax.text(x+.78, 1.42, m, color=ORANGE, fontsize=11, ha="left", bbox=dict(facecolor="#f6f8fb", edgecolor="none", pad=.6)) ax.text(0, -.34, r"$e=\sum_{n\geq1}e_n=\sum_{n\geq1}\alpha^n(e_n)$", fontsize=14, color=NAVY) ax.text(0, -.77, "Band widths carry no trace or probability. [IC7–12]", fontsize=10.5, color=MUTED) # B: exact horizontal times. All arrows remain in a finite window. ax = fig.add_axes([.525, .585, .425, .285]) ax.set_xlim(-1.25, 11.3); ax.set_ylim(-.2, 4.8); ax.axis("off") ax.text(-1.05, 4.47, "B Pair the first hit in each occupied interval", fontsize=14, weight="bold", color=NAVY) for y, title in [(3.25, r"$\Omega_1$"), (2.0, r"$\Omega_2$")]: arrow(ax, (-.45, y), (10.7, y), color=LINE, width=1.2, scale=9) ax.text(-1.0, y, title, ha="center", va="center", color=NAVY, fontsize=13) for x in [0, 4, 8]: ax.scatter([x], [3.25], s=49, color=BLUE, zorder=4) ax.text(x, 3.01, str(x), ha="center", va="top", color=BLUE) for y in [1, 7, 10]: ax.scatter([y], [2.0], s=49, color=TEAL, zorder=4) ax.text(y, 1.77, str(y), ha="center", va="top", color=TEAL) for (x, y), label in zip(h["displayed_pairs"], [r"$a=1$", r"$a'=3$", ""]): arrow(ax, (x, 3.13), (y, 2.13), color=ORANGE, width=1.8 if label else 1.0, scale=12) if label: ax.text((x+y)/2+.08, 2.66, label, fontsize=12, color=ORANGE, bbox=dict(facecolor="#f6f8fb", edgecolor="none", pad=.5)) arrow(ax, (0, 3.8), (4, 3.8), style="<->", scale=10) ax.text(2, 3.95, r"$R_1=4$", color=BLUE, ha="center", fontsize=12) arrow(ax, (1, 1.24), (7, 1.24), color=TEAL, style="<->", scale=10) ax.text(4, .96, r"$R_2=6=4-1+3$", color=TEAL, ha="center", fontsize=12) ax.text(-1.05, .39, "Coincident hits:", color=NAVY, fontsize=10.5) for x in [3.4, 6.3, 9.2]: ax.scatter([x], [.38], s=76, facecolors="none", edgecolors=BLUE, linewidth=1.8) ax.scatter([x], [.38], s=16, color=TEAL, zorder=4) ax.text(6.3, .02, r"$a=b=0,\quad W=\mathrm{id}$", ha="center", color=TEAL, fontsize=11) ax.text(-1.05, -.18, "Finite orbit windows; no periodic closure. [IC41–46]", color=MUTED, fontsize=10.5) # C: commuting point square for the unsheared full product map. ax = fig.add_axes([.055, .19, .895, .325]) ax.set_xlim(0, 13.2); ax.set_ylim(-.85, 4.4); ax.axis("off") ax.text(0, 4.12, "C The unsheared product map commutes with the deck maps", fontsize=16, weight="bold", color=NAVY) node = dict(boxstyle="round,pad=.5", facecolor="white", edgecolor=BLUE, linewidth=1.4) for xy, text in [((2.1, 3.03), r"$(9,x)$"), ((10.7, 3.03), r"$(8,Wx)$"), ((2.1, .77), r"$(5,x')$"), ((10.7, .77), r"$(2,Wx')$")]: ax.text(*xy, text, fontsize=17, ha="center", va="center", color=NAVY, bbox=node) arrow(ax, (3.2, 3.03), (9.4, 3.03), color=ORANGE, width=2) ax.text(6.3, 3.36, r"$\mathcal{J}:\ s\mapsto s-a,\quad a=1$", fontsize=13, color=ORANGE, ha="center") arrow(ax, (3.2, .77), (9.4, .77), color=ORANGE, width=2) ax.text(6.3, .40, r"$\mathcal{J}:\ s\mapsto s-a',\quad a'=3$", fontsize=13, color=ORANGE, ha="center") arrow(ax, (2.1, 2.62), (2.1, 1.17), color=BLUE, width=2) ax.text(.3, 1.89, r"$\Gamma_1^E$"+"\n"+r"$-R_1=-4$", fontsize=13, color=BLUE, ha="left", va="center") arrow(ax, (10.7, 2.62), (10.7, 1.17), color=TEAL, width=2) ax.text(11.16, 1.89, r"$\Gamma_2^E$"+"\n"+r"$-R_2=-6$", fontsize=13, color=TEAL, ha="left", va="center") ax.text(6.3, 2.09, r"$9-4-3=9-1-6=2$", color=NAVY, fontsize=17, ha="center") ax.text(6.3, 1.50, r"$\mathcal{B}(5,x')A_{1,x}=A_{2,Wx}\mathcal{B}(9,x)$", color=NAVY, fontsize=13, ha="center") ax.text(0, -.26, "The arrows include the full fiber maps and normal inverses. [IC50–59]", color=MUTED, fontsize=11) ax.text(0, -.76, r"After the shear: $D=H\mathcal{J}$, $(HG)(s,y)=G(s-a(Vy),y)$, " r"$D(1\otimes x)=1\otimes\Phi(x)$.", color=NAVY, fontsize=12) fig.text(.055, .106, "Height alignment extracts the coefficient conjugacy; it does not claim that D intertwines the full variable-roof decks.", fontsize=11.2, color=MUTED) fig.text(.055, .066, "Exact objects and proofs: OA-FLOW-IC, IC7–12, IC41–46 and IC50–60.", fontsize=11.2, color=NAVY) fig.text(.055, .038, "Original mathematical illustration • reproducible Python / Matplotlib • CC0-1.0; bundled fonts retain their license.", fontsize=10.2, color=MUTED) fig.savefig(ROOT / "induced-corners.png", dpi=180, metadata={"Software": "Original induced-corners renderer"}) fig.savefig(ROOT / "induced-corners.svg", metadata={"Date": None, "Creator": "Original induced-corners renderer", "Title": DATA["title"]}) plt.close(fig) for name in ["induced-corners.svg", "induced-corners.png"]: p = ROOT / name print(name, hashlib.sha256(p.read_bytes()).hexdigest())