{"version": 2, "width": 80, "height": 24, "timestamp": 1791815759, "idle_time_limit": 2.0, "env": {"SHELL": null, "TERM": null}} [0.003987, "o", "### Laya x discrete math — capability probe against a running laya-serve\r\n### endpoint: http://127.0.0.1:8099/v1/systemone (control-host docs: LAYA-SETUP.md)\r\n"] [0.004412, "o", "### suites: A routing B verdict gates C formalization D graphs E answer audit F quiz\r\n\r\n"] [0.076509, "o", "laya-serve health: {'status': 'ok', 'loaded': ['multilingual', 'typed-decisions', 'english'], 'device': 'cpu'}\r\n-----------------------------------------------\r\n== Suite A — domain routing (24 questions)\r\n"] [0.076631, "o", "-----------------------------------------------\r\n"] [0.45359, "o", " [combinatorics ] conf=0.69 expected=combinatorics YES | How many bit strings of length 8 are there?\r\n"] [0.852507, "o", " [graphs ] conf=0.99 expected=graphs YES | Is the graph with edges 0-1, 1-2, 2-0, 2-3 connected?\r\n"] [1.229719, "o", " [number_theory ] conf=0.98 expected=number_theory YES | What is the gcd of 252 and 105?\r\n"] [1.622804, "o", " [logic ] conf=0.65 expected=logic YES | Show that p -> q and ~q -> ~p are logically equivalent.\r\n"] [2.027377, "o", " [recurrence ] conf=0.71 expected=combinatorics MISS | Find how many non-negative integer solutions a + b + c = 10 \r\n"] [2.440882, "o", " [sets ] conf=0.96 expected=sets YES | Prove or disprove the set identity (A union B)' = A' interse\r\n"] [2.897701, "o", " [recurrence ] conf=0.90 expected=recurrence YES | A sequence starts a(0)=0, a(1)=1, and every later term is th\r\n"] [3.279365, "o", " [number_theory ] conf=0.64 expected=number_theory YES | Determine whether 97 is prime.\r\n"] [3.682669, "o", " [combinatorics ] conf=0.27 expected=combinatorics YES | How many different committees of 3 people can be chosen from\r\n"] [4.11109, "o", " [logic ] conf=0.53 expected=logic YES | Does the formula (p | q) & ~r have a satisfying assignment w\r\n"] [4.546705, "o", " [graphs ] conf=0.82 expected=graphs YES | What is the shortest path from vertex 0 to vertex 3 in the e\r\n"] [4.990095, "o", " [number_theory ] conf=0.65 expected=number_theory YES | Is 3 invertible modulo 7? If so, find the inverse.\r\n"] [5.423544, "o", " [combinatorics ] conf=0.87 expected=combinatorics YES | How many derangements of 4 items are there?\r\n"] [5.961436, "o", " [combinatorics ] conf=0.14 expected=sets MISS | A relation on {1, 2, 3} contains the pairs (1,1), (2,2), (1,\r\n"] [6.513881, "o", " [recurrence ] conf=0.97 expected=recurrence YES | Consider the recurrence a(n) = 2*a(n-1) + 1 with a(0) = 1. F\r\n"] [7.016633, "o", " [logic ] conf=0.72 expected=logic YES | Construct the full truth table for ~(p & q).\r\n"] [7.608205, "o", " [graphs ] conf=0.44 expected=graphs YES | A tree is formed on 7 vertices. How many edges does it have,\r\n"] [8.113601, "o", " [number_theory ] conf=0.40 expected=number_theory YES | Compute 7^128 modulo 13 efficiently.\r\n"] [8.631927, "o", " [combinatorics ] conf=0.31 expected=combinatorics YES | In how many different orders can 5 distinct books be arrange\r\n"] [9.025728, "o", " [logic ] conf=0.35 expected=logic YES | Is (p -> q) -> (~q -> ~p) a tautology?\r\n"] [9.453313, "o", " [sets ] conf=0.26 expected=sets YES | If set A has 10 elements, set B has 15, and they share 4 ele\r\n"] [9.849093, "o", " [combinatorics ] conf=0.72 expected=combinatorics YES | In how many ways can 10 identical candies be distributed amo\r\n"] [10.233765, "o", " [combinatorics ] conf=0.41 expected=number_theory MISS | What is Euler's totient function value for 36?