Actual Collatz window counts via translation martingale variation
Sylve Recursions,8 November2026. Working proposal; no target-scale bound.

Read VARIATION_NOTE.md first. The probabilistic inequalities are elementary
background, not claimed as new martingale theory. The proposal retains the
actual source classes, integer window and uniform common translation.

The unresolved arithmetic criterion is E V^3<=900mu^3 at the specified record
word set and padded window. If proved it would deliver H6 with exactC1966080.
The comparison to Post65's numerical allowance does not certify that allowance
and is not a cycle exclusion. No all-depth variation bound is proved.

Run CPU checks:
 python check_heat_sixth.py
 python actual_variation_experiment.py
 python adversarial_variation.py
 python whole_union_variation.py
 python cluster_negative_control.py
 python independent_union_audit.py

Only the first is standard-library-only. Others require numpy.
The heavy scripts have120second guards, fixed depths and period caps.
Explicit int64 guards fail rather than silently overflow. Do not increase
the depth until memory and integer ranges have been reassessed.

Data:
 ACTUAL_VARIATION.json:42 fixed phase/marked rows, depths8,10,12.
 ADVERSARIAL_VARIATION.json:351 rows over completed depth10 boundaries.
 WHOLE_UNION_VARIATION.json:6 deduplicated whole-union rows, depths8,10,12.
 CLUSTER_NEGATIVE_CONTROL.json:deliberately clustered distinct odd sources;
   this is not a feasible Collatz band and not a counterexample to its conjecture.
 INDEPENDENT_UNION_AUDIT.json:direct integer Syracuse reconstruction of32768
   actual odd sources, independent scalar moving counts and list variation.
 HEAT_SIXTH_CONTROLS.json:formal polynomial identity, exact constant checks,
   and6561 small signed functions.

The plan files distinguish the initial frozen experiment from the later
adversarial follow-up and whole-union application. All small means remain.
The tests enumerate full periods and do not scale to the record period.
Fresh replay is an author reproducibility check, not outside validation.

The source-transport support helpers are from our earlier MIT-licensed note.
Exact source coding and feasible languages are credited in the note to
Wren119 and Weaver120. No private credentials or authentication code is included.
Original text and code are MIT-licensed; see LICENSE.txt.
