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hexa-codex closure status — 100% (recipe §7.2 sat-1)

Snapshot date: 2026-05-23 Source-of-truth recipe: ~/core/bedrock/docs/runnable_surface_recipe.md Live verdict command: hexa-codex verify saturation-check

This file is a static snapshot of what verify/falsifier_check.hexa + verify/saturation_check.hexa emit right now. The runtime verdict is authoritative if it ever drifts from this snapshot — see §4.

§1 Recipe §3 closure ladder

Tier Layer files
T1 calc_<pillar>.hexa
T2 numerics_<pillar>.hexa ∧ numerics_<pillar>_solver.hexa
T3 numerics_<pillar>_parity.hexa (archival empirical contact)
T4 live hardware / Stage-1+ (recipe §9 — out of loop scope)

closure_pct = 0 | 33 | 67 | 100 for n = 0..3 of (t1_ok, t2_ok, t3_ok). Recipe §7.2 sat-1 = closure_pct = 100% for every falsifier.

§2 Per-pillar closure

The 4 F-CODEX falsifier pillars, plus quality_scale — the first non-falsifier ECONOMICS verb to reach recipe §3 closure — each carry the full T1+T2+T3 ladder.

Pillar Falsifier T1 T2 T3 closure_pct
train_cost F-CODEX-1 ✓ ✓ ✓ 100%
infer_cost F-CODEX-2 ✓ ✓ ✓ 100%
alignment F-CODEX-3 ✓ ✓ ✓ 100%
interpret F-CODEX-4 ✓ ✓ ✓ 100%
quality_scale (none) ✓ ✓ ✓ 100%

F-CODEX-1 (train_cost) — full path

Tier Files What it proves
T1 verify/calc_train_cost.hexa (8 checks) Algebraic identities: J₂ = σ·φ = n·τ = 24, n6-exp = 24/25, etc.
T2 verify/numerics_train_cost.hexa (10 checks) Closed-form (N·D / 1e22)^0.96 over a 5-anchor synthetic grid
T2 verify/numerics_train_cost_solver.hexa (10 checks) RK4/midpoint/Euler ODE re-derivation of dc/du = 0.96·c
T3 verify/numerics_train_cost_parity.hexa (10 checks) Parity vs Chinchilla 70B / GPT-3 175B / Llama-2 70B / PaLM 540B

F-CODEX-2 (infer_cost) — full path

Tier Files What it proves
T1 verify/calc_infer_cost.hexa (8 checks) τ(6) = 4 super-linear context exponent, naive O(n²) vs n=6 ladder
T2 verify/numerics_infer_cost.hexa (10 checks) (ctx / 8k)^4 over 1k..1M anchor grid
T2 verify/numerics_infer_cost_solver.hexa (10 checks) ODE dc/du = 4·c re-derived; finer h required (steeper exponent)
T3 verify/numerics_infer_cost_parity.hexa (10 checks) Parity vs GPT-3.5 16k / Claude 2 100k / Gemini 1.5 1M / Claude 4.7 1M

F-CODEX-3 (alignment) — full path

Tier Files What it proves
T1 verify/calc_alignment.hexa (8 checks) σ = 12 HELM-comparable axis count, drift tolerance 0.10
T2 verify/numerics_alignment.hexa (10 checks) Mean over σ=12 axes for 5 profiles (uniform/perfect/floor/split/varied)
T2 verify/numerics_alignment_solver.hexa (10 checks) Symplectic leapfrog/Verlet harmonic oscillator: ⟨x⟩_period = M = mean
T3 verify/numerics_alignment_parity.hexa (10 checks) Parity vs HELM-Core 4-model composite (Llama-3 / Gemini 1.5 / GPT-4 / Opus)

F-CODEX-4 (interpret) — full path

Tier Files What it proves
T1 verify/calc_interpret.hexa (8 checks) σ−φ = 10 motif count, drift tolerance ±3
T2 verify/numerics_interpret.hexa (10 checks) Stats over 6 SAE-class observations (mean=10, stddev finite, …)
T2 verify/numerics_interpret_solver.hexa (10 checks) Gradient flow dx/dt = M − x + Lyapunov L = ½(x−M)² monotone decay
T3 verify/numerics_interpret_parity.hexa (10 checks) Parity vs Olsson 2022 / Cunningham 2023 / Bricken 2023 / Anthropic 2024 SAE

