[jwr404]

Summary

Under the hypotheses ||B_i|| ≤ 9 p^2, ||C_i|| ≤ 9 p^2 + ε and ||B_i - C_i|| < 2 ε, with ε = p^6 exp(-p^2) and ||X ⊗ Y|| = ||X|| ||Y||,

⊗_i B_i - ⊗_i C_i = sum_k T_k,
||T_k|| < 2 (9 p^2 + ε)^{g-1} ε,
||⊗_i B_i - ⊗_i C_i|| < 2 g (9 p^2 + ε)^{g-1} ε.

The factor 2 is two section errors on the active axis. HALO's 2g rectangles stay a volume partition. The scalar shadow uses caps 9, 10 and 2; the displayed factors are 8, 7, 6 and 7, 9, 5. A difference of size 3 exceeds the cap 2 when g = 1.

The three norm hypotheses are not proved. The comparison with 2^{-C p} is #4506 and is not re-proved. No new κ. The selected record remains 23/10000.

This answers the open question of #4506. It does not replay #4506. #4488 is the same telescope at ceiling 10 p^2. Splitting one axis through the section polynomial is left open.

Test plan

• python3.12 -B scripts/research_package.py --package research/gaussian-tensor-nine-axis
• Prints PASS_GAUSSIAN_TENSOR_NINE_AXIS and outcome=completed
• Maintainer replay was not run

Base bbde3b0bedb8f7ce17159dfbe913b7e3e5194bab, priority revision 7. Upstream had moved from 2a13eb18; κ stayed 23/10000. The pre-submit fetch f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc left the HALO blob 5f601b3c8ac368aa79aa1007effe5933a360237b and the selected-result blob ed33caef5c5827693e9572d252a66f99cbb73d40 unchanged, so this package keeps the bbde3b0 baseline.

Prepared by James Reed with substantial Cursor Grok 4.7 assistance.