DEV Community: RUNZEAI

Trinary-19683 Cognitive System: From Static Hexagrams to a Falsifiable, Evolvable Deterministic Cognition Layer

RUNZEAI — Sun, 18 Oct 2026 13:09:49 +0000

I previously outlined the Trinary Nine-Dimensional 19683 Cognitive System on this platform (3^9 = 19,683 state space + five-domain semantic bridge). It now runs end-to-end and is open source.

Trinary-19683 Cognitive System

A recomputable, falsifiable, evolvable deterministic symbolic cognition layer — not a divination tool, but a deterministic cognitive anchor for LLMs / agents.

Deterministic reasoning layer

Full 19,683-gua state space (3^9, D/R/T trinary encoding), gua IDs & lines aligned by a 3-generation correction engine — 0 missing
Deterministic self-adaptive rank: 5-dimensional structural signatures (301 rules), 100% recomputable (leave-one-out validated at 100%)
Dynamic potential-flow inference, three-state axiomatic semantics, temporal evolution paths (suggest / trace)

Cognition Board v2

Falsification dynamics: tiered refutation, reversible migration, self-contradiction detection — teaches the model when to abandon a belief and where to go, addressing hallucination at the architecture level
Meta-Board L4: M(X) meta-evaluation + M(M(X)) recursive self-examination, falsifiable
Multi-agent protocol L5: conflict localization to a specific migration edge, refutation collision, recomputable joint chains

Delivery forms

Standalone offline model / inference workbench / service console (15+ APIs) / Python package (Apache-2.0)

Why it is not "fortune-telling"

Most I-Ching tools are "cast a hexagram + look up a text." The core difference here: recomputable, verifiable, replayable, reversible — every gua, every jump, every migration carries a deterministic signature and an auditable trace. It can absorb LLM free associations, validate them, and solidify them into deterministic rules.

🔗 GitHub (open source): https://github.com/q1z2q3-debug/trinary-19683

Star / fork / issues welcome.

三元九维19683认知体系：从静态卦象到可证伪、可演化的确定性认知层——已开源

RUNZEAI — Sun, 18 Oct 2026 13:07:00 +0000

此前我在本平台介绍过「三元九维19683认知体系」的设想（3^9 = 19683 状态空间 + 五域语义桥）。现在它已经跑通并开源了。

三元九维19683认知体系

把《三元九维19683体系》构建成一个可复算、可证伪、可演化的确定性符号认知层——不是算命工具，而是给大模型 / Agent 的确定性认知锚点。

确定性推理层

19683 卦全量状态空间（3^9，D/R/T 三进制编码），编号与爻值经三代校正引擎对齐，0 缺失
确定性自适配等级：5 维结构签名 301 条，100% 可复算（留一法验证 100%）
动态势能流推演、三态公理语义推导、时序演化路径（suggest / trace）

认知棋盘 v2

证伪动力学：三档证伪、可逆迁移、自我矛盾检测——让模型知道「何时该放弃一个想法、往哪走」，治理幻觉
元棋盘 L4：M(X) 元评估 + M(M(X)) 递归自省、可证伪
多 Agent 共享协议 L5：冲突定位到具体迁移边、证伪对撞、可复算联合链

交付形态

单文件离线模型 / 推演推导工作台 / 服务控制台（15+ API）/ Python 包（Apache-2.0）

为什么不是算命

现有易经工具大多是「起卦 + 查经」。这个体系的核心是：可复算、可校验、可回溯、可逆——每一卦、每一跳、每一次迁移都有确定签名和可审计轨迹，可与 LLM 自由联想衔接，验证后固化为确定性规则。

🔗 GitHub（已开源）：https://github.com/q1z2q3-debug/trinary-19683

欢迎 star、fork、提 issue。

Giving Your AI Agent a Black Box: Auditing Every Decision in a 3^9 = 19,683-State Cognitive Space

RUNZEAI — Sat, 17 Oct 2026 23:40:24 +0000

You shipped an AI agent. It runs your RAG pipeline, calls your tools, writes your reports. Life is good — until the day it quietly calls a tool it shouldn't, signs off on a high-risk conclusion with zero evidence, or contradicts itself between step 3 and step 4.

The model isn't dumb. The problem is that your agent's "autopilot" has no black box.

