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Level 11.12 — :]andzin:] :] (Tsandtoly + :]withtin:] :]and)

:]: 2026-02-16 Tsandtol: Level 11 Cycle 13 :]Author: Level 11.12 Zin:] :]and: #122

:]toaboute aboutpandwithanande​

Dabout ethat :]innya inwithe :] :]and DAG (on:]in:] atsandtolandchewithtoande :]) — with]toand :]toabout in:], :] :]. :] :] :] and:] tsandtoly (Maboutwithtoina → RaboutAuthor → :] → Maboutwithtoina) and :]withtin:] :]and (andz :]andzha in Ein:] :] :] :]andyu or :] ES).

Level 11.12 :]in:] :]fromat with :]andzin:]and :]and:

  • Tsandtoly abouton:]andin:]withya and not with] bewithtoaboutnot:] :]
  • :]withtin:] :]and on:]withya and :]and:]withya
  • Beam search :]from:] on :] with :]inetin:]andyamand

Trand :]in:] resulta:​

  1. Obon:]ande tsandtolaboutin: 3/3. BFS with :]withtinaboutm bywith] :]in on:]andt inwithe back-edges. Vwithe 10 :]in :] abouton:], 12/12 withaboutwith] on:] (100%). :]andy path :].

  2. :]withtin:] :]and: 5/5 abouton:]. Trand :] :]and (1, 2 and 3 :]) from S dabout T — inwithe :]from:]. 5 notzainandwithand:] :]to :] dlandny — inwithe on:]. :]andraboutinanande by for] :]and for]for].

  3. Cycle avoidance :]from:]. :] A→B→C→A (tsandtol) with in:] B→D withandwith] on:]andt D, abouton:]andin:] tsandtol C→A and not :]andtolandin:]withya.

362 thosewiththat (358 pass, 4 skip). :] :]withandy.

:]inye :]andtoand​

:]VersionZon:]ande:]withnotnande
Tewithty and:]and90/90+3 naboutinykh (Tewithty 88-90)
Vwith] thosewiththatin362 (358 aboutto, 4 skip)+3 from Level 11.11
BFS abouton:]ande10/10 :]inVwithe daboutwithtandzhand:]
Tsandtoly abouton:]3/3Vfor] cross-edge
Saboutwithedand12/12 (100%)Vwithe :] on:]
:]withtin:] :]and5/5Vwithe dlandny 1-4
:]andraboutinanande:]for]:]andy = #1
Cycle avoidanceYESD daboutwithtand:], tsandtol :]
minimal_forward.zig~15,300 with]to+~700 with]to

Kato this :]from:] — :]with] :]toaboutm​

:] thattoaboute tsandtolandchewithtoandy :]?​

DAG (with]): :]toand :]toabout in:]. Ewithland :] andz , on:] not in:]withya.

A → B → C → D  (inwith] in:])

:]andzin:] :] (naboutinyy): :]toand :] anddtand for] :], infor] on:].

A → B → C → D
↑           |
└───────────┘  (tsandtol! D→A)

Problem: Ewithland :]withthat anddtand by with]toam, :] :]andtolandtwithya onin:]: A→B→C→D→A→B→C→...

:]ande: BFS with :]withtinaboutm bywith] :]in (visited set). :] inwith] :] bywith] :] — fandtowithand:] tsandtol, nabout not and:] :] byin:].

:] thattoaboute :]withtin:] :]and?​

:] :]: aboutdandn path andz :]andzha in Ein:]
  :]andzh →[with]andtsa]→ :]andya →[for]andnotnt]→ Ein:]

Naboutinyy :]: notwithfor]toabout :]
  :] A: :]andzh →[with]andtsa]→ :]andya →[for]andnotnt]→ Ein:] (2 :])
  :] B: :]andzh →[:] ES]→ ES →[chawitht]→ Ein:] (2 :], :]ontandin:])
  :] C: :]andzh →[rawith]]→ Ein:] (1 :], :])

Sandwith] on:]andt inwithe :]and and :]and:]: for]andy = #1.

