Enter, I-B-ECHO-v3, 2026, pp. 1-48
I-B-ECHO: Diffracted echoes and finite supplied-report instruments
Ngo Cheung
October 2026
Abstract
We study the apex-diffracted part of the massless Friedrichs Green operator on the prescribed conical product used in the Enter spacetime framework. The cone, its deficit, the bundle holonomy, and the extension are inputs. The continuum-to-register preparation is a separate assumption; a destructive finite instrument does not acquire an unknown continuum amplitude.
Starting from the explicitly stated I-B-G kernel, we derive the general twisted front coefficient and its high-frequency asymptotic. For the untwisted scalar, the leading coefficient agrees, in the declared Fourier convention, with the difference-angle term of Keller's wedge coefficient. The remainder is stated additively, including when the leading coefficient vanishes.
Two admissible time windows define a direct-pulse integral and an echo integral. Their calibrated ratio is a nonnegative weighted average of a closed scalar function. On 1/2 < α ≤ 1, it vanishes exactly at zero deficit. On every compact parameter sector avoiding backscatter shadow values, including sectors with α < 1/2, appropriately isolated windows satisfy explicit separation estimates. A sufficiently short, nonzero window also gives an injective averaged functional on each such sector. Supplied finite preparations, the X-J signal instrument, and complete X-K composition then give a total-variation lower bound with explicit implementation-error allowances. The actual classical outputs are finite codes and stochastic symbols, not exact real amplitudes.
For neutral smooth curvature cores, we prove agreement before a round-trip core time and convergence of spatially smeared records. We give a quantitative record-error bound in terms of exterior resolvent discrepancies and derive the associated Bessel matching coefficient. An explicit profile-uniform decay rate still requires additional estimates. The resulting non-reconstruction conclusion is finite-precision indistinguishability, not a theorem that finitely many exact real functionals are necessarily non-injective.
Twisted-scalar and spin-1 front identities are retained with their channel conventions. Twisted-core, vector-core, and curvature-regular spin-2 echo extensions remain open at specified interfaces. Numerical discrepancies from the supplied version are retained as unexecuted reports, not certificates. Standing refusals are frozen in the I-B-G Book Ledger v1; O.1 remains NOT_CLOSED; no downstream quantum admission or sourcing claim is made.
Bibliographic record
- Title
- I-B-ECHO: Diffracted echoes and finite supplied-report instruments
- Author
- Cheung, Ngo
- Publication date
- 2026/10/01
- Institution
- Enter
- Report number
- I-B-ECHO-v3
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 48
- Language
- en