[CubeJerry]

Result

No new κ. This package gives actual fixed finite ADD/SCALE transition
tables for the current three-bit coded lifecycle ABI. They execute through
the unchanged published execute_table and Controller.primitive, with no
runtime numerical callback or decoded length. The all-width theorem accepts
exactly the common-grid outputs that fit the original signed word, stages the
entire field before target writes, preserves borrowed sources, returns heads
and physically erases its two work tapes on success.

This supplies one concrete missing scalar-provider implication in the current
compiler/owned-lifecycle composition. It covers 366,842 original ADD/SCALE
occurrences in the exact 642,410-event selected caller, using 42 tables with
58,544 rows. It does not discharge the five assumptions as a whole or improve
the selected conditional κ = 0.003125804.

Why this is new

#3098 already executes inherited scalar recipes on
aligned sequential packets and leaves their actual caller/owner binding open.
This package binds the current exact source tokens and ordered owners to
tables accepted by the newer coded lifecycle, with complete copying, head
return, backing and erasure costs. It also removes recipe-specific temporary
headroom requirements: four-bit SCALE(-1/2) accepts -8 → +4, and ADD(2) accepts
(-7,+7) → +7, without storing either overflowing intermediate word.

The 31-coefficient/denominator-16 census is credited to
#6928 and is not claimed anew. The general fixed
rational theorem does not prove the unfinished-context grid condition of
#6932 or #6934.

Exact sources

• Canonical base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
• Selected local word from Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030 and the original
  productive controller, pinned by Git blob and SHA256 in SOURCES.json.
• Unchanged published lifecycle machine and source compiler,
  pinned in DEPENDENCIES.json at
  ab239cb6ee884e7a900dd9101c34448077fad0b0.
• Unchanged Implement a local continuation stack with exact linear cost #5356 physical continuation source.

Verification

python3 -B scripts/research_package.py --package research/current-scalar-flat-tables

The manifest registers eight bounded normal/optimized checks, with exact
committed receipts. The physical oracle covers all 10,870 width-1-through-4
signed cases for the actual table catalogue, wider complete fields through
width 129, and 400 additional rational cases. A real unchanged-controller
fixture executes the complete initial scalar block at source events 1..9895
on 799 coded fields, totaling 41,088,794 physical cell actions, and compares
every endpoint to a separate exact Fraction interpretation.

Twenty-five controls detect arithmetic, shape, source, alias and erasure
failures, including mutants of the final-carry sign and sign extension. An
independent lead AI mathematical audit derived the terminal equation and
checked a separate 14,260-case integer-digit/Fraction domain. It is described
separately from physical executor tests in VERIFICATION.md. The all-size
proof is in PROOF.md; finite tests do not establish it alone.

Limits and next obligations

Successful execution requires aligned complete operands on the same grid and
the stated final signed range. Source owner maps and original lifecycle
contracts remain premises. Arithmetic rejection preserves public contents but
can leave heads advanced and work occupied; no physical rollback is claimed.

The positive complete scalar bill is O_q(V+D+Q), with two used work tapes and
current backing at most 2V+3+O(1); retained erased history remains counted.
This does not certify the complete old numerical allowance. Native maps,
row/recursive services, whole-caller precision/error returns, global ownership
and analytic recovery remain open composition obligations.

Credit and assistance

Prepared for @CubeJerry, with substantial OpenAI assistance in mathematics,
implementation, source analysis and checking. Prior credit is preserved for
Jose Manuel/jmbarrancoml (#3098), Nick Petalas
(#3078 and #3090),
Sagar Thakrar (#696), James Chang
(#1869), the encoded arithmetic of
#3091, Ali Romman's productive caller/continuation
work, DreamingOfClouds' selected word, Mark/Matarener's occurrence sources,
and the retained native/compiler/lifecycle lineage. The geometry and precision
work in #6878, #6900 and
#6901 retains its scope and credit. Separate AI
review is not independent human or proof-kernel admission.