callensxavier/hyperbolic-resistor-networks

Hyperbolic vs flat resistor networks: conditioning of the inverse conductance problem

Data accompanying the preprint Logarithmic boundary depth and the conditioning of the discrete inverse conductance problem on hyperbolic lattices (X. Callens, 2026), included as paper.pdf.

Contents

File	What it contains
graphs/*.json	Layer-truncated {7,3} tilings (L=1..6) and square/triangular lattice disks: node coordinates (Poincare disk / plane), edge list, boundary nodes (face incidence)
dtn/*.npz	Dirichlet-to-Neumann map Lambda (unit conductances) for graphs with N <= 900
conditioning.csv	log10 condition number of the DtN sensitivity Jacobian; empty and numerically_singular_float64=True where float64 cannot resolve it
probe_matched.csv	DtN and Neumann-to-Dirichlet conditioning, full vs subsampled boundary
exact_rank.csv	Exact Jacobian ranks over GF(p) for two primes; deficiency vs number of unmeasured degree-2 nodes; condition number on the identifiable subspace
exact_rank_full_boundary.csv	Exact full-boundary Jacobian ranks over GF(p), two primes: full-rank certificates
conditioning_arb.csv	(v1.1) log10 condition number in 512-bit ball arithmetic for the float64-singular flat lattices, with certified radii and the two unsaturated controls
disorder.csv	(v1.1) log10 kappa (log-parametrised and raw Jacobian) under U[0.5,1.5] and log-uniform [0.1,10] conductances (5 seeds) and x100 / x0.01 defects
subspace_control.csv	(v1.1) probe-matched dimensionality control: square lattice sigma_1/sigma_r vs hyperbolic identifiable-subspace kappa
tda_defect.csv	(post-v1.1, not in the paper) persistent homology (Gudhi) of the boundary resistance metric with and without a bulk defect, vs a global-disorder null. The null was mis-sized; see TDA_RESULTS.md
tda_noise.csv	(post-v1.1, not in the paper) defect detection vs measurement-noise level (eps_max), metric and H1 detectors
localize_defect.csv	(post-v1.1, not in the paper) single-node defect localisation from two noisy NtD maps (oracle-dictionary matched filter); 60/60 cells perfect at noise 3e-4, so it is a ceiling, not a measurement of the failure boundary
tilings_kappa.csv	(post-v1.1, not in the paper) log10 condition number for (7, 3), (8, 3), (5, 4), (6, 4), (4, 5) at L=1..6, with d_max and float64 error bounds (Gram-matrix method, controls in the repository)
localize_tolerance.csv	(post-v1.1, not in the paper) localisation top-1 on random boards with component tolerance 0.1 %, 1 %, 5 % and an ideal-model decoder; tolerance has no effect in this differential setting
localize_noise.csv	(post-v1.1, not in the paper) localisation top-1 vs noise level and eps_loc (largest noise with top-1 >= 0.9) at the deepest node, contrasts x1.25 and x2
tolerance_null.csv	(post-v1.1, not in the paper) defect detection vs component tolerance (0.1 %, 1 %, 5 %), model-based and differential regimes; only the extreme x100 contrast is tested
exact_rank_tilings.csv	(v1.2) exact full-column-rank certificates (random row-combination method, two primes) for 11 instances of {7,3}, {8,3}, {5,4}, {6,4}, {4,5} up to E = 1604
rc_benchmark_tilings.csv	(v1.2) RC relaxation time, stiffness and the K1/K2 integrator controls (SciPy BDF and rusty-SUNDIALS CVODE) on {7,3} L=2, {8,3} L=2, {5,4} L=3, {6,4} L=2, {4,5} L=4
minimum_contrast.csv	(v1.2) localisation top-1 vs true contrast (x0.5 to x2) and noise (1e-4 to 3e-3) at the deepest node of four lattices; both geometries localise +-10 % at the 3e-4 budget
hardware_noise.csv	(v1.2) localisation top-1 under common-mode offset, gain drift and ADC quantisation at N~112, contrast x2; a floor (49/50 cells at 1.00), not a failure boundary
coherence_depth.csv	(v1.2) per edge depth and instance: exhaustive abs-cosine statistics between Jacobian columns of equal-depth edges and the effective dimension fraction (participation ratio / count) of their normalised Gram matrix
coherence_matched.csv	(v1.2) per depth on the largest instance of each family: log10 kappa of the Jacobian restricted to columns of depth <= d, the full-class effective dimension fraction and the six-column matched-size median of 50 draws
coherence_mechanism_test.csv	(v1.2) test of the band-counting argument on unseen instances ({7,3} L=5, {4,5} L=7, square R=16, triangular R=10.75): effective dimension fraction and depth-restricted log10 kappa per depth
flat_rate_windows.csv	(v1.2, exploratory) growth rate of the depth-restricted log10 kappa over windows fixed in relative depth on square R=6..22 and triangular R=3.2..17.2, with per-class effective dimension fraction and smallest normalised-Gram eigenvalue
spectral_gap.csv	Dirichlet spectral gap, RC relaxation time and stiffness; exploratory=True rows were not preregistered
interior_degree.json	Integer check that interior nodes of the {7,3} truncations have degree 3, and that the interior of G_L is G_(L-1) (coordinates and edge sets)
integrator_controls.csv	K1 (matrix-exponential known answer) and K2 (steady state = DtN column) controls per integrator; rows with status other than run were not executed
rc_step_response.csv	Reference (matrix-exponential) RC step response V_i(t), C=1, on {7,3} L=2 and square R=6

Provenance and reproduction

Generated from commit ccfc30dddab42c801d7aedb7d0ff99e0fff4139b of https://github.com/xaviercallens/SocrateAI-Scientific-CondensedMatterTheory, directory experiments/track_h_hyperbolic_network:

python3 hyperbolic_network.py --self-test && python3 hyperbolic_exact.py --self-test
python3 hyperbolic_exact.py && python3 probe_matched.py && python3 identifiability.py && python3 rc_network.py
python3 h2_explore.py && python3 interior_degree.py
python3 release/export.py

Each claim built on these data carries an evidence tier in docs/elenchus/ledger.json of that repository.

Known limitations

• Condition numbers are float64 SVD values; "numerically singular" means unresolved, not infinite.
• The two-integrator (SciPy BDF, rusty-SUNDIALS CVODE) cross-validation covers two networks of ~110 nodes.
• The probe-matched identifiable-subspace metric was chosen post hoc (deviation from preregistration).

License

Data and paper: CC BY 4.0. Code (see the companion model repository and the Zenodo archive): MIT.

Citation

Callens, X. (2026). Logarithmic boundary depth and the conditioning of the discrete inverse conductance problem on hyperbolic lattices. Preprint.