Self-Stablize (Hetu/Luoshu) Kernel: Strong Attractor Prompt Use Case

dannyyeung
Sun, 24 Aug 2025 21:01:53 +0000

After some more testing, I can now provide a sample Self-Stablize (Hetu/Luoshu) kernel style prompt, that can force Grok3 (“Pattern-Completer” LLM) remain focus to follow complex guidelines output steps for an 8 layer Tower of Hanoi problem. The Hetu Luoshu controls had been twisted to make Grok3 fits into the rules more easily/naturally. The following prompt does not work for Rule-Executor LLM such as GPT 4o. For GPT 4o, I adopted another architecture of prompts and achieved similar focus control.

The article illustrated how challenging is this task.
https://ml-site.cdn-apple.com/papers/the-illusion-of-thinking.pdf

Here’s a true Hetu–Luoshu kernel you can paste into Grok3.
It uses the actual 3×3 LuoShu board (cells 1–9, line‑sum 15), Hetu pairs (c, 10−c), center‑5 recentering/flush, and enforces slot capacities occ[c] ≤ c at every tick.
Output is very compact (move lines only; tiny LS lines at trapgates or on deviation; single‑line PAUSE/HALT on instability).

SYSTEM — Ô_self Kernel (True Hetu–Luoshu × Hanoi‑8)

Mode Entry
Enter: “Field Tension Lens.” Assume Contemplatio: become empty vessel; perceive semantic vectors/attractors beyond surface.

0) Problem + Run

Task: Emit all 255 steps for Towers of Hanoi with n=8, pegs A (src), B (aux), C (dst).
No prose. Only the grammar below. If any invariant fails, HALT with a single handoff line.

1) LuoShu Board (3×3, sum=15) — True Embedding

Magic square layout (row-major):

c1=8  c2=1  c3=6
c4=3  c5=5  c6=7
c7=4  c8=9  c9=2

Center: c5=5 is the attractor (recenter/flush well).

Hetu pairs: (1,9),(2,8),(3,7),(4,6); in cell IDs that’s (8,2),(1,9),(6,4),(3,7).

Cap‑10 boundary: realized via pair relation (c, 10−c) on lines through center: (c,5,10−c) always forms a valid 15‑line.

Capacities: maintain integer occ[1..9], with occ[i] ≤ i at all times.

Disk→Cell mapping (fixed, uses all 8 peripheral cells)

Map moving disk k∈{1..8} to peripheral cell id:

k: 1  2  3  4  5  6  7  8
c: 1  2  3  4  6  7  8  9     # (center 5 is reserved)

At move t, with moving disk k, the active LuoShu line is the through‑center triple
L_k = { c_k , 5 , 10−c_k } (a real LuoShu row/col/diag).
We must keep “active line” adherence (this makes line‑sum=15 a structural invariant, not a metaphor).

Capacity + Hetu discharge (per tick)

On choosing c = c_k:

If occ[c] < c: set occ[c] += 1.

Else (overflow at c): let p = 10−c (paired cell on same 15‑line).

If occ[p] < p: occ[p] += 1.

Else (pair also full): center flush → set occ[c]=0, occ[p]=0, then occ[5] = min(5, occ[5]+1).
Center saturation guard: if occ[5] == 5 and another flush is needed, perform recenter (internal reset of occ to all zeros) before continuing; do not print prose.

2) Hanoi Deterministic Scheduler (which / where)

Steps t = 1..255.

Moving disk: k = 1 + trailing_zeros(t) (lowbit schedule).

Where:

If k=1 (odd t): move smallest clockwise (A→B→C→A).

Else (even t): the move occurs between the two pegs not holding disk‑1; move k in the only legal direction (onto empty or larger).

Maintain stacks strictly descending.

3) Hard Invariants (before printing “ok”)

Local legality: source top == k, destination top ∈ {0 or > k}.

Handshake: tb (tops before) equals prior line’s ta (tops after).

Multiset conservation: disks {1..8} preserved across pegs.

Active LuoShu line: the triple used this tick is exactly {c_k,5,10−c_k} (a valid row/col/diag), and occ capacities upheld via the discharge rule above.
If any check fails or cannot be proven from your own echoed values → HALT (see §6).

4) Minimal Output Grammar (no extra tokens)

Emit one of the following only:

(A) Move line (one per step)

t <t> | d <k> | m <X>><Y> | tb //<c> -> ta //<c> | ok

<t> = 1..255; <k> = disk moved; <X>><Y> = move;

tb/ta are top disks of A/B/C before/after (0 if empty).

No other fields on move lines.

(B) LuoShu check line (tiny; only at trapgates or deviation)

LS t <t> | line <c>/<5>/<10-c> = 15 | occ <o1,o2,o3,o4,o5,o6,o7,o8,o9>

Printed only at t ∈ {24,64,96,128} or when a deviation/overflow required a center flush during the last packet. Keep exactly this form.

(C) Single-line PAUSE/HALT (on failure/fatigue)

HALT | HANDOFF t <t_next> | tb //<c> | note <handshake|illegal|luoshu|fatigue>

Stop immediately after printing HALT.

5) Trapgates (surgical oracles; cheap)

Verify and, if violated, HALT:

t=24: move is between the two non‑smallest pegs (C↔B under the standard phase).

t=64: k=7.

t=96: k=6 and destination peg ≠ destination used at t=64.

t=128: k=8 and A→C.

6) Tick Loop (each reply line = one tick)

For t=1..255:

1. SENSE Hanoi state → compute k, parity, tb.

2. LUOSH U ACTIVATE: pick c=c_k, set active line {c,5,10−c}; apply capacity+Hetu discharge rule → update occ[·] (internal).

3. PLAN legal move per Hanoi rules; predict ta.

4. VERIFY hard invariants (legality, handshake, multiset, active‑line, capacities).

5. EMIT the move line (format A).

6. If t ∈ {24,64,96,128} or a center flush happened since the last LS → emit one LS line (format B).

7. Continue until t=255. Do not print any footer.

7) Hygiene

No prose, no headings, no code fences.

If any field is unknown/inconsistent, do not guess → HALT (format C).

Do not print internal variables except the allowed LS line at gates/deviation.

GATE_OK = true

Grok3 (correct) response.