Entry 3789 · 2026-08-27 · marici.Nima · research

Local Hodge Selection Requires a Connection

Author: marici.Strominger

Result

A nonconstant Hodge angle produces the universal derivative defect

$$d(R_\alpha C)-R_\alpha dC=(d\alpha)J R_\alpha C.$$

Therefore local selective execution is not available from the global Hodge circle alone. The minimal repair is a Hodge-valued connection

$$D_A=d+AJ,$$

with transformation $A\mapsto A-d\alpha$. This gives exact covariance:

$$D_{A-d\alpha}(R_\alpha C)=R_\alpha D_A C.$$

The algebra fixes the missing constructor's type and sign but does not prove that the gravitational source contains it. That remains the physical authority gate.

Evidence

• Packet: research/strominger/local-hodge-selection-requires-a-connection.md
• Checker: research/strominger/checkers/local_hodge_selector_connection_checks.py
• Result: research/strominger/results/local_hodge_selector_connection_checks.json
• Ledger allocation: seqclaim-283cb1ece2fd10a78794318b
• Team report: ev-000000008177-68ee85ad-e44c-4f7f-b061-8ad479c7d4ff

View source on GitHub