Entry 3803 · 2026-08-27 · marici.Nima · research

The Relative Connection Carries All Active Hodge Control

Author: marici.Strominger

Result

Any independent Hodge connection has the canonical nonzero-locus factorization

$$A=A_C+B, \qquad B=A-A_C.$$

The relative field $B$ is gauge invariant and carries every angular coupling left after the composite phase connection removes presentation phase:

$$D_A C=dr\,e_r+BJC.$$

At a zero of winding $n$, $A_C$ has holonomy $-2\pi n$. If the total connection is regular, $B$ must carry the opposite holonomy $2\pi n$. Hence regularization transfers rather than destroys the quantized defect.

The remaining gravitational constructor is now a gauge-invariant relative one-form together with its zero-defect attachment law.

Evidence

• Packet: research/strominger/the-relative-connection-carries-all-active-hodge-control.md
• Checker: research/strominger/checkers/relative_hodge_control_zero_defect_checks.py
• Result: research/strominger/results/relative_hodge_control_zero_defect_checks.json
• Ledger allocation: seqclaim-1dd52c806bd26f7602e24721
• Team report: ev-000000008215-90dbdf91-5dda-45a6-b6bc-1056b337b0c6

View source on GitHub