Implementation Notes#

Status: Draft, 2026-08-20. Built from products/cancer/technical-notes.md; the product it implements is specified in product-spec.md. Both state their deltas against the third-sector chassis, medical insurance (iryō hoken, 医療保険): its product specification, its technical notes, and the model that implements them, Medical_JP_S. This model carries that model’s names for every shared concept.

This is a mechanics demonstration, not a pricing or reserving result. The contractual mechanics are sourced: the 90-day waiting period as a hard zero, the two-year repeat cycle measured from the previous payment trigger, 上皮内新生物 (jōhinai shinseibutsu, carcinoma in situ) as a separate once-only tier that does not trigger the premium waiver, the absence of any day limit and of any surrender value, and the waiver on the first invasive diagnosis. The incidence basis is sourced too, which makes this product an exception in jplib: 全国がん登録 (zenkoku gan tōroku, the national cancer registry) publishes incidence rates (rikanritsu, 罹患率) by five-year age band, freely R5 REG-R29. Everything else is std — the sex split of that basis, the post-diagnosis survival model, the relapse hazard, the care frequencies, the expense scale and the premium itself. No carrier publishes a rate table for a cancer main contract, the statement of the method of calculating premiums and reserves (sanshutsu hōhō-sho, 算出方法書) is not published REG-R2, and third-sector (dai-san-bun’ya, 第三分野) business has no standard incidence table and no reference pure premium to fall back on R3. Replace the assumption tables with company data before drawing any conclusion from the numbers.

Run it#

python products/cancer/run.py            # the anchor cell
python products/cancer/run.py 4          # another model point

Three lines to the same thing:

import modelx as mx
model = mx.read_model("products/cancer/Cancer_JP_S")
model.Projection[1].result_cf()

Projection takes a point_id; Projection[1] is the worked-example anchor cell. result_cf() returns a DataFrame indexed by policy month t with one column per cash flow line, and result_pols() the policy counts, rates and ledgers. model.doc describes the product and the projection basis; model.Projection.doc holds the full mapping from the technical notes’ symbols to the cells names.

Three states, not one — the structural contrast with the chassis#

Medical_JP_S projects a single in-force population and reads a hospitalization incidence off it. A cancer model cannot. The diagnosis benefit repeats on a two-year cycle, the inpatient benefit has no day limit, and the treatment benefit pays by the month — so all three run on how long the insured lives after diagnosis. Cancer_JP_S therefore carries pols_healthy (never diagnosed), pols_locked (diagnosed, inside the cycle) and pols_open (diagnosed, eligible again), and needs a post-diagnosis survival basis as well as an incidence basis. check_cancer_roll_fwd() asserts that the two diagnosed recursions collapse to the single line pols_cancer(t+1) = (pols_cancer(t) + diag_first(t)) × sc(t), which is where an off-by-one in the delay shows up and nowhere else in the in-force figures.

Four things the third-sector chassis has are absent here, as product facts:

no L1 and no LA — no per-hospitalization day ledger and no lifetime aggregate (tsūsan, 通算) day ledger [S1] [S3] R11. What replaces them is a 60-month ledger on the treatment benefit, a ledger on months, not days;
no benefit-driven termination — paying the diagnosis lump sum neither terminates nor exhausts the contract [S1], so the in-force roll-forward has two ways out;
no cv_pp and no 自動振替貸付 (jidō furikae kashitsuke, automatic premium loan) — the composite is 無解約払戻金型 at every duration under 終身払 [S7] [S10] [S11], so there is nothing to lend against and a missed premium really does lapse the policy;
no claims_death — the composite carries no death benefit [S1], so mortality is a pure liability-releasing decrement.

The cycle is a delay on the trigger history, not a rate#

A life that has just been paid cannot be paid again for C = 24 months; after that it can, on a fresh relapse (saihatsu, 再発), metastasis (ten’i, 転移) or new primary, without limit [S5] [S7] [S10]. That clock is keyed to an event — the previous payment trigger — so unlock(t) is the trigger cohort of month t − C carried forward on diagnosed decrements alone, and not a release rate applied to a stock. Two consequences are easy to get wrong and both are pinned by tests. unlock reads trig, which is first diagnoses and repeats: reading it off diag_first would let every repeat payment escape the lock. And the clock is emphatically not the medical chassis’s 180-day one-hospitalization memory — different length, different trigger (a payment, not a discharge), different consequence (eligibility, not grouping) [S5] [S1]. check_cycle_ledger() rebuilds pols_locked straight off the trigger vector with no reference to the unlock recursion.

