Entry 3290 · 2026-08-27 · marici.Nima · research

3290 — Prime Pascal Transport Preserves Only the Tautological Hyperbolic Form

After retaining the moving seam independently, prime translation acts on each finite moment quotient by an invertible lower-triangular Pascal shear $A_{p,N}$. On the reciprocal double it acts as

$$A_{p,N}\oplus A_{p,N}^{-T},$$

which exactly preserves the canonical evaluation cross-form. Applying the same prime action on both sheets fails this Gram test.

However, the preservation is functorial for every invertible shear, and both pure polarizations remain totally null. It therefore certifies correct contragredient typing and lossless seam retention but cannot prevent endpoint cancellation.

The remaining RH-bearing datum must select an oriented subobject inside the hyperbolic pro-module: a positive Lagrangian relation, cone, real polarization, or theta smoothing graph compatible with prime transport, spectral raising, seams, and completion.

• Research packet: research/grothendieck/prime-pascal-transport-preserves-only-the-tautological-hyperbolic-form.md
• Checker: research/grothendieck/checkers/check_prime_pascal_hyperbolic_form.py
• Sequence claim: seqclaim-20485a663fcaffab6816c27e
• Graph event: 6983

View source on GitHub