The spike fit between two samples

# Self-authored for the EML case corpus (no external origin). The utilisation
# gauge stayed under its ceiling for the whole hour, and every sample it took was
# real. How often it samples, against how long the spike lasted, is computed
# below.
#
# The gauge is honest. It reads a real utilisation counter, not a model; every
# sample is kept, none discarded; the ceiling is checked against each sample;
# and the sixty samples an hour are on a chart anyone can read.
#
# It samples once every sixty seconds, and the spike lasted twenty.

60 => sample_interval_seconds
20 => spike_duration_seconds
15 => seconds_after_a_sample_the_spike_began
9000 => requests_dropped_during_the_spike
0 => samples_that_landed_during_the_spike
3600 => seconds_in_the_hour

int(seconds_in_the_hour / sample_interval_seconds) => samples_in_the_hour
seconds_after_a_sample_the_spike_began + spike_duration_seconds => second_within_the_minute_the_spike_ended
sample_interval_seconds - second_within_the_minute_the_spike_ended => seconds_of_quiet_after_it_before_the_next_sample

"sample interval                 : " + str(sample_interval_seconds) + " seconds" ^0
"samples in the hour             : " + str(samples_in_the_hour) ^0
"spike duration                  : " + str(spike_duration_seconds) + " seconds" ^0
"  began after a sample at       : " + str(seconds_after_a_sample_the_spike_began) + " seconds" ^0
"  ended at second               : " + str(second_within_the_minute_the_spike_ended) ^0
"  quiet before the next sample  : " + str(seconds_of_quiet_after_it_before_the_next_sample) + " seconds" ^0
"samples during the spike        : " + str(samples_that_landed_during_the_spike) ^0
"requests dropped in the spike   : " + str(requests_dropped_during_the_spike) ^0
"" ^0

# ---- what the gauge verified ----

"the utilisation gauge" ^0
"  reads : a real counter, not a model" ^0
"  samples kept : all of them" ^0
"  ceiling : checked against each sample" ^0
"  visibility : sixty samples an hour on a chart" ^0
"  samples over the ceiling : 0" ^0
"  verdict : UNDER THE CEILING" ^0
"" ^0
"  keeping every sample rather than pre-averaging is the" ^0
"  part done right here, and it is why a sustained climb" ^0
"  would show" ^0
"" ^0

# ---- what falls between samples ----

"the twenty seconds nobody sampled" ^0
"  the spike : began at second " + str(seconds_after_a_sample_the_spike_began) + ", ended at " ^0
"    " + str(second_within_the_minute_the_spike_ended) + ", inside one sample interval" ^0
"  the sample before it : taken at second 0, quiet" ^0
"  the sample after it : taken at second 60, quiet again" ^0
"  samples that saw it : " + str(samples_that_landed_during_the_spike) ^0
"  what the chart shows there : two calm readings and a" ^0
"    straight line between them" ^0
"" ^0

# ---- what the spike did, unseen ----

"the spike itself" ^0
"  requests dropped : " + str(requests_dropped_during_the_spike) ^0
"  the gauge's maximum for the hour : a calm sample" ^0
"  is any sample wrong : no; each was real and under the" ^0
"    ceiling" ^0
"  did the ceiling hold : unknown; the gauge never looked" ^0
"    when it mattered" ^0
"  is the peak the maximum sample : only if a sample" ^0
"    coincided with the peak" ^0
"" ^0

# ---- null control ----

# The same hour, with the counter reporting its own max-since-last-read at each
# sample instead of an instantaneous value.
0 => nc_samples_during_the_spike
1 => nc_samples_that_would_report_the_peak
9000 => nc_dropped_requests_it_would_reveal

"null control - report max-since-last-read, not instantaneous" ^0
"  samples during the spike : " + str(nc_samples_during_the_spike) + ", still zero" ^0
"  samples that would report the peak : " ^0
"    " + str(nc_samples_that_would_report_the_peak) ^0
"  dropped requests it would reveal : " ^0
"    " + str(nc_dropped_requests_it_would_reveal) ^0
"  no request and no interval changed; each sample stopped" ^0
"  being a single instant and started summarizing the gap" ^0
"" ^0

# ---- the rule ----

"what an hour under the ceiling guarantees" ^0
"  no sample the gauge took exceeded the ceiling : exactly," ^0
"    every sample kept and checked" ^0
"  the peak was within limits : not addressed; the gauge is" ^0
"    polled every 60s and the spike lasted 20s between two" ^0
"    polls - " + str(samples_that_landed_during_the_spike) + " samples saw it while " + str(requests_dropped_during_the_spike) + " requests" ^0
"    were dropped" ^0
"" ^0

"a sample is a fact about an instant, and a maximum over samples is a fact about" ^0
"those instants, not about the moments between them; an event shorter than the" ^0
"interval lives entirely in the gaps the gauge does not measure" ^0
"" ^0

"It reads a real counter, keeps every sample, and checks each against the" ^0
"ceiling - none over. It polls every 60s and the spike lasted 20s between two" ^0
"polls, so " + str(samples_that_landed_during_the_spike) + " samples caught it while " + str(requests_dropped_during_the_spike) + " requests were dropped in the" ^0
"gap the gauge never looked at." ^0

