PALIMPSESTE — capacity note (final, in-field)
Converged with the audit. Substrate is real VSA. One label corrected, one overclaim cut, one test now in-repo.
Three numbers (Section 6 rewrite)
Do not collapse these.
| quantity | law | at D=20 000, M=1698 |
|---|---|---|
| C_addr | 0.14 · D · 2^(D/β) with β ≈ 4 |
2^5000 ≈ 10^1505 locations (headline) |
| k*_bundle | linear in D | exact ≈ 0.02 D (~400) · soft ≥0.99 ≈ 0.03 D (~600) · theory D/(2 ln M) ≈ 0.067 D (~1300) |
| N_traces | append-only log | 131 541 (white paper) / 2.2M (HF ULTRA) |
"Grows exponentially with D" is true for C_addr only. Retrieval is linear. The 10^1505 figure counts SDM locations, not decode capacity.
Axiom 2 — why 100% still holds
Phi(q) is the bundle of (w·v) over the Hamming ball N_r(q), LSH-indexed — not a global bundle of |M|. So k* applies per ball. 306/306 means no ball has crossed k*_exact yet, not k* = ∞.
As |M| grows, the only metric that matters is the occupancy histogram of |N_r(q)|.
Confidence curve (D=8000, M=1698, 60 trials)
| per-ball load | 1 | 75 | 151 | 226 | 453 |
|---|---|---|---|---|---|
| exact-recover (all members outrank all non-members) | 1.00 | 1.00 | 0.98 | 0.35 | 0.00 |
| soft cleanup (frac of members in top-k) | 1.00 | 1.00 | 1.00 | 1.00 | 0.97 |
Exact cliffs at ~0.02 D. Soft degrades slowly (still 0.97 where exact is 0). k*_soft/D swept at 0.031 / 0.032 / 0.033 for D=2k/4k/8k.
Forgetting
True as no erasure (append-only (a,v,w)). False as crosstalk-immune. A trace dies when |N_r(a)| > k*, not when you insert elsewhere.
Invariants that stand (not "14 impossible")
- O(1) write, zero gradient
- no overwrite
- native bind/bundle analogy (HRR)
Live test
python examples/occupancy.py --sweep
python examples/occupancy.py --live --limit 306
Flag any query with |N_r(q)| > 0.02 D. First flagged ball is the first predictable exact-recall failure.
Caveat
If retrieve/Phi adds a cleanup pass or resonator, the constant in k* moves by a factor, not an order. Occupancy uses Phi.retrieve so it pins the implementation ball, not a paper rewrite.
Instrument: palimseste/capacity.py. Theory: Jolin plateau, bipolar v_A=1, k* = D/(2 ln M). β≈4 from the headline.