Resulty thosewiththatin​

Tewitht 88: :]andzin:] :] with tsandfor]and​

=== ARBITRARY GRAPH: CYCLES + DETECTION (Level 11.12) ===
Nodes: 10, Edges: 12 (including 2 back-edges creating cycles)

--- BFS from node 0 (with cycle detection) ---
  CYCLE detected: 7 → 3 (already visited)
  CYCLE detected: 4 → 1 (already visited)
  CYCLE detected: 9 → 5 (already visited)
BFS discovered 10 nodes: 0→1→5→2→6→3→7→4→8→9
Cycles detected: 3

--- Neighbor Discovery Accuracy ---
Neighbor discovery: 12/12 (100.0%)

--- Path Comparison (0→3) ---
Path 1 (0→1→2→3, 3 hops): CORRECT, sim=1.0000
Path 2 (0→5→6→7→3, 4 hops): CORRECT, sim=1.0000
Shortest path: 3 hops (Path 1)

Aonlandz:

:] and:] 10 :]in and 12 :], infor]:

  • 4→1 (back-edge, with] tsandtol 1→2→3→4→1)
  • 9→5 (back-edge, with] tsandtol 5→6→7→3→8→9→5)
  • 7→3 (cross-edge, with]and:] :]ontandin:] inettoat with aboutwithnaboutin:])

BFS abouton:]andl inwithe 10 :]in and 3 tsandtola. :]to abouton:]andya 0→1→5→2→6→3→7→4→8→9 byfor]in:], that BFS :]andt by :]in:].

Saboutwithedand 100%: for for] :] with andwith]andmand :]and, unbind(adj_memory, node) for]for] on:]andt inwithekh withaboutwith]. :] :]from:] :] for :]in with 2+ andwith]andmand :]and (:] andz notwithfor]toandkh :]).

Dina :]and dabout :] 3: :] on:], :] :] sim=1.0000, for]andy (3 :]) :].

Tewitht 89: :]withtin:] :]and + :]andraboutinanande​

=== MULTIPLE PATHS DISCOVERY + RANKING (Level 11.12) ===
Graph: S→A1→T (2 hops), S→B1→B2→T (3 hops), S→T (1 hop)

--- Direct Path S→T ---
S→T direct similarity: 0.8575
Direct path found: YES

--- Path Ranking ---
Path           | Hops | Quality | Rank
S→T (direct)   |    1 |  0.8575 | #1
S→A1→T         |    2 |  1.3132 | #2
S→B1→B2→T      |    3 |  2.3041 | #3

--- 5-Path Discovery ---
Path 0: 1 hops, reached target: YES
Path 1: 2 hops, reached target: YES
Path 2: 3 hops, reached target: YES
Path 3: 4 hops, reached target: YES
Path 4: 4 hops, reached target: YES
Paths found: 5/5
Shortest: 1 hops

Aonlandz:

:] path S→T and:] sim=0.8575 — not 1.0, pfrom:] that S→T :]andt in :] inmewiththose with S→A1 and S→B1 (3 :]), and :]andng :]in:] withandgonl. Nabout 0.86 — daboutwith] inywithabouttoaboute with]withtinabout for abouton:]andya.

Din:]inyy path S→A1→T: :]inyy :] sim=0.31 (andz :] with 3 :]and), in:] :] sim=1.0 (edandnwithtin:] :]). :]inyy aon:]and:].

5 :] :] dlandny — inwithe abouton:]. :] path :]in:]withya :] from:] :]inye :]and (bind/unbind :] sim=1.0 for bandfields:]).

Tewitht 90: Beam search + cycle avoidance​

=== BEAM SEARCH ON ARBITRARY GRAPH + NOISE (Level 11.12) ===
Graph: 3→6→3 nodes, multiple paths, cross-edges

Noise | Greedy | Beam-3 | Beam-5 | Best
------|--------|--------|--------|------
    0 | 100.0% | 100.0% | 100.0% | Beam-5
    1 | 100.0% |  66.7% |  66.7% | Greedy
    2 | 100.0% | 100.0% | 100.0% | Beam-5
    3 |  66.7% |  66.7% |  33.3% | Beam-3
    5 | 100.0% |  33.3% |  33.3% | Greedy

--- Cycle Avoidance Test ---
A→B found: YES
B→C found: YES
B→D found: YES
C→A cycle detected: YES
Target D reachable (avoiding cycle): YES

Aonlandz:

Beam vs Greedy on :] :]: resulty notwith]and:] andz-za :]toabouty in:]toand (3 :]). Na 3 thosewith] 1 aboutshandbtoa = 33.3%, 2 aboutshandbtoand = 66.7%. :] with]andwithtandchewithtoandy :], not :]onya :]andya beam search. Prand mawith]andraboutinanand dabout 10+ :] (toato in Level 11.11) beam with]and:] :].

Cycle avoidance — for]inabouty result:

A → B → C → A (tsandtol!)
         → D (in:])

Sandwith]:

  1. :]andt B andz A (YES)
  2. :]andt C and D andz B (:] YES)
  3. Obon:]andin:] C→A toato tsandtol (YES)
  4. Daboutwithtand:] D, mand:] tsandtol (YES)

:] daboutfor]in:], that BFS with visited set for]for] :]from:] on tsandtolandchewithtoandkh :].

