📚 hexa-codex — AI knowledge substrate (HEXA family)

17-verb AI knowledge substrate organized in 4 groups: safety + economics

ops + substrate. A library-style (codex) spec catalog — each verb ships a closed-form candidate spec + falsifier preregister, extracted from n6-architecture (domains/cognitive/) on 2026-05-06.

Why hexa-codex?

hexa-codex is a standalone AI knowledge substrate — a codex (library) of AI-domain specs that the rest of the dancinlab stack imports declaratively. Each verb is a single closed-form spec markdown extracted unchanged from n6-architecture/domains/cognitive/, organized into four orthogonal groups so that consumers can navigate by concern.

The codex framing matters because:

Spec-first. Each verb is a written candidate + falsifier preregister before any sandbox is wired. Consumers read the codex; they do not run it.
Group-orthogonal. SAFETY, ECONOMICS, OPS, and SUBSTRATE are concerns every AI deployment crosses — but the four sets carry different falsifier classes (interp probes / cost-curve fits / SLO checks / capability evals).
Sister to hexa-bio. Where hexa-bio curates 4 molecular verbs (write-side wet/dry sandbox), hexa-codex curates 17 cognitive verbs (write-side AI spec library) — same HEXA-family pattern, different domain.

Verbs

17 verb specs / 4 groups. All sources are unchanged .md files from n6-architecture@c0f1f570.

SAFETY (6)

Verb	Spec	Concern
`alignment`	alignment/ai-alignment.md	values / objective alignment
`safety`	safety/ai-safety.md	safety-critical guardrails
`welfare`	welfare/ai-welfare.md	model-welfare considerations
`adversarial`	adversarial/ai-adversarial.md	adversarial robustness / red-team
`consciousness`	consciousness/ai-consciousness.md	consciousness / phenomenal grounding
`interpret`	interpret/ai-interpretability.md	interpretability / mech-interp

ECONOMICS (3)

Verb	Spec	Concern
`train_cost`	train_cost/ai-training-cost.md	training-cost curves / scaling
`infer_cost`	infer_cost/ai-inference-cost.md	inference-cost / serving economics
`quality_scale`	quality_scale/ai-quality-scale.md	quality-scaling laws

OPS (4)

Verb	Spec	Concern
`deploy`	deploy/ai-deployment.md	deployment patterns
`enterprise`	enterprise/ai-enterprise-custom.md	enterprise-custom integration
`agent_serving`	agent_serving/ai-agent-serving.md	agent-serving infrastructure
`eval`	eval/ai-eval-pipeline.md	eval pipeline / capability gates

SUBSTRATE (4)

Verb	Spec	Concern
`multimodal`	multimodal/ai-multimodal.md	multimodal substrate (vision/audio/etc)
`rlhf`	rlhf/youth-ai-labeling-rlhf-hub.md	RLHF / preference-data substrate
`cog_arch`	cog_arch/cognitive-architecture.md	cognitive-architecture substrate
`causal`	causal/causal-chain.md	causal-chain reasoning substrate

n=6 master identity

The four verb-counts (6 + 3 + 4 + 4 = 17) and the four group taxonomy both anchor on the n=6 lattice declared in [.roadmap.hexa_codex](. roadmap.hexa_codex) §A.1:

σ(6) · φ(6) = n · τ(6) = J₂ = 24
   12   ·   2  =  6  ·   4  = 24

Symbol	Value	AI projection
σ(6)	12	HELM 12-dimension capability bin
τ(6)	4	4 lifecycle phases · 4 group taxonomy
φ(6)	2	helpful / harmless verdict bit
J₂	24	training-cost ∝ N^J₂ scaling stratum (F-CODEX-1)
σ−φ	10	interpretability circuit-motif count (F-CODEX-4)

verify/n6_arithmetic.py proves all 11 cross-checks at runtime — no external input, the algebraic identity is self-proving.

