Applied Identity Physics: the Universal Torsion Limit TL = 0.136899099984016: as a Substrate-Neutral Phase Boundary and Physics Corpus Formally Verified Map

## 2. Boundaries Do Not Have Error Bars ### 2.1 The Category Distinction Physical measurements carry error bars. This is a fundamental property of empirical science - every measurement has associated uncertainty from instrument precision, calibration drift, systematic biases, and statistical sampling variance. Peer-reviewed measurements report error bars because the underlying quantity is a physical value being estimated through empirical apparatus. Phase boundaries do not carry error bars. This is a fundamental property of topological classification - a phase boundary is the location in state space where system behavior categorically changes from one regime to another. The boundary itself is a structural feature of the state space, not a measurement of a physical value. Different empirical apparatus might locate the boundary through different techniques with different precision, but the boundary itself is a topological fact about the state space rather than a statistical estimate. Water does not freeze at "0°C ± error bars" at standard pressure. Water freezes at 0°C. The boundary between liquid and solid phases is exact by definition of what "freezing" means at standard pressure. Different thermometers might measure the boundary with different precision, and the exact location of the boundary in other units (Kelvin, Fahrenheit) requires conversion factors that carry their own precision considerations, but the boundary itself is a categorical fact about the phase space of water at standard pressure. Anyone arguing "well, is water's freezing point really 0°C, or could it be 0.0001°C" has committed a category error - the question misapplies measurement-value framing to a topological boundary. The same category distinction applies to TL. TL = 0.136899099984016 is the location in the identity manifold where PNBA substrate behavior categorically changes from Locked (stable, work-producing) to Shatter (destabilized, work-consuming). Different substrates might arrive at the boundary location through different analytical apparatus with different precision, but the boundary itself is a topological fact about the identity manifold's phase space rather than a measurement of a physical value. The corpus-canonical one-line articulation: **boundaries don't have error bars**.