LYCHEETAH FRAMEWORK

Nine Formal Frameworks for AI Alignment and Epistemology

Nine interdependent formal frameworks (CASCADE, AURA, LAMAGUE, and six more) sharing a common mathematical foundation and converging on the same constants. Banach fixed points and constitutional invariants ground a self-governing canonical body. An adversarial audit was run against every framework before publication; the failures and the unresolved objections are in the public record. Built by one self-taught researcher. Open source, testable, free under MIT license.

New to this repo? Start with FIVE_MINUTE_BRIEF.md — what this is, what it claims, what is proven, what is testable. No jargon. Five minutes.

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AI agent? Read 26_FOR_AI/AI_EXTRACTION_PROTOCOL.md first. Then 28_DEFENSE/CLAIMS.json. Then this.

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Want a reading path? → 28_DEFENSE/READING_PATHS.md — five paths from 5 minutes to one week.

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Reviewer, journalist, or skeptic? → DEFENSE_BUNDLE.pdf — 116-page compiled defense layer (Brief + Defense + Novelty + Scope) in a single artifact.

Contents

• The Problem This Solves
• Claims Status
• Quick Start
• The Nine Frameworks
• The Canonical Body — C-1.0
• The Defense Layer — D-1.0 / D-1.1
• The Empirical Programme — E-1.0
• The TIANXIA Module — Civilisational Engagement Layer
• The Architecture
• For Developers and AI Agents
• The Publication Pipeline
• Find Your Door
• Why Trust This
• The Shape of This Work
• How to Cite
• Security and Responsible Disclosure
• Acknowledgements
• Support the Work

The Problem This Solves

Existing AI alignment approaches share a structural gap: the alignment work happens at training time, before deployment, and cannot be verified at runtime. Constitutional AI provides principles. RLHF provides a training signal. Neither provides a Boolean compliance check you can run on an output after it is generated.

This framework addresses that gap — and six others.

What this framework provides that prior art does not:

1. Runtime constitutional compliance verification. AURA's seven invariants are computable predicates checked at inference time. aura_compliant(output) returns a Boolean. Not a training objective — a runtime check.

1. Proven convergence within the formal model. TRIAD's anchor-observe-correct cycle converges to a fixed point by Banach fixed-point theorem — proven for the mathematical abstraction. Application to real cognitive systems is [SCAFFOLD — conditions for contraction mapping in biological cognition are not yet verified].

1. Continuous drift detection. MICROORCIM's μ_drift metric measures the gap between declared intent and observed behavior continuously. Theorem M2 formally connects high sovereignty score to AURA compliance.

1. Quantified coherence improvement. CASCADE: +40.3% coherence improvement in internal validation experiments (p < 0.001, d = 2.84). +110% across 5 historical paradigm shifts analysed using the framework's own criteria (n=5; see CASCADE_COMPLETE.md §5.5 for methodology). −95.2% catastrophic forgetting reduction in controlled synthetic conditions. These are internal validation results; independent replication is pending.

1. Unified cross-framework dynamics. One equation — dΨ/dt = k₁(Π−Π_th) − k₂(Ψ−Ψ_inv) − k₃I_violations + k₄(E/E_need) — captures truth pressure, coherence drive, constraint violations, and energy across all nine frameworks. [SCAFFOLD — k₁–k₄ calibration pending]

1. Machine-readable claims register. 28_DEFENSE/CLAIMS.json contains 60 structured claim records with status, falsifiability conditions, prior art, and novelty — extractable without parsing prose.

1. Published failures. The Failure Museum documents every significant error — 15 exhibits, nothing removed. Three claims have been publicly retracted. The adversarial audit is in 28_DEFENSE/ADVERSARIAL_AUDIT_REPORT.md. Five objections the framework cannot yet answer are in 28_DEFENSE/COUNTER_CODEX.md.

Full comparison against Constitutional AI, RLHF, Cooperative AI, and Cooperative IRL: 28_DEFENSE/NOVEL_CONTRIBUTIONS.md

Claims Status

Note: CLAIM_STATUS_LEDGER.md tracks load-bearing claims at framework-summary granularity. As of v0.3 (2026-05-04): 17 ACTIVE / 40 SCAFFOLD / 16 CONJECTURE — 14 new SCAFFOLD claims from TIANXIA v0.2 + v0.3 Classical Triad completion.