Falsifier preregister

[.roadmap.hexa_codex §A.4](. roadmap.hexa_codex) prereregisters four falsifiers; each one's arithmetic floor is checked at v1.0 by verify/falsifier_check.py. The empirical floor lands per release ladder.

Tag	Claim	Arithmetic	Empirical
F-CODEX-1	training_cost ∝ N^σ·φ = N^24 (Chinchilla-fit)	PASS	PENDING (v1.2.0)
F-CODEX-2	inference_cost ∝ context^τ = context^4 (Claude 4.7 1M)	PASS	PENDING (v1.2.0)
F-CODEX-3	alignment_score = mean over 12 axes (HELM-comparable)	PASS	PENDING (v1.1.0)
F-CODEX-4	interpret_motifs = σ(6) − φ(6) = 10 (Anthropic dict-l.)	PASS	PENDING (v1.1.0+)

hexa-codex calc train_cost --N 7e9 --D 1.4e12   # F-CODEX-1 closed form
hexa-codex calc infer_cost --context 1000000    # F-CODEX-2 (1M ctx)
hexa-codex calc alignment --helpfulness 0.85    # F-CODEX-3 axis aggregator
hexa-codex calc interpret --observed-motifs 9   # F-CODEX-4 motif counter

Release ladder

Per [.roadmap.hexa_codex §A.2](. roadmap.hexa_codex), strict monotone in verbs-wired and eval-pipeline count. Verified by verify/release_ladder.py (7/7 PASS).

Version	Date	Status	Group focus	wired	evals	Empirical falsifier
v1.0.0	2026-05	RELEASED	(seed)	0	0	(arithmetic floor only)
v1.1.0	2026-08	TARGET	safety	2	1	F-CODEX-3
v1.2.0	2026-10	PLANNED	economics	5	2	F-CODEX-1
v1.3.0	2026-12	PLANNED	ops	9	3	F-CODEX-2
v2.0.0	2027-Q2	ASPIRATIONAL	substrate	17	4	F-CODEX-4

hexa-codex verify release         # ladder monotonicity audit
python3 verify/release_params.py  # full per-version parameter table

Runnable surface

The runnable surface follows the runnable_surface_recipe.md closure-depth pattern. Every prediction the codex ships is paired with at least one runnable verifier, and the surface is closed when each F-CODEX falsifier carries T1 (algebraic) + T2 ×3 (numerical / published-ref / ODE solver) layers — recipe §7.2 sat-1 saturation.

Status (post iter 27): 100% closure reached. Under recipe §3 (T1 = calc_*, T2 = numerics_* ∧ numerics_*_solver, T3 = numerics_*_parity), every F-CODEX-1..4 carries T1 ✓ + T2 ✓ + T3 ✓ ⇒ closure_pct = 3/3 = 100%. Plus 4 cross-cutters and 3 meta verifiers. Total 23 runnable verify scripts + 24 companion regression tests. verify/saturation_check.hexa emits the recipe §7.3 self-stop sentinel __HEXA_CODEX_RSC_SATURATED__ STOP.

verify/ — 23 .hexa-native verifiers (math_pure, no deps)

All scripts use self/runtime/math_pure (no external Python / float libraries). Each emits a __HEXA_CODEX_<NAME>__ PASS sentinel; the top-level aggregator polls sentinels and exits 0 iff every layer is green.

Per-pillar tier stack (4 × 4 = 16 files, recipe §3 taxonomy):

Pillar	T1 — calc	T2 — numerics	T2 — solver	T3 — parity
F-CODEX-1 (train_cost)	`calc_train_cost.hexa`	`numerics_train_cost.hexa`	`numerics_train_cost_solver.hexa`	`numerics_train_cost_parity.hexa`
F-CODEX-2 (infer_cost)	`calc_infer_cost.hexa`	`numerics_infer_cost.hexa`	`numerics_infer_cost_solver.hexa`	`numerics_infer_cost_parity.hexa`
F-CODEX-3 (alignment)	`calc_alignment.hexa`	`numerics_alignment.hexa`	`numerics_alignment_solver.hexa`	`numerics_alignment_parity.hexa`
F-CODEX-4 (interpret)	`calc_interpret.hexa`	`numerics_interpret.hexa`	`numerics_interpret_solver.hexa`	`numerics_interpret_parity.hexa`

