Material Gate Calibration Table

Purpose

This note records the first material-calibration layer for the information-theoretic emergent throat and virtual Sidon selector model.

The proposed table is useful as a hypothesis table, but the listed sigma values must be treated as model outputs to be calibrated, not as measured facts. Material speed of sound and shock velocity alone do not determine Sidon density.

Core Correction

Material acoustic properties can parameterize the selector.
They do not directly measure Sidon density.

Correct dependency chain:

material parameters
  -> acoustic horizon / bandgap / damping parameters
  -> recoverable active-cell set I_active(N)
  -> finite-window active-cell counting
  -> nonseparable encoding Phi_N
  -> Sidon pair-sum audit
  -> compact-density receipt

Candidate Materials

Material type	Role in model	Expected behavior
Fused silica	low-loss stiff baseline	strong propagation; needs engineered isolation to suppress echoes
Lead	high-loss damping baseline	strong attenuation; may over-damp recoverable modes
Engineered resonator metamaterial	tunable selector candidate	best candidate because bandgap, damping, resonance, and horizon-like gradient can be tuned
Beryllium	high-rigidity low-loss baseline	useful contrast material; likely sparse unless engineered with lossy structure

Required Calibration Variables

Define a measured/calibrated identity quotient:

Q_id(N) = Recoverability(N) * Selectivity(N) * Compactness(N)

where:

Recoverability(N) = exp(-L_total) * R_repair
Selectivity(N)    = active fraction produced by shock/bandgap/phonon gates
Compactness(N)    = encoding-range efficiency after Phi_N or virtual pair-state projection

A physical material quotient can be written schematically as:

Q_mat = Z_eff * T_window * Gamma_bandgap * eta_mode * R_repair / gamma_diss

All factors must be nondimensionalized before comparison.

Acoustic Horizon Calibration

The Hawking-equivalent temperature cannot be determined from v and c_s alone. It depends on a gradient scale near the horizon:

T_eff = hbar/(2*pi*k_B) * kappa_eff
kappa_eff = |partial_x(c_s - v_flow)| at v_flow = c_s

Approximation:

kappa_eff ~ |c_s - v| / ell_h

Therefore the table must include:

ell_h = horizon gradient length scale

or the Hawking-temperature column remains schematic.

Audit Classification

Receipt: MaterialGateCalibrationTable
Status: HYPOTHESIS_CALIBRATION_DRAFT
Gate: U_scope
Reason: useful for selecting candidate substrates, but sigma values are not empirical receipts until derived from calibrated active-cell counts, loss model, and nonseparable encoding audit.

Required Receipts

MaterialParameterReceipt
AcousticImpedanceReceipt
GradientLengthScaleReceipt
BandgapTransmissionReceipt
DampingCoefficientReceipt
ModeOverlapReceipt
RepairOperatorReceipt
FiniteWindowActiveCountingReceipt
NonseparableEncodingReceipt
CompactDensityReceipt

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