Shockwave Eigenvalue Comparison

Date: 2026-05-09

Status: EIGEN_GAP_AUDIT

Claim boundary: this note checks the external stellar shock / CIGaRS equation layer against the repo's current eigenvalue surfaces. It does not claim astrophysical validation, cosmological validation, or a new physical spectrum. It records where the current basis already has signal, and where it has a visible gap.

External Equation Layer

The CIGaRS paper is not a shock-hydrodynamics paper. Its useful contribution to this stack is the joint latent forward-model pattern:

host galaxy state + supernova occurrence + dust + selection + cosmology
  -> simulated observation
  -> simulation-based inference

The concrete equations that matter for the stack are:

SFH^h = [SFH^{h,j}]_{j=1..7}
sum_j SFH^{h,j} = M_*^h

DTD(t_*) = A * (t_* / Gyr)^b * M_sun^-1 * yr^-1

<N_SN^{h,j}> =
  T / (1 + z^h) * SFH^{h,j} * DTD(t_*^{h,j})

N_SN^{h,j} ~ Poisson(<N_SN^{h,j}>)

Sources:

Phys.org summary: https://phys.org/news/2026-05-universe-sharpen-cosmic-expansion-dark.html
Nature Astronomy CIGaRS paper: https://doi.org/10.1038/s41550-026-02842-5

The stellar shockwave layer is different. It gives the physical bow/front equations that can sharpen the local shock model:

R_s(t) = xi * (E * t^2 / rho_0)^(1/5)
v_s(t) = (2/5) * R_s(t) / t

rho_1 * u_1 = rho_2 * u_2
P_1 + rho_1 * u_1^2 = P_2 + rho_2 * u_2^2
h_1 + u_1^2 / 2 = h_2 + u_2^2 / 2

tau ~= c / v_s
t_diff ~= (delta R)^2 / (c * l)
t_dyn ~= delta R / D_s
breakout when t_diff ~= t_dyn

Shock-breakout source:

MNRAS, "Coupling of matter and radiation at supernova shock breakout": https://doi.org/10.1093/mnras/sts577

Current Repo Eigen Surface

The current physics eigen map records these relevant clusters:

Layer	Repo surface	Eigenvalue	Strength	Local meaning
Radiation / absorption	Cluster 1: Electromagnetism & Circuits	`0.968750`	`0.176777`	Beer-Lambert, EM wave, Poynting layer
Diffusion / material transport	Cluster 2: Condensed Matter & Superconductivity	`0.969697`	`0.174078`	Einstein diffusion relation
Radiation spectrum	Cluster 3: Quantum Mechanics & Particle Physics	`0.970588`	`0.171499`	Planck / radiation-law layer
Acoustic impedance / material boundary	Cluster 4: Materials Science & Engineering	`0.992063`	`0.089087`	Klemens acoustic mismatch
Local stack shock alignment	Cluster 5: Cognitive & Semantic Systems	`0.998464`	`0.039193`	Shockwave alignment / relaxation
Classical hydrodynamic shock laws	Detonics & Shock Physics entries	current cluster entry	`0.000000`	ZND, Taylor-Sedov, Rankine-Hugoniot, CJ, Mie-Gruneisen are present but not active

Local evidence:

3-Mathematical-Models/physics_eqs_eigenvector_mapped.md
3-Mathematical-Models/eigenvector_tsm/eigenvector_hyperfluid_150_steps.json
0-Core-Formalism/otom/formal/lean/SidonAudit/ShockBurgersCoupling.lean
0-Core-Formalism/otom/formal/lean/SidonAudit/ShockwaveAlignmentRelaxation.lean
shared-data/network_topology_database.json

Result

The external shock equations do not contradict the current eigenvalues. They expose a missing physical-shock axis.

What the stack already has:

shock as local alignment / discharge / relaxation
shock as discrete Burgers-style flux / dissipation
shock as rain-impulse / statolith threshold gate

What the stack does not yet strongly encode:

shock as radiation-hydrodynamic breakout
shock as Rankine-Hugoniot conservation surface
shock as Sedov-Taylor self-similar expansion
shock as optical-depth release gate

So the correct decision is:

HOLD_ADD_PHYSICAL_SHOCK_EIGEN_AXIS

Proposed Sharpened Axis

Add a physical shock eigen lane with five required components:

front propagation:
  R_s(t), v_s(t)

jump conservation:
  mass, momentum, enthalpy Rankine-Hugoniot receipts

radiation escape:
  tau ~= c / v_s

diffusion release:
  t_diff ~= t_dyn

host / context prior:
  CIGaRS-style latent context and systematic-residual lane

Minimum gate:

if missing Rankine-Hugoniot receipt:
  HOLD_PHYSICAL_SHOCK_AXIS
elif tau > c / v_s and t_diff > t_dyn:
  HOLD_BURIED_SHOCK
elif abs(tau - c / v_s) <= epsilon_tau
     and abs(t_diff - t_dyn) <= epsilon_t:
  ADMIT_BREAKOUT_GATE
else:
  HOLD_RESIDUAL_CONTEXT

Interpretation For The Drawn Shock-Bow Map

Your 2D shock-bow diagram can be treated as a compressed projection of this new axis:

curved bow fronts     -> shock