Public research · 2026-09-21
Narrow CNG confirmation, not a global one
This pipeline’s predeclared oscillation passed on an unseen window. Discovery grades from 20 September stay on their own page. Global structure is not established.
2026-09-21 · narrow
A completed window, not a global confirmation
This pipeline’s predeclared oscillatory structure across the tested window. Not global asymptotics, not a validated infinite-frequency integral, not full HH RSET, not gate physics.
- Status
- CNG_CONFIRMATION_PASS
- Window
- 10.40 ≤ ω ≤ 10.90
- Angular gate
- 51/51 angular-accepted
- ε₁
- 37.5, held fixed, not fitted
- Grades
- The accepted record reports C1–C6 PASS.
Provenance
C5 was corrected. Both R² pairs are shown.
C5 was corrected from sequential residual fitting to joint-H1 source A/B transfer, with a fresh cubic fit on the target half. The older C5 audit contains intermediate variants. Those are not the final corrected statistic.
- Accepted directional R²
- 0.9988049064965246 · 0.9985764043986991
- Replay 2026-10-09
- 0.9988049064965255 · 0.9985764043986983
The last digits differ at floating-point roundoff. The replay agrees with the accepted pair. It is not a new fit and not an independent recomputation by this website.
Grid SHA-256 3b85d57c14510e1c53b008e792860b9376e3236d55cdd5b4954e4bd26a6b0289. The grid file is not in the public package. It is not a download.
History stays
Discovery grades are not rewritten
September 20 discovery grades D = FAIL and F = CRITERIA_GAP stay historical. Earlier HOLD and PASS_CONDITIONAL marks are not erased.
OUR_NUMERICAL_CNG_STRUCTURE_CONFIRMED stays false. ASYMPTOTIC_STRUCTURE_MIXED remains the literature classification. This is not a validated infinite-frequency integral, not full Hartle–Hawking RSET, and not gate physics.
Do not invent
What the public package does not contain
Individual definitions of C1, C2, C3, C4, and C6 are not in the public package. Only “C1–C6 PASS” plus the C5 correction is stated. The confirmation grid and the older C5 audit JSON are not published. Intermediate C5 variants are not given numbers here.
Plain-language terms
- PMR
- Pragmatic mode-sum regularization. Levi–Ori t-splitting: subtract a local frequency polynomial, then integrate the regularized remainder in a generalized sense.
- CNG
- Connecting-null geodesic. A remote caustic of the two-point function. After local subtraction it can remain as an oscillation in frequency, not as a term in F_sing.
- RSET
- Renormalized stress-energy tensor. The quantum source that would enter the semiclassical Einstein equation. Not yet independently reproduced here.
- HH
- Hartle–Hawking state. The thermal quantum state regular on both past and future horizons of an eternal black hole.
- GI / self-cancellation
- Generalized integral of a non-decaying oscillatory remainder. Finite-support numerical success is not a proof of the infinite-frequency limit.
- Ward
- Covariant conservation of the stress tensor. A stored primary-tolerance diagnostic is not full independent closure of that identity.
- E
- The finite local Hadamard counterterm removed after the frequency integral. A derivation candidate is not E_VALIDATED.
- B1
- First calibration benchmark: known Schwarzschild Hartle–Hawking physics. Partial. Not a portal test.
- φ²
- Renormalized field variance ⟨φ²⟩. On this Ricci-flat background the scalar variance does not depend on curvature coupling; the stress tensor does.
- Mτ
- Mixed Euclidean-time derivative of the Green function. The displayed-sign question is paused and unconfirmed.