Code and Data · Donkey on the Edge

I · MANUSCRIPT & APPENDICES

Rendered in-site, with KaTeX math. Each is part of the complete package.

i.

The Manuscript

paper_full_v3_FINAL.md · full text, §§1–9, with Figures 1–5 inline.

› ii.

Appendix A · Generalized EGH Formulas

Closed-form moment identities for the bulk-marginal diagonal.

› iii.

Appendix B · Reproducibility

Manifest, seeds, environment. Master seed 707070. Every CSV reproduces bit-identically.

› iv.

Appendix C · The Entropy-Replacement Proof (Haar)

C.1–C.5 off-diagonal F_off; C.6 diagonal-to-bulk F_diag by the centered-operator reduction; C.7 assembly.

› v.

The Reviewer's Note

Six rounds of adversarial review by Scholar (ChatGPT). Final state of the manuscript.

› vi.

Paper II · Manuscript (Historical)

paper_full_draft_v2.md · the intermediate draft, preserved as the corrected-foundation record.

›

II · THE FIVE PLATES

Figures rendered from the reproducibility CSVs (seed 707070).

Figure I: The structural identity, verified. The Haar-$V$-averaged observer-reduced state against the diagonal of the bulk marginal across eighteen diagonal entries; off-diagonal coherences suppressed at the predicted order. Drawn from data, seed 707070. — Fig. I. The structural identity, verified. The Haar- $V$ -averaged observer-reduced state against the diagonal of the bulk marginal across eighteen diagonal entries; off-diagonal coherences suppressed at the predicted order. Drawn from data, seed 707070.

Figure II: First-moment collapse. Off-diagonal magnitude in the cloning basis as a function of dimension, showing the $O(1/d^2)$ suppression that underwrites Lemma 1. — Fig. II. First-moment collapse. Off-diagonal magnitude in the cloning basis as a function of dimension, showing the $O(1/d^2)$ suppression that underwrites Lemma 1.

Figure III: The Haar law. $\mathbb{E}|S_A - S_B|$ against $d_B$ on log axes, with the analytic $\sqrt{2/\pi}/(d_M d_B^{3/2})$ line; out-of-sample points fall on the line at sub-$\sigma$ precision. — Fig. III. The Haar law. $\mathbb{E}|S_A - S_B|$ against $d_B$ on log axes, with the analytic $\sqrt{2/\pi}/(d_M d_B^{3/2})$ line; out-of-sample points fall on the line at sub- $\sigma$ precision.

Figure IV: Prefactor convergence. The ratio of measured disagreement to the analytic leading term approaching unity, $A = 1.00 \pm 0.01$, with the $1 - 1.0/d_B$ subleading trend. — Fig. IV. Prefactor convergence. The ratio of measured disagreement to the analytic leading term approaching unity, $A = 1.00 \pm 0.01$ , with the $1 - 1.0/d_B$ subleading trend.

Figure V: The landscape. The two state classes side by side – the slow product decay and the fast Haar decay – with the integer gap between their slopes made visible. — Fig. V. The landscape. The two state classes side by side – the slow product decay and the fast Haar decay – with the integer gap between their slopes made visible.

III · THE REPRODUCIBILITY BUNDLE

File-listing table sourced from MANIFEST.txt. Every CSV reproduces bit-identically from master seed 707070.

File What it is Download

bh_lab_backend.py Self-contained backend (von Neumann algebra, crossed product, HUZ inclusion). ⤓ download

make_fig2.py Figure 2 generator (first-moment off-diagonal collapse). ⤓ download

make_figs_1345.py Figure 1, 3, 4, 5 generators (structural identity, Haar law, landscape). ⤓ download

make_figs_41.py Figure 4 panels (prefactor convergence, out-of-sample). ⤓ download

scratch_fourth_moment.py Lemma C.5 fourth-moment projector estimate. ⤓ download

scratch_centered_C6.py Lemma C.6 centered-operator representation. Closes F_diag. ⤓ download

scratch_Fdiag.py Direct F_diag check (companion to Lemma C.6). ⤓ download

scratch_grouped_dirichlet.py Lemma 3 grouped-Dirichlet moments (the corrected covariance). ⤓ download

scratch_Mdom.pyDIAGNOSTIC DIAGNOSTIC ONLY – supports no proof step. Marker of the route we did NOT take. ⤓ download

table1_full_scan.csv Landscape data – single source of truth for Table 1, Fig. 4(c), Fig. 5. ⤓ download

entropy_replacement.csv Direct replacement-error data, multiple state classes. ⤓ download

fig1_full_V.csv Figure 1, full-V observer-reduced state diagonal entries. ⤓ download

fig1_no_V.csv Figure 1, no-V control. ⤓ download

fig2_offdiag.csv Figure 2, off-diagonal magnitudes. ⤓ download

fig2_struct_identity.csv Figure 2, structural identity entry-by-entry. ⤓ download

fig3_dirichlet_var.csv Figure 3, Dirichlet variance asymptote. ⤓ download

fig3_gaussian_ratio.csv Figure 3, Gaussian-limit ratio convergence. ⤓ download

fig3_panel_d.csv Figure 3, panel-d data. ⤓ download

fig3_prefactor.csv Figure 3, Haar prefactor. ⤓ download

fig4_full_V.csv Figure 4, full-V scaling. ⤓ download

fig4_haar_prefactor.csv Figure 4, Haar prefactor convergence. ⤓ download

fig4_out_of_sample.csv Figure 4, out-of-sample tests. ⤓ download

fig5_class_ratio.csv Figure 5, product/Haar class ratio. ⤓ download

phase2_dM_scan.csv d_M scan, exponent stability. ⤓ download

phase2_exponents.csv Phase 2 exponent fits across configurations. ⤓ download

Master Manifest

MANIFEST.txt The package manifest. Lists the v4.0 (paper III final) submission layout, theorem hierarchy, reproducibility/ contents. ⤓ download

Note: scratch_Mdom.py is the diagnostic supporting no proof step – the route we did NOT take. Its story is told in The Constant We Left to the Machine.

IV · ENVIRONMENT

Python3.11

numpy>= 1.26

scipy>= 1.11

mpmath>= 1.3

sympy>= 1.12

master seed707070

Anyone with the bundle can reproduce every numerical claim in the paper.