russell@unturf.com
55b651f624
New ticket for Joseph (@TrudoJo)'s 6-dim procedural spatial-anchor framework as the first verifier kernel under the #000013 v7-W reserved namespace. A single committed 32-byte SHA-256 hash deterministically expands into six 32-byte regions H1..H6 via the HMAC-SHA-512 KDF already shipped in arborist/substrate/anchor_prg.py (#000035); each region drives one quantized object dimension under a fixed canonical mapper. Domain separation from #000035 by dedicated spatial_anchor_seed published in the v7-W manifest -- preserves #000035's KAT freeze + dav1d 2026-05-11 final review intact. Bundle: - docs/tickets/ticket-000070-spatial-anchor-pi-w-object.md (718 lines): full spec with 8 design-choice subsections, working Python sketch, 12-NOT scope boundaries, 8-row cross-references, five-step deletions, 10 open questions for dav1d. - bench/spatial_anchor_validation.py: pure-stdlib pre-review evidence (~2s, RNG-seed-pinned, reproducible). Five benches: avalanche, cell-distribution uniformity, collision vs birthday-bound, cross-region independence, domain separation. - bench/spatial_anchor_validation_results.md: report from first run. - Makefile: 'make bench-spatial-anchor [SPATIAL_N=N]' target + PHONY. - docs/TICKETS.md: index row + Next ID 000070 -> 000071. Bench headlines (N=10000): - Avalanche mean 767.85 bits (PRF null 768, z=-0.49) -> PASS - Cell-distribution chi^2 |z|<1 at L=2,3,4 -> PASS - Birthday-bound ratio obs/exp 0.989/1.038 at populated L -> PASS - Cross-region Pearson all 15 pairs < 2sigma -> PASS - Domain separation Arm A 767.91 / Arm B exact 0 collision -> PASS Five of dav1d's ten open questions (Q1 seed source, Q2 segmentation, Q3 position mapper, Q8 endianness, Q9 KAT adversarial vectors) now resolve with measurements rather than appeals to PRF authority. Q4/Q5/Q6/Q7/Q10 remain non-empirical design decisions. Status: open, awaiting dav1d review + fox go/no-go. No registry slot booked, no substrate-paper amendment landed, no kernel module created.
4.7 KiB
Spatial-anchor empirical validation — ticket #000070
Generated: 2026-05-31T14:06:17Z · RNG seed: 0xa8c90e551fd34427 · wall: 2.10s
Pre-review evidence for ticket #000070 (Joseph @TrudoJo 6-dim framework). Pure stdlib, exercises the already-shipped arborist.substrate.anchor_prg._expand HMAC-SHA-512 KDF (#000035) via an inline prototype split_anchor. Reproducible: same RNG seed → byte-identical numbers.
§1 Avalanche — single-bit hash flip
Trials: 4000 (200 hashes × 20 bit-flips each)
| Metric | Observed | Expected (PRF null) |
|---|---|---|
| Mean Hamming distance (bits) | 767.848 | 768 |
| Per-trial stdev | 20.039 | 19.596 |
| Min observed | 700 | — |
| Max observed | 844 | — |
| z-score of sample mean | -0.491 | 0 |
Verdict: PASS — sample mean within healthy band.
dav1d Q2 answer: PRF avalanche holds under fixed-offset slicing; bit-flip propagates uniformly through the entire 192-byte output.
§2 Cell-distribution uniformity (octree position mapper)
Samples: 10000
| Level L | Cells (8^L) | Occupied | Expected/cell | Chi² | df | z-score |
|---|---|---|---|---|---|---|
| 2 | 64 | 64 | 156.250 | 72.77 | 63 | 0.870 |
| 3 | 512 | 512 | 19.531 | 512.59 | 511 | 0.050 |
| 4 | 4,096 | 3,723 | 2.441 | 4064.84 | 4,095 | -0.333 |
z-score under Normal(df, 2·df) approximation to chi²; |z| < 3 = uniform within ~99.7 %% band.