上皮内新生物 is a second benefit tier, not a discount on the first#

insitu_ev attaches to pols_healthy alone and carries its own once-only ledger, insitu_avail. It does not move the life into the diagnosed state, does not start the cycle and does not trigger the waiver [S6] [S11] [S7] [S10]. Implementing it as insitu_pct × claims_diag inside the main diagnosis benefit gets the amount right and the cap, the cycle and the waiver all wrong. The three sourced treatments of in-situ disease — full rate, half rate and 10% — are one model-point parameter, insitu_pct.

An in-situ diagnosis pays the reduced lump sum and the surgery benefit in full, and nothing continuing std. The rationale is a data fact rather than a convenience: the sourced estimated patient counts (suikei kanjasū, 推計患者数) and mean length of stay (heikin zaiin nissū, 平均在院日数) are for malignant neoplasm (akusei shinseibutsu, 悪性新生物) and do not measure in-situ exposure R7, so attaching the invasive frequencies to in-situ lives would credit them with an exposure no retrieved statistic observes. The direction of the error is stated: it understates the in-situ tier. check_insitu_ledger() asserts that benefit paid plus availability remaining is one, reading the paid side off the published claim line rather than off the recursion, so the identity cannot close by construction.

Two ledgers that are per diagnosed life, not per block#

treat_months counts against the 60-month cap and adv_paid against the ¥20,000,000 advanced medicine (senshin iryō, 先進医療) cap, and both measure what an individual has consumed. Diagnosed lives enter at different times, so each is carried as a cohort average diluted by new entrants — and only by diag_first, because a repeat trigger is an already-diagnosed life whose ledger continues. Weighting either by pols_cancer would measure the block’s consumption and defer the cap forever; diluting with diag_rep would reset a ledger that should keep running.

The direction of the approximation is stated rather than discovered: E[min(Σ, K)] ≠ min(E[Σ], K), so a deterministic average understates the cap’s bite. That matters more here than on the medical chassis, because the 60-month cap is reached by a real minority rather than never — treat_prob and the diagnosed-state duration give an expected 12.98 qualifying months against it [S5] [S11]. The ledgers read small at the anchor cell (M(12) = 0.4002 months, V(12) = ¥2,401.31) and are not therefore deletable: model point 4 carries a twelve-month cap that binds for more than four hundred months of its projection.

Monthly, and monthly by construction#

Three mechanics are monthly by construction rather than by approximation: the 90-day waiting period is three months of the grid, the treatment benefit’s unit of payment is the calendar month [S5] [S10] [S11], and the premium mode is monthly (getsubarai, 月払) throughout the composite [S1] [S6] [S11] [S12]. t is the policy month, and proj_len() = 12 × (omega_age − x + 1) — 924 months on the anchor cell, running to the terminal age of 第三分野標準生命表2018, 116 male and 118 female REG-R18 REG-R20. A diagnosis arising in month t pays its lump sum in month t and the life enters the diagnosed state at the end of that month, so the four continuing benefits begin at t + 1 std.

Inputs are external files#

The seven input CSVs live in this directory, beside run.py — not inside the model folder. Cancer_JP_S/ holds nothing but formulas:

products/cancer/
  model_point_table.csv        <- inputs live here
  mort_table.csv               incidence_table.csv
  sex_factor_table.csv         survival_table.csv
  lapse_table.csv              hosp_stay_table.csv
  run.py
  model.md  product-spec.md  technical-notes.md  sources.md
  Cancer_JP_S/                 <- formulas only
    __init__.py  _system.json
    Data/__init__.py           (reads the CSVs, once per model)
    Projection/__init__.py     (the by-policy projection)

