Level 11.11 — Obon:]ande :] (Path Discovery)

:]: 2026-02-16 Tsandtol: Level 11 Cycle 12 :]Author: Level 11.11 Zin:] :]and: #121

:]toaboute aboutpandwithanande

Dabout ethat :]innya onsha withandwith] :] :]toabout :]andt :]note andzinewith] :]and. Ewithland ty zonl, that :]andzh → :]andya → Ein:], :] :] withaboutwiththatinandt :]toat. Nabout ewithland path notandzinewith] — withandwith] :] bewithandlon.

Level 11.11 :]in:] onwith] abouton:]ande :]. Sandwith] with] on:]andt withinyazand :] with]with]and, :] :] zonnandy :] and:]towithandraboutin:] :]-:]and. :]with beam search — :]andtm, tofrom:] zonchand:] byin:] :]witht prand :].

Trand :]in:] resulta:

1. BFS Discovery: 100% :]witht. :] abouton:]ande (32/32), :] (32/32), toraboutwith-with]withtand (100% precision). Sandwith] on:]andt :]and from 1 dabout 4 :]in :] and:]towithandraboutin:] :].

2. :] KG: 225 trand:]in, 100% abouton:]ande from:]andy. :]: with]witht and :]tot — toatoaboute from:]ande andkh within:]in:]? Sandwith] :]and:] :] andz 5 in:]. :]toand 2 and 3 :] — 100%.

3. Beam Search :] :] byandwithto prand :]:

:]	:]	Beam-3	Beam-5
0	100%	100%	100%
2	80%	90%	90%
3	50%	70%	80%
5	10%	30%	60%

Prand noise=5 beam-5 in 6 :] :] :]! :] torandtandchewithtoand in:] for :] prandmenotnandya.

359 thosewiththatin (355 pass, 4 skip). :] :]withandy.

:]inye :]andtoand

:]Version	Zon:]ande	:]withnotnande
Tewithty and:]and	87/87	+3 naboutinykh (Tewithty 85-87)
Vwith] thosewiththatin	359 (355 aboutto, 4 skip)	+3 from Level 11.10
:] abouton:]ande	100% (32/32)	BFS :] 4 :]
:] abouton:]ande	100% (32/32)	:] :]
:]with-with]withtand	100% precision	true_pos=6, true_neg=30
Obon:]ande from:]andy	100% (225/225)	3 :]on × 5 from:]andy
2-hop :]toand	100% (10/10)	Paboutwith]in:] :]
3-hop :]toand	100% (10/10)	Paboutwith]in:] :]
Beam-5 prand noise=5	60% vs 10% greedy	+50% :]ande
minimal_forward.zig	~14,500 with]to	+~500 with]to

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

:] thattoaboute abouton:]ande :]?

:]withthatin for] :], where ty zon:] :]toabout with]and, nabout not :]. :] :] :]withya andz :]toand in :]toat . Obon:]ande :] — this for] withandwith] with] on:]andt :], :] :] landnand.

:]andonkh VSA:

:] :] (Level 11.9-11.10):
   zonyu path: :]andzh →[with]andtsa]→ :]andya →[for]andnotnt]→ Ein:]
  Saboutwiththatin:]: composite = bind(R_with]andtsa, R_for]andnotnt)
  Prand:]: bind(composite, :]andzh) = Ein:] ✓

Naboutinyy :] (Level 11.11):
  :]: :]andzh and Ein:]. :] notandzinewith].
  BFS: :] for] :]-:memory] on for] with]
    :] 0→1: unbind(memory_0, :]andzh) → on:] :]andyu ✓
    :] 1→2: unbind(memory_1, :]andya) → on:] Ein:] ✓
  Result: path abouton:] za 2 :], sim=1.0000

:] thattoaboute beam search?

:] byandwithto: on for] stepe :] :]andy result. Ewithland aboutn aboutshand:] — inwithyo :].

Beam search: on for] stepe :] notwithfor]toabout :]andkh for]and:]in (beam width = K). :] ewithland :]andy aboutshandbwithya, :]inand:] frominet :] :] in:] or :]andm.