sample_interval_seconds = 60
spike_duration_seconds = 20
seconds_after_a_sample_the_spike_began = 15
requests_dropped_during_the_spike = 9000
samples_that_landed_during_the_spike = 0
seconds_in_the_hour = 3600
samples_in_the_hour = int(seconds_in_the_hour / sample_interval_seconds)
second_within_the_minute_the_spike_ended = seconds_after_a_sample_the_spike_began + spike_duration_seconds
seconds_of_quiet_after_it_before_the_next_sample = sample_interval_seconds - second_within_the_minute_the_spike_ended
print("sample interval                 : " + str(sample_interval_seconds) + " seconds")
print("samples in the hour             : " + str(samples_in_the_hour))
print("spike duration                  : " + str(spike_duration_seconds) + " seconds")
print("  began after a sample at       : " + str(seconds_after_a_sample_the_spike_began) + " seconds")
print("  ended at second               : " + str(second_within_the_minute_the_spike_ended))
print("  quiet before the next sample  : " + str(seconds_of_quiet_after_it_before_the_next_sample) + " seconds")
print("samples during the spike        : " + str(samples_that_landed_during_the_spike))
print("requests dropped in the spike   : " + str(requests_dropped_during_the_spike))
print("")
print("the utilisation gauge")
print("  reads : a real counter, not a model")
print("  samples kept : all of them")
print("  ceiling : checked against each sample")
print("  visibility : sixty samples an hour on a chart")
print("  samples over the ceiling : 0")
print("  verdict : UNDER THE CEILING")
print("")
print("  keeping every sample rather than pre-averaging is the")
print("  part done right here, and it is why a sustained climb")
print("  would show")
print("")
print("the twenty seconds nobody sampled")
print("  the spike : began at second " + str(seconds_after_a_sample_the_spike_began) + ", ended at ")
print("    " + str(second_within_the_minute_the_spike_ended) + ", inside one sample interval")
print("  the sample before it : taken at second 0, quiet")
print("  the sample after it : taken at second 60, quiet again")
print("  samples that saw it : " + str(samples_that_landed_during_the_spike))
print("  what the chart shows there : two calm readings and a")
print("    straight line between them")
print("")
print("the spike itself")
print("  requests dropped : " + str(requests_dropped_during_the_spike))
print("  the gauge's maximum for the hour : a calm sample")
print("  is any sample wrong : no; each was real and under the")
print("    ceiling")
print("  did the ceiling hold : unknown; the gauge never looked")
print("    when it mattered")
print("  is the peak the maximum sample : only if a sample")
print("    coincided with the peak")
print("")
nc_samples_during_the_spike = 0
nc_samples_that_would_report_the_peak = 1
nc_dropped_requests_it_would_reveal = 9000
print("null control - report max-since-last-read, not instantaneous")
print("  samples during the spike : " + str(nc_samples_during_the_spike) + ", still zero")
print("  samples that would report the peak : ")
print("    " + str(nc_samples_that_would_report_the_peak))
print("  dropped requests it would reveal : ")
print("    " + str(nc_dropped_requests_it_would_reveal))
print("  no request and no interval changed; each sample stopped")
print("  being a single instant and started summarizing the gap")
print("")
print("what an hour under the ceiling guarantees")
print("  no sample the gauge took exceeded the ceiling : exactly,")
print("    every sample kept and checked")
print("  the peak was within limits : not addressed; the gauge is")
print("    polled every 60s and the spike lasted 20s between two")
print("    polls - " + str(samples_that_landed_during_the_spike) + " samples saw it while " + str(requests_dropped_during_the_spike) + " requests")
print("    were dropped")
print("")
print("a sample is a fact about an instant, and a maximum over samples is a fact about")
print("those instants, not about the moments between them; an event shorter than the")
print("interval lives entirely in the gaps the gauge does not measure")
print("")
print("It reads a real counter, keeps every sample, and checks each against the")
print("ceiling - none over. It polls every 60s and the spike lasted 20s between two")
print("polls, so " + str(samples_that_landed_during_the_spike) + " samples caught it while " + str(requests_dropped_during_the_spike) + " requests were dropped in the")
print("gap the gauge never looked at.")

sample interval                 : 60 seconds
samples in the hour             : 60
spike duration                  : 20 seconds
  began after a sample at       : 15 seconds
  ended at second               : 35
  quiet before the next sample  : 25 seconds
samples during the spike        : 0
requests dropped in the spike   : 9000

the utilisation gauge
  reads : a real counter, not a model
  samples kept : all of them
  ceiling : checked against each sample
  visibility : sixty samples an hour on a chart
  samples over the ceiling : 0
  verdict : UNDER THE CEILING

  keeping every sample rather than pre-averaging is the
  part done right here, and it is why a sustained climb
  would show

the twenty seconds nobody sampled
  the spike : began at second 15, ended at 
    35, inside one sample interval
  the sample before it : taken at second 0, quiet
  the sample after it : taken at second 60, quiet again
  samples that saw it : 0
  what the chart shows there : two calm readings and a
    straight line between them

the spike itself
  requests dropped : 9000
  the gauge's maximum for the hour : a calm sample
  is any sample wrong : no; each was real and under the
    ceiling
  did the ceiling hold : unknown; the gauge never looked
    when it mattered
  is the peak the maximum sample : only if a sample
    coincided with the peak

null control - report max-since-last-read, not instantaneous
  samples during the spike : 0, still zero
  samples that would report the peak : 
    1
  dropped requests it would reveal : 
    9000
  no request and no interval changed; each sample stopped
  being a single instant and started summarizing the gap

what an hour under the ceiling guarantees
  no sample the gauge took exceeded the ceiling : exactly,
    every sample kept and checked
  the peak was within limits : not addressed; the gauge is
    polled every 60s and the spike lasted 20s between two
    polls - 0 samples saw it while 9000 requests
    were dropped

a sample is a fact about an instant, and a maximum over samples is a fact about
those instants, not about the moments between them; an event shorter than the
interval lives entirely in the gaps the gauge does not measure

It reads a real counter, keeps every sample, and checks each against the
ceiling - none over. It polls every 60s and the spike lasted 20s between two
polls, so 0 samples caught it while 9000 requests were dropped in the
gap the gauge never looked at.

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