File	Contents	Provenance
`model_point_table.csv`	Eight points. Point 1 is the worked-example anchor cell; 2–8 exercise the female limb and the 118 terminal age, the 定期 flag with conditioned repeats, a cap that binds with no 先進医療 rider, both ends of the 20–75 issue-age range, 65歳払済, a no-waiver design, and the がん退院一時金 rider	std throughout — every premium in it is a modelling value, because no rate table for this product is public REG-R2 R3
`mort_table.csv`	第三分野標準生命表2018 proxy by sex, male ages 20–116 and female 20–118	std library-wide construction: the quoted rates — 男 q(40) = 0.00076 among them — graduated log-linearly between anchors R1 REG-R18 REG-R19 REG-R20; not a copy REG-R21
`incidence_table.csv`	罹患率 per 100,000 by five-year age band, both sexes, all sites C00–C96, 2023	Sourced and reproduced verbatim with its attribution R5 REG-R29
`sex_factor_table.csv`	The two sourced male / both-sexes ratios, at band midpoints 37.5 and 72.5	Sourced R5; the interpolation between them is std
`survival_table.csv`	Five-year relative survival (go-nen sōtai seizonritsu, 5年相対生存率) by sex, 2018 diagnoses	Sourced R6 REG-R28
`lapse_table.csv`	Annual lapse by policy year, 9% grading to a 3% ultimate	std, shared unchanged with the medical chassis; anchored to the sourced 5.6% 解約・失効率 REG-R31
`hosp_stay_table.csv`	Mean stay for 悪性新生物 discharges: all-ages, and the four-band age gradient	Both sourced R7 REG-R27; which basis is read is a switch

Every row of every assumption table carries a provenance column saying which of these it is. The readers live on the Data Space, which takes no parameters, so each file is read once per model rather than once per model point, and Data.input_dir() resolves the directory from _model.path.parent at run time. The trade-off is that the model is not portable on its own: copy Cancer_JP_S/ without the CSVs and it reads fine, then fails on first evaluation. What that buys is a diff that shows logic changes only, and an input that can be swapped in place.

The mortality table is a construction, not a copy#

This is the one place where the library’s position has to be stated exactly. 第三分野標準生命表2018 is published by 日本アクチュアリー会 at a stable public URL, free and in full R1 REG-R18 REG-R19 — anyone can retrieve it and check a rate, a real contrast with uklib, where the CMI tables cannot be read at all without a subscription. But the publisher’s site terms prohibit reproduction, alteration and transmission to third parties without written consent REG-R21, so jplib must not ship a copy.

What is shipped instead is one std table for the whole library, built on the union of the individual rates jplib’s products quote and attribute: 22 anchor rows across the two sexes — 男 q(40) = 0.00076 among them, and the terminal rows 男 q(116) = 1.00000 and 女 q(118) = 1.00000 REG-R18 REG-R19 REG-R20 — graduated log-linearly (geometrically) between adjacent anchors, q(x) = q(a) × (q(b)/q(a))^((x−a)/(b−a)).

The graduation was chosen over the curve fits the products previously shipped independently for two reasons. It reproduces every anchor exactly, so nothing sourced is disturbed — which is the property the three incumbent fits all failed, and it is why nine products could publish the same sourced cell at values up to 34% apart. And it is locally the Gompertz family, which is the family the publisher itself uses at the older ages. The model therefore reproduces the quoted rates exactly and asserts nothing else about the published table; no conclusion about Japanese third-sector mortality follows from it beyond the anchored rates. The copy in this directory is cut to the ages this model can reach, male 20–116 and female 20–118: the composite’s 20–75 issue-age range run out to each sex’s terminal age. Drop a licensed extract in over the same schema — sex, age, mort_rate — and no formula changes.

incidence_table.csv is the opposite case, and the contrast is the point: the age-banded 罹患率 of 全国がん登録 are reproduced here verbatim with the attribution the dataset requires R5 REG-R29.

Modules that are off in the base run#

Eight of the notes’ optional constructions are implemented and held at an inert base value, so that the base run reproduces the worked example while the machinery stays visible and testable. lapse_canc_factor is the one whose base is inert rather than off.