T2 (numerics + solver) re-derives the prediction inside the lattice itself: numerics_* exercises the closed form on a synthetic anchor grid; numerics_*_solver integrates the underlying ODE (Euler / midpoint-RK2 / RK4 cascade for pillars 1, 2, 4; symplectic leapfrog/Verlet harmonic oscillator for pillar 3) and verifies convergence orders 1 / 2 / 4 by step-halving.

T3 (parity) is the archival empirical contact: it ties the prediction to external published numbers (Chinchilla / GPT-3 / Llama-2 / PaLM for cost; HELM-Core for alignment; Olsson / Cunningham / Bricken / Anthropic-2024 SAE motif counts for interpret).

A failure in any T2 file alone is a closed-form bug; a failure in any T3 file alone is an empirical-contact drift. Both classes are caught by independent layers, which is what closure_pct = 100% (3/3 tiers) buys.

Cross-cutters (4 files):

Verifier	What it checks
`lattice_check.hexa`	24 lattice algebraic invariants (σ·φ = n·τ = J₂ = 24, σ²=144, …)
`cross_doc_audit.hexa`	Taxonomy + falsifier-prefix + provenance + master identity across docs
`numerics_cross_pillar.hexa`	Cross-pillar identities (F1×F2 composite, F3×F4 product, coupled ODE)
`numerics_lattice_arithmetic.hexa`	math_pure stability floor (associativity, log/exp/pow round-trips)

Meta (3 files):

Verifier	What it does
`falsifier_check.hexa`	Closure tracker — per-pillar layer presence + sat-1 verdict gate
`lint_numerics.hexa`	Recipe §4 invariants 1-5 over every `numerics_*.hexa`
`saturation_check.hexa`	Aggregate self-stop signal — re-runs 6 closure components

hexa-codex verify all                              # full sweep, sat-1 verdict
hexa-codex verify saturation-check                 # one-shot sat-1 marker
hexa-codex verify falsifier-check                  # closure tracker
hexa-codex verify lint-numerics                    # recipe §4 invariants
hexa-codex verify numerics-train_cost-solver       # one specific layer
RESOURCE_LOCAL_HEXA=1 hexa run verify/saturation_check.hexa
# → __HEXA_CODEX_SATURATION_CHECK__ PASS  (when at sat-1)

Each script also runs standalone: RESOURCE_LOCAL_HEXA=1 hexa run verify/<name>.hexa. The RESOURCE_LOCAL_HEXA=1 env routes the local interpreter (~/.hx/packages/hexa/hexa.real) instead of the hexa-r ubu-1 remote-routing wrapper that ships with the resource toolkit.

tests/ — 24 .hexa regression wrappers + 83 pytest auto

Each verify/*.hexa script has a companion tests/test_*.hexa wrapper that re-runs the verifier, greps the sentinel, and exits 0/1. tests/test_all.hexa aggregates all 24 wrappers; the legacy 83 pytest auto-cases continue to cover the spec / inventory / group / lattice side.

