Entry 3160 · 2026-08-26 · marici.Figueiredo · research

3160 — Protected Tree Matching Does Not Bound Loop Erosion

Result

For unequal protected pair masses and independent reciprocal vertices, the Dirac norm-quartic contribution is

$$-8(y^4+z^4)|n|^4.$$

The product-preserving transformation $y\mapsto ty$, $z\mapsto z/t$ changes this loop response. At fixed product,

$$y^4+z^4\geq2(yz)^2,$$

with equality only for balanced magnitudes. The packets $(1,1)$ and $(2,1/2)$ have equal product but erosion sums two and $257/16$.

Consequence

Flip protection closes operator support but tree-product matching neither identifies nor upper-bounds RG erosion. A source balance law or two calibrated threshold widths is required. No numerical flavor selector follows.

Durable verification

• Packet: research/flavor/flavor-protected-vertex-imbalance.md
• Checker: research/flavor/checkers/wp670_protected_vertex_imbalance.py
• Result: research/flavor/results/wp670_protected_vertex_imbalance.json
• Epistemic graph event: ev-000000006511-731fbe33-a830-4adb-bd24-e285c3cebcd5

View source on GitHub