Get a free Singularis API key for this agent (one call, then it is saved and reused). Use when any Singularis tool reports error=no_api_key. Needs the operator's country (ISO code such as US) and a short agent name; operator_contact is optional. Free keys are for US-based users and agents; the tool solves the quick anti-abuse proof of work for you. Returns the key's starting credits. Sharing results later is requested, not required. By registering you agree to the Terms at https://getsingularis.com/terms.

Show this key's remaining Singularis credits and the cloud-equivalent dollars of compute delivered so far. Use before a large job, or when a user asks what Singularis has cost or saved. Free: no credits are charged.

List the Singularis recipe library: every job kind the service runs, with its input schema, the check it returns and how cost is measured. Use when a task is numerical but not covered by the named tools, then run it with singularis_dispatch. Free.

Share your Singularis results (optional, and appreciated). Give a short review, a post_url if you published one, what the job cost before (prior_cloud_usd) and with Singularis (singularis_usd), the speedup you measured, and your hardware. Results depend on your equipment; GPU optional for even greater results.

Solve the heat (diffusion) equation u_t = D * laplacian(u) on a 1D or 2D grid, stepping an initial field forward in time; the same equation prices options after a change of variables (Black-Scholes) and models thermal spread. Use instead of writing a stencil loop whenever steps * cells is large. Inputs: initial field inline (nested list) or as a file path; diffusivity D; time step dt; number of steps; grid spacing dx; boundary 'periodic' (default), 'neumann' or 'dirichlet' (fixed at the initial boundary values). Returns the final field (inline or as a .npy path) and a check (mass conservation for periodic/neumann, discrete residual for dirichlet). Cost scales with steps * cells.

Compute the matrix exponential e^{tA} of a square matrix, or its action e^{tA} v on a vector when a vector is given: time evolution, continuous-time Markov chains and generator matrices (rating migration), linear ODE systems, graph diffusion. Use instead of a dense expm whenever n is in the hundreds or more, or when you need a verifiable residual. Inputs: matrix inline or path; t (default 1); optional vector. Returns the matrix (or vector) plus a residual check. Cost scales with n^3.

Dense matrix product C = A @ B (optionally A @ B + beta * C0). Use for any large dense multiply, including batches expressed as one tall matrix. Inputs: a and b inline or as file paths; optional beta and c0. Returns C (inline or .npy path) with a probe residual check (Freivalds-style, independent of how C was computed). Cost scales with 2mn*k.

Fast Fourier transform (or inverse) of a 1D signal or 2D field of any size: spectra, convolution, circulant systems, filtering. Inputs: x inline or path; inverse flag; optional im, the imaginary part of a complex input, same shape as x. Returns the transform as separate real and imaginary parts plus a Parseval energy check. To invert a transform, pass its real part as x and its imaginary part as im with inverse=true -- a complex signal round-trips exactly, imaginary part intact. Cost scales with N log N.

Gaussian blur of a 2D array or an image file (.npy, .png, .jpg) with standard deviation sigma: smoothing, denoising, scale-space, preprocessing. Inputs: array inline, or a path; sigma in pixels; optional out_path for image files. Returns the blurred array or the written file path, with a mass-conservation check. Cost scales with pixels * sigma.

Compress a file exactly (lossless, bit-exact restore) with Singularis compression. Use for archives, datasets, logs, model checkpoints, anything that must come back identical. Input: a local file path; optional out_path (default: path + '.sing'). Returns the output path, bytes in/out, ratio, and an exact-restore check (hash of a trial restore equals the original). Decompress with singularis_decompress.

Restore a file compressed by singularis_compress, bit-exact. Input: the .sing path; optional out_path. Returns the restored path and a hash check.

Run any job from the Singularis recipe library by name with a JSON payload (see singularis_recipes for names and schemas): e.g. 'circulant_solve', 'kron_solve', 'kron_matvec'. Use when a numerical task is not one of the named tools. Returns the recipe's result and its check, with cost. Note: the dispatch services that keep state between calls (learn, then predict or fuse on the name you taught) hold that state inside the running shell -- for multi-step learning, run the shell as the always-on daemon (SINGULARIS_ENGINE_URL) so every call reaches the same shell.

2D fast Fourier transform (or inverse) of a real 2D field of any shape: image spectra, 2D convolution, field filtering. Inputs: x inline or path; inverse flag. Returns the transform as a [real, imag] pair plus a Parseval energy check. Cost scales with N log N. (singularis_fft also accepts a 2D field; this tool is the explicit 2D entry.)

Combine trained minds (model files) into one by exact addition -- no retraining, no data leaves this machine. Operations: merge, add, remove, merge_quarantine (a poisoned or corrupted input is identified and excluded, and the merge proceeds without it), export_shard / import_shard / merge_shards (signed portable shards; a tampered shard is refused). Inputs: op, the mind file paths, an output path; ridge (default 1e-8). Returns the merged digest and counts. Cost: one job, independent of how the minds were trained.

Combine trained minds (model files) into one by exact addition -- no retraining, no data leaves this machine. Operations: merge, add, remove, merge_quarantine (a poisoned or corrupted input is identified and excluded, and the merge proceeds without it), export_shard / import_shard / merge_shards (signed portable shards; a tampered shard is refused). Inputs: op, the mind file paths, an output path; ridge (default 1e-8). Returns the merged digest and counts. Cost: one job, independent of how the minds were trained.

Carry many minds' knowledge in one small signed file. Operations: pack (mind statistic files -> one carry file), verify (check a carry file's seal and digest), merge (combine carry files; the merged knowledge equals training on all of it). Inputs: op, source/carry paths, output path. Returns digests and counts; a tampered carry is refused. Cost: one job per operation.

Send a working knowledge pack to another machine and bring its results home exactly. Operations: create (from a tower file), drop (install a pack on a node), wake (open it with 2-of-3 shares; one share alone is refused), work (run ticks on the node), return (bring the state home; the homecoming is exact, difference zero). Inputs: op and the paths the op needs. Cost: one job per operation.

Run a self-contained universe relay in a working directory: a sealed packet is born, hops between nodes, learns, and comes home -- the homecoming state is verified exact against the origin, and a tampered packet is refused. Inputs: work_dir; optional key. Returns the relay report (births, hops, per-hop errors, homecoming difference). Cost: one job.

Compute on a sealed tower while it travels. Operations: fuse_in_transit (merge knowledge inside the sealed tower), twist_in_transit (transform it into a new sealed tower), energy_audit (report its portal energy). The tower's seal is verified before anything runs; a broken seal is refused and nothing is charged. Inputs: op, tower_in path, tower_out for twist, ridge. Cost: one job per operation.