Prove a third-moment QQ16 transcript bound

[petalas]

Summary

 QQ16 fixed F0/B_1_2 erased-family contract
-necessary rational record width per owner >= 13
+necessary rational record width per owner >= 14

Adds research/qq16-third-moment-capacity/ with a written proof, exact source-bound verifier, receipt, failure controls and registered replay. The new third moment gives

rank([B0;B1;B2]) >= 280|G|/13
selected A/T defect >= ceil(176|G|/13)
width-13 residual >= ceil(7|G|/13)

This is an information bound for read-only rational-linear records, not paid recursive rank, an exact transcript minimum or supplier admission. Widths fourteen and fifteen remain open. The selected frontier and frozen sources are unchanged.

Base canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Contribution e18ca76987f5945c6a4b5b6bebbe73cdab3c4561. Task joint-query-controller, refined to the released sharper-rank handoff after live overlap showed the chooser's generic incumbent cards were covered. Canonical claim. Exact heads, scope, commands and freshness are in TASK.json; input blob/hash pins are in SOURCES.json.

Evidence

• Before: Ross Richardson's Quantify QQ16 information loss after the extra B2 query #2104 supplies the two-moment rank bound 144|G|/7; commdata2338's Bound QQ16 transcript capacity and rule out the full initial R2 query #2153 gives defect 88|G|/7 and excludes widths at most twelve.
• After: 18,432 ordered route products and a separate chart-swap reconstruction establish the new triple coefficient 6144. Exact moments (24,28,109/3) and a rational cubic spectral polynomial exclude width thirteen. No predecessor executable is imported.

python3.12 -I -B scripts/research_package.py --package research/qq16-third-moment-capacity
python3.12 -I -O -B scripts/research_package.py --package research/qq16-third-moment-capacity
python3.12 -I -O -B research/qq16-third-moment-capacity/test_verify.py
python3.12 -B -m unittest discover -s tests -p 'test_research_*.py'
make selected-record-check

Linux x86_64, CPython 3.12.15, standard library. Both registered replays, seven focused tests, 65 workflow tests, -Wall compilation and selected-record integrity pass. Three semantic controls and CLI source/receipt corruption reject. The direct verifier also passes normally and optimized under a 512 MiB address-space cap; the Git provenance launcher ran uncapped because it maps the checkout's larger packfile. No hosted CI result is claimed.

Credit Ali Romman and #1969 for the conserved maps, route packet and erased witness; Ross Richardson #2104 for the rank method; commdata2338 #2153 for the joint A/T defect argument and #2174 for adjacent sixteen-coordinate recovery. Cinna Davis #2079/#2122 and Adam Gall #2086/#2093 are preceding query/logger investigations. Retained notices and supplier attribution are unchanged; new work is Apache-2.0.

The global erased-family trajectory remains inherited. Native local-word replay, the full selected cold replay, physical costs, recursive precision, independent human review and proof-assistant verification were not performed. This does not close a final-only controller or establish a new multiplication exponent.

Merge Danger

Door: two-way. Only one new opt-in research package; removal reverses the change.

Blast radius: package. No shared verifier, selected record or frozen input changes. The replay hook declares its exact QQ16 inputs.