OMEGA NAUGHT -- SUCCESSOR-SEARCH EXACT CERTIFICATE
Arithmetic: integers + frozen 60-decimal open enclosure of lambda
Scope: finite-domain search; does not rewrite OMEGA_NAUGHT/1.0
frozen_1.0=339949771344778/1000000000000000  gcd=2  reduced=169974885672389/500000000000000
frozen_first_mismatch=42189065
I_15=[4196/12343, 7039/20706)
I_15_active_lower=[12343, 24686]  active_upper=20706
I_15_endpoint_det=1  I_15_width=1/255574158
farey_neighbor_min_denominator=33049
q_min=4196/12343  A=45392  floors=15430_vs_15431
q_min_is_unique_denominator_below_33049: yes (Farey-neighbor theorem)
profile  Q/S  reduced  in_I15  bitsQ,bitsS  Q*32767  signed32
  frozen_1.0  339949771344778/1000000000000000  reduced=False  in_I15=True  bits=49,50  Qd_max=11139134157654340726  signed32=False
  globally_normalized  169974885672389/500000000000000  reduced=True  in_I15=True  bits=48,49  Qd_max=5569567078827170363  signed32=False
  minimum_modulus  4196/12343  reduced=True  in_I15=True  bits=13,14  Qd_max=137490332  signed32=True
  signed32_horizon  49136/144539  reduced=True  in_I15=True  bits=16,18  Qd_max=1610039312  signed32=True
  baseline_horizon_min  846547/2490212  reduced=True  in_I15=True  bits=20,22  Qd_max=27738805549  signed32=False
  first_admissible_dyadic  22813643/67108864  reduced=True  in_I15=True  bits=25,27  Qd_max=747534640181  signed32=False
signed32_A=2490212
signed32_next_interval=[846547/2490212, 797411/2345673)
signed32_next_det=1  min_numerator_beyond=846547  Q_cap=65538
no_signed32_candidate_has_A_greater_than_2490212: yes
baseline_horizon_min=846547/2490212  A=42189065
dyadic=22813643/2^26  A=33049
normalized_A=42189065
extinction_table  depth  states  largest_fiber  branch_bits
  k=0  states=32768  largest_fiber=1  branch_bits=0
  k=1  states=11140  largest_fiber=3  branch_bits=2
  k=2  states=3787  largest_fiber=9  branch_bits=4
  k=3  states=1288  largest_fiber=27  branch_bits=5
  k=4  states=438  largest_fiber=80  branch_bits=7
  k=5  states=149  largest_fiber=236  branch_bits=8
  k=6  states=51  largest_fiber=695  branch_bits=10
  k=7  states=17  largest_fiber=2045  branch_bits=11
  k=8  states=6  largest_fiber=6016  branch_bits=13
  k=9  states=2  largest_fiber=17697  branch_bits=15
  k=10  states=1  largest_fiber=32768  branch_bits=15
max_predecessor_set=3  two_branch_bits=yes  hist={1: 1, 2: 650, 3: 10489}
certificate_sha256=26d230fba560a5e08f2380207afc5f8b43cdea25ac67de3de1761ab56fc21e5e
THEOREM: I_15, q_min, signed-32 horizon bound, baseline-horizon min, and D_15 extinction are exact
NOT A SUCCESSOR ACCEPTANCE: serialization, verifier surface, and guarantee-set scoring are not claimed
CERTIFICATE PASS (36.49 seconds)