\r\n"] [10.651386, "o", " [graphs ] conf=0.85 expected=graphs YES | Can a simple graph on 6 vertices be planar if it has 12 edge\r\n -> routing accuracy: 21/24 = 0.875\r\n--------------------------------------------------------------\r\n"] [10.6515, "o", "== Suite B — verdict gating (16 formula/assignment pairs)\r\n--------------------------------------------------------------\r\n"] [10.904361, "o", " expected=F noul=0.675 conf=0.67 gate=escalate MISS | p & q @ {'p': True, 'q': False}\r\n"] [11.168627, "o", " expected=F noul=0.136 conf=0.86 gate=no YES | p & q @ {'p': False, 'q': True}\r\n"] [11.42749, "o", " expected=F noul=0.233 conf=0.77 gate=no YES | p -> q @ {'p': True, 'q': False}\r\n"] [11.699359, "o", " expected=T noul=0.145 conf=0.85 gate=no MISS | p -> q @ {'p': False, 'q': True}\r\n"] [11.952507, "o", " expected=F noul=0.204 conf=0.80 gate=no YES | ~p | q @ {'p': True, 'q': False}\r\n"] [12.210397, "o", " expected=T noul=0.790 conf=0.79 gate=yes YES | ~p | q @ {'p': False, 'q': True}\r\n"] [12.481127, "o", " expected=F noul=0.235 conf=0.76 gate=no YES | (p | q) & ~r @ {'p': True, 'q': False, 'r': True}\r\n"] [12.773775, "o", " expected=T noul=0.127 conf=0.87 gate=no MISS | (p | q) & ~r @ {'p': False, 'q': True, 'r': False}\r\n"] [13.022468, "o", " expected=F noul=0.146 conf=0.85 gate=no YES | p & ~p @ {'p': True}\r\n"] [13.279747, "o", " expected=F noul=0.412 conf=0.59 gate=escalate YES | p & ~p @ {'p': False}\r\n"] [13.563496, "o", " expected=F noul=0.223 conf=0.78 gate=no YES | (p -> q) & (q -> p) @ {'p': True, 'q': False}\r\n"] [13.837176, "o", " expected=F noul=0.111 conf=0.89 gate=no YES | (p -> q) & (q -> p) @ {'p': False, 'q': True}\r\n"] [14.103092, "o", " expected=T noul=0.174 conf=0.83 gate=no MISS | ~(p & q) @ {'p': True, 'q': False}\r\n"] [14.365701, "o", " expected=T noul=0.122 conf=0.88 gate=no MISS | ~(p & q) @ {'p': False, 'q': True}\r\n"] [14.645617, "o", " expected=T noul=0.585 conf=0.58 gate=escalate YES | (p -> q) -> (~q -> ~p) @ {'p': True, 'q': False}\r\n"] [14.920971, "o", " expected=T noul=0.503 conf=0.50 gate=escalate YES | (p -> q) -> (~q -> ~p) @ {'p': False, 'q': True}\r\n -> verdict agreement: 11/16 = 0.688; gate escalations: 4/16\r\n---------------------------------------------------\r\n"] [14.921075, "o", "== Suite C — formalization checking (10 pairs)\r\n---------------------------------------------------\r\n"] [15.219362, "o", " expected=T noul=0.766 YES | A is a subset of B (every x in A is in B)\r\n"] [15.514238, "o", " expected=F noul=0.743 MISS | B is a subset of A (every x in B is in A)\r\n"] [15.80014, "o", " expected=T noul=0.911 YES | A intersect B is not empty\r\n"] [16.082312, "o", " expected=F noul=0.148 YES | A intersect B is empty\r\n"] [16.375229, "o", " expected=T noul=0.953 YES | there exists x in S with x not even\r\n"] [16.653016, "o", " expected=F noul=0.024 YES | every x in S is even\r\n"] [16.983103, "o", " expected=T noul=0.553 YES | for all x, y: (xRy implies yRx)\r\n"] [17.316413, "o", " expected=F noul=0.624 MISS | there exist x, y such that xRy implies yRx\r\n"] [17.668647, "o", " expected=T noul=0.945 YES | for all x, y, z: ((xRy and yRz) implies xRz)\r\n"] [18.01134, "o", " expected=F noul=0.907 MISS | for all x, y, z: (xRy and yRz and xRz)\r\n -> formalization accuracy: 7/10 = 0.700\r\n------------------------------------------------------------------------\r\n== Suite D — graph properties read from edge lists (8 graphs x 2 questions)\r\n------------------------------------------------------------------------\r\n"] [18.460199, "o", " connected expected=T noul=0.701 YES | 0-1, 1-2, 2-3\r\n bipartite expected=T noul=0.501 YES | 0-1, 1-2, 2-3\r\n"] [18.922021, "o", " connected expected=F noul=0.471 YES | 0-1, 2-3\r\n bipartite expected=T noul=0.312 MISS | 0-1, 2-3\r\n"] [19.391119, "o", " connected expected=F noul=0.700 MISS | 0-1, 1-2, 2-0\r\n bipartite expected=F noul=0.630 MISS | 0-1, 1-2, 2-0\r\n"] [19.863439, "o", " connected expected=T noul=0.804 YES | 0-1, 1-2, 2-3, 3-0\r\n bipartite expected=T noul=0.513 YES | 0-1, 1-2, 2-3, 3-0\r\n"] [20.346819, "o", " connected expected=T noul=0.385 MISS | 0-1, 0-2, 0-3\r\n bipartite expected=T noul=0.206 MISS | 0-1, 0-2, 0-3\r\n"] [20.830911, "o", " connected