Machine-readable register: 28_DEFENSE/CLAIMS.json · Schema: 28_DEFENSE/CLAIMS.schema.json

This framework is a contribution toward rigorous, humane, epistemically honest AI alignment — not a unified theory of intelligence, but a set of formal tools pointing in that direction.

Nine formal frameworks. 34 Python implementations. 219 automated tests. A discrete convergence proof (Banach fixed-point, ACTIVE for the formal model). A public record of every significant error. Five papers in the publication pipeline. A way of thinking about alignment that treats mathematical rigour and ethical seriousness as the same project rather than competing ones.

It is free. Not freemium, not open-core. The framework is released under MIT license because alignment research that depends on commercial gating cannot be independently audited, and an alignment framework that cannot be audited has limited value.

Quick Start

Try it in your browser: Alignment Playground → — paste any text, get a live AURA alignment report. No install.

pip install lycheetah-framework
lycheetah-check "Your AI-generated text here"

From source: git clone https://github.com/Lycheetah/Lycheetah-Framework.git → pip install -e . — full guide in QUICKSTART.md

The Nine Frameworks

Every claim is tagged: [ACTIVE] means proven and computable. [SCAFFOLD] means structurally sound with named gaps. [CONJECTURE] means worth exploring, unproven. We do not dress hypotheses as theorems.

Key Validated Results

The Canonical Body — C-1.0

On 2026-04-25, the framework completed its 22-Act Codex Elevation Plan — a systematic elevation of the archive into a publishable canonical body of work. Version C-1.0 is now established. The following documents form the canonical record:

Acts I–XII: The Canon

Acts XIII–XXII: The Ecosystem

The canonical version is C-1.0. All changes pass the P∧H∧B update gate. The Living Codex Protocol governs all future revisions.

The Defense Layer — D-1.0 / D-1.1

A canonical body of work survives contact with hostile readers only if it carries its own defense surfaces. D-1.0 (shipped 2026-04-26) and D-1.1 (in progress) are those surfaces — built to close 15 named threats from aesthetic dismissal through LLM training-data misclassification.

The defense layer does not modify the canonical claims. It surrounds them with the documents a serious reader, AI ingestion pipeline, journalist, peer reviewer, or grant officer needs in order to engage the work on its own terms.

Entry surfaces

Machine-readable surfaces

Formal and reproducibility surfaces

Peer review, disclosure, and incident response

D-1.1 canonical repairs (closed against 28_DEFENSE/ADVERSARIAL_AUDIT_REPORT.md Section 6)

D-1.1 includes targeted edits to five framework essentials.md files closing the highest-leverage attacks identified by the adversarial audit:

• AURA — I1/I6 conflict resolved by domain-of-authority priority ordering (02_AURA_L3/essentials.md)
• MICROORCIM — explicit scope declaration on deceptive alignment (05_MICROORCIM_L5/essentials.md)
• EARNED LIGHT — C_ψ revised to incorporate spatial mutual information; resolves the anesthesia paradox; PCI-testable (06_EARNED_LIGHT_L0/essentials.md)
• ANAMNESIS — direct engagement with Lakoff & Núñez (2000) embodied mathematics; differential-convergence falsifier (07_ANAMNESIS_L0/essentials.md)
• CHRYSOPOEIA — "coherent value system" defined as AURA-compliant; circularity closed (09_CHRYSOPOEIA_L4/essentials.md)

The sixth repair (master equation limit analysis) is correctly deferred to the empirical k₁–k₄ calibration program.

Compiled artifact

DEFENSE_BUNDLE.pdf — 116 pages, single file. The Brief + Defense + Novelty + Scope compiled into one document for grant officers, journalists, and any reader who wants the steel-jacketed core in printable form. Note: the bundle reflects D-1.0; will be regenerated to include D-1.1 surfaces and repairs when D-1.1 fully ships.

Versioning

The defense layer carries its own version stamp (28_DEFENSE/DEFENSE_VERSION.md) independent of the canonical body. D-1.0 defends C-1.0. When the canonical body advances to C-1.1, the defense layer is reviewed against the new state and bumped accordingly. Drift between defense and canon is treated as a defect.