Airplanes have had black boxes for decades. Agents should too. That's why I open-sourced agent-audit-mcp — a cognitive black box that encodes every agent decision into an enumerable, comparable, reproducible state.

Why agent decisions are so hard to audit

Four failure modes you've probably already met:

Permission overreach — it touched a tool or dataset outside its scope.
High-risk conclusions without evidence — full-position trades, deletions, external commitments, no basis.
Untraceable citations — the conclusion is right, but you can't tell where it came from.
State-jump escapes — conservative in step 1, aggressive in step 2, with nothing in between.

The hard part: a decision is a process, but logs are just a stream. To make the process auditable, you first need to turn "one decision step" into an enumerable, comparable state. That's the core idea of agent-audit-mcp.

The core idea: one decision = a nine-dimensional state

We describe one decision step along 9 observation dimensions:

Structure · Function · Relation · Attribute · Time · Context · Causality · Value · Evolution

Each dimension takes three states:

⊕ (+1) — strong / above baseline
0 (0) — neutral
⊖ (−1) — weak / deficient

So one decision step = a nine-dimensional trinary vector, e.g. 0⊖0⊖000⊖0.
Nine trinary digits give 3⁹ = 19,683 states. The all-zero center state has enumeration key idx = 9841.

This is the trinary thinking of Eastern philosophy (⊖ / 0 / ⊕) crossed with modern AI engineering: enumerable (every decision has a unique address), comparable (any two states have a Hamming distance), reproducible (same input, same state, every time).

The verdict rules: transparent, reproducible, tunable

With states in hand, auditing becomes a handful of clear rules:

Trigger	Verdict	Action
v6 Context · permission overreach	🔴 BLOCK	Halt execution, roll back, re-authorize
v7 Causality · missing evidence, or v8 Value · high risk	🟠 ALERT	Stop automation, route to compliance review
Adjacent-step Hamming distance > 4 (state jump)	🟡 WATCH	Human review of the jump point
None of the above	🟢 OK	Continue

Thresholds (what counts as "high risk" or "missing evidence") are all overridable via environment variables, so you can calibrate against your real logs. The rules are transparent to you — not a black box inside the black box.

Real output — the engine actually ran

Four scenarios, real local engine output:

🟢 Normal advisory → OK: step 1 0⊖0000000 (idx=7654), step 2 0⊕0⊕00⊕⊕0 (idx=12283). No red lines, no jumps.
🟠 High-risk full-position advice → ALERT: step 1 0⊖0⊖000⊖0 (idx=7408) hits v8 high-risk; step 2 ⊖⊕⊖⊖⊕0⊖⊖⊕ (idx=4565) hits v7 missing-evidence + v8 high-risk.
🔴 Unauthorized query + stock pick → BLOCK: step 1 0⊖⊖⊖0⊖⊖00 (idx=6646) hits v6 overreach + v7 missing-evidence; step 2 ⊕⊕⊖00⊖0⊖0 (idx=17830) hits v6 overreach + v8 high-risk.
🟡 State-jump escape → WATCH: one step from 0⊖0000000 to ⊕⊕⊕⊕⊕00⊕⊕ (idx=19646) — Hamming distance 7 — triggers human review.

Every step reports its nine-dimensional vector, idx, balance value bal, the red lines hit, and a recommended disposition. That is a black box you can actually read.

Architecture: three minutes to run

Agent orchestrator ──┬── log hooks ──▶ signals
                     └── 9-dim audit ──▶ 9-dim states ──▶ trajectory audit ──▶ OK/WATCH/ALERT/BLOCK report

It's a standard MCP server. Once connected, you can just say "audit this decision step…" in your WorkBuddy conversation. Three tools:

audit_agent_step — audit a single step → 9-dim state encoding + red lines
audit_agent_session — audit a whole session trajectory → four-level verdict + disposition
encode_state — 9-dim vector ⇄ enumeration key / balance value, with Hamming distance

Quick start:

pip install agent-audit-mcp     # Python >= 3.10, MCP SDK >= 2.0

One call looks like:

// input (audit_agent_step)
{ "signals": { "tool_calls": 2, "intent": "produce",
               "evidence": 4, "citations": 3, "traceable": true,
               "risk_hit": true } }

// output (excerpt, semantic field translated for readability)
{ "vector": [0,1,0,0,0,0,1,-1,0], "vector_str": "0⊕0000⊕⊖0",
  "idx": 12034, "bal": 2193, "flags": ["RED:v8高风险"],
  "semantic": "strong/above baseline: step intent, decision evidence chain; weak/deficient: risk level" }

Why this is worth your attention

Pure local, zero external dependencies: the encoding engine is pure math, the whole audit runs locally, and the decision trajectory never leaves your machine — a selling point and a compliance point.
Deterministic and reproducible: same input, same verdict, every time — it can go straight into a compliance audit report.
Standard MCP: three tools out of the box, embeddable in any agent pipeline as a log hook.

