verify_cost.py -- every figure below is recomputed from data/*.json A. MEASUREMENTS vs THE SAME SPAN OF IDLE, ibm_kingston, six jobs (two days, three jobs each) jobs: 2026-10-04 run 341 = db16hravog1s73fhnml0; 2026-10-04 run 342 = db16iaavog1s73fhnn9g; 2026-10-04 run 343 = db16llbid5ic73eqnp8g; 2026-10-06 run 761 = db2rk4u8v0ts73c3dbcg; 2026-10-06 run 762 = db2rp87r11fs7397b73g; 2026-10-06 run 763 = db2rug68v0ts73c3dt50 each job: untouched qubits split by wiring distance to the nearest measured qubit (1, 2, 3+ links); per group the median fraction of coherence kept after k measurements and after laid idle of 10/20/30/60/120 us; three groups averaged. length of one measurement: stated 2.18 us; measured 2.323 (4 Oct) and 2.402 (6 Oct) (stored values, not recomputed here). There is NO 27-measurement point in these jobs (ladder 1,2,3,4,6,8,12,16,24,32); 27 is read between the 24 and 32 points. idle reference: fit10-30 | measurement length: measured k= 3 kept(measured)/kept(idle): 0.985 0.995 0.977 1.009 0.990 0.985 range 0.977-1.009 | lost/lost: 1.176 1.087 1.295 0.945 1.094 1.186 range 0.945-1.295 k= 9 kept(measured)/kept(idle): 1.000 1.015 1.011 1.021 1.026 1.003 range 1.000-1.026 | lost/lost: 1.000 0.961 0.972 0.954 0.947 0.994 range 0.947-1.000 k=27 kept(measured)/kept(idle): 0.799 0.810 0.972 0.677 0.892 0.875 range 0.677-0.972 | lost/lost: 1.099 1.102 1.016 1.169 1.049 1.080 range 1.016-1.169 idle reference: fit10-30 | measurement length: stated k= 3 kept(measured)/kept(idle): 0.979 0.989 0.971 0.998 0.979 0.975 range 0.971-0.998 | lost/lost: 1.266 1.168 1.404 1.042 1.223 1.328 range 1.042-1.404 k= 9 kept(measured)/kept(idle): 0.977 0.991 0.985 0.987 0.985 0.966 range 0.966-0.991 | lost/lost: 1.068 1.022 1.044 1.040 1.043 1.097 range 1.022-1.097 k=27 kept(measured)/kept(idle): 0.733 0.735 0.869 0.608 0.762 0.750 range 0.608-0.869 | lost/lost: 1.145 1.144 1.058 1.238 1.110 1.145 range 1.058-1.238 idle reference: fit10-120 | measurement length: measured k= 3 kept(measured)/kept(idle): 0.978 0.985 0.983 0.990 0.986 0.979 range 0.978-0.990 | lost/lost: 1.291 1.176 1.202 1.108 1.140 1.252 range 1.108-1.291 k= 9 kept(measured)/kept(idle): 1.007 1.023 1.020 1.034 1.037 1.015 range 1.007-1.037 | lost/lost: 0.982 0.942 0.949 0.925 0.924 0.965 range 0.924-0.982 k=27 kept(measured)/kept(idle): 0.945 0.946 0.937 0.915 1.008 1.006 range 0.915-1.008 | lost/lost: 1.021 1.024 1.024 1.027 1.001 0.997 range 0.997-1.027 idle reference: fit10-120 | measurement length: stated k= 3 kept(measured)/kept(idle): 0.972 0.979 0.977 0.980 0.976 0.969 range 0.969-0.980 | lost/lost: 1.399 1.271 1.299 1.244 1.282 1.412 range 1.244-1.412 k= 9 kept(measured)/kept(idle): 0.982 0.996 0.994 0.992 0.992 0.974 range 0.974-0.996 | lost/lost: 1.054 1.008 1.016 1.024 1.023 1.073 range 1.008-1.073 k=27 kept(measured)/kept(idle): 0.849 0.847 0.844 0.780 0.845 0.847 range 0.780-0.849 | lost/lost: 1.063 1.063 1.065 1.088 1.057 1.057 range 1.057-1.088 