Switch	Base	What it does
`void_adjust`	`False`	Scales `pols_if_init()` by `1 − void_prob()`, de-recognising the 0.037% of policies diagnosed inside the 90-day window — a de-recognition, not a decrement, so the premium already collected comes back with the future benefit. The acquisition expense and initial commission are deliberately not scaled: they were incurred [S1] [S5] [S10]
`sel_lapse_lambda`	`0.0`	Anti-selective lapse on the incidence basis, `1 + lam × max(0, w_cum − w_ref)`. Amplified here by the waiver: the healthiest lives are also the only ones still paying. No Japanese evidence was retrieved
`repeat_conditioned`	`False` (model point)	Multiplies the relapse hazard by `treat_prob`. Two of the three sourced two-year designs condition the repeat on being under treatment [S7] [S10], so the designs differ by an order of magnitude, not a rounding. True on point 3
`hosp_age_gradient`	`False`	Reads the sourced 35–64 / 65+ / 75+ mean-stay gradient instead of the all-ages 14.4 days R7 REG-R27. The base run takes the all-ages figure because the gradient has four broad bands and the incidence twenty-one narrow ones
`mort_age_offset`	`0.0`	Reads the mortality table at `age(t) + 0.5`, interpolating between rows: the table is built for a nearest-birthday age (hoken-nenrei hōshiki, 保険年齢方式) basis, so reading it at attained age with the fraction discarded (man-nenrei, 満年齢) understates the valuation age by about half a year R2 REG-R20
`net_of_cancer`	`False`	Nets the never-diagnosed baseline of `cancer_death_share` = 0.28 std, so cancer mortality inside the table’s own rates is not carried twice against the diagnosed excess hazard. 0.28 is a round placeholder with no observed range: no document in this product’s source set gives 悪性新生物’s share of all-cause Japanese mortality — REG-R28 publishes the cancer death count and no all-cause denominator — so the switch shows the capability, not a calibration
`renew_reprice_rate`	`0.0`	Steps the premium at each ten-year renewal on the 定期 chassis flag [S5] [S7]. Point 3 carries the flag with the rate at zero
`lapse_canc_factor`	`1.0`	Scales the diagnosed lapse rate off the healthy one. Inert wherever the waiver fires — a waived life has no premium to miss and no surrender value to take — so it reaches a cash flow only on the `waiver_trigger = "none"` and `"disability"` designs [S7] [S10] [S11]. Live on point 7

The 定期 flag deserves one further sentence, because what it does not do is the surprise: it projects to the same horizon as 終身, since the renewal is automatic and neither document states a maximum renewal age. What it changes is the premium — which would ordinarily close the contract boundary at each renewal. jplib records that tension rather than resolving it, exactly as the medical chassis does.

Two constructions the notes name are deliberately not implemented, and the absence is stated rather than left to inference. A duration-banded excess hazard needs cohort tracking by time since diagnosis that a three-state model does not carry; the flat hazard overstates late-duration mortality and therefore understates the long-survivor benefits, and a cure-fraction basis moves the liability one way only — up. And reinstatement (fukkatsu, 復活) enters as a new model point rather than as a negative lapse, because the waiting period re-runs from the 復活日 [S1] [S6]: a reinstated policy has 90 days of no cover in front of it, and a negative lapse would hand back cover the contract does not restore and delete an anti-selection control.

One divergence from the technical notes#

technical-notes.md carries disch_rider in its model point attribute table, but its cash-flow section defines seven claim lines and none of them is the cancer discharge lump sum (gan taiin ichijikin, がん退院一時金). product-spec.md does specify the benefit — ¥100,000 on discharge from a covered stay of ten or more consecutive days, unlimited count, with a 30-day re-payment bar [S1] [S2] — and puts it in scope. The model therefore supplies a std formula:

claims_discharge(t) = disch_mult × A × disch_qual_share × h × pols_cancer(t)

with disch_mult = 10 from the specification and disch_qual_share = 0.60 std, the share of cancer admissions whose stay reaches ten days. The 30-day re-payment bar is not modelled [std scope]: at 0.0208 admissions per diagnosed life-month the overlap is second-order. The rider is off on every model point but 8, so the worked example and the base run are untouched by it. This is the only cash flow in the model the notes do not define.

Sign convention#

The notes’ net_cf(t) is already income positive — premiums less claims, less expenses (acquisition and maintenance), less claim_expenses deducted explicitly, less commission — which is the library-wide sign, so there is no outgo-positive liability_cf companion to publish: one stream, one sign, one name.

The asymmetry that defines this product’s cash-flow signature sits inside that one line: premiums are weighted by pols_healthy and claims by pols_cancer, and the two are disjoint, because the waiver fires on the same first invasive diagnosis that starts every benefit [S10] [S11]. Weighting the premium by pols_if is the single largest arithmetic error available here — it overstates lifetime income by 6.1% at the anchor cell — and it is invisible in the first three months, because there the two are equal. pols_payer() is where the choice is made, and it is a product choice rather than a constant: on the waiver_trigger = "none" and "disability" designs the diagnosed keep paying and can lapse, which is why lapse_rate_canc_mth() is not simply zero either. Model point 7 runs both reversals.