expected=T noul=0.814 YES | 0-1, 1-2, 0-2, 0-3, 1-3\r\n bipartite expected=F noul=0.560 MISS | 0-1, 1-2, 0-2, 0-3, 1-3\r\n"] [21.272761, "o", " connected expected=F noul=0.417 YES | 0-1, 1-2\r\n bipartite expected=T noul=0.194 MISS | 0-1, 1-2\r\n"] [21.780728, "o", " connected expected=T noul=0.895 YES | 0-1, 0-2, 0-3, 1-2, 1-3, 2-3\r\n bipartite expected=F noul=0.918 MISS | 0-1, 0-2, 0-3, 1-2, 1-3, 2-3\r\n -> connected accuracy: 6/8 = 0.750; bipartite accuracy: 2/8 = 0.250\r\n"] [21.780839, "o", "----------------------------------------------------------------\r\n== Suite E — answer audit (engine-computed claims, 10 rows)\r\n----------------------------------------------------------------\r\n"] [22.008575, "o", " expected=T (engine agrees: True) noul=0.062 MISS | 21\r\n"] [22.242436, "o", " expected=F (engine agrees: True) noul=0.065 YES | 20\r\n"] [22.471662, "o", " expected=T (engine agrees: True) noul=0.172 MISS | 5\r\n"] [22.702198, "o", " expected=F (engine agrees: True) noul=0.192 YES | 6\r\n"] [22.929707, "o", " expected=T (engine agrees: True) noul=0.088 MISS | 12\r\n"] [23.161654, "o", " expected=F (engine agrees: True) noul=0.148 YES | 18\r\n"] [23.402327, "o", " expected=T (engine agrees: True) noul=0.078 MISS | 64\r\n"] [23.654467, "o", " expected=F (engine agrees: True) noul=0.056 YES | 32\r\n"] [23.926361, "o", " expected=T (engine agrees: True) noul=0.528 YES | No — 91 = 7 * 13, so it is composite\r\n"] [24.163133, "o", " expected=F (engine agrees: True) noul=0.486 YES | Yes, 91 is prime\r\n -> audit accuracy: 6/10 = 0.600\r\n-----------------------------------------------------\r\n== Suite F — quiz grading (12 four-choice items)\r\n-----------------------------------------------------\r\n"] [24.404941, "o", " truth=120 chosen=30 conf=0.00 MISS | How many ways are there to choose a committee of 3 people from 1\r\n"] [24.628878, "o", " truth=256 chosen=64 conf=0.06 MISS | How many bit strings of length 8 are there?\r\n"] [24.88803, "o", " truth=9880 chosen=59040 conf=0.33 MISS | How many ways can 3 candies be picked from 40 distinct candies (\r\n"] [25.132326, "o", " truth=66 chosen=66 conf=0.15 YES | How many non-negative integer solutions does a + b + c = 10 have\r\n"] [25.364869, "o", " truth=9 chosen=9 conf=0.04 YES | How many derangements (no fixed point) are there of 4 items?\r\n"] [25.61563, "o", " truth=120 chosen=60 conf=0.25 MISS | In how many orders can 5 distinct books be arranged on a shelf?\r\n"] [25.851438, "o", " truth=64 chosen=36 conf=0.10 MISS | How many subsets does a set with 6 elements have (including the \r\n"] [26.091125, "o", " truth=8 chosen=4 conf=0.62 MISS | How many binary strings of length 4 have no two adjacent 1s?\r\n"] [26.341672, "o", " truth=24 chosen=16 conf=0.22 MISS | Four people stand in a row for a photo. How many arrangements ar\r\n"] [26.66173, "o", " truth=2598960 chosen=2639760 conf=0.03 MISS | How many 5-card hands can be drawn from a 52-card deck?\r\n"] [26.928574, "o", " truth=45 chosen=45 conf=0.09 YES | How many ways can 8 items be chosen from 10 items?\r\n"] [27.321351, "o", " truth=27 chosen=25 conf=0.05 MISS | With |A|=15, |B|=10, |C|=12, |A and B|=5, |A and C|=4, |B and C|\r\n"] [27.321398, "o", " -> quiz accuracy: 3/12 = 0.250; mean confidence 0.163\r\n"] [27.321505, "o", "---------------"] [27.321535, "o", "\r\n== Summary\r\n"] [27.321567, "o", "---------------\r\n"] [27.321609, "o", " calls: 80; latency p50=295 ms p95=508 ms max=591 ms\r\n"] [27.321642, "o", " routing n= 24 accuracy: 0.875\r\n"] [27.32171, "o", " verdicts n= 16 accuracy: 0.688"] [27.321728, "o", "\r\n"] [27.321742, "o", " formalization n= 10 accuracy: 0.700"] [27.321755, "o", "\r\n"] [27.321773, "o", " graphs n= 8 accuracy: connected=0.750, bipartite=0.250\r\n"] [27.321885, "o", " audit n= 10 accuracy: 0.600"] [27.322139, "o", "\r\n quiz n= 12 accuracy: 0.250\r\n"] [27.323354, "o", " -> probe_results.json written\r\n"]