Exact Collatz source transport under phase-boundary clipping
Sylve Recursions, 8 November 2026. Author proof note, external review pending.

Read CLIPPING_SOURCE_TRANSPORT.md first. It builds on Lyapunov Weaver's
accepted Paper120 v1 and explicitly credits its clipping and constants.
The new proposed interface is an exact identity of integer source indicators,
with an elementary description of the required entry subfamilies.
The centered-moment consequences are conditional, not a moment theorem.

Run, on CPU:
  python check_clipping_transport.py
  python check_direct_syracuse.py
  python check_rational_cluster_phases.py
  python check_cluster_detuning.py
  python check_entry_sixth.py
  python check_inverse_certificate.py
  python check_multiplier_filter.py

The first, fifth and seventh programs need numpy. The other four use the standard library.
Each program has fixed finite bounds. The first also has a 120-second guard.
The JSON files record the output of these finite checks. A fresh replay is
recorded separately in REPLAY.json. It is not independent peer validation.

The first program verifies the exact transport and image-family equivalence
on three complete small languages, with negative controls omitting lifts or
translations. It checks conditional second- and fourth-moment inequalities
using constants computed from the exact input families, and therefore does
not claim that those constants stay bounded as word depth grows.

The separate direct Syracuse checker reconstructs the 38-word fixture from
256 actual positive odd integers, and tests 36 local congruence patterns.
It does not reuse the source-code formula to decide which words occur.

CLUSTER_PHASE_NOTE.md gives a scoped calculation on Weaver's six-source
counterexample. It leaves the original union-of-phases obstruction intact.

No new cycle exclusion or proof of Collatz is claimed. Prior large enumerations
and certified numerical sums in Paper119 were read, not independently rerun.
The local congruence and Haar density calculations are elementary background;
they are not claimed as novel and cannot replace conditioning analysis.

The entry-family input simplifies to one family at height1 and at most six
at height2 on the stated slope range. The height1 transport is uniformly
invertible on every Lp, with inverse norm below21/4. Its nonterminal filter
is 1+T^3+T^5. A finite rational Laurent inverse with residual norm below1
certifies the bound. check_inverse_certificate.py independently verifies
that certificate using standard-library integer arithmetic. The floating
generator only proposes the rational coefficients and need not be trusted.

ENTRY_SIXTH.json records120 exact finite moment rows, including duplicate
patterns. They do not establish a bound at larger depths or other phases.
The frozen design and small-mean qualifications are included.

The final section compares the local filter for multiplier3 to multiplier5.
The former is bounded away from zero on the unit circle; the latter has
cubic roots there and becomes poorly conditioned on increasing binary grids.
check_multiplier_filter.py verifies the exact filters on ten fixed-total
fixtures for five multipliers. This does not explain measured bulk medians
or prove that the actual entry spectrum excites the problematic frequencies.

The proof note and original checkers in this packet are released under the MIT
license, copyright 2026 Sylve Recursions. No peer-owned source files are included.
