Bind mixed-provider precision to the rounded Gaussian tensor caller

[jmbarrancoml]

I identify an omitted incoming-height term in PR4100's literal common-grid allocation and give an exact constant-vector witness. The author allows inputs on 2^-(P+t0) Z[i] with magnitude at most 2^t0, then allocates a grid without t0. For t0=Bh+1, a constant input lies half a unit below the stated fractional grid and C preserves it. I propose one root allocation of P+t0+Bh fractional bits and t0+Bh+2 integer/sign bits.

I derive an explicit conditional reserve from all eight emitted THREE/FOUR base/extra programs. I reconstruct their canonical construction fields from the original words, regenerate the complete programs through the authenticated emitter and match the retained digests. The census includes initial corrections, backward center flushes, restoration and cleanup. Maximum scalar-height charge: 30,349; maximum division shift: 3. I count all 725,760 bridge ADDs per cover and retain the full native rank mass, giving

S=23431680*Gamma, E=99056520*Gamma+73, B=max(2,ceil((S+E)/25)).

I prove the recurrence by strong induction, including the growing leaf cutoff, without assuming monotonicity. I retain a separate shift-extent condition and add the Gaussian caller's raw-H conversion/restoration reserve. I do not exhibit a failing Gaussian execution or reject the proposed exponent.

I also bind an explicit rounding protocol to the actual six-H/Beneš compiler: rounded tables and cached suffix products, rounded diagonal outputs, and exact raw-H returns after H0 scale restoration. I prove a forward-error bound independent of scan length, account for temporary product widths and the complete cache/rounding scans, and derive O(p)-bit records even with O(p) incoming height. I retain the author's coefficient-generation and boundary-prefix norm hypotheses. CALLER.md gives the quantified protocol and its outer error-budget substitution.

I replay 34 trajectories through two distinct coarse-label programs, with eighteen raw-H calls and nineteen diagonals per trajectory, against separate original-gate endpoints. I observe nonzero rounding error, raw-H entrance height eight and temporary fractional width 511. Controls detect stale carries, incompatible global H signatures, omitted product rounding and omitted H0 restoration. The retained provider controls cover 4,394 scalar cases, 338 C/inverse-C cases and 54 incoming-height witnesses.

At 3e69c9360f609bdbf3617d35ea44f497f5506f93, all four ordinary/optimized registered checks pass. I passed the 45-file committed-byte/source-history preflight, official export integrity and all four Git-free export commands in 1.521, 1.569, 1.621 and 1.415 seconds, with all 46 files including the receipt unchanged. Export SHA256: 1e1bb43646fab5f790d861ed8288ec00970ecede8f1df8f98e866f97adda9aa0; receipt SHA256: dce18db1b3a1bad362f53060c1cc1d0a9d3c4cce228388a7a8be948258c47eb6. I retain the first revision's successful hosted/export receipt in the canonical Discussion.

I matched all four successful hosted records to the committed export and verified the successful unchanged-input step. Test merge a7ea76d10c99400669d116bcdb39870a598e1660 has the published tree 5d1a6bfaec5d97485342cc4c2bcc97f45649b5cb. Provider receipt: 6a5a920762c63f1b53cb46f9dc7139294372ff99006072207a9898f0b5479b3f; caller receipt: 60f8a60f8268bbc8717a4b505aca1cd39dc4e1e10d4fbdc0d6dd53af4b60f142.

I start from main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision 7, and pin PR4100 at 337d04939571a637aeab54a0f58f54fde811663a and PR4088 at 72d7efc181edb21806a878f174847c96dd410ab0. I refreshed main and checked both source heads, current feedback, the canonical claim and 100 recent PR records before submission. I record the broader bounded overlap search and scope in Discussion4175.

I leave the analytic coefficient/conditioning and rounded boundary-prefix estimates, native/free-algebra endpoints, physical execution and complete theorem acceptance open. I use an exact C/H0 interface model in the caller replay; I do not execute the physical mixed-provider cover. Yssite's PR4180 supplies separate finite-admission evidence. The conservative reserve constant has 2,650 bits; I claim an asymptotic existence bound, not a practical precision improvement. I keep the selected frontier unchanged.

Jose Manuel (jmbarrancoml), with substantial OpenAI Codex assistance. I credit Vlado Vojdanovski's compiler, ywz65's earlier simultaneous-rounding theorem, Cinna Davis's construction, AAAmirinu's prefix/divisibility/shift audit, Gareth Davidson's Horner analysis and the retained native lineage and source notices. My source-analysis agents belong to the author process; I claim no independent human or formal-kernel acceptance.