fix(k1 tax basis): odd cents of property basis run cumulatively (B-36, D-38)

The tax-basis K-1 shared each entry's built-in gain, property without a
basis, prepaid at book and property distributed among the members entry
by entry, every tied odd cent to the first member: three equal odd-cent
properties contributed 50/50 left the members three cents apart.

Apply D-38's rule (the closes' cumulative largest remainder, through
kernel::apportion_cumulative): tax_capital::RunningSplit keeps each
member's exact running share, rounds the running shares afresh to the
cent and hands out the change, so no member's running share is ever a
cent from exact and tied cents alternate. A negative running whole is
rounded as its magnitude, a zero one by the sign of the whole just
split, so a run of losses mirrors its gains part for part. Exact running
shares are taken to ten places before rounding: a sum of Decimal thirds
can sit a hair under its cent (the law found 399.93 as 399.9299...).

tax_capital::entry_parts runs the splits over every posted entry from
the books' first, in date order, whatever span is asked for, with one
count per set of members with a part in the entry: a member never takes
a cent of an entry they had no part in (Item L's capital contributed is
the basis of the property that member contributed), and the count never
restarts, since its weights are each entry's own amounts, not shares.
An entry's reversal takes its original's split back out of the count
(RunningSplit::unsplit), so an entry's cents are the same in every span
and next year's beginning is this year's ending. The K-1's per-entry
lines come from k1::entry_lines, which k1_detail now uses too.

The book property each member contributed in an entry stays split entry
by entry (each member's property must stay within their own credit);
B-36 says so.

Tests: tied_odd_cents_of_property_basis_run_cumulatively (fails on the
per-entry split: 665.86 / 665.83); a_member_outside_an_entry_never_
takes_its_cents (three members; fails with one count for all members),
an_entrys_odd_cent_is_the_same_in_every_span (a reversal across the
span's start; fails with the count carried span by span or the reversal
not taken out), the_split_runs_in_date_order (fails in posting order);
the law a_running_split_never_drifts_a_cent (5,000 cases: the
largest-remainder rounding of exact integer shares, ties to the first,
and the negated run mirrored; fails with ties to the later member or a
zero running whole rounded as a gain); unit tests for one split,
alternating ties, a member outside a split, the mirror at zero, unsplit
and the thirds case; bookspec example partnership-k1-tax-basis-odd-cents.
rules.md B-36, the handbook (tracing figures), STATUS, testing.md and
verification.md updated.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01T3gXMVt7XJPi6ens1or9Dj

docs/testing.md

@@ -1611,7 +1611,40 @@ basis. Mutation runs wait for P12 (D-33); none was run.
   worth less than basis, one more, one equal; the plan at book with its
   note; the gain property's disposal flagged with its built-in gain),
   property subject to a liability (negative tax property), and three
-  members with unequal shares, one contributing nothing);
+  members with unequal shares, one contributing nothing; and, from the
+  owner's ask of 2026-10-22 (B-36 with D-38), three odd-cent devices
+  contributed 50/50 whose built-in loss runs cumulatively, a cent apart
+  for the year and from June on a beginning carried from January
+  (`tied_odd_cents_of_property_basis_run_cumulatively`; it fails with
+  the per-entry split, 665.86 / 665.83), and the law
+  `a_running_split_never_drifts_a_cent` (5,000 cases, up to four
+  members, two dozen splits each with its own weights, small ratios
+  scaled by a cent amount up to ten million, wholes to ten billion
+  either sign, a third of them a few cents so the running whole often
+  returns to zero: each split sums to its whole, the running totals to
+  everything split, each member's running total is the
+  largest-remainder rounding of the exact running totals, ties to the
+  first, so never a cent from exact, checked in integers, and the run
+  with every whole negated gives every part negated; it found the
+  Decimal thirds case `RunningSplit` now takes to ten places, kept as a
+  regression and as the unit test `thirds_summed_are_the_cents_they_are`;
+  with ties given to the later member it fails on the rounding, and
+  with a zero running whole rounded as a gain it fails on the mirror);
+  from the P4 review (2026-10-22), three worksheet tests:
+  `a_member_outside_an_entry_never_takes_its_cents` (three members, a
+  later entry by two of them: the third's line is nothing at all, and
+  each year's built-in shares and tax property sum to its entries'; it
+  fails with one count for all members, the first cut, which gave the
+  third −0.01 of tax property), `an_entrys_odd_cent_is_the_same_in_every_span`
+  (a reversed contribution across the span's start: the desk's cent is
+  the same from January, June, August and October; it fails with the
+  count carried span by span, and with the reversal not taken back
+  out), and `the_split_runs_in_date_order` (a 2027 entry posted before a
+  2026 one: next year's beginning is this year's ending; it fails with
+  the count in posting order); the unit tests in `src/tax_capital.rs`
+  (one split, tied cents alternating, a member outside a split trued
+  up, a loss mirroring a gain at a running whole of zero, a split taken
+  back out);
   `spec_asset_basis.rs` `a_duplicated_run_line_is_carried_once`; `properties.rs`
   `prop_basis_figures_laws` (5,000 cases); `kernel_bridge.rs`
   `basis_figures_agree`; Kani `basis_figures_laws` (`src/proofs.rs`, 83
@@ -1670,7 +1703,10 @@ reversal test; `check_depreciation_run`'s arms; the register filter
 `check_journaled` and `check_legacy_journaled` arms; the acquisition and
 in-service date refusals; the disposal floor; the MCP `aliased` logic
 (both given and differing); `asset_basis_from_journal` (newer vs corrupt);
-the projection loader's two key sets; `tax_capital::share` and
+the projection loader's two key sets; `tax_capital::RunningSplit` (the
+sign, its zero case, the snap to ten places, `unsplit`),
+`tax_capital::entry_parts` (the member set, the date order, the
+reversal's take-back) and
 `entry_property` (the mismatch branch, the unknown sum), the open-item
 conditions (`in_service`, the disposal window), and the reconciliation's
 signs.