Compose shared radix and forward admission across actual pooled preparation

research/r437-preparation-composition/.gitattributes

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+* -text

research/r437-preparation-composition/PREDECESSORS.json

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+  "transport": "Byte-identical materialized vendor directory; historical archive retained locally outside published package."
+}

research/r437-preparation-composition/PROOF.md

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+# Preparation composition and phase contract
+
+This is a source-action theorem for successful valid inputs. It is not the
+complete Pi term, a physical allocator tariff, or an exponent improvement.
+
+## Interval
+
+Borrow a canonical Program, old raw-directory tape, positive old-prefix Count,
+encoded history depth, modulus and Ring. Their complete bytes, heads and live
+numerical ownership are protected. Actively used Program/directory/Count tapes,
+modulus, Ring operands, encoded depth and arena templates enter at their canonical
+head1 positions; the runtime rewinds these inputs and does not promise restoration
+of arbitrary active-input entry heads. Unused spectator Words may enter at other
+valid heads (the fixtures use head2), and those heads are preserved.
+Specifications are independently compiled
+from the pinned pooled R437 catalogue. Create Context; create frame control
+Words; produce the full next directory and prefix Count; read its first prefix,
+run SelectedBinding.validate_residual, clear the prefix; read the first prefix
+again, run SelectedBinding.child_program, clear the prefix; then clear both
+returned tapes, close the returned Count and Context and release frame controls.
+This is precisely the preparation sequence used by residual_begin and
+prepare_child at these named component boundaries, with geometry, child_extents,
+fixed handoff copies and payload roles explicitly factored out. It does not
+execute the entire Machine methods or establish literal top-level reachability.
+
+The Context constructor and final disposer are included. Input construction,
+source/low-vocabulary compilation, Ring construction, old Program/directory
+construction and later child consumption are outside this interval, and retain
+separate charges. The frozen low specification is real; the admitted history is
+a generic legal fallback history, not a projected good-class assertion.
+
+## Two radix families
+
+For dimension d, M=d², modulus q^w, both Context.high_count and directory.produce
+invoke high_power. The original implementation repeats digit_suffix M times;
+ToikY's #4025 adapter validates radix_power once and repeats the same ordered
+M(w-1) Count multiplications by q. Its mathematical count is unchanged. Both
+implementations exhaust the radix validator even when w=1. A complete traversal
+has source-residue invoice rho; the saving is (M-1)rho per high_power.
+
+This package applies the identical credited adapter at **both** original
+bindings, including counts.high_power reached by Context.high_count. Therefore
+the full interval saves exactly 2(M-1)rho source-residue actions. Count and record
+actions, cardinality, output bytes/order and physical duplicate prefix
+multiplicity are unchanged. It introduces no tape, numerical Word or extra
+simultaneously live storage. Context still creates and later closes its high
+Count and cap, and the producer retains its M-digit odometer. No Context charge
+is silently borrowed from an already-live fixture.
+
+## Chronological admission composition
+
+The #4011 adapter changes only monotone Program/Fields admission. Both validation
+and child creation construct one Callback over the same history and first
+prefix. Each checks exactly the same chronological predicates and finishes with
+the original random-access Program restored. The child extension's later access
+and output copy are unchanged. Hence there are exactly two admission savings.
+
+Let n=h+1, r=2I+L+5, c=Q+2I+90, F=Q+2+4096(L+1). For one admission, the removed
+Program reads and moves are
+
+    3r n + (3c-1)h n/2,       n(2r+2+ch).
+
+The removed Fields reads and moves are
+
+    (3F-1)n(n+1)/2 - 3nF + 3nQ + 6n,
+    F n(n-1) + n(2Q+6).
+
+Writes are unchanged. Twice their sum is the complete interval's record saving.
+The source index-Word saving is separately metered; it is not inferred from
+record actions. The adapter preserves residue actions and adds no live tape or
+Word. Its AST guards fail on unreviewed admission shapes.
+
+## Composition argument
+
+Directory production returns byte-identical canonical prefixes under either
+radix implementation; therefore both original and cursor Callback receive the
+same bytes. Cursor admission returns the same accepted state and preserves
+borrowed fields; therefore the subsequent extension and disposal are identical.
+The two changes affect disjoint source-action lanes (residue versus record/index)
+and restore the same protected boundary state. Sequential composition gives the
+sum of savings without a cross term. The verifier executes all four combinations
+and checks this equality in every action lane, and checks that phase invoices
+partition the entire measured interval. It also checks identical created-tape
+inventory, numerical peak and slot count; this is source runtime storage, not a
+full physical backing/metadata tariff.
+
+## Actual finite source boundary
+
+The pinned #4010 replica catalogue independently resolves native IDLE896352,
+rank14, and old common COPY1603, rank7, at low identity over q=3. Both low source
+specifications are compiled by the actual Specifications path; the current
+source is fallback. Its actual compiled plan begins with a UNIT child. Q=6512
+includes the five-bit pooled source-code widening. At h=2 the old history uses
+the distinct COPY and IDLE source codes, and every field belongs to its actual
+compiled context. Roots are 2048*64^h, root unit2; admitted current width2048
+extends to32. The tests cover h=0/B=1 and h=2/B=2, including duplicate physical
+prefixes. They are complete dimension64 high cubes only at cap1 (modulus3);
+no nontrivial 3^4096 cube is executed.
+
+The universal source-code composition proof assumes every old/current context
+is admitted, enough capacity, positive cardinalities and no concurrent mutation.
+Malformed-input general rollback, selected source reachability, physical gather,
+transport, geometry, coefficient evaluation, full CALL/RETURN, stock and kappa
+remain separate obligations. This package cannot promote the low-level saving
+to a complete recurrence.