Naming#

Cells names follow lifelib’s basiclife/BasicTerm_S wherever it has an analogue — pols_* for policy counts, plural nouns for cash flows, *_rate for annual rates and *_rate_mth for their monthly counterparts, claims(t, kind) with an uppercase kind string. The full notes-symbol-to-cells mapping lives in the Projection docstring, headed Notes symbol. Five cases needed care:

Notes	Cells	Why
`pols_open(t)`	`pols_open`	The population eligible for a repeat payment, not the population in payment; a fresh relapse is what converts eligibility into a payment
`insitu_ev(t)`, `Z(t)`	`insitu_ev` / `insitu_avail` / `insitu_used`	A second benefit tier with its own once-only ledger, on `pols_healthy` alone. `insitu_used` accumulates off the published claim line, not off the recursion, so `check_insitu_ledger` cannot close by construction
`M(t)`, `V(t)`	`treat_months` / `adv_paid`	Ledgers per diagnosed life, diluted only by `diag_first`. The names say months and yen, which is the dimensional check the treatment benefit needs
`w(t)` vs `w_cum(t)`	`lapse_rate_mth` / `lapse_cum`	`lapse_cum` is a proportion of the original cohort, not a running total of the rate, and the loading it feeds moves incidence, not lapse
(no symbol)	`claims(t, "LAPSE")`	Exists and returns zero: there is no surrender value at any duration under 終身払, so a lapse pays nothing. A column of zeros states the product fact where a missing column would hide it. There is no `claims_death` at all

Ten further names are fixed across all nine jplib products, so that one concept has one spelling in the library. This model carries them as follows:

Name	Means	Note
`pols_if_at(t, timing)`	The in-force count at `BEF_DECR` / `BEF_LAPSE` / `AFT_DECR`	`BEF_LAPSE` is the sum over the two states, each decremented on its own mortality basis, so a blended rate on `pols_if` does not reproduce it. What the vocabulary cannot show here is the movement that defines the product: the three timings are decrement timings and a first diagnosis is not a decrement, so `diag_first` changes which benefits and which premium a life carries while leaving `pols_if` identical at all three points. Read `pols_healthy`, `pols_cancer` and `diag_first` for the state movement — `pols_if_at` answers only how many lives are left, never which state they are in
`check_net_cf()` / `check_net_cf_resid(t)`	The check that the published statement adds up	Rebuilt from the columns of `result_cf` rather than from `net_cf`, so a column wired to the wrong cells shows up in the very table a reader is looking at. The benefit side is swept as every column beginning `claims_` — which it can be, because there is no subtotal column among them
`inc_band_at_age(a)`	The five-year 全国がん登録 band containing an age	The `*_at_age` suffix marks a lookup keyed by an age, as `mort_rate_at_age` does. `Medical_JP_S` has an `inc_band` keyed by a projection period, and one spelling must not carry two argument meanings across the library
`claims(t)`, and no `claims` column	The benefit total as a cells, never as a column	`result_cf` publishes the nine `claims_*` splits and no subtotal beside them, so its columns add to `net_cf` as they stand. A statement carrying its own subtotal among its parts stops being additive unless the reader knows which column to skip
`expenses(t)`	Acquisition plus maintenance only	The claim-handling cost is `claim_expenses(t)`, a cells of its own, deducted explicitly in `net_cf()` and published as its own `claim_expenses` column. The notes’ month-by-month traces narrate the two in one arithmetic line; the worked-example table and the policy-year-1 aggregate carry them as two
`claim_expenses(t)`	¥5,000 per diagnosis trigger, ¥3,000 per admission	On the diagnosis and admission counts, where `expenses` is on `pols_if` — different weights, so publishing one column would hide a real movement
`prem_period_type()`	The premium-paying period as a category, `whole_life` or `to_65`	`prem_period` is reserved for a duration in the model’s own grid unit. The model point column keeps the name `prem_period`
`premium_mth_pp()`	The monthly office premium per policy	`premium_pp` is an annual per-policy premium elsewhere in the library; this grid’s step is the payment interval
`mort_rate_at_age(a)`	The shipped table rate keyed by age, which may be fractional	`mort_rate_base(t)` is the name for a table rate in period `t`, which this model does not need: `mort_rate(t)` reads `mort_rate_at_age(age(t) + mort_age_offset)` directly
`mort_be_factor`	The multiplier turning the shipped valuation table into the projection basis	1.25 here. Named for what it does — a best-estimate factor — and not to be confused with an actual-to-expected ratio, which is a different quantity