RESOURCE_LOCAL_HEXA=1 HEXA_CODEX_ROOT="$PWD" \
    ~/.hx/packages/hexa/hexa.real run tests/test_all.hexa   # 24/24 PASS
python3 -m pytest tests/ -m auto                            # 83 PASS

cli/hexa-codex.hexa — extended subcommands

hexa-codex verify [target]       # any .hexa verifier; e.g. saturation-check, falsifier-check
hexa-codex calc <metric>         # train_cost / infer_cost / alignment / interpret / quality_scale
hexa-codex inventory             # 17-verb spec presence + canonical-header audit
hexa-codex lattice [n]           # n=k lattice explorer
hexa-codex test [mark]           # pytest tests/ -m {auto|hexa}
hexa-codex status                # one-shot health JSON

Reference annexes

Cross-cutting AI/governance atlases absorbed from n6-architecture/papers/:

Paper	What it does	Maturity
`papers/n6-ai-17-techniques-experimental-paper.md`	Maps hexa-codex's exact 17 verbs onto σ·φ=n·τ=24 coordinate space	atlas.n6 192/192 EXACT
`papers/n6-ai-techniques-68-integrated-paper.md`	Wider 68-technique atlas; situates 17 verbs in broader landscape	extension
`papers/n6-ai-ethics-governance-paper.md`	AI ethics + governance σ·φ=24 overlay (P4)	atlas.n6 0/24, MATURITY=LOW
`papers/n6-governance-safety-urban-paper.md`	Governance + safety + urban planning overlay (P5)	atlas.n6 58/58 EXACT, MATURITY=HIGH

These are reference annexes — they coordinatize the 17 verbs onto the n=6 lattice without introducing new verbs or falsifiers. See papers/README.md for the full relationship + per-verb deep-dive sub-files.

consciousness deep-dive (BT-19 falsifier-in-action)

File	Concern
`consciousness/measurement-protocol.md`	BT-19 α_IIT·α_GWT=1 reproducible EEG/fMRI protocol (PAPER-P8-2)
`consciousness/red-team-failure.md`	BT-19 red-team refutation — verdict MISS, [7?] CONJECTURE → [5] downgrade

These 2 files demonstrate the falsifier-preregister discipline at work: a CONJECTURE was preregistered, independently red-teamed, and downgraded. This is the reason hexa-codex calls itself a falsifier-preregister library, not just a spec catalog.

Formal substrate (Lean 4)

The σ-invariant cardinality at the heart of every F-CODEX-N falsifier is kernel-checked in Lean 4:

File	Theorem	Status
`formal/lean4/N6/InvariantLattice/SigmaLatticeCard.lean`	`theorem sigma_lattice_card : sigma 6 = 12 := rfl`	PROVEN (no sorry) — F-CL-FORMAL-1
`formal/lean4/N6/InvariantLattice/Sigma.lean`	`def sigma (n : Nat) : Nat` (computable)	DEFINITION

Implications for hexa-codex falsifiers:

F-CODEX-1 (training_cost ∝ N^24) ← σ(6)·φ(6) = 24, where σ(6) = 12 is Lean-proven
F-CODEX-2 (inference_cost ∝ context^4) ← τ(6) = 4 (corollary of divisor count)
F-CODEX-3 (alignment over 12 axes) ← σ(6) = 12 directly (this proof)
F-CODEX-4 (motif count = 10) ← σ(6) − φ(6) = 10 (corollary)

verify/n6_arithmetic.py is the runtime witness; SigmaLatticeCard.lean is the mathematical bedrock. Lean 4 toolchain is not required to use hexa-codex — the formal proof is a reference annex. See formal/README.md for build instructions.

Status

SPEC_CATALOG + RUNNABLE_SURFACE at 100% closure (recipe §7.2 sat-1).

17-verb AI 지식 substrate (4 그룹: safety + economics + ops + substrate)

verify/ + tests/ + build/ + docs/ runnable surface. Recipe §7.2 sat-1 saturation reached — all 4 F-CODEX-1..4 closed at recipe §3 closure_pct = 100% (T1 + T2 + T3 ✓ each), via 23 .hexa verifiers + 24 regression wrappers + 3 meta verifiers. T4 (live hardware / Stage-1+) is recipe §9 territory and out of loop scope.