research/r437-preparation-composition/README.md

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+# Compose two preparation improvements on actual pooled R437 sources
+
+This package joins ToikY's #4025 shared radix traversal with #4011 chronological
+Callback admission and independently compiles #4010's actual pooled source
+contexts. It measures a complete named interval: Context construction, full
+next-directory production, both first-prefix read/validate and read/child-program
+phases, and disposal of every owned result and Context.
+
+The new composition applies radix sharing to Context.high_count as well as the
+directory producer. Both variants exhaust validation and retain every ordered
+Count multiplication. The interval saves **8190 validated radix traversals**
+worth **4,283,370 reads, 778,050 writes and 4,553,640 moves** of source residue
+Words in each dimension64/cap1 case. No tape or numerical word is added.
+The chronological adapter separately saves two complete admissions; the four
+original/candidate combinations prove exact additive savings without cross terms.
+
+| Actual-source fixture | Original total source actions | Composed total | Reduction |
+|---|---:|---:|---:|
+| h=0, one old physical prefix | 11,709,798 | 2,023,876 | 82.716% |
+| h=2, two duplicate old physical prefixes | 21,090,379 | 10,356,737 | 50.894% |
+
+Totals sum separately recorded record-Tape, residue-Word and index-Word reads,
+writes and unit moves. They are source-operation counts, not wall-clock or a
+physical bit-machine tariff. RESULT.json preserves all lanes and phase invoices.
+At h=2 the record lane alone drops 7,331,381 to 6,247,715 actions, and numerical
+peak remains 4097 additional residue Words and 16 index Words (including Context
+and frame controls). Created tapes and backing slots agree in all four modes.
+
+The current source is **native IDLE896352, rank14, Q=6512**; the old history also
+uses **common COPY1603, rank7**. Actual Specifications compilation checks the low
+identity contexts over q=3. The IDLE is fallback, and its actual plan starts with
+a UNIT child. Legal generic histories reach current width2048 and produce a
+width32 child. Active inputs enter at canonical head1; unused spectators also test head2.
+Every borrowed byte/head, spectator Word, input Count and numeric
+ownership set is restored after complete disposal. The first prefix is cleared
+and reread between validation and extension, matching the real caller boundaries.
+
+These are complete dimension64 high cubes at cap1 (modulus3). They do not execute
+a nontrivial 3^4096 cube. Source compilation is real; top-level selected-history
+reachability and a full physical CALL/RETURN are not established. Geometry,
+child_extents, transport/gather/scatter, handoff copies, coefficient evaluations,
+control/allocator tariffs, original-width stock and remaining Pi terms stay
+explicit. There is no new kappa or selected-frontier change.
+
+## Evidence and reproduction
+
+Run `python3 -B scripts/research_package.py --package research/r437-preparation-composition`.
+The package is self-contained: its authenticated 154-file materialized pooled export preserves
+all frozen notices and complete loader inventory; exact #4025 sources and the
+#4011 adapter are retained with original hashes. PREDECESSORS.json and
+POOLED-SOURCES.json bind bytes and upstream heads. Shared/frozen files are never
+edited. The checker independently compiles both source specifications, then runs
+four modes for each fixture. An independent serializer checks every returned child byte and its width32 extent. The independent invoice checker imports no runtime.
+Eleven controls include two actual same-output losing compositions: leaving
+Context unoptimized and silently skipping validation. Checks remain active under
+optimized Python. This is AI-assisted reviewable source evidence, not independent
+human acceptance or formal kernel verification.
+
+## Open next questions
+
+PROOF.md states the success contract and exact formulas. Input/low-vocabulary
+compilation and construction of the borrowed Ring/old history are separate entry
+charges. Successful valid-input cleanup is proved; general malformed-input
+rollback is not promised. TASK.json records scope, overlap and structured next
+questions. The next useful join prices geometry/child extents and fixed handoff
+copies on this same pooled context, including arbitrary dirty acquisition before
+the residual; it must not reuse an unpooled rank26 fixture as rank14 evidence.
+
+## Credit
+
+ToikY/#4025 supplies high_power_shared, complete producer metering and the exact
+validated radix invoice. ywz65/#2590 supplied the prior cubic repeated-setup
+analysis and explicitly requested shared traversal; ywz65/#2566 supplies primitive
+analysis. Ross Richardson's numerical peak audit retains its credit. Chris R /
+Clear1nsight #4011 supplies the forward admission adapter and source invoices;
+#4010 supplies actual replica-indexed pooled source compilation. Jose Manuel /
+jmbarrancoml supplies the physical caller and encoded runtime; David Arias/#2753,
+Nick Petalas and the retained controller/record lineage retain their notices.
+The R437/OQ4, pooling and chart work retains ai-nanachi/#3647, zxv/#3690,
+Ali Romman/#1043, Sagar Thakrar/#3700, #3936/#3950/#3967, #3958/#3959/#3995,
+and the authors credited by those packages. New composition, lifecycle boundary,
+exact joined invoice and controls: Chris R / Clear1nsight with substantial OpenAI
+Codex assistance and a separate AI review. Apache-2.0.
+
+Publication uses the154 unchanged upstream source files under vendor/, with exact
+file/directory inventory, SHA256 and no-link checks before execution. Missing,
+extra, linked and corrupted inputs reject. The original compressed archive was
+retained as local evidence outside this package; transport changed, science did not.