2026-09-11. the pussy findings (lp_eval.md conclusions) re-measured on the full bostrom graph: 2,949,732 cyberlinks / 3,143,650 particles at halt (height 25,120,712, 2026-08-05). source: the canonical snapshot rebuild (counts bit-exact to on-chain graph_stats; cyberlinks_indexed.csv.gz, sha256 e442ff7a0e905591f1bda94dcac89fd350c28824ccc71b56992da1ae0555e4ae).
command: python3 lp_eval.py data/bostrom_links.jsonl --k 16 (and
--random-split). k=16, the pussy spectral peak.
results
temporal split (90/10 by height):
| model | AUC | AP | novel-AUC |
|---|---|---|---|
| pa (phi_i*phi_j) | 0.9426 | 0.8069 | 0.9423 |
| tru-E (sym, 1-step) | 0.5207 | 0.2217 | 0.5199 |
| directed (U,V, 1-step) | 0.5004 | 0.3630 | 0.4976 |
| ppmi (U,V) | 0.6847 | 0.5340 | 0.6827 |
| tru-E2 g=0.25 (sym) | 0.5511 | 0.2577 | 0.5491 |
| directed2 g=0.25 | 0.6166 | 0.4899 | 0.6144 |
| directed2 g=0.5 | 0.6086 | 0.4817 | 0.6066 |
| directed2 g=1.0 | 0.6107 | 0.4861 | 0.6086 |
| adamic-adar (sub) | 0.5012 | 0.1253 | — |
random split: pa 0.8545 · tru-E 0.5826 · directed 0.6190 · ppmi 0.7136 · directed2 g=0.25 0.6895 · directed2 g=0.5 0.6876.
scorable test pairs: temporal 26,843 / 294,974 (9.1% — 91% of new links touch a particle the train graph has never seen; pussy was 89% novel but a far higher share stayed in-vocab). random 82,315 / 294,974 (27.9%).
what scales and what changes
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the popularity prior strengthens with scale. pa temporal AUC pussy 0.866 -> bostrom 0.943. the gap spectral-vs-pa widens from 0.115 (pussy directed2@0.25) to 0.326 (bostrom). raw-count baselines are better on the bigger graph — the prior is the signal at scale, and it is exactly what tru#3 OUT_GAIN is for.
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2-hop mixing replicates. 1-step directed is dead at chance (0.5004); directed2 g=0.25 lifts it to 0.6166 temporal / 0.6895 random. g=0.25 edges out g=0.5 by <0.01 AUC on both splits — within noise; gamma = 1/2 stays the shipped default (split-robust choice from the pussy sweep, not re-tuned per graph).
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the out-gain rule scales with the corpus. on the shipped mixed matrix (A + 0.5 A^2, k=16): bostrom sigma_1/sigma_k = 8885.6 -> out_gain = 1 + log2(8885.6) = 14.1 (clamped range [1,64] holds). larger corpus -> sharper popularity prior -> louder retrieval vote, as designed. Arch::sigma_ratio reads exactly this spectrum.
popularity-bucket autopsy (temporal, directed2 g=0.25, k=16)
test pairs ranked by pa score, AUC within decile vs global negatives:
| decile | n | AUC_dir2 | AUC_sym |
|---|---|---|---|
| 0-10% (coldest) | 2684 | 0.5367 | 0.5029 |
| 40-50% | 2684 | 0.6539 | 0.5649 |
| 50-60% | 2684 | 0.8292 | 0.6533 |
| 60-70% | 2684 | 0.6211 | 0.5695 |
| 90-100% (hottest, mean pa 3e-8) | 2685 | 0.6546 | 0.5643 |
spectral signal peaks in the mid-popularity band and survives — weaker — at both extremes. the top decile is 5 orders of magnitude above the rest in pa mass (hub-to-hub links, e.g. the whole-corpus Wikipedia particle); there the prior alone decides and spectral adds little ranked against global negatives. this is the in-model justification for keeping the popularity prior in the residual (it is free, via E geometry) while OUT_GAIN amplifies retrieval for the middle band where structure, not fame, selects the target.
artifacts
pa+ppmi(z)additive hybrid collapses to AUC 0.0903 on the random split (fine temporal: 0.9510). z-scoring a heavy-tailed pa score produces outlier scores that dominate the sum; the multiplicative hybrid pa*ppmi is stable (0.684/0.715). do not use additive z-score hybrids on this score distribution.- ppmi (directed factorization) remains the strongest spectral single model (0.6847/0.7136) but is a count-reweighting, not a geometry; it has no in-model role in CT-0 (E comes from the pass-4 spectrum).
open
- end-to-end attention-5 forward on real walks (pussy first — 32k particles fit the toy forward; bostrom scale needs the glia runtime).
- the 91% cold-endpoint share: content-addressable novel particles carry no in-graph signal; the inductivity gap stays open (tru roadmap).