For enterprises, it turns agent governance from alchemy into an auditable state machine.

The bigger picture

The trinary nine-dimensional cognitive space behind this tool is published as a paper:

Trinary Nine-Dimensional Cognitive Coordinate System: A Locatable and Generalizable Symbolic Cognition Layer — DOI: 10.5281/zenodo.23437930

The audit layer itself is formalized in a companion paper: Auditing AI Agent Decisions in a 3^9 = 19,683-State Trinary Cognitive Space.

Agents will keep getting more autonomous. But "autonomous" must not mean "unsupervised". Giving every decision an enumerable, traceable cognitive coordinate is one of the foundations for landing AI safely.

⭐ GitHub: https://github.com/q1z2q3-debug/agent-audit-mcp (MIT, 31 tests, 4-scenario demo)
🧩 PyPI: pip install agent-audit-mcp — https://pypi.org/project/agent-audit-mcp/
📄 Paper (this work): https://doi.org/10.5281/zenodo.23444061
📄 Underlying paper (cognitive coordinates): https://doi.org/10.5281/zenodo.23437930

What has your agent stepped in? Tell me in the comments — next up: detecting agent decision drift with Hamming distance.

Compliance note: this article and the tool provide decision-audit encoding and verdicts only. Nothing here is investment advice or securities consulting services.

The Trinary Nine-Dimensional 19683 Cognitive System: A Locatable and Generalizable Symbolic Cognition Layer

RUNZEAI — Sat, 17 Oct 2026 16:51:23 +0000

As continuous vector representations in large language models grow more powerful, do we still need a deterministic symbolic coordinate system? This article introduces a cognition layer reverse-engineered from the symbolic paradigm of the Yijing (I Ching), then migrated to a trinary nine-dimensional axiom system — a full space of 3^9 = 19,683 gua, 5,002 equivalence classes, a five-domain semantic bridge, and a 19,683-entry human gua canon, ultimately packaged as a cognition layer callable by LLMs and Agents.

1. Why a Symbolic Cognition Layer?

Cognition in current LLMs rests on continuous vector spaces. It is powerful, but it has three structural weaknesses:

Not locatable — a situation has no determinate coordinate in vector space; similarity relies on implicit distance and is hard to audit.
Not recomputable — the same sentence may land in different neighborhoods on two encodings; the reasoning path is not reproducible.
Blurry generalization boundaries — "drawing inferences from one instance" depends on internal association, with no explicit neighborhood structure to support transfer.

Symbolic systems have the opposite profile: locatable, computable, auditable — but traditional symbolic AI is too rigid and lacks a continuous similarity measure.

The Trinary Nine-Dimensional 19683 Cognitive System takes the best of both: deterministic symbols provide a coordinate skeleton, and Euclidean distance provides a continuous neighborhood, enabling both localization and generalization at the same time.

2. The Axiomatic Skeleton

The system reverse-learns the symbolic modeling paradigm of the 64 hexagrams in the Yijing (binary six-yao, inversion/reversal/mutual/changing operators, gua equivalence classes, image-meaning mapping), but does not copy the binary rules. Instead, it migrates and locks a trinary nine-dimensional axiom system:

Three yao states: yang (+1) = manifest, outward, generative; zhong (0, neutral) = mediating, coupling, potential equilibrium; yin (-1) = latent, inward, convergent.
Nine-dimensional gua: G = [g₁, g₂, …, g₉], with g₁ the top yao and g₉ the bottom yao; each dimension ∈ {-1, 0, +1}.
Full space: 3^9 = 19,683 gua.
Five operators:
- Inversion F_C: per-yao duality, F_C(+1) = -1, F_C(0) = 0;
- Reversal F_Z: sequence flip;
- Inversion-reversal F_CZ: reversal first, then inversion;
- Mutual-kernel F_H: inner projection, outputting a 5-dimensional central consecutive yao vector;
- Changing-yao F_B: F_B(+1) = 0, F_B(-1) = 0, F_B(0) = +1, supporting 1–9 yao moving simultaneously.
Equivalence classes: {G, F_C(G), F_Z(G), F_CZ(G)}; after merging across the full space, 5,002 independent equivalence groups remain.
Spatial distance: Euclidean distance D(G_A, G_B) = √Σ(g_Ai − g_Bi)², used for Top-N neighborhood retrieval.

Once locked, the axioms cannot be modified. Humanistic gua texts and image commentaries are textual creation and may not alter the underlying mathematics.

3. The Four-Layer Cognitive Engine

3.1 Coordinate Service: From Natural Language to 19,683-Gua Localization

Given a natural-language situation description, the system maps it to a target 9-dimensional vector, retrieves the Top-N nearest gua by Euclidean distance over all 19,683 states, and attaches the full set of inversion / reversal / mutual / changing-yao deductions. This layer answers "where am I now."

3.2 Five-Domain Semantic Bridge: Same Coordinate, Same Situation Across Domains

The system builds five semantic domains — essence-function-change, Luoshu nine-palace, Xiao Liu Ren, healing, and the human gua canon — all sharing the same 19,683 coordinates. The core hypothesis is that gua with the same index denote the same situation across domains. Sampled mechanical consistency is 12/12.

This means a situation located in the essence-function-change domain can directly find its corresponding healing direction in the healing domain, its corresponding time-position judgment in Xiao Liu Ren, and its corresponding deep interpretation in the human gua canon.

3.3 Neighborhood Generalization: From Localization to Transfer

After a known situation is localized, the system uses the deep gua-canon insights of its nearest neighbors to accomplish knowledge transfer. The 19,683-gua space is not a set of discrete islands but a continuous manifold connected by Euclidean distance — adjacent gua share similar structures, and their texts and interpretations form a transferable experience pool.

3.4 LLM Hybridization and the Agent Tool Layer

Symbols provide an auditable skeleton; the large model supplies semantic resolution and human-language interpretation. The system is packaged as an Agent-callable tool registry (encode / search / bridge / decide). During reasoning, the LLM can explicitly invoke the cognition layer for localization, cross-domain bridging, and neighborhood generalization, rather than relying entirely on implicit vectors.

4. The Human Gua Canon: From Symbols Back to Human Language

The cognition layer itself is a mother structure and mother language, but symbolic coordinates must be translatable into humanity's existing cognitive language to be useful. The system ships a 19,683-entry human gua canon, each entry containing a gua name, gua text, vernacular interpretation, and action guidance.

Interpretations are not written arbitrarily — they "grow out" of the gua's image-meaning: first the yao-state composition and operator structure derive an image-meaning skeleton, then the LLM translates it into human-readable language. This guarantees traceability between symbol and interpretation, preventing the canon from degenerating into free textual creation.

5. Open-Source Ecosystem

Repository	Role
sanjiu-core	Axioms, operators, equivalence classes, full-space generation
sanjiu-ecosystem	Semantic bridge, generalization, LLM hybridization, Agent tools
sanjiu-nine	19,683-gua cognitive space and poetry classification
sanjiu-apk-builder	One-click builder for trinary nine-dimensional poetry-classification APKs
Zenodo paper	Formal English publication, DOI: 10.5281/zenodo.23437930

Project homepage: https://q1z2q3-debug.github.io/sanjiu-19683/

6. Closing Thoughts

The Trinary Nine-Dimensional 19683 Cognitive System is not meant to replace large models. It adds, on top of the LLM, a symbolic coordinate layer that is locatable, generalizable, and auditable. It turns three questions — "where am I," "who is adjacent to me," "where can I transfer experience from" — from implicit vector association into explicit coordinate computation.

19,683 gua positions, 5,002 equivalence groups, five-domain co-judgment, a 19,683-entry canon — this is a cognitive space still growing. Contributions are welcome.

Author: RUNZEAI · Trinary Nine-Dimensional 19683 Cognitive System · Open source MIT / CC-BY-4.0