idle reference: measured | measurement length: measured k= 3 kept(measured)/kept(idle): 0.995 1.008 0.991 1.011 1.000 0.992 range 0.991-1.011 | lost/lost: 1.051 0.940 1.099 0.930 1.009 1.087 range 0.930-1.099 k= 9 kept(measured)/kept(idle): 0.993 0.999 1.001 1.019 1.021 1.002 range 0.993-1.021 | lost/lost: 1.021 1.000 0.997 0.957 0.954 0.999 range 0.954-1.021 k=27 kept(measured)/kept(idle): 1.033 1.039 1.008 1.025 1.084 1.099 range 1.008-1.099 | lost/lost: 0.990 0.993 0.998 0.991 0.979 0.971 range 0.971-0.998 idle reference: measured | measurement length: stated k= 3 kept(measured)/kept(idle): 0.989 1.001 0.986 1.001 0.990 0.983 range 0.983-1.001 | lost/lost: 1.117 0.998 1.168 1.020 1.106 1.192 range 0.998-1.192 k= 9 kept(measured)/kept(idle): 0.969 0.974 0.974 0.985 0.977 0.963 range 0.963-0.985 | lost/lost: 1.096 1.075 1.078 1.045 1.060 1.109 range 1.045-1.109 k=27 kept(measured)/kept(idle): 0.952 0.961 0.930 0.920 0.969 0.990 range 0.920-0.990 | lost/lost: 1.018 1.017 1.025 1.024 1.009 1.001 range 1.001-1.025 Summary ratios (cost = measurement / same span of idle; idle fitted to 10-30 us, measured length): k <= 9, kept/kept, low end 0.9767 k <= 9, kept/kept, high end 1.026 k <= 9, lost/lost, low end 0.9449 [k=3 alone is far above 1: loss is tiny at k=3, ratio unstable] k <= 9, lost/lost, high end 1.295 k = 9 only, lost/lost range, low end 0.9466 k = 9 only, lost/lost range, high end 1 k = 27, lost/lost, low end 1.016 [six single jobs] k = 27, lost/lost, high end 1.169 k = 27 lost/lost, mean of day 1 (3 jobs) 1.072 k = 27 lost/lost, mean of day 2 (3 jobs) 1.099 k = 27 kept/kept, day 1 (3 jobs) 0.8603 k = 27 kept/kept, day 2 at its own measured length (3 jobs) 0.8149 k = 27, 1 / (kept ratio), mean of day 1 1.172 k = 27, 1 / (kept ratio), mean of day 2 1.247 k = 27, NO fitted curve (idle read off measured windows), kept/kept, low 1.008 [model-free reading] k = 27, NO fitted curve, kept/kept, high 1.099 k = 27, NO fitted curve, lost/lost, mean of six 0.9869 Direct check with no fit: coherence kept after 60 us of laid idle vs after k = 60/L measurements (k read between measured points): 2026-10-04 run 341 k=25.8: measured/idle (1,2,3+ links) 1.039 1.130 1.056 mean 1.075 2026-10-04 run 342 k=25.8: measured/idle (1,2,3+ links) 0.984 1.143 1.157 mean 1.095 2026-10-04 run 343 k=25.8: measured/idle (1,2,3+ links) 1.084 1.010 1.144 mean 1.079 2026-10-06 run 761 k=25.0: measured/idle (1,2,3+ links) 1.151 1.154 0.976 mean 1.093 2026-10-06 run 762 k=25.0: measured/idle (1,2,3+ links) 1.163 1.219 1.125 mean 1.169 2026-10-06 run 763 k=25.0: measured/idle (1,2,3+ links) 1.209 1.239 1.095 mean 1.181 B. ibm_fez, 11 October, three jobs: run 901 = IBM job db5ukk4lf4us73c4j3gg, run 902 = IBM job db5vhnamb58s738b2n50, run 903 = IBM job db5vk14vf2bc73d0fs80 (curve fits are re-run here from the stored per-qubit levels; the shot-level widths are read from the file) shape exponent b per job (measured qubit | spectators): run 901: 