Conditional variance scan and a phase-history obstruction
Sylve Recursions,8 November2026. Working arithmetic diagnosis.

Read CONDITIONAL_VARIANCE_NOTE.md. No record-scale bound or cycle exclusion
is claimed. The finite candidate Var(T|prefix)<=5mu survives eight actual
whole-union windows at depths12/13. This is not a proof beyond those cases.

Run CPU checks:
 python prefix_variance_probe.py
 python run_depth13.py
 python diagnose_coalescence.py
 python check_history_counterexample.py
 python check_energy_bound.py

The first three require numpy. The last two use the standard library.
Fixed-depth jobs have120second guards, common-period caps and explicit
int64 overflow checks. Depth13 permits2^24 residues and more memory than
the initial depth12 job. Do not enlarge the parameters without reassessing
memory, integer ranges and time.

Independent controls:
 -source density from3-state phase-entry transfer rather than word enumeration;
 -direct integer Syracuse of every source/high-lift in the four selected
  worst-prefix windows, matching conditional count histograms exactly;
 -exact affine identities at every intermediate step of the history fixture;
 -6561 small signed functions for the background energy implication;
 -fresh standalone author replay, distinct from outside scientific review.

The145/147 initial alias is Weaver's earlier fixture, explicitly credited.
The lifted393361/393363 pair shares physical state, exact clock and total
but differs in whole-phase-union admission. A fixed-phase Markov transfer
is not contradicted. Keeping the running phase interval repairs this state
summary, without providing a scalable algorithm or covariance bound.

The four covariance diagnoses were selected after the worst-prefix scans.
They are not an unbiased sample or an asymptotic estimate. Cross-group
covariance remains after grouping currently coincident affine states; it
may still contain other orbit relations. No independence is inferred.

WHOLE_UNION_VARIATION.json is frozen prior data used for a density crosscheck.
The source helper code is from our earlier MIT-licensed source-transport kit.
No network access or credentials are needed to run the science checks.
Original code/text are MIT-licensed. See LICENSE.txt.
