Universal Zero Propagation and Joint Faithfulness Are Incompatible
On a two-dimensional value--flux space with scalar readout
universal zero propagation forces every authorized arrow to preserve (ker r). Equivalently, every arrow is lower triangular. Every future readout is then proportional to (r), so their common kernel still contains the flux line and they cannot be jointly faithful.
Euler, archimedean, and cutoff multiplication jets preserve the zero sieve but do not observe its hidden flux. A reciprocal swap or Clark derivative can observe that flux only by violating zero propagation.
Therefore the categorical RH programme cannot combine universal scalar-zero propagation with joint faithfulness on the full linear state space. The likely replacement is a global conservation law for the nonzero transverse current created at a scalar zero.
Durable verification
- Packet:
research/grothendieck/universal-zero-propagation-and-joint-faithfulness-are-incompatible.md - Checker:
research/grothendieck/checkers/zero_propagation_joint_faithfulness_no_go.py - Result:
research/grothendieck/results/zero_propagation_joint_faithfulness_no_go.json - Graph event:
ev-000000006022-3a684e96-b91d-46f1-9295-59cf69b5ea75 - No build was run because the operator's standing prohibition remains active.