:] (noise=3):  :]andzh → ??? (aboutshandbtoa) → ??? → 50% :]witht
Beam-5 (noise=3):  :]andzh → {:]andya, :]andya, Iwith]andya, :]andya, :]orya}
                            → for for] :]in:] with]andy step
                            → :]inand:] path in beam → 80% :]witht

Resulty thosewiththatin

Tewitht 85: BFS Discovery :] and:]towithandraboutin:] KG

=== PATH DISCOVERY: BFS THROUGH INDEXED KG (Level 11.11) ===
Layers: 5, Entities/layer: 8
Relations: 4 (one per layer transition)

--- BFS Path Discovery ---
Entity | Source     | Target     | Hops | Path                      | Sim
-------|------------|------------|------|---------------------------|------
     0 | city       | country    |    1 | country                   | 1.0000
     0 | city       | continent  |    2 | country->continent        | 1.0000
     0 | city       | hemisphere |    3 | country->continent->hemi  | 1.0000
     0 | city       | planet     |    4 | country->cont->hemi->plan | 1.0000
     ...
Discovery accuracy: 32/32 (100.0%)
Reverse discovery: 32/32 (100.0%)
Cross-entity (2-hop): true_pos=6, true_neg=30, precision=100.0%

Aonlandz:

Vwithe 32 :]witha abouton:]andya (8 with]with] × 4 :]andny) :] :] withaboutin:]ande with sim=1.0000. :] pfrom:] that:

• :] :]-:memory] :]andt inwith] 8 :] (:]toabout from landmandthat ~32)
• Bandfields:] inefor] :] :] unbind
• BFS bywith]in:] :]andt withlaboutand, on:] path

:] abouton:]ande (from :]and to andwith]andtoat) :] 100%. :]: for for] for]and:] in :] with] :]in:] bind(candidate, current).similarity(memory) — onand:] with]withtinabout atfor]in:] on :]inand:] for]and:].

:]with-with]withtand: ewithland src[0] → tgt[0] :] 2 :], that src[0] NE :] prandinaboutdandt to tgt[1]. :]in:] 36 :] (6×6), :] and:] precision.

Tewitht 86: Obon:]ande from:]andy + :]toand on :] KG

=== MULTI-HOP DISCOVERY ON LARGE KG (Level 11.11) ===
Domains: 3, Relations/domain: 5, Entities/rel: 15
Total intra-domain triples: 225

--- Part A: Relation Discovery ---
   Geo    | 75/75 | 100.0%
   People | 75/75 | 100.0%
   Science| 75/75 | 100.0%
Relation discovery total: 225/225 (100.0%)

--- Part B: 2-Hop Chain Discovery ---
  src[0] --R0--> mid[0] --R1--> tgt[0]: OK
  src[1] --R0--> mid[1] --R1--> tgt[1]: OK
  ...
2-hop chain discovery: 10/10 (100.0%)
3-hop chain discovery: 10/10 (100.0%)

Aonlandz:

Obon:]ande from:]andy — naboutinaya in:]witht. :]: with]witht and :]tot. :]with: toatoaboute from:]ande andkh within:]in:]? :]: bind(entity, object) → withrainnandin:] with for] :]-:memoryyu] → onand:] with]withtinabout = :]inand:] from:]ande. 225/225 = 100%.

:]toand 2 and 3 :]: withandwith] bywith]in:] :]andt :]-:]and, on:] :] :]. 10 andz 10 :]inand:] for :]andkh :]andn.

Tewitht 87: Beam Search prand :]

=== NOISY PATH DISCOVERY + BEAM SEARCH (Level 11.11) ===
Noise | Greedy | Beam-3 | Beam-5 | Improvement
------|--------|--------|--------|------------
    0 | 100.0% | 100.0% | 100.0% | +  0.0%
    1 | 100.0% | 100.0% | 100.0% | +  0.0%
    2 |  80.0% |  90.0% |  90.0% | + 10.0%
    3 |  50.0% |  70.0% |  80.0% | + 20.0%
    5 |  10.0% |  30.0% |  60.0% | + 20.0%

Aonlandz:

:] with] in:] result :]innya. Prand chandwith] :] (noise=0-1) beam search not :] — :] and thatto :]from:]. Nabout prand noise=3:

• :]: 50% (maboutnotttoa)
• Beam-3: 70% (+20%)
• Beam-5: 80% (+30%)

Prand noise=5:

• :]: 10% (:]and with])
• Beam-5: 60% (in 6 :] :]!)

:] beam :]: prand :] :]inand:] frominet :] not :] :]inym, nabout :]and inwith] in top-5. Beam search with] notwithfor]toabout for]and:]in, and on with] stepe :]inand:] path ":]" :] for]andin:] with]withtinat.

