THE PROVING GROUND

The tools in the corpus that actually ran — real models, measured numbers, proven algorithms — collated in one place, and separated honestly from the figures.
THE BAR. A tool earns a place here only if a real computation happened and produced a number you can point to: a real trained model was run (GPT-2, DistilGPT-2, BERT, a WikiText transformer), a proven algorithm is recomputed live, or a cryptographic seal recomputes itself. Everything else in the ~1,400-sphere corpus is the interpretive / figurative layer — real ideas, but not this.
Each entry was adversarially verified — 41 candidates read one-by-one, default-to-reject; 24 were sent back (15 are real algorithms on toy data, 9 are figures). What follows is what survived.
⟳ LIVE recomputed in your browser  ·  ▪ RAN OFFLINE real model ran offline; the page renders the recorded result
①

Ran a real model

12 · real GPT-2 / BERT / DistilGPT-2 / WikiText
▪transformer-fusion-kit
A from-scratch 76.5M-param transformer trained on WikiText-103; measured test perplexity 52.45, fused with count + kNN models down to 25.25 — run on an RTX 4050.
A runnable Python kit (no in-browser view). Honest correction shipped: the aspirational ~20/~48 numbers were targets; a v1/v2 "−1.21 gate win" was retracted after leak-free re-measurement.
▪transformer-block
A GPT-2 block rebuilt in numpy from DistilGPT-2's real weights, verified against HuggingFace to 2.3e-7; then quantized to MXFP4 — weights ~20-25% error, but block output drifts ~35% (error compounds).
Numbers from one offline run, rendered by the canvas; the 2.3e-7 match is the internal witness that the reconstruction is real.
▪trained-on-the-cross
A from-scratch char-transformer A/B on TinyShakespeare: a custom "seeded cross" attention trains to within 1.2% of softmax perplexity (6.80 vs 6.72), at ~1.75× compute.
A 0.6M-param CPU run, numbers baked into the page — a small-scale floor-holding result, explicitly not a GPT-scale quality claim.
▪the-seeded-cross
The seeded-cross kernel swapped for softmax in real DistilGPT-2 attention (all 12 heads): stays valid (Σ=1), 100% top-token agreement, sharper (entropy ratio ~0.58), block drift ~0.16.
Renders precomputed constants; a drop-in swap on softmax-trained weights — "sharper" means different-from-softmax, not better.
▪jlens-tone-inflection
A Jacobian lens on real GPT-2 124M: exact affine reconstruction proven by three fp32-floor witnesses (3.81e-5); reads how words, tone and tense come into focus across the stack.
Precomputed JSON rendered client-side; the recorded witnesses are the proof, not an in-browser re-run.
▪the-attention-fracture
GPT-2 124M attention read out under emotional/intentional load: retrieval survives (a relay L6H4→L10H0), integration and priors fracture — real offline measurements (row-sum residual 4.8e-7).
Replays a static JSON blob; the "five fractures" narrative is interpretation layered on real numbers.
▪the-toroidal-audit
GPT-2 124M logit-lens audit: KL(final‖layer k) peaks 1.86 nats at L1 and drops below 1 nat only by L8 — the lens is an unreliable witness for the first two-thirds of the stack.
Baked KL trajectories (final-layer self-KL ≈ 2e-7, the numerical sanity check); the affect axes are crude.
▪two-basins
Real BERT-tiny embeddings: two near-orthogonal word-neighborhoods (principal angles ~75°) that share exactly one word — measured, not modeled.
Values hardcoded into the page; README asserts node-verification of the angles.
▪the-word-silo
A word's "weight" = its real measured GPT-2 input-embedding L2 norm (love 0.502 lightest → rage 0.799 heaviest).
The nine-layer "confinement" physics wrapped around it is a toy ODE — only the embedding norms are real. See its honest sibling the-weight-of-a-word below.
⟳attention-observatory
Real BERT attention through one live eigendecomposition → dimension / curvature / coherence / flow — and each claim is audited against a shuffle null (curvature honestly reads ARTIFACT).
BERT ran offline (attention matrices embedded); the eigendecomposition and the null audit run live in-browser.
⟳dimension-leapfrog
Tours real BERT-tiny attention geometry with a live geodesic→MDS eigendecomposition: intrinsic dim ~5, curvature 10.2% (reproduced exactly in numpy); paste your own matrix.
The BERT forward pass was offline (matrices hardcoded); the geometry is computed live.
⟳the-flooding
Attention-as-random-walk: diffusion computed exactly as Aᵗ on real row-stochastic BERT attention (every row sums to 1.0000), with live stationary-distribution and spectral (Jacobi) math.
The shuffle-test headline (0.91→−0.02, function vs content words) is asserted in prose, not recomputed; the diffusion substrate is what runs live.
②

Proven algorithm, live

4 · no trained model — verifiable math, recomputed in-browser
⟳the-draft
Speculative decoding, live: accept/reject + residual (p−q)₊ resampling, and the emitted distribution provably equals the target at any speculation length (exactness demonstrated in-browser; I confirmed it in node to within 0.001).
Toy 6-word distributions, an idealized cost model — the mechanism and the exactness are what's real. Part of A Scanner Darkly.
⟳perceptron-convergence
The perceptron convergence theorem run live: real w ← w + y·x updates on separable data, mistake count provably capped by ⌈(R/γ)²⌉ and shown obeying the bound every run.
Synthetic separable data; it demonstrates the exact convergence math, separable case only.
⟳forward-observers
A network-free canary detector (word-boundary regex + SHA-256 dedupe) whose reproducible self-test passes; the in-browser port recomputes the identical SHA-256.
Shallow string-match + hash, not learned math; the self-test proves the detector primitive only (the GitHub-polling upstream is unverified).
⟳the-weight-of-a-word
Live Pearson correlations on 33 real GPT-2 embedding norms: the norm sorts register (r≈0.86) with length entangled (r≈0.76), and the 8 lightest words are exactly the 8 function words — the norm is a frequency/register ladder, not semantic mass.
Uses the real GPT-2 norms from the-word-silo; the live computation is the correlation + set-membership proof.
③

Self-verifying provenance

the seal that checks itself
⟳the-chain
Recomputes the corpus's whole SHA-256 seal-chain client-side, zero network — the genesis independently confirmed against Node crypto; tamper any seal and watch the chain break.
Proves internal intactness (each link commits to the previous), not mint-time or repo authenticity. The same live mechanism powers the series ring-seals and akasha-constellation.

Also real — but on toy data, not a real model

These 15 run a genuine algorithm live in your browser, but on synthetic / hand-built data — no trained model, no real-world measurement. Real mechanism; not verified against reality. Kept honest and separate. FIG-adjacent

the-cleave · early-exit, toy field the-swarm · gradient ascent, toy mixture jacobi-space · basins on scattered points the-jacobian-lens · real math, untrained toy net attention-geometry · MDS/Isomap, tree tokens attention-synthesis · eigendecomp, constructed rows attention-tail · softmax on set logits the-mule-detector · kernels on synthetic crowd the-heart · live Jacobi, toy field the-trinity-engine · Cayley kernel, synthetic input perceptron-capacity · Cover's formula exact perceptron-in-two-cubits · quantum kernel, XOR ripple-inference · 6 checks, toy priors surfacing · real crypto, synthetic canaries transformer-silo · self-test passes, planted data