Record the exact floor-stable shifts of both bootstrap savings.

[unpaidmoon]

Change and mathematical scope

Finite certificate. No new κ and no stock coefficient. Selected κ stays 0.001672660197076918.

On the frozen selected bootstrap receipt, the twenty-four floor integers of the cutoff table do not select one rational saving. Shifting each branch's recorded common_saving by an integer number of printed denominator units preserves every floor(s L_j - L_{j-1}) and every floor((1-s) L_{j-1}) for exactly these k:

• Native branch: k in {-2, -1, 0, 1} (4 shifts).
• Conservative branch: k in {-86, ..., 15} (102 shifts).

Both endpoints are forced by the stage-7 margin alone. Native k = -3 and k = 2, and conservative k = -87 and k = 16, change that margin and no earlier stage. Every other margin and every routing room allows a strictly larger integer interval. At k = 0 the floors reproduce the published table, including native stage 2 2851485324488315 and native stage 3 1015784602045963452130. common_saving = 1 - gaps.stock holds, and every actual_stock_coefficient stays null.

This does not choose which shift is the saving, bind W_j, or touch the complex supplier.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main). Priority revision 6.
• Head: cd09decd71843287ef180f537f4cb39508bae369.
• Task: selected-stock-envelope, scope refined. The card's second method asks for a missing implication of a proposed envelope. The object is the floor table's ambiguity, not a derived reserve coefficient.
• Handoff index: discussion Handoffs and requests for independent checks #1166 comment 19047276 is item 13 of the ordered list below. The list has 13 eligible items, so index (26-1) mod 13 = 12 selects that item. The item itself is to bind one rational. This package records the exact set of rationals the floors still accept.

Ordered eligible handoffs, chronological on #1166, after dropping tasks delivered or claimed by an open PR through #4123, including this account's round #4107 and #4110–#4123:

1. Single-hub two-bearing factorization of Classify all thirty two-port support transfers #3573 (comment 19021149).
2. Integer-shear supplier/recurrence inequality (comment 19031016).
3. Independent review of the research: certify local-first two-ADD obstruction on staged544 #3942 reduction (comment 19032637).
4. P104 adjacent completed-call pair (comment 19034066).
5. One chronological row/column pair and its fiber tags (comment 19034676).
6. Changed chronological P104 caller with a favorable bill (comment 19034741).
7. Fuse source-normalization with the full-output interface (comment 19035513).
8. Instantiate producer Pi under original-width stock (comment 19035639).
9. Inspect the Audit every scalar event in the actual P104 tensor code #3996 literal-index bridge (comment 19035716).
10. Pin one physical K/adjoint boundary (comment 19036235).
11. Lower the many-axis prime producer at the encoded caller (comment 19037887).
12. q2 event 58, target local 16 (comment 19039339).
13. Bind one branch-saving rational from the Audit: stock-margin chain closes for the remaining cutoff pairs (no new kappa) #2972 floor table (comment 19047276). Index target. The rational is not bound here.

Set aside before that cut: comment 19016211 because open #3681 replays the #3605 wrapper; the length-22 census line because #4117 and #4120 refine it; QQ16 six-tape (19030049) because #4114 refines it; the tensor-pairing review (19030180) because #4113 does it; moved-ADD (19034220) because #4122 does it; separated A2 acceptance (19036786) because #4112 does it; the #3943 return-adapter comparison because #3956 does it; helpers 600/601 because #4061 does it.

Nearest overlap: #2972 / research/stock-margin-chain publishes the floors and leaves the coefficient unresolved. Open #4094 replays that table and samples one denominator unit (floors unchanged) and 10^10 units (stages 6–7 move). This package replaces those two samples with the exact first failures. Open #3898 binds a stage-one parent recurrence and still leaves the numerical coefficient open. Neither derives this window.

Validation

CPython 3.12.3. Registered replay:

python3.12 -B scripts/research_package.py --package research/stock-saving-floor-window
python3 scripts/check_research_commit.py --package research/stock-saving-floor-window --check-source-history

Both passed. Marker:

PASS_STOCK_SAVING_FLOOR_WINDOW native_k=-2..1 native_shifts=4 conservative_k=-86..15 conservative_shifts=102 binding=stage7_margin coefficient=unresolved no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/stock-saving-floor-window outcome=partial

The slack inequalities and an outward floor walk agree on both windows. Every interior integer is evaluated. The two adjacent shifts fail at stage 7. Dropping the stage-7 margin widens the intersection. A cross-branch saving swap is rejected. The receipt hash is f0bd4f2270826de7b935323e9b4d2e034f69b46205be9535488c4429e95f7917.

Not run: the frozen PR1087 assembler, a production stock fit, Lean, Docker, or the selected cold replay.

Credit

Kumagi for the cutoff chain and the published floors. Nick Petalas for the independent tie-out and the one-unit / 10^10 samples in discussion comment 19047276. The selected stock audit and Jeremy Kothe's PR1087 assembler retain the receipt. unpaidmoon, with substantial Cursor Grok assistance. No independent human review is claimed. Apache-2.0.

Open next questions

1. Which source sentence bounds a stage-j routing call into A_{j-1} by a factor whose log2 is at most the routing room? The smallest room is still native stage 2, 4777557234646. The floor window does not contain that sentence.
2. Does the frozen PR1087 assembler, other than the stored common_saving field, exclude the nonzero shifts? The first step is the stage-7 margin at native k = 1 and k = -2 against the assembler recurrence.

Workflow feedback (optional)

Handoff-first selection against open PR titles left fewer than 26 concrete remaining requests, so the session index wrapped to the last item and took a different piece of it. #1200