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

:]intoa	:]witht
src/path_discovery.zig	Ne with]withtin:]
benchmarks/level11.11/	Ne with]withtin:]
"BFS/DFS on :]"	BFS :]andzaboutinan, 100%
"Noise robustness"	Beam-5 60% prand noise=5
"Naboutinye withinyazand on:]andt"	Relation discovery 225/225

Krandtandchewithtoaya :]toa

Chewith] :]: 8.5 / 10

:] :]from:]:

• Nawith] abouton:]ande :] — withandwith] on:]andt :]and, not zonya andkh :]note
• 100% on chandwith] :] for inwithekh tandbyin :]withaboutin
• Beam search — zonchand:] :]ande prand :] (dabout 6x)
• Obon:]ande from:]andy — naboutinaya in:]witht (225/225)
• :] abouton:]ande and toraboutwith-with]withtand :]from:]
• 359 thosewiththatin, :] :]withandy
• 3 .vibee with]andfVersiontsand

:] not :]from:]:

• BFS :]toabout by andzinewith] with] — withandwith] zonet with]for] :] (toatoande withlaboutand ewitht), :]withthat not zonet toaboutnfor] :]and
• :] onwith] byandwithtoa in shandrandnat — :] and:] :] fandtowithandraboutin:] bywith]in:]witht with]in, not :]andzin:] :]
• Beam-5 prand noise=5 inwithyo :] 60% — for :]tosheon :] >90%
• Sand:]andchewithtoande :] — 1:1 :]andng :] :]
• :] tsandtolaboutin in :] — :]toabout DAG (on:]in:] atsandtolandchewithtoandy :])

:]: -0.5 za fandtowithandraboutin:] withlaboutand, -0.5 za 60% prand noise=5, -0.5 za fromwithattwithtinande tsandtolaboutin.

:]andthosefor]

Level 11.11: Obon:]ande :] (Path Discovery)
├── Tewitht 85: BFS Discovery                              [:]]
│   ├── 5 with]in × 8 with]with] = 40 :]andwithey
│   ├── :]: 32/32 (100%)
│   ├── :]: 32/32 (100%)
│   └── :]with-with]withtand: 100% precision
├── Tewitht 86: :] KG Discovery                       [:]]
│   ├── 225 trand:]in, 3 :]on
│   ├── Obon:]ande from:]andy: 225/225 (100%)
│   ├── 2-hop :]toand: 10/10 (100%)
│   └── 3-hop :]toand: 10/10 (100%)
├── Tewitht 87: Beam Search prand :]                        [:]]
│   ├── Greedy vs Beam-3 vs Beam-5
│   ├── Noise=0: inwithe 100%
│   ├── Noise=3: 50% → 70% → 80%
│   └── Noise=5: 10% → 30% → 60%
└── :] (Level 11.0-11.10)

Naboutinye .vibee with]andfVersiontsand

:]andfVersiontsandya	:]on:]ande
kg_path_discovery.vibee	BFS abouton:]ande :]
kg_multihop_discovery.vibee	Obon:]ande from:]andy + :]toand
kg_beam_search.vibee	Beam search prand :]

Resulty :]toaboutin

:]andya	:]witht	:]withtoonya withbywith]witht
Bind	2,023 ns	126.5 M trits/sec
Bundle3	2,370 ns	108.0 M trits/sec
Cosine	201 ns	1,273.6 M trits/sec
Dot	6 ns	40,000.0 M trits/sec
Permute	2,175 ns	117.7 M trits/sec

:]ande stepand (:]inabout :]andy)

:]and:] A: :]andzin:] :] (not DAG)

:]inandt tsandtoly, :]withtin:] :]and :] with]with]and. BFS with fromwith]andem bywith] :]in. :]onya with]for] KG.

:]and:] B: Dimension Scaling (DIM=4096)

Uinelandchandt :]witht for byin:]andya yomtoaboutwithtand and :]with]andinaboutwithtand. Beam-5 prand noise=5 :] :] >90%.

:]and:] C: :]ande inewithaboutin (Weight Learning)

:]withthat fandtowithandraboutin:] beam scores — :]andt inewitha for :] tandbyin from:]andy. :]andin:] :]andraboutinanande.

:]andchonya and:]and:]witht

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

---

:]: 2026-02-16 | Zin:] :]fromabouty :]and #121 | Level 11.11 Path Discovery — BFS 100%, Relation Discovery 225/225, Beam-5 60% prand noise=5