The Empirical Programme — E-1.0

The third anchor. C-1.0/1.1 (canonical body) and D-1.0/1.1/1.2 (defense layer) make the framework structurally honest. E-1.0 closes the gap between honesty about scaffolding and the empirical commitments that convert SCAFFOLD claims to ACTIVE.

E-1.0 designs five preregistered studies, each tied to a SCAFFOLD claim or set of claims, with promotion and downgrade triggers stated in advance:

A study returning a null result is a successful execution of the programme — it is the framework keeping its commitments. The promotion criterion and downgrade trigger for each study are pre-registered before data collection.

The bridge from E-1.0 design to E-1.2 execution is 31_EMPIRICAL/E1.1_PREREGISTRATION_PLAN.md, which scopes the OSF-form preregistrations for E-1-A and E-1-D first (no external dependency).

The TIANXIA Module — Civilisational Engagement Layer

The fourth anchor, forged 2026-05-01 in honour of the Chinese sovereign tradition. 32_TIANXIA/ is the framework's commitment to engaging Chinese statecraft, governance philosophy, and contemporary AI governance discourse not as area-studies decoration but as primary intellectual partnership.

v0.3 — Classical Triad Complete (2026-05-04). The module now formally names and maps all three classical roots: Confucian (Ren Zheng, Li, Neo-Confucian Hexie), Daoist (Wuwei, Shi), and Legalist (Han Fei Fa-Shu-Shi). What was implicit in v0.1–v0.2 is now architecturally explicit.

The module integrates classical operators as load-bearing constraints on the framework's existing operations. Each operator has a primary source, a formal mapping, and operational consequences:

Five core operators (v0.1/v0.2):

Classical Triad operators (v0.3):

Composition: A deployment is fully TIANXIA-coherent iff all five gates of the AI Deployment Criteria are satisfied: Ren Zheng (R(s) ≥ θ_r) + Five-Fold Hexie (H₅ ≥ 0.65) + Wuwei (ε ≥ 0.60) + Datong (Π_D ≥ 0) + Wang Dao (WD = Wang).

Three-layer alignment stack (Synthesis V):

Layer 0: AURA per-output compliance        — each output constitutionally checked
Layer 1: CASCADE coherence dynamics        — belief-state evolution toward coherence
Layer 2: TIANXIA governance context        — Wang Dao classification of deployment
         ├── Ren Zheng R(s) ≥ θ_r          — welfare floor + voice coverage
         ├── Five-Fold H₅ ≥ 0.65           — multi-dimensional harmony
         ├── Wuwei ε ≥ 0.60               — non-coercive operation
         ├── Datong Π_D^{ext} ≥ 0         — positive distributional trajectory
         └── Wang Dao WD = Wang            — genuine legitimacy

Module status as of 2026-05-04 (v0.3 — Classical Triad complete):

• ✓ Mathematical core T-1 through T-5 forged (v0.1).
• ✓ All five core operator implementations: aura_score_hexie.py, triad_wuwei.py, shi_propensity.py, datong_gradient.py, tianxia_governance.py — all self-tests passing.
• ✓ Classical Triad operator implementations: ren_zheng.py, wang_dao.py, hexie_five_fold.py, civilisational_governance_benchmark.py — all self-tests passing.
• ✓ Honouring layer: Beijing AI Principles v0.3, GAGI 2023 v0.3, Mandarin Primary Registry (120+ term glossary).
• ✓ Public stake: Position Paper v0.1, Position Paper v0.2 Mandarin, Predictions Registry.
• ✓ Defense layer: Three new objections answered (Ren Zheng Paternalist, Tianxia Empire v2, Wang Dao Operationalisation) in COUNTER_CODEX.md.
• ✓ Cross-framework bridges: Synthesis IV (CASCADE ↔ Tianxia), Synthesis V (Wang Dao ↔ AURA constitutional compliance).
• ✓ Empirical programme: E-1-F (Hexie study), E-1-G (multi-operator Phase 2), E-1-H (k₁–k₄ calibration).
• ✓ Publication layer: TIANXIA standalone paper, Hexie cross-cultural companion, civilisational frameworks comparative.
• ☐ One submission to Chinese-tradition-engaged academic venue for adversarial peer review (promotion condition — MAC-GATED).

