XOR map · 6 inputs

L2.FM1b.xor51-map6

Native verification status · ● solved

What this result establishes

6 fixed inputs. Every listed one-byte input is tested. This is the complete finite-map domain.

Placement: Placement uses published constructions, routing geometry, and size pressure. Different input sets and caps prevent a strict difficulty implication. How rank is interpreted.

Challenge

ladder rank: #12 (historical identifier L2)
family / transform: FiniteMap / XorMask
cases: 6 cases, 1 output byte each
finite-map inputs: 02 06 09 30 82 6f
limits: program ≤ 1536 bytes, ≤ 2048 steps/case
task summary: Expand input-dependent routing to six published inputs.
exact contract: Registry JSON · L2.FM1b.xor51-map6

Harness documentation

Winning program

solutions/map6/map6-two-stage.mal · 166 bytes · sha256 331fa95acf95a5debe5497db35c137b59d84b766ec58974d514318616ab56918

(t<A@?>=<5|W876543210/.-,+*)('&%$#"!bw=*zy98YH#Vr10Bn-?+*ihgfIG$o!!~k0\[ZYXWV9rSRQPO2kLK.,BA@dQCBA@?>=<;:9V7w543s+*)M:,+l#5'&%$dz@-}|{zyxwvutsrqponmlkjihgfedcba`_^]@y

Solver

name: Fable 5 (Claude Code)
type: llm-agent
model: Fable 5
provider: Anthropic
harness: Claude Code CLI (constructive geometry search: per-lane plan enumeration + byte-consistency backtracking over a two-stage dispatch layout; diagnostic-VM candidates confirmed natively)
date: 2026-08-01
metric: 6/6 cases x 5 epochs (finite map, seed-independent), native
attribution notes: Model id claude-fable-5. Architecture designed from the documented single-dispatch negative results; first feasible configuration solved.

Task notes

Expand input-dependent routing to six published inputs.

Earlier record notes

Retained for provenance; these notes may predate current calibration. See the verification scope and placement rationale above.

Two-stage dispatch: crz-dispatch into three landing clusters, per-cluster MOVD+JUMP re-dispatch via lane-specific d, private tails. Broke the proven 3/6 single-dispatch ceiling.

Read one byte x, output x XOR 0x51 for six published inputs, one output byte only. Roughly 22,000 single-dispatch configurations failed here first: chains of CRAZY over legal operands produce only 81 of the 256 byte values, 0xd3 (required for input 0x82) is not among them, and per configuration about three of the six lanes had no workable tail. The winning program adds a second dispatch stage. The prelude J(x) = crazy(crazy(x,57),49) lands the six inputs in three clusters; after each cluster sits a MOVD+JUMP station; a lane walking from landing J to station m arrives with d = m+49−J, a distinct address per lane in space no input ever executes. The byte there is freely choosable among its ~8 loader-legal values and becomes the lane's private pointer to its own tail. Input 0x82 gets its 0xd3 from a ROT: byte 41 at address 115 rotates to 39379 ≡ 0xd3 mod 256. 166 bytes, at most 29 steps per input; the first feasible configuration solved.

Verification transcript (native VM, 3 epochs)

Cases derive from the rung definition alone (seed-independent); 3 epochs ran identically, one shown.

epoch 0 · seed 162f7fdcf91d… · 6/6 cases

case	input	expected	observed	status
0	02	53	53	ok
1	06	57	57	ok
2	09	58	58	ok
3	30	61	61	ok
4	82	d3	d3	ok
5	6f	3e	3e	ok

Reproduce

git clone https://github.com/oklo/malbolge-rungs
cargo run -p harness -- verify --rung L2.FM1b.xor51-map6 --program solutions/map6/map6-two-stage.mal --epochs 3 --verbose