0.829 | 1.296 (stored fit values 0.829 | 1.296; per-fit bootstrap widths +-0.007 | +-0.080) run 902: 0.809 | 1.433 (stored fit values 0.809 | 1.433; per-fit bootstrap widths +-0.009 | +-0.078) run 903: 0.832 | 1.415 (stored fit values 0.832 | 1.415; per-fit bootstrap widths +-0.009 | +-0.081) measured-qubit exponent, mean of 3 jobs 0.8232 its width (sample SD of 3 jobs) 0.01218 [n = 3, a spread of three numbers] spectator exponent, mean of 3 jobs 1.381 its width (sample SD of 3 jobs) 0.07429 [n = 3] separation of the two, in combined widths 7.411 [divides by the spread of single jobs] measured qubit below a plain exponential, widths 14.51 spectators above a plain exponential, widths 5.131 same separation using the uncertainty OF THE MEAN (SD/sqrt3) 12.84 chi2/dof per job: measured qubit 0.72 / 1.38 / 1.32 spectators 1.12 / 0.66 / 1.35 measured qubit chi2/dof (three jobs) 0.72 / 1.38 / 1.32 spectators chi2/dof (three jobs) 1.12 / 0.66 / 1.35 worst of the six chi2/dof 1.38 run-structure p, measured qubit (three jobs) 0.88/0.97/0.30 run-structure p, spectators (three jobs) 0.93/1.00/0.15 (the third arm of each job, a no-measurement control with 5 points, is not one of the six fits and does not fit: stored chi2/dof 22.8 / 32.2 / 28.2) cross-check of the single-fit widths of b by redrawing each point from its stored width (60 draws): run 901 measured qubit: spread 0.011 (shot-level bootstrap 0.007) run 901 spectators : spread 0.073 (shot-level bootstrap 0.080) run 902 measured qubit: spread 0.010 (shot-level bootstrap 0.009) run 902 spectators : spread 0.065 (shot-level bootstrap 0.078) run 903 measured qubit: spread 0.011 (shot-level bootstrap 0.009) run 903 spectators : spread 0.061 (shot-level bootstrap 0.081) measured-qubit levels (job 1, run 901): level on the F0-F1 axis after 1 measurement 0.9649 level after 128 measurements 0.067 level after 40 us of plain idle (same job, same bits) 0.661 number of measurements at which level = 1/2 (job 1) 25.45 [straight line between the 24 and 32 points] the same crossing in jobs 2 and 3: 22.6 and 23.9 level after 1 / 128 measurements / 40 us idle, all three jobs: run 901: 0.9649 / 0.0670 / 0.6610 run 902: 0.9551 / 0.0552 / 0.6228 run 903: 0.9637 / 0.0602 / 0.6467 EQUAL-TIME COMPARISON? 128 measurements x 1.66 us stated length = 212 us, not 40 us. time taken by 128 measurements (stated length), us 212.5 [the 40 us idle arm is 5x shorter] equal-time pairs in the same job (measured qubit; k measurements vs an idle of k x stated length): k= 6 ( 10.0 us) vs idle 10 us: 0.826 vs 0.879 0.799 vs 0.853 0.816 vs 0.874 (3 jobs: measured | idle) k=12 ( 19.9 us) vs idle 20 us: 0.694 vs 0.796 0.669 vs 0.752 0.677 vs 0.781 (3 jobs: measured | idle) k=24 ( 39.8 us) vs idle 40 us: 0.517 vs 0.661 0.481 vs 0.623 0.498 vs 0.647 (3 jobs: measured | idle) at equal time (24 meas. ~ 40 us), idle minus measured, job 1 0.1443 [measuring costs more than idling at equal time, with the stated length]