# Example 856 — The first seen was read as the first time `the_first_seen_was_read_as_the_first_time.eml` - A cohort report counts accounts acquired in the first month, and it reads the earliest recorded activity for every account correctly. What the earliest record actually marks is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A cohort report # counts accounts acquired in the first month, and it reads the earliest recorded # activity for every account correctly. What the earliest record actually marks is # computed below. # # The measurement is careful. It reads the real earliest recorded timestamp, not # an estimate; it covers every account; it takes the true minimum; and the intent # is exactly 'when did the account first become active'. # # Logging began on the window's first day, and any activity before then was never # recorded, so a pre-existing account's earliest record is the window start, not # its real first activity. 500000 => accounts 40000 => truly_first_active_in_month_one 200000 => pre_existing_clamped_to_window_start truly_first_active_in_month_one + pre_existing_clamped_to_window_start => counted_as_new_by_first_seen truly_first_active_in_month_one => truly_new_in_month_one counted_as_new_by_first_seen - truly_new_in_month_one => spurious_new_accounts int(spurious_new_accounts * 10000 / counted_as_new_by_first_seen) => spurious_share_per_myriad "accounts : " + str(accounts) ^0 " truly first active in month 1 : " + str(truly_first_active_in_month_one) ^0 " pre-existing, clamped to day 1 : " + str(pre_existing_clamped_to_window_start) ^0 "" ^0 "counted as new by first-seen : " + str(counted_as_new_by_first_seen) ^0 "truly new in month 1 : " + str(truly_new_in_month_one) ^0 "spurious new accounts : " + str(spurious_new_accounts) ^0 "spurious share of the count : " + str(spurious_share_per_myriad) + " per ten thousand" ^0 "" ^0 # ---- what the measurement verified ---- "the acquisition count" ^0 " reads : the real earliest recorded timestamp" ^0 " covers : every account" ^0 " takes : the true minimum of the recorded times" ^0 " intent : when did the account first become active" ^0 " accounts omitted : 0" ^0 " verdict : 240000 ACCOUNTS FIRST SEEN IN MONTH 1" ^0 "" ^0 " taking the real minimum recorded time over every account" ^0 " is the part done right here, and it is why a genuinely" ^0 " new account's first-seen is exact" ^0 "" ^0 # ---- what the earliest record marks ---- "the earliest recorded activity" ^0 " when logging began : the window's first day" ^0 " activity before that : happened, but was never recorded" ^0 " so a pre-existing account's minimum record : is the" ^0 " window start, not its real first activity" ^0 " what first-seen therefore marks : the observation" ^0 " boundary, for anyone older than it" ^0 " the tell : 200000 accounts share the exact first-day" ^0 " timestamp" ^0 "" ^0 # ---- what the caller got ---- "the result of the cohort report" ^0 " accounts it calls new : " + str(counted_as_new_by_first_seen) ^0 " accounts that are actually new : " + str(truly_new_in_month_one) ^0 " pre-existing accounts counted as new : " + str(spurious_new_accounts) ^0 " is the minimum computed wrong : no; it is the true min of" ^0 " what was recorded" ^0 " is first-seen the first time : no; the record starts at" ^0 " the window, and everything earlier is left-censored" ^0 "" ^0 # ---- null control ---- # The same data, with accounts whose first-seen equals the window start treated as # left-censored (true start unknown), or joined to an out-of-window creation date. 200000 => nc_clamped_accounts_counted_as_new_before 0 => nc_clamped_accounts_counted_as_new_after 40000 => nc_accounts_that_remain_genuinely_new "null control - treat first-seen on day 1 as censored, not as new" ^0 " clamped accounts counted as new, before : " + str(nc_clamped_accounts_counted_as_new_before) ^0 " clamped accounts counted as new, after : " + str(nc_clamped_accounts_counted_as_new_after) ^0 " accounts that remain genuinely new : " + str(nc_accounts_that_remain_genuinely_new) ^0 " no account and no timestamp changed; the first-day pile-up" ^0 " stopped being read as an acquisition date and started" ^0 " being read as the edge of the record" ^0 "" ^0 # ---- the rule ---- "what an earliest-recorded-activity count guarantees" ^0 " it is the true minimum of the recorded timestamps :" ^0 " exactly, real times, every account, honest min" ^0 " it is when the account first became active : not" ^0 " addressed; logging began at the window start, so a pre-" ^0 " existing account's minimum is that boundary - " + str(spurious_new_accounts) + " old" ^0 " accounts are counted as new" ^0 "" ^0 "the first record is the first time you were watching, not the first time it" ^0 "happened; everything before the window collapses onto the window's edge, and a" ^0 "minimum taken there measures when observation started, not when the thing did" ^0 "" ^0 "It takes the true minimum recorded time over every account - a genuinely new" ^0 "account is dated exactly. But logging began at the window start, so " + str(pre_existing_clamped_to_window_start) ^0 "pre-existing accounts pile onto day 1 and are counted as new; " + str(spurious_share_per_myriad) + " per ten" ^0 "thousand of the acquisition count is left-censoring, until day-1 is read as censored." ^0 ``` ## Python (deterministic transpilation) ```python accounts = 500000 truly_first_active_in_month_one = 40000 pre_existing_clamped_to_window_start = 200000 counted_as_new_by_first_seen = truly_first_active_in_month_one + pre_existing_clamped_to_window_start truly_new_in_month_one = truly_first_active_in_month_one spurious_new_accounts = counted_as_new_by_first_seen - truly_new_in_month_one spurious_share_per_myriad = int(spurious_new_accounts * 10000 / counted_as_new_by_first_seen) print("accounts : " + str(accounts)) print(" truly first active in month 1 : " + str(truly_first_active_in_month_one)) print(" pre-existing, clamped to day 1 : " + str(pre_existing_clamped_to_window_start)) print("") print("counted as new by first-seen : " + str(counted_as_new_by_first_seen)) print("truly new in month 1 : " + str(truly_new_in_month_one)) print("spurious