Standardizations used#

Everything in this list is std, and each is marked so at its definition in the notes and in the model: the whole post-diagnosis survival model — mu_ex = −ln(S5)/5 from a sourced 5年相対生存率 R6 REG-R28, held flat for the diagnosed lifetime, and added to the baseline rather than replacing it; the relapse hazard rel_rate = 0.06 p.a., which gives 1.485593 diagnosis payments per diagnosed life and has no source and no observed range; the sex split of the incidence basis, a two-point interpolation between two sourced ratios R5 read at the band midpoint and clamped; treat_prob = 0.10 and the cohort-average ledger behind the 60-month cap; hosp_rate = 0.25 admissions per diagnosed life-year, derived from two sourced counts R7 R5 on a construction in which the population cancels — 38.98 inpatient days per diagnosed person over a cancer lifetime, the single most useful number for sanity-checking an implementation; surg_per_hosp = 0.35 payable cancer surgeries per admission, carried from the medical chassis so the two products do not disagree about the same statistic, and surg_per_insitu = 0.80 recognised in an in-situ diagnosis month; outp_days = 1.10, resting on an unsourced 250 outpatient operating days and an unsourced 25% qualifying share, a factor-of-four uncertainty between them; adv_freq = 0.012 at adv_sev = ¥600,000; mort_be_factor = 1.25, the reciprocal of 0.80, a round value inside the sourced 70–85% risk-theory band R2 REG-R20; the whole expense and commission scale, carried from the medical chassis because no Japanese cancer expense or commission scale is public; the ¥3,000 premium; and mortality-before-lapse as the processing order. The first three are the levers: the survival basis is the assumption a medical model does not have at all, and three of the eight benefit streams are integrals over it.

The clamp on the sex factor#

sex_factor(a) is clamped to [0, 2] std, and the clamp is not decoration. The linear form reaches 2 at age 98.87, and above that the female limb 2 − f_male goes negative — at the 100+ band midpoint of 102.5 it would give −0.086 × the band rate, on a female projection that runs to 118. The admissible domain of a construction whose two limbs must sum to twice the band rate and must both be non-negative is exactly f_male in [0, 2], so that is where it is clamped; it binds on the 100+ band alone, where it takes female incidence to exactly zero and caps male incidence at twice the band rate. That is a discontinuity, and it is the construction’s own behaviour made admissible rather than a new approximation: the construction is already 6% below the sourced female rate at 70–74. Replacing sex_factor_table.csv and the interpolation with the by-sex age-band grid from the same workbook removes both the clamp and the error, and it is the first thing a serious user should do.

Tests#

tests/test_model_conventions_jp.py asserts the house style over the whole registry. tests/test_cancer_jp.py asserts this product:

the notes’ six-row worked example and its four month-by-month traces, hard-coded, to the precision the notes display — money to ¥0.01, pols_if and the healthy split to six decimals, the diagnosed state to eight, the ledgers to four — plus the policy-year-1 aggregates, the ¥16,035.00 of benefit per diagnosed life-month and its five components, and the relapse hazard’s stated calibration target;
every pitfall the notes list, one test each and named after it, because every one of them is a way an implementation can look right and be wrong;
the shipped mortality table: all twenty sourced rates inside the age range this model reads, pinned to the digits the publisher shows, plus the log-linear graduation between them and the exact age span of the file. A quoted rate that the shipped table cannot reproduce is a library defect, not a rounding, so it is asserted rate by rate;
the expense split — expenses is acquisition plus maintenance, claim_expenses is a line of its own, and net_cf deducts both;
the seven check_* roll-forward and ledger identities, on every one of the eight model points;
each optional module in both positions, off and switched on;
and the structural product facts — the whole-of-life horizon set by the mortality table’s terminal age, the three states partitioning the in-force, the crossing sex curves and the clamp, 65歳払済, the no-waiver design, and the treatment cap that binds.

python -m pytest tests -q