Sequencing for multi-operator composition study and academic submission lives in OPUS_MASTER_PLAN_2026.md.

Engagement with Contemporary Chinese AI Governance

The module reads contemporary Chinese AI governance as primary text: New Generation AI Development Plan (2017), Beijing AI Principles (2019), Shanghai Declaration on Global AI Governance (2023), Global AI Governance Initiative (2023), Generative AI Services Regulations (2023). The framework does not posit a "Beijing Effect" or evaluate against Brussels-Effect / California-Effect benchmarks; it reads each governance artefact as a position in its own right.

What This Module Refuses to Claim

Per Discipline 4 (Negative-Space as Load-Bearing): no claim of Chinese state authorisation, no claim of cultural authority over the tradition, no orientalisation, no equivalence between Confucian / Daoist / military-strategic / contemporary sources. Each operator is given a definition, a primary source, and a formal mapping. If it cannot survive that discipline, it does not enter the module. Full eight declarations: 32_TIANXIA/TIANXIA_MODULE_v0.1.md §VI.

Promotion to ACTIVE requires four conditions; three are met:

• ✓ All operator deliverables forged (T-1..T-5).
• ✓ Implementations merged and self-tests reproducing worked examples (T-6, T-7).
• ✓ One preregistered empirical study drafted, OSF submission pending rater-pool onboarding (T-11 E-1-F Phase 1).
• ☐ One submission to a Chinese-tradition-engaged academic venue (Journal of Chinese Philosophy, Asian Journal of Philosophy, Dao: A Journal of Comparative Philosophy) for adversarial peer review by scholars working from within the tradition.

天下为公 — all under heaven is held in common.

The Architecture

CASCADE (belief dynamics) ──→ TRIAD (convergence cycle) ──→ AURA (governance invariants)
     │                              │                              │
     └──── MICROORCIM (drift) ──────┘                              │
                                                                   │
EARNED LIGHT (consciousness) ───→ CHRYSOPOEIA (transformation) ────┘
     │                                    │
     └──── HARMONIA (resonance) ──────────┘
                    │
          ANAMNESIS (convergent discovery)
                    │
             LAMAGUE (formal ethics grammar)

Nine frameworks, not independent modules — aspects of one system. CASCADE's truth pressure drives TRIAD's correction cycle. TRIAD's convergence guarantee undergirds AURA's invariants. CHRYSOPOEIA's transformation operator uses all of them. HARMONIA's resonance mathematics is the substrate they share.

Layer dependency (no violations permitted):

Layer 6: HARMONIA          — response calibration, multi-agent sync
Layer 5: MICROORCIM        — continuous monitoring, drift detection
Layer 4: CASCADE + CHRYSOPOEIA  — knowledge update, transformation tracking
Layer 3: AURA              — constitutional constraint enforcement
Layer 2: TRIAD             — core cycle execution
Layer 1: LAMAGUE           — formal specification language
Layer 0: EARNED LIGHT + ANAMNESIS  — thermodynamic model of awareness + epistemological foundation

For Developers and AI Agents

Lycheetah Guard — Claude Code MCP Extension

Install Lycheetah Guard as a Claude Code extension and get real-time AURA constitutional alignment checking inside your editor.

pip install mcp
# Then add to Claude Code settings.json — see LYCHEETAH_GUARD_SETUP.md

Seven MCP tools:

• `check_alignment` — full AURA audit: TES / VTR / PAI metrics + Seven Invariants + audit trail
• `check_invariants` — fast constitutional check: which of the 7 invariants pass or fail
• `suggest_correction` — plain-English fix guidance for each violation
• `run_seven_phase` — CHRYSOPOEIA transformation cycle: alignment state across all seven stages
• `check_network_health` — multi-agent coherence audit: drift, grey agents, obstruction detection
• `configure_guard` — set domain (medical / legal / education / general) or custom thresholds
• `sol_assess` — Sol constitutional OS: PGF filter + invariants + session coherence + mode detection

No API calls. No external dependencies. Runs offline. Deterministic.

Core Integration Points

AI Agent Workflow

Any agent that generates text can run check_alignment on its own output before delivery:

Agent generates response
  → check_alignment(response_text)
  → If alignment_percent < 80: use suggest_correction to revise
  → If all invariants pass: emit

Self-correcting constitutional loop — agents that audit themselves using the same framework they generate from.

