closes: a run of members closes splits cumulatively

Each close into members' capital rounded on its own, ties to the
earlier member, so twelve monthly 50/50 closes of odd-cent income could
leave one member several cents ahead of half the year (docs/testing.md
#12, found with the members' equity fix).

- CloseTo::Members now splits cumulatively over a run (closes back to
  back with the same members and shares): each close gives a member
  allocate(run total so far) - allocate(run total before). Periods
  record their close order and a cumulative close's members and net
  (Period::close_seq, member_close) so the next close continues the run
  and replay recomputes it exactly. A close to anything else, or other
  shares, ends the run.
- Journaled "rounding": "cumulative". The per-close rule is kept as
  CloseTo::MembersPerClose for closes journaled "largest_remainder";
  older closes still replay with the last member absorbing it.
- Lean: runPart_telescopes (a member's total from a run is their
  allocation of the run's total) and closePart_total (each close hands
  out exactly its net), audited to the standard axioms.
- Tests: hand-computed three one-cent months (per close A 0.03 / B 0;
  cumulative A 0.02 / B 0.01), a run ending, a property that each member
  stays within a cent of their share (fails on the per-close rule), and
  a store contract that each rule journals and replays as itself.

Wanderland's books have no closes yet, so all of theirs use the new rule.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01GWVo7x3UHw5kwCUaWxiejX

docs/spec/rules.md

@@ -217,6 +217,14 @@ closed period).
 - **No authority** says how to round a share to the cent. Largest
   remainder, ties to the earlier member: DECISION (Stephen, 2026-10-13).
   Closes made before then replay with the last member absorbing it.
+- Rounding never piles up: a run of members closes (same members and
+  shares, back to back) splits cumulatively, each close giving a member
+  their allocation of the run's total so far less their allocation before
+  it, so each member's total from the run is within a cent of their exact
+  share (follows from the running capital account below; found
+  2026-10-13: closing each month on its own gave every tied cent to the
+  earlier member). Journaled as `"rounding": "cumulative"`; closes
+  journaled `"largest_remainder"` replay one at a time.
 - A capital account is one running balance: Form 1065 Schedule K-1
   instructions, Item L: "The partnership must report your beginning
   capital account and ending capital account for the year", "based on the
@@ -229,8 +237,12 @@ closed period).
 
 **Enforced:** `CloseTo::Members`, `periods::allocate`,
 `kernel::apportion`, `members_equity`. **Checked:** Kani
-`apportion_is_exact`, `apportion_is_fair`; properties `prop_split_*`,
-`each_members_capital_chains_across_statements`;
+`apportion_is_exact`, `apportion_is_fair`; Lean `runPart_telescopes`,
+`closePart_total`; properties `prop_split_*`,
+`each_members_capital_chains_across_statements`,
+`each_member_stays_within_a_cent_of_their_share`;
+`a_run_of_closes_never_piles_up_rounding`,
+`members_closes_replay_under_the_rule_they_were_journaled_with`;
 `closes_journaled_under_the_old_rule_replay_with_it`.
 
 ## B-14 Statements: P&L for a period; cash flow by the indirect method

docs/testing.md

@@ -79,7 +79,7 @@ accounting question), CHANGE (a source says otherwise; work pending).
 | 9 | An asset's life ends at purchase + life months, that day not held; day-count proration | CONVENTION | Exactly N months of service; day proration and the mid-month convention are both accepted book policies (ASC 360-10-35-4 not read: login) |
 | 10 | A payroll entry has one line per account total | CONFIRMED | The per-employee detail the IRS requires ("Amounts and dates of all wage ... payments", Employment Tax Recordkeeping) is kept in the run; a summary entry is standard |
 | 11 | A period with exactly the dates of an existing one is allowed | DESIGN | Nothing governs duplicate periods; harmless (the second close locks only). Refusing exact duplicates is an option |
-| 12 | Each close into members' capital rounds on its own (ties to the earlier member) | CHANGE (pending) | Found 2026-10-13 with #7: twelve monthly 50/50 closes can leave one member several cents ahead of half the year's income. Closes should split cumulatively too (year-to-date allocation minus what earlier closes gave); a new journaled rounding rule, older closes replaying as booked |
+| 12 | Each close into members' capital rounds on its own (ties to the earlier member) | CHANGED 2026-10-13 | Twelve monthly 50/50 closes could leave one member several cents ahead. A run of members closes now splits cumulatively (rules.md B-13; Lean `runPart_telescopes`; property `each_member_stays_within_a_cent_of_their_share` fails on the per-close rule); journaled `"cumulative"`, older closes replay as booked |
 
 Questions are settled from the sources, not by any one company's CPA
 (wanderbooks is general software). Where the standards leave a real

docs/verification.md

@@ -124,6 +124,13 @@ sequence of commands, of any length**:
     other shares were rounded, and only the last share changes.
     - Kani `plug_last_sums_exactly` · Lean `plugLast_total`,
       `plugLast_keeps`
+17. **A run of member closes telescopes**: each member's total from a run
+    of cumulative closes is their allocation of everything the run closed
+    (so its rounding is one allocation's, never a sum of them), and each
+    close hands out exactly its net, for any allocation whose parts sum to
+    the whole (rules.md B-13).
+    - Lean `runPart_telescopes`, `closePart_total` · property
+      `each_member_stays_within_a_cent_of_their_share`
 
 ## What the proofs found