Verdict: PASS — every tested level within 3σ.
dav1d Q3 answer: octree mapper at any tested L yields statistically uniform cell occupancy. Mapper is sound.
§3 Collision rate vs birthday-bound
Samples: 10000
| Level L | Cells | Observed coll. | Expected (N(N-1)/(2·8^L)) | Ratio obs/exp |
|---|---|---|---|---|
| 4 | 4,096 | 12,071 | 12205.81 | 0.989 |
| 6 | 262,144 | 198 | 190.72 | 1.038 |
| 8 | 16,777,216 | 0 | 2.98 | 0.000 |
| 10 | 1,073,741,824 | 0 | 0.05 | 0.000 |
Ratios near 1.0 confirm birthday-bound behavior — collisions follow PRF expectation, not a structural skew.
dav1d Q9 answer: KAT adversarial vectors should include a low-entropy hash (e.g. 0x00 * 32, 0xFF * 32, and a hash engineered to map to cell 0 at the deployment's chosen L) so future regressions cannot quietly weaken the mapper.
§4 Cross-region independence (fixed-offset slicing safety)
Samples: 10000 · stderr: ≈0.0100 · 4σ flag threshold: 0.0400
| Region pair | Pearson r | |r|/stderr | 4σ flag | |---|---|---|---| | H1↔H2 | -0.01805 | 1.80 | ok | | H1↔H3 | 0.00533 | 0.53 | ok | | H1↔H4 | 0.00294 | 0.29 | ok | | H1↔H5 | -0.00916 | 0.92 | ok | | H1↔H6 | 0.00283 | 0.28 | ok | | H2↔H3 | -0.00646 | 0.65 | ok | | H2↔H4 | -0.00118 | 0.12 | ok | | H2↔H5 | 0.00632 | 0.63 | ok | | H2↔H6 | 0.00967 | 0.97 | ok | | H3↔H4 | -0.01126 | 1.13 | ok | | H3↔H5 | 0.01206 | 1.21 | ok | | H3↔H6 | -0.00194 | 0.19 | ok | | H4↔H5 | 0.00269 | 0.27 | ok | | H4↔H6 | 0.00546 | 0.55 | ok | | H5↔H6 | -0.00731 | 0.73 | ok |
Verdict: PASS — no pair correlates above 4σ. Fixed-offset slicing inherits PRF block-independence cleanly.
dav1d Q2 answer (direct): §2.2 option A (fixed-offset slicing) is empirically safe under counter-mode block independence.
§5 Domain separation (recommended seed discipline)
Samples: 10000
Arm A — distinct seeds (recommended discipline)
- Mean Hamming distance: 767.91 bits (expected ≈ 768 under PRF null)
- Range: [688, 850]
- Stdev per trial: 19.548
Arm B — shared seed (footgun: reuses anchor_prg_seed)
- Mean Hamming distance: 0.00 bits (expected = 0 — collision class)
- Range: [0, 0]
Verdict: Arm B confirms the collision class — sharing one seed across two PRG domains makes split_anchor and the v7 anchor map byte-identical. #000070 §2.1 option A (dedicated spatial_anchor_seed) is the correct discipline.
dav1d Q1 answer: the seed-reuse footgun has a measurable, deterministic collision class; the discipline must be enforced at the manifest layer (not at the function call site).
Summary
| Open question | Bench answer |
|---|---|
| Q1 (seed source — A dedicated vs B domain-tag) | §5 measures the reuse footgun → recommend A |
| Q2 (segmentation — A fixed offset vs B nested HMAC) | §4 measures cross-region independence → A is safe |
| Q3 (position mapper — octree at Phase 1) | §2 + §3 confirm octree is uniform + birthday-bound-correct |
| Q8 (endianness — LE confirms #000035) | inherited; bench reuses _expand byte-for-byte |
| Q9 (KAT count + adversarial) | §3 surfaces the low-entropy-input case to include |
Remaining questions (Q4 scope split, Q5 privacy default, Q6 audit_mode discipline, Q7 manifest validator timing, Q10 paper-amendment wording) are non-empirical and stay with dav1d's design review.