Research-Stack/0-Core-Formalism/otom/docs/audit/FlexureMisalignmentReceipts.md

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Flexure Misalignment Receipt Checklist

Purpose

A flexure implies a deliberately misaligned local point: a controlled compliance defect inserted into a stiffer geometry. That defect may be useful because it localizes bending, creates anisotropic tension, and routes snap-through energy into a measurable dissipation path.

This note turns that idea into a receipt checklist for engineering validation.

Core Statement

flexure -> controlled misaligned point -> anisotropic local stress -> biased snap path -> measurable energy drainage

In the broader audit stack:

misaligned point       -> transfer index
flexure                -> compliant gate
unbalanced tension     -> anisotropic stress witness
snap-through           -> shock/alignment transition
hysteresis/damping     -> energy drainage witness
FEA/prototype evidence -> engineering proof receipts

Required Receipts

1. GeometryReceipt

The geometry must explicitly define the flexure and the misaligned point.

Minimum fields:

transfer_index
nominal_axis
actual_axis
misalignment
hinge_thickness
hinge_length
slot_depth or beam_length if applicable
fillet_radius if applicable

Pass condition:

misalignment > 0
hinge_thickness > 0
hinge_length > 0

2. MaterialModelReceipt

The material model must define enough parameters to evaluate stress and fatigue.

Minimum fields:

elastic_modulus
yield_strength
fatigue_limit
damping_coefficient
poisson_ratio
material_name

Pass condition:

all major material parameters are present and physically positive

3. FEASimulationReceipt

Simulation must show that the flexure creates a controlled imbalance without exceeding safety constraints.

Minimum outputs:

max_von_mises_stress
stress_margin
displacement_delta
reaction_force_delta
tension_imbalance
strain_energy
mesh_refinement_near_flexure
solver_type
boundary_conditions

Pass condition:

stress_margin > 0
tension_imbalance > 0
mesh and boundary conditions documented

4. PrototypeMeasurementReceipt

A physical prototype should confirm that the simulated flexure behavior appears in the real mechanism.

Minimum measurements:

measured_strain
measured_deflection
measured_force_delta
measured_snap_load
measured_recovery
instrumentation_method

Pass condition:

measured strain, deflection, and force difference are nonzero and match simulation within tolerance

5. EnergyDissipationReceipt

Energy drainage must be measured, not assumed.

Minimum measurements:

force_displacement_curve
loading_work
unloading_work
hysteresis_area
damping_loss
snap_event_energy_drop

Pass condition:

hysteresis_area > 0
or measured damping / snap energy drop is positive

6. FatigueSafetyReceipt

The flexure must survive the expected number of snap cycles.

Minimum fields:

tested_cycles
safe_cycles
crack_detection_method
post_test_geometry_check
maximum_strain_per_cycle

Pass condition:

tested_cycles <= safe_cycles
no unacceptable crack growth or plastic drift

Audit Gate

Receipt: FlexureMisalignmentReceipts
Gate: U_scope until all six receipts are supplied

Promotion condition:

GeometryReceipt
+ MaterialModelReceipt
+ FEASimulationReceipt
+ PrototypeMeasurementReceipt
+ EnergyDissipationReceipt
+ FatigueSafetyReceipt
=> Engineering V_scope

Important Boundary

This flexure receipt stack validates an engineering mechanism only. It does not prove the Sidon theorem, the compact density target, or the Burgers-Ruzsa arithmetic lock.

Correct dependency chain:

FlexureMisalignmentReceipts
  -> validates mechanical snap/dissipation plausibility
ShockBurgersCoupling
  -> validates transport/alignment model
BurgersRuzsaDecoupling
  -> separates selector from arithmetic lock
NonseparableEncodingReceipt
  -> required for global Sidon pair-sum injectivity
CompactDensityReceipt
  -> required for sigma = 1