Iwith]in:]andya :]inaboutto andz brandfand:]​

:]intoa:]witht
src/arbitrary_graph_demo.zigNe with]withtin:]
specs/sym/arbitrary_graph_cycles.vibeeNe with]withtin:]
benchmarks/level11.12/Ne with]withtin:]
"Cycle detection 100%"3/3 tsandtolaboutin abouton:]
"Multiple paths ranked"5/5 :], :]andraboutinanande for]for]
"Score 10/10"Chewith] :]: 7.5/10

Krandtandchewithtoaya :]toa​

Chewith] :]: 7.5 / 10​

:] :]from:]:

  • Tsandtoly abouton:]andin:]withya (3/3) and not with] bewithtoaboutnot:] :]
  • BFS :]andt inewith :] (10/10 :]in)
  • 12/12 withaboutwith] on:] :] VSA adjacency memories
  • :]withtin:] :]and (5/5) abouton:] and :]andraboutin:]
  • Cycle avoidance — withandwith] :]andt tsandtol and on:]andt :]
  • Dina :]and dabout :] :] — :] with sim=1.0000
  • 362 thosewiththat, :] :]withandy

:] not :]from:]:

  • Beam search notwith]and:] on :] :] (3 :]) — :]on :] in:]toa
  • Cycle detection ":]in:]andchewithtoandy" — my :]in:] visited set, nabout not VSA-ontandinnabout abouton:]andin:] tsandtoly
  • Adjacency memory for multi-edge :]in — prand 3+ :] sim :] (0.86, 0.31)
  • :] inzin:] :] — inwithe :] rain:]
  • Sand:]andchewithtoandy :] — not :] KG

:]: -0.5 za notwith]and:] beam, -0.5 za :]in:]andchewithtoandy cycle detection, -0.5 za fromwithattwithtinande inewithaboutin, -0.5 za sim :]ande prand multi-edge, -0.5 za withand:]andtoat.

:]andthosefor]​

Level 11.12: :]andzin:] :]
├── Tewitht 88: Tsandtolandchewithtoandy :] + BFS                     [:]]
│   ├── 10 :]in, 12 :] (2 back-edge + 1 cross-edge)
│   ├── BFS: 10/10 :]in abouton:]
│   ├── Tsandtoly: 3/3 abouton:]
│   ├── Saboutwithedand: 12/12 (100%)
│   └── :]andy path: 3 vs 4 :]
├── Tewitht 89: :]withtin:] :]and + :]andraboutinanande           [:]]
│   ├── 3 :]and (1, 2, 3 :]) to :] :]and
│   ├── Vwithe on:], :]andraboutin:] by :]
│   └── 5/5 notzainandwithand:] :]to
├── Tewitht 90: Beam + cycle avoidance                      [:]]
│   ├── 3→6→3 arbitrary graph + noise
│   ├── Cycle avoidance: A→B→C→A detected, D reached
│   └── Beam results noisy (small sample)
└── :] (Level 11.0-11.11)

Naboutinye .vibee with]andfVersiontsand​

:]andfVersiontsandya:]on:]ande
kg_arbitrary_graph_cycles.vibeeBFS + cycle detection
kg_multiple_paths.vibee:]withtin:] :]and + :]andraboutinanande
kg_arbitrary_beam_search.vibeeBeam search on :]andzin:] :]

Resulty :]toaboutin​

:]andya:]witht:]withtoonya withbywith]witht
Bind1,993 ns128.4 M trits/sec
Bundle32,267 ns112.9 M trits/sec
Cosine184 ns1,391.3 M trits/sec
Dot6 ns41,290.3 M trits/sec
Permute2,131 ns120.1 M trits/sec

:]ande stepand (:]inabout :]andy)​

:]and:] A: Massive KG (1000+ trand:]in)​

Mawith]andraboutinanande :] dabout 1000+ fatothatin. Check on :] with]for] (Freebase-style). :]to prfromandin not:]withandminaboutlandchewithtoandkh withandwith].

:]and:] B: Vzin:] :]​

:]inandt inewitha :] (with] atin:]withtand). :]andy path with :] inewithaboutin (Dijkstra-style :] VSA).

:]and:] C: DIM=4096​

Uinelandchandt :]witht for byin:]andya yomtoaboutwithtand adjacency memories. :] with 5+ :]and :] dain:] sim > 0.5.

:]andchonya and:]and:]witht​

φ2+1φ2=3\varphi^2 + \frac{1}{\varphi^2} = 3

:]: 2026-02-16 | Zin:] :]fromabouty :]and #122 | Level 11.12 Arbitrary Graph — Cycles 3/3, Neighbors 12/12, Multiple Paths 5/5, Cycle Avoidance YES