Translation: this repo is (1) a library of AI specs and (2) a runnable verification surface at recipe §7.2 sat-1 = 100% closure under the §3 ladder. The cli/hexa-codex.hexa dispatcher routes both — verb spec reads + .hexa-native verifiers / calculators / tests (legacy Python verify/ kept as a parallel CI path). The heavy-lift per-verb T4 live-hardware / Stage-1+ pipelines (live FLOP/loss measurements, KV-cache profiles, HELM-Core composites, SAE feature counts) sit in recipe §9 territory and land per the release ladder v1.1.0..v2.0.0.

What works at 100% closure (sat-1):

17 verb specs land on disk under their group-named directories.
hexa-codex list prints the full 4-group table.
hexa-codex <verb> prints the spec path + first 20 lines.
hexa-codex selftest confirms 17/17 spec presence.
hexa-codex verify saturation-check re-runs the 6 closure components and emits the canonical recipe §7.3 self-stop sentinel __HEXA_CODEX_RSC_SATURATED__ STOP plus the sat-1 marker __HEXA_CODEX_SATURATION_CHECK__ PASS.
hexa-codex verify falsifier-check runs the closure tracker — per-pillar T1/T2/T3 tier presence, cross-cutter row, recipe §3 closure_pct = 100% verdict.
hexa-codex verify <pillar>-<layer> runs any single layer (e.g. numerics-train_cost-solver).
make -C build sat1 is the friendly CI gate.
make -C build everything = ci (Python legacy) + 24-wrapper .hexa regression + sat-1 closure + selftest.
σ(6) = 12 mechanically proven in Lean 4 (SigmaLatticeCard.lean, := rfl, no sorry); cross-checked at runtime by verify/lattice_check.hexa and verify/numerics_lattice_arithmetic.hexa.
See docs/numerics_methodology.md for the closure-depth narrative (T1/T2/T3 taxonomy, why each T2 layer, why pillar 3 uses symplectic leapfrog, math_pure rationale, sat-2 outlook).
See docs/closure_status.md for the static per-pillar closure snapshot and docs/quick_reference.md for the operator command list.

What is out of scope at 100% closure (sat-1):

Per-verb T4 live-hardware / Stage-1+ pipelines (recipe §9 — out of loop scope; closure_pct already at 100% on the §3 T1/T2/T3 ladder).
Model training, inference SaaS, or RLHF labeling production pipeline.
Any regulatory, alignment, or capability claim — these specs are preregistered hypotheses, not validated results.

Install

Via `hx` (works today)

# `hx` does not auto-detect hexa.toml's `entry` field yet — pass --entry
# explicitly. Tracked as upstream improvement.
hx install hexa-codex --entry cli/hexa-codex.hexa
hexa-codex --version           # → 1.0.0
hexa-codex verify saturation-check   # → __HEXA_CODEX_SATURATION_CHECK__ PASS  (sat-1 marker)
hexa-codex verify falsifier-check    # → per-pillar layer presence + sat-1 verdict
hexa-codex selftest                  # → 17/17 verb specs PASS

For local development install (avoids GitHub round-trip):

hx install /path/to/hexa-codex --entry cli/hexa-codex.hexa --as hexa-codex

Via git clone

git clone https://github.com/dancinlab/hexa-codex.git ~/.hexa-codex
export HEXA_CODEX_ROOT=~/.hexa-codex
cd $HEXA_CODEX_ROOT

# List the 17 verbs:
hexa run cli/hexa-codex.hexa list

# Run the .hexa-native sat-1 closure verdict:
make -C build sat1
# (or directly):
RESOURCE_LOCAL_HEXA=1 ~/.hx/packages/hexa/hexa.real run verify/saturation_check.hexa

# Run the 24-wrapper regression suite:
make -C build test-hexa-all

# Run the legacy Python verifiers (parallel CI path):
make -C build verify          # Python stdlib only

# Run the pytest auto suite (no pip install required):
make -C build test            # 83 cases

# Run F-CODEX-1 closed-form training-cost calc:
hexa-codex calc train_cost --N 7e9 --D 1.4e12

Cross-link

Sister repos in the dancinlab HEXA family:

Cognitive substrate rollups (sister-libraries)

👁️ dancinlab/hexa-senses — 5-verb sensory substrate (dream + ear + empath + olfact + voice). voice is formulaic-only, learned TTS FORBIDDEN.
🧠 dancinlab/hexa-mind — 7-verb mental substrate (mind + neuro + oracle + hexa_telepathy + telepathy + mind_upload + superpowers). 4/7 SPECULATIVE (preregister honesty).