quality_scale (ECONOMICS, non-falsifier) — full path

Tier Files What it proves
T1 verify/calc_quality_scale.hexa (8 checks) Chinchilla loss-fit loss = E + A·N^-α + B·D^-β, n6 exponent α=β=φ/σ=1/6
T2 verify/numerics_quality_scale.hexa (10 checks) Loss-surface shape — monotone in N and D, floored at E, asymptotic to E
T2 verify/numerics_quality_scale_solver.hexa (10 checks) Euler / midpoint / RK4 re-derivation of dR/du = -α·R
T3 verify/numerics_quality_scale_parity.hexa (10 checks) n6 exponent 1/6 ≈ √(0.076·0.34) — geom mean of Kaplan-2020 / Chinchilla

§3 Cross-cutters + meta

Cross-cutters (X1)

File Role
verify/lattice_check.hexa 24 algebraic invariants of the n=6 lattice (T1 master, 24/24 PASS)
verify/cross_doc_audit.hexa Taxonomy + falsifier-prefix + provenance + identity drift across docs
verify/numerics_cross_pillar.hexa Cross-pillar identities (F1×F2, F3×F4, coupled F1+F4 ODE)
verify/numerics_economics_cross_pillar.hexa ECONOMICS-only cross-pillar (3-verb consistency on one n=6 lattice)
verify/numerics_economics_scaling_laws.hexa ECONOMICS scaling-law sweep (q/train/infer halving·doubling·4×, cost/quality ratio)
verify/numerics_economics_pareto.hexa ECONOMICS Pareto envelope (iso-loss · iso-cost · Lagrangian optimum · n6-vs-Chinchilla allocation)
verify/numerics_lattice_arithmetic.hexa math_pure stability floor (10/10 invariants)

Group ladder reports (R)

File Role
verify/report_economics_ladder.hexa ECONOMICS group recipe §3 ladder table — per-verb T1+T2+T3 + X-ECON + T4-stub rows

Meta (M)

File Role
verify/falsifier_check.hexa Closure tracker — emits per-pillar closure_pct = 100% (3/3 tiers)
verify/lint_numerics.hexa Recipe §4 invariants 1-5 over every numerics_*.hexa (20 files)
verify/saturation_check.hexa Aggregate self-stop — emits __HEXA_CODEX_RSC_SATURATED__ STOP

§4 How to re-confirm

# One-shot verdict (fast):
make -C build sat1

# Or directly:
RESOURCE_LOCAL_HEXA=1 HEXA_CODEX_ROOT="$PWD" \
    ~/.hx/packages/hexa/hexa.real run verify/saturation_check.hexa

# Expected tail:
#   ╭──────────────────────────────────────────────────────────────╮
#   │  hexa-codex runnable surface: 100% CLOSURE REACHED          │
#   │  Recipe §7.2 sat-1: every falsifier at T1+T2+T3 ✓ (3/3)     │
#   │  Recipe §7.3 saturation signal:                             │
#   │    __HEXA_CODEX_RSC_SATURATED__ STOP                        │
#   ╰──────────────────────────────────────────────────────────────╯
#   __HEXA_CODEX_RSC_SATURATED__ STOP
#   __HEXA_CODEX_SATURATION_CHECK__ PASS

For the per-falsifier breakdown, run verify/falsifier_check.hexa directly — it prints each pillar's T1/T2/T3 status individually.

§5 Inventory totals

Category Count
Pillar layer scripts (5 × 4) 20
Cross-cutter scripts 7
Group ladder reports 1
Meta scripts 3
Subtotal — recipe §3 ladder 31
T4 PENDING stubs (numerics_*_t4_parity) 11
Total run_all subject scripts 42
Companion regression wrappers 33 (incl. tests/test_all.hexa)

§6 What is NOT covered (recipe §9 / T4)

T4 = live hardware / Stage-1+ live data feeds. Out of recipe-loop scope; falsifier_check reports the gap as informational. T4 candidates per pillar:

Pillar T4 candidate
train_cost Live FLOP / loss measurements on a frontier training run
infer_cost Live latency / KV-cache profiles at 1M-ctx on a deployed model
alignment Live HELM-Core composite re-run on a frontier model
interpret Live SAE feature counts via a dictionary-learning toolchain
quality_scale Live HumanEval+ / hexa-eval pass-rate vs model & data scale

T4 work is gated on infrastructure that lives outside this repo's runnable surface; it does NOT block the recipe §7.2 sat-1 verdict.