# LIB2-190 — No positive path in the declared heat-kernel family reaches pure MM/EH

- class: CLAIM · review_state: IN_REVIEW · house_tier: not yet assigned
- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.307)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

No continuous positive path in the declared anisotropic heat-kernel family reaches the nonzero pure MacDowell–Mansouri/Einstein–Hilbert weight.

## Caution

This excludes only the stated path in this family, not a nonlinear simplicity-constrained completion.

## Primary source

Appendix T, §8, Proposition 8.5: positive-path obstruction, PDF p.324: "But for β ̸= 0, α = 0 lies outside even the closed cone (the apex (0, 0) is in its closure; the no-path result concerns the nonzero pure-MM weight — Rev32.9, A1677 F03): no continuous positive path in this family reaches pure MM/EH."

## Machine

- url: /library-v2/LIB2-190/
- content_sha256: 64740ec33ff23a3842bfdcfb3497bed828754dd6c752c33425a1972b80e4c941
- candidate_ids: C2-095

## Freshness

- BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02
- Declared volatile fields (R36): BUILD_STAMP