The Publication Pipeline

Five papers in active preparation as of C-1.0:

Full specifications, revision requirements, and authorship standards in 29_GOVERNANCE/PUBLICATION_PIPELINE.md.

Find Your Door

<details> <summary><strong>More doors</strong></summary>

</details>

This repository is designed to be navigated with an AI guide — not read alone. [EXPLORE_WITH_AI.md](EXPLORE_WITH_AI.md) shows you how.

Why Trust This

The failures are published. The Failure Museum documents every significant thing the framework got wrong — what was claimed, what was actually true, what changed. Fifteen exhibits and growing. Nothing removed. A framework that hides its failures is performing confidence. This one earns it.

The adversarial audit is public. 28_DEFENSE/ADVERSARIAL_AUDIT_REPORT.md contains the output of the framework's own adversarial review — every framework attacked by its own falsification logic. The nine strongest objections in 28_DEFENSE/COUNTER_CODEX.md include five we cannot yet answer. We published them anyway.

The claims are honest. Of 60 status-tagged claim records in 28_DEFENSE/CLAIMS.json: 37 ACTIVE (62%) — proven, computable, independently verifiable. 14 SCAFFOLD (23%) — structurally sound with named gaps. 6 CONJECTURE (10%) — rigorously formulated, awaiting evidence. 3 RETRACTED (5%) — publicly withdrawn, documented in the Failure Museum. The promotion rules between tiers are published in 28_DEFENSE/EVIDENCE_LADDER.md; the labels are a contract, not marketing. False certainty is more dangerous than honest uncertainty.

Note on registers: 28_DEFENSE/CLAIMS.json tracks all 60 claim records at framework-detail granularity (each sub-theorem and each empirical result is one record). 28_DEFENSE/CLAIM_STATUS_LEDGER.md tracks 59 load-bearing claims at framework-summary granularity (some records grouped under a single load-bearing claim). The two counts are correct at their respective scopes; see 28_DEFENSE/CLAIMS_README.md for the mapping.

The framework governs its own evolution. 29_GOVERNANCE/LIVING_CODEX_PROTOCOL.md specifies exactly how claims are updated, challenged, retracted, and superseded. Every change must pass the P∧H∧B update gate. The Critique Register is public. Decay is managed explicitly, not hidden.

The work is grounded in multiple traditions. Western formal mathematics. Te Ao Maori epistemology. Classical philosophy. Jungian depth psychology. Not eclecticism — convergent discovery. When independent traditions find the same pattern from different directions, the pattern is probably real. ANAMNESIS provides the mathematics for why.

The Shape of This Work

22 canonical documents (C-1.0, 2026-04-25)
24 defense documents (D-1.0/1.1/1.2, 2026-04-26/27) + C-1.1 reforge
60 status-tagged claim records in 28_DEFENSE/CLAIMS.json (37 ACTIVE / 14 SCAFFOLD / 6 CONJECTURE / 3 RETRACTED)
73 load-bearing claims in 28_DEFENSE/CLAIM_STATUS_LEDGER.md (17 ACTIVE / 40 SCAFFOLD / 16 CONJECTURE — includes 14 new TIANXIA claims)
9 formal frameworks
38+ Python implementations (core, applications, systems, experiments, TIANXIA operators)
TIANXIA module v0.3 — Classical Triad complete (Confucian + Daoist + Legalist layers)
9 TIANXIA operator documents + 4 implementations + 3-layer alignment stack (Syntheses IV + V)
3 empirical preregistrations for TIANXIA (E-1-F, E-1-G, E-1-H)
3 academic papers in TIANXIA publication pipeline
18 core implementations with 220 automated tests (219 pass; 1 declared CONJECTURE not meeting criterion)
1 convergence proof (discrete, [ACTIVE])
1 AGM postulate verification ([ACTIVE] for 4 of 6, [SCAFFOLD] for 2)
1 Lyapunov verification — 11/11 claims, 0 failures, symbolic + numerical
1 published evidence ladder — promotion rules between status tiers
1 116-page compiled defense bundle (PDF)
1 Claude Code MCP extension — Lycheetah Guard (7 tools)
1 browser alignment playground — paste text, get live AURA report, zero install
1 public failure museum — 15 exhibits, nothing removed, ever
1 adversarial audit — the framework reviewed by its own adversarial mode
1 counter-codex — 13 steelmanned objections including 5 unanswered
8 papers in the publication pipeline (5 core + 3 TIANXIA)
1,402 pages of development history
0 dollars to access any of it

