CT-0 eval — link prediction on live cybergraphs

the measurable half of "compile a transformer without training": can the compiled geometry predict new links in a graph that real users built?

data

• space-pussy (live testnet): 48,370 cyberlinks / 30,017 train particles, fetched from the node tx index (fetch_links.py over tx_search "cyberlink.neuron EXISTS", attributes base64-decoded). heights recorded per link — temporal split is real.
• bostrom (halted mainnet, snapshot at height 25,120,712): 2,949,732 cyberlinks / 3,143,650 particles, rebuilt bit-exact to the on-chain graph_stats by a full-history block scan (see the bostrom snapshot manifest: cyberlinks_indexed.csv.gz, IPFS QmUFrsLYUK8USpNMEGBbUyi3nTuq12QcLiVWiyVMMVyyFf, sha256 e442ff7a…e4ae). too big for git — fetch from deimos:/archive/snapshot/pub/cyberlinks_indexed.csv.gz (or any IPFS gateway) and convert to jsonl; see data/.gitignore. results: lp_bostrom.md; spectral gap observed from convergence (March 2026, uniform weights): spectral-gap-bostrom.md.

setup

python3 -m venv .venv && .venv/bin/pip install scipy numpy
.venv/bin/python fetch_links.py https://rpc.space-pussy.cybernode.ai data/pussy_links.jsonl
.venv/bin/python lp_eval.py data/pussy_links.jsonl --k 64

task

temporal split: first 90% of links by height → train; last 10% → test. negatives: same-vocab pairs that are non-edges in the full link set. φ* is computed with the preferential dangling fix (cyberia-to/tru#1).

coverage caveat: only 519 / 4,837 test links are scorable — 89% of future links touch particles that did not exist in train. the scorable subset is therefore popularity-biased by construction; the numbers below describe "which old nodes get linked next", not "what new content arrives".

results — space-pussy, temporal split (n=519, novel n=372)

random-split control (k=64, n=3,272): directed 0.797 and ppmi 0.794 beat pa 0.752 — spectral structure is real but transductive: it ranks links among known nodes, not arrivals of new links.

update (tru#2) — 2-hop mixing fixes the fine-structure floor

with M <- diag(√φ)(A + 0.5·A²)diag(√φ) (lp_eval.py, --k 16 and 64):

the sibling-signal gap closes by ~0.11 AUC temporal / ~0.15 novel-AUC; γ=0.5 is the split-robust default. shipped in rs/pass/arch.rs (hop2_mix) + spec §6.1-rev.

what this says

1. the live graph grows by preferential attachment. popularity (φ*) is the single strongest predictor of future links on a temporal split. no spectral variant beats it; hybrids (pa*ppmi, pa+ppmi(z)) do not close the gap.
2. direction-blindness costs on real data too. tru-E (current pass 4, symmetric U√Σ) sits at the bottom at every k. the V-side fix is confirmed on live data, not only the toy: directed factorization beats it by ~0.10–0.14 AUC.
3. small rank generalizes, large rank memorizes. ppmi peaks at k=16 and degrades monotonically with more components (σ₆₄ = 0.0006 — dead dimensions). tru's d* = effective-rank heuristic is load-bearing; the 64 floor may already be too high for this graph.
4. 89% of new links are unscorable — embeddings cannot rank particles they have never seen. for the compile to matter for the real graph, pass 4 needs an inductive route to unseen particles (content-hash features, not only structural ids) — or the honest claim narrows to "ranks among known particles".

pass 4 at scale — bostrom

see lp_bostrom.md — the pussy findings re-measured on the full halted graph. headline: the popularity prior strengthens with scale (pa temporal AUC 0.866 -> 0.943), 2-hop mixing replicates (1-step directed at chance 0.5004 -> directed2 g=0.25 0.6166), and the tru#3 out-gain rule scales: sigma_1/sigma_k = 8885.6 on the shipped mixed matrix -> gain 14.1.

fine-tuning ablation

see ft_ablation.md — the compiled init vs random, under walk-LM and contrastive link-prediction objectives, with seen/unseen controls. headline: no training configuration learns unseen-link prediction at this scale; the compiled init remains the best unseen-link model; the exact spectrum is the better learning substrate (the Fx artifact's advantage is init-only).

pass 5: the attention half

see attn_eval.md — llama forward over the compiled per-layer weights. findings: (1) the spec'd construction self-collapses at init (softmax self-wins, pinv(W_V) ≈ identity, multi-power layers invisible, RoPE net-negative); (2) the weight-only fix shipped in rs/pass/attn.rs — Q/K from the DIRECTED projection Eᵀ(Aˡ)ᵀE (self-transition killed, U≠V), retrieval head W_V = I, W_O = c·I; (3) the fine-grained ceiling is pass 4: structurally equivalent tokens get parallel embeddings, 2-hop sibling signal lives in low-σ components that the rank heuristic discards.

reproduction notes

• tx_search order_by 500s on the public node; heights are re-sorted locally.
• the earlier corpus-toy result (all variants MRR 1.000) was a NaN artifact: unclamped Rayleigh quotients in the toy's f64 SVD made every score comparison false → rank 1 everywhere. fixed by clamping; tru's own fixed-point SVD already clamps (svd.rs). lesson recorded: assert finite on all scores in an eval harness.