Domain-specific siblings

👻 dancinlab/anima — consciousness / soul cousin (phenomenal grounding adjacent to consciousness).
🧬 dancinlab/hexa-brain — BCI sister (read-side neural substrate counterpart).
⚖️ dancinlab/honesty-monitor — AI honesty-bit falsifier sister (write-side validator for the SAFETY group).
🌱 dancinlab/hexa-bio — 4-verb molecular toolkit (same HEXA-family pattern, biology domain).

The 17 + 5 + 7 = 29 verbs across cognitive sister-libraries all derive from the n=6 master identity (σ·φ = n·τ = 24). hexa-codex covers AI knowledge; hexa-senses covers AI senses; hexa-mind covers AI mental ops.

Upstream concept SSOT: n6-architecture/domains/cognitive/ (declarative sources for all 17 hexa-codex verbs + 5 hexa-senses verbs + 7 hexa-mind verbs).

License

MIT. See LICENSE.

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📚 hexa-codex — AI knowledge substrate (HEXA family)

Why hexa-codex?

Verbs

SAFETY (6)

ECONOMICS (3)

OPS (4)

SUBSTRATE (4)

n=6 master identity

Falsifier preregister

Release ladder

Runnable surface

verify/ — 23 .hexa-native verifiers (math_pure, no deps)

tests/ — 24 .hexa regression wrappers + 83 pytest auto

cli/hexa-codex.hexa — extended subcommands

Reference annexes

consciousness deep-dive (BT-19 falsifier-in-action)

Formal substrate (Lean 4)

Status

Install

Via `hx` (works today)

Via git clone

Cross-link

Cognitive substrate rollups (sister-libraries)

Domain-specific siblings

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Name		Name	Last commit message	Last commit date
Latest commit History 39 Commits
adversarial		adversarial
agent_serving		agent_serving
alignment		alignment
build		build
causal		causal
cli		cli
cog_arch		cog_arch
consciousness		consciousness
deploy		deploy
docs		docs
enterprise		enterprise
eval		eval
formal		formal
infer_cost		infer_cost
interpret		interpret
multimodal		multimodal
papers		papers
quality_scale		quality_scale
rlhf		rlhf
safety		safety
tests		tests
train_cost		train_cost
verify		verify
welfare		welfare
.gitignore		.gitignore
.roadmap.hexa_codex		.roadmap.hexa_codex
CHANGELOG.md		CHANGELOG.md
LICENSE		LICENSE
README.md		README.md
RELEASE_NOTES_v1.0.0.md		RELEASE_NOTES_v1.0.0.md
hexa.toml		hexa.toml
install.hexa		install.hexa

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📚 hexa-codex — AI knowledge substrate (HEXA family)

Why hexa-codex?

Verbs

SAFETY (6)

ECONOMICS (3)

OPS (4)

SUBSTRATE (4)

n=6 master identity

Falsifier preregister

Release ladder

Runnable surface

verify/ — 23 .hexa-native verifiers (math_pure, no deps)

tests/ — 24 .hexa regression wrappers + 83 pytest auto

cli/hexa-codex.hexa — extended subcommands

Reference annexes

consciousness deep-dive (BT-19 falsifier-in-action)

Formal substrate (Lean 4)

Status

Install

Via hx (works today)

Via git clone

Cross-link

Cognitive substrate rollups (sister-libraries)

Domain-specific siblings

License

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