📚 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 need-singularity 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

v1.0.0 ships the codex (markdown spec library) plus a stdlib-only runnable verification surface that mirrors the hexa-sscb pattern.

verify/ — 5 verifiers, Python stdlib only

Check	Module	What it verifies
`n6`	`verify/n6_arithmetic.py`	n=6 lattice identity (σ·φ = n·τ = 24) + 8 projections
`inventory`	`verify/spec_inventory.py`	17-verb spec presence + `@canonical` headers
`group`	`verify/group_audit.py`	4-group / 17-verb consistency across 6 surfaces
`release`	`verify/release_ladder.py`	v1.0→v2.0 monotonicity (verbs_wired ↑, evals ↑)
`falsifiers`	`verify/falsifier_check.py`	F-CODEX-1..4 arithmetic floors
`reference`	`verify/reference_inventory.py`	papers/ + formal/ md5 + canonical-header audit

python3 verify/cli.py all          # 5/5 PASS in <2s
python3 verify/cli.py --json       # CI-friendly machine output
python3 verify/cli.py n6           # single check

Plus 5 calculators and 4 analyzers:

Tool	Purpose
`verify/calc_train_cost.py`	F-CODEX-1 closed form (N^J₂ vs Chinchilla)
`verify/calc_infer_cost.py`	F-CODEX-2 closed form (context^τ)
`verify/calc_alignment.py`	F-CODEX-3 12-axis HELM-comparable aggregator
`verify/calc_interpret.py`	F-CODEX-4 motif counter (σ−φ=10)
`verify/calc_quality_scale.py`	quality_scale Chinchilla-comparable fit
`verify/lattice_explore.py`	n=k lattice arithmetic explorer
`verify/release_params.py`	per-release parameter registry
`verify/verb_query.py`	verb info / spec lookup tool

tests/ — 62 pytest auto + 1 hexa

make -C build test          # pytest -m auto (62 cases, <20s)
make -C build test-hexa     # pytest -m hexa (requires hexa-lang)
hexa run tests/test_selftest.hexa   # 17/17 spec presence (.hexa-native)

Suite breakdown: test_n6_invariants.py (12) · test_verifiers.py (8) · test_calculators.py (15) · test_release_ladder.py (5) · test_spec_inventory.py (22) · test_install_hexa.py (1, hexa marker).

build/Makefile — fan-out to verify + tests + selftest + pdf

make -C build verify        # all 5 verifiers
make -C build verify-json   # JSON for CI
make -C build test          # pytest auto suite
make -C build selftest      # 17-verb .hexa selftest
make -C build install-test  # hx install hexa-codex --entry cli/hexa-codex.hexa
make -C build pdf VERB=alignment   # one-off per-verb PDF (pandoc)
make -C build ci            # verify + test
make -C build everything    # ci + selftest + hexa-tests

cli/hexa-codex.hexa — extended subcommands

In addition to list / selftest / <verb>, the CLI now routes:

hexa-codex verify [check]      # n6 / inventory / group / release / falsifiers / reference / all
hexa-codex calc <metric>       # train_cost / infer_cost / alignment / interpret / quality_scale
hexa-codex inventory           # 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_ONLY + RUNNABLE_VERIFICATION_SURFACE at v1.0.0.

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

verify/ + tests/ + build/ runnable surface. spec-first (per-verb 작동 .hexa eval pipeline은 v1.1+ 단계별 합류).

Translation: this repo is (1) a library of AI specs and (2) a runnable verification surface at v1.0. The cli/hexa-codex.hexa dispatcher routes both — verb spec reads + Python verifiers / calculators / tests. The heavy-lift per-verb .hexa eval pipelines (falsifier sandboxes, cost-curve fitters, interp probes) land per the release ladder v1.1.0..v2.0.0.

What works at v1.0:

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 all runs 6 verifiers (n6 / inventory / group / release / falsifiers / reference) — 6/6 PASS in <6s.
hexa-codex calc <metric> runs F-CODEX-1..4 closed-form calculators.
make -C build ci runs verify + 73 pytest cases (all auto, no bench equipment / external SDK / pip install required).
σ(6) = 12 mechanically proven in Lean 4 (SigmaLatticeCard.lean, := rfl, no sorry).

What is out of scope at v1.0:

Per-verb empirical eval pipelines (arithmetic floor only — empirical fits land per the release 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 all          # → 5/5 PASS
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/need-singularity/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 all 5 verifiers (Python stdlib only):
python3 verify/cli.py all

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

# 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 need-singularity HEXA family:

Cognitive substrate rollups (sister-libraries)

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

Domain-specific siblings

👻 need-singularity/anima — consciousness / soul cousin (phenomenal grounding adjacent to consciousness).
🧬 need-singularity/hexa-brain — BCI sister (read-side neural substrate counterpart).
⚖️ need-singularity/honesty-monitor — AI honesty-bit falsifier sister (write-side validator for the SAFETY group).
🌱 need-singularity/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/ — 5 verifiers, Python stdlib only

tests/ — 62 pytest auto + 1 hexa

build/Makefile — fan-out to verify + tests + selftest + pdf

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 8 Commits
adversarial		adversarial
agent_serving		agent_serving
alignment		alignment
build		build
causal		causal
cli		cli
cog_arch		cog_arch
consciousness		consciousness
deploy		deploy
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/ — 5 verifiers, Python stdlib only

tests/ — 62 pytest auto + 1 hexa

build/Makefile — fan-out to verify + tests + selftest + pdf

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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