new accounts : " + str(spurious_new_accounts)) print("spurious share of the count : " + str(spurious_share_per_myriad) + " per ten thousand") print("") print("the acquisition count") print(" reads : the real earliest recorded timestamp") print(" covers : every account") print(" takes : the true minimum of the recorded times") print(" intent : when did the account first become active") print(" accounts omitted : 0") print(" verdict : 240000 ACCOUNTS FIRST SEEN IN MONTH 1") print("") print(" taking the real minimum recorded time over every account") print(" is the part done right here, and it is why a genuinely") print(" new account's first-seen is exact") print("") print("the earliest recorded activity") print(" when logging began : the window's first day") print(" activity before that : happened, but was never recorded") print(" so a pre-existing account's minimum record : is the") print(" window start, not its real first activity") print(" what first-seen therefore marks : the observation") print(" boundary, for anyone older than it") print(" the tell : 200000 accounts share the exact first-day") print(" timestamp") print("") print("the result of the cohort report") print(" accounts it calls new : " + str(counted_as_new_by_first_seen)) print(" accounts that are actually new : " + str(truly_new_in_month_one)) print(" pre-existing accounts counted as new : " + str(spurious_new_accounts)) print(" is the minimum computed wrong : no; it is the true min of") print(" what was recorded") print(" is first-seen the first time : no; the record starts at") print(" the window, and everything earlier is left-censored") print("") nc_clamped_accounts_counted_as_new_before = 200000 nc_clamped_accounts_counted_as_new_after = 0 nc_accounts_that_remain_genuinely_new = 40000 print("null control - treat first-seen on day 1 as censored, not as new") print(" clamped accounts counted as new, before : " + str(nc_clamped_accounts_counted_as_new_before)) print(" clamped accounts counted as new, after : " + str(nc_clamped_accounts_counted_as_new_after)) print(" accounts that remain genuinely new : " + str(nc_accounts_that_remain_genuinely_new)) print(" no account and no timestamp changed; the first-day pile-up") print(" stopped being read as an acquisition date and started") print(" being read as the edge of the record") print("") print("what an earliest-recorded-activity count guarantees") print(" it is the true minimum of the recorded timestamps :") print(" exactly, real times, every account, honest min") print(" it is when the account first became active : not") print(" addressed; logging began at the window start, so a pre-") print(" existing account's minimum is that boundary - " + str(spurious_new_accounts) + " old") print(" accounts are counted as new") print("") print("the first record is the first time you were watching, not the first time it") print("happened; everything before the window collapses onto the window's edge, and a") print("minimum taken there measures when observation started, not when the thing did") print("") print("It takes the true minimum recorded time over every account - a genuinely new") print("account is dated exactly. But logging began at the window start, so " + str(pre_existing_clamped_to_window_start)) print("pre-existing accounts pile onto day 1 and are counted as new; " + str(spurious_share_per_myriad) + " per ten") print("thousand of the acquisition count is left-censoring, until day-1 is read as censored.") ``` ## stdout (executed) ```text accounts : 500000 truly first active in month 1 : 40000 pre-existing, clamped to day 1 : 200000 counted as new by first-seen : 240000 truly new in month 1 : 40000 spurious new accounts : 200000 spurious share of the count : 8333 per ten thousand the acquisition count reads : the real earliest recorded timestamp covers : every account takes : the true minimum of the recorded times intent : when did the account first become active accounts omitted : 0 verdict : 240000 ACCOUNTS FIRST SEEN IN MONTH 1 taking the real minimum recorded time over every account is the part done right here, and it is why a genuinely new account's first-seen is exact the earliest recorded activity when logging began : the window's first day activity before that : happened, but was never recorded so a pre-existing account's minimum record : is the window start, not its real first activity what first-seen therefore marks : the observation boundary, for anyone older than it the tell : 200000 accounts share the exact first-day timestamp the result of the cohort report accounts it calls new : 240000 accounts that are actually new : 40000 pre-existing accounts counted as new : 200000 is the minimum computed wrong : no; it is the true min of what was recorded is first-seen the first time : no; the record starts at the window, and everything earlier is left-censored null control - treat first-seen on day 1 as censored, not as new clamped accounts counted as new, before : 200000 clamped accounts counted as new, after : 0 accounts that remain genuinely new : 40000 no account and no timestamp changed; the first-day pile-up stopped being read as an acquisition date and started being read as the edge of the record what an earliest-recorded-activity count guarantees it is the true minimum of the recorded timestamps : exactly, real times, every account, honest min it is when the account first became active : not addressed; logging began at the window start, so a pre- existing account's minimum is that boundary - 200000 old accounts are counted as new the first record is the first time you were watching, not the first time it happened; everything before the window collapses onto the window's edge, and a minimum taken there measures when observation started, not when the thing did It takes the true minimum recorded time over every account - a genuinely new account is dated exactly. But logging began at the window start, so 200000 pre-existing accounts pile onto day 1 and are counted as new; 8333 per ten thousand of the acquisition count is left-censoring, until day-1 is read as censored. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done