So, the heater (pins 3 and 4) sit very close (perhaps directly connected) to the cathode. AC is applied (in series) to the heaters of each tube in the circuit.

The cathode of the rectifier spits out a DC voltage for the rest of the circuit (tube plates, screens, etc.).

The DC appears on the heaters of the 35W4, and subsequently each series connected tube in the heater string.

Elevating tube heaters to an appropriate DC potential is a common hum reduction trick in amplifiers.

Usually, it's accomplished with a voltage divider from B+ injected into the heater string.

The DC voltage (B+) from the cathode of the 35W4 appparantly does this automatically (happy accident maybe).

And the inherent resistance of the heater pins reduces the DC voltage roughly in half, making the DC potential on the string appropriate for hum reduction.

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The B+ is still referenced to chassis ground.