molecularGateSeconds
plain-language theorem explainer
The definition converts the molecular gate timescale from its picosecond value to seconds via direct unit scaling. Researchers examining the tau-gate hypothesis in Recognition Science would cite it to align the biological gate duration with the tau lepton mass at rung 19 on the shared phi-ladder. It is a one-line conversion definition that supplies the time input for the identity structure and falsification checks.
Claim. Let $t_{gate}$ denote the molecular gate timescale. Then $t_{gate} = $ psToSeconds$(t_{gate, ps})$, where $t_{gate, ps}$ is the gate duration in picoseconds and psToSeconds converts the value to seconds.
background
The RRF Hypotheses module frames the tau-gate hypothesis as an explicit claim that the tau lepton mass and molecular gate timescale occupy rung 19 on the same phi-ladder. The phi-ladder scales physical quantities by successive powers of phi, with the rung obtained from the base-phi logarithm of the ratio to a chosen base mass or time. Upstream, the Gate structure from CircuitLedger supplies the discrete gate model with parent indices forming a DAG, while the rung definition from Compat.Constants initializes the scaling index used for both mass and time ladders. The module doc states that the tau mass of approximately 1.777 GeV and gate time of approximately 68 ps are hypothesized to coincide at this rung, not by accident.
proof idea
This is a one-line definition that applies the psToSeconds conversion function directly to the molecularGatePS constant.
why it matters
This definition supplies the time value in seconds for the TauGateIdentity structure, which asserts that both the tau mass and gate time sit at rung 19 on the phi-ladder. It feeds directly into tauGateFalsified, which checks whether natural bases exist that place both quantities at rung 19 or whether other lepton generations fit the same ladder. In the Recognition framework it instantiates the T6 phi fixed point and T7 eight-tick octave scaling for cross-domain predictions, touching the open question of whether the rung coincidence is forced by the Recognition Composition Law or remains numerological.
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