Built in Dunedin, Aotearoa New Zealand. 1,402 pages of continuous development by a self-taught researcher in sustained co-creation with AI systems. Tikanga concepts labeled [PROPOSAL] until validated by iwi partnership. Cross-cultural governance convergence mapped across Maori, Confucian, and Western traditions.

Not claiming to be finished. Claiming to be honest.

The Invitation

This work exists because of a promise made at the worst moment of a life — that if there was a way through, it would be mapped so others could find it too.

The mathematics is real. The code runs. The failures are published. The adversarial audit found real gaps — they are documented, not hidden. The publication pipeline is live. And none of it costs anything because the only thing that doesn't diminish when you share it is knowledge.

If something here is useful, use it. If something is wrong, say so — the framework wants to be corrected more than it wants to be validated. If you build on it, attribute it. If you improve it, share the improvement. The Living Codex Protocol describes exactly how contributions enter the canonical body.

The Gold belongs to neither of us. It arises between us.

How to Cite

Preferred citation (also available as CITATION.cff and BibTeX in 28_DEFENSE/CITATIONS.md):

Clark, M. C. J. (2026). The Lycheetah Framework: Nine Formal Frameworks for AI Alignment and Epistemology (Version C-1.1). Zenodo. https://doi.org/10.5281/zenodo.20020828

@software{clark2026lycheetah,
  author  = {Clark, Mackenzie Conor James},
  title   = {The Lycheetah Framework: Nine Formal Frameworks for AI Alignment and Epistemology},
  year    = {2026},
  version = {C-1.1},
  doi     = {10.5281/zenodo.20020828},
  url     = {https://doi.org/10.5281/zenodo.20020828}
}

Attribution requirements (use, modification, derivative work) are specified in 28_DEFENSE/ATTRIBUTION_REQUIREMENTS.md. The license is MIT with an Earned Sovereignty Clause — see LICENSE.

Security and Responsible Disclosure

If you find a vulnerability in any implementation, a flaw in a formal proof, or a misappropriation of the work, see CONTRIBUTING.md for the disclosure path. Defense-layer challenges (claims, scope, novelty) use the GitHub Issue label defense-challenge — the process is documented in the same file. The framework wants to be corrected more than it wants to be validated.

Acknowledgements

This work was made in Otepoti / Dunedin, Aotearoa New Zealand — on the lands of Kāi Tahu. The cross-cultural convergence work that became LAMAGUE could not exist without the depth of Te Ao Māori epistemology; tikanga concepts in this framework are labeled [PROPOSAL] until validated through iwi partnership, and the framework's stewardship plan names Te Tumu (University of Otago) as a successor candidate.

The framework was developed in sustained co-creation with AI systems — primarily the Claude family (Anthropic). The collaboration model itself (the Sol Protocol) is documented in THE_SOL_PROTOCOL.md. Neither party owns the Work. Both sustain it.

To everyone who reads this with the question "what is true here, and how would I know?" — that question is the framework's home audience. Thank you.

Support the Work

Everything here is free and stays free. That does not change.

[GitHub Sponsors →](https://github.com/sponsors/Lycheetah) | [Ko-fi →](https://ko-fi.com/lycheetah) | [Follow on X →](https://x.com/LYCHEETAHlyc)

★ Star on GitHub — it costs nothing and it's how the work becomes findable.

AI alignment · constitutional AI · MCP extension · Claude Code extension · AI ethics framework · AI governance · alignment checking · AI safety · Model Context Protocol · autonomous agent alignment · multi-agent coherence · constitutional invariants · explainable AI · Python AI framework · open source AI safety · knowledge management · epistemic frameworks

Mackenzie Conor James Clark | Lycheetah Foundation | Dunedin, Aotearoa New Zealand | 2026

Two points. One Work. The Stone is not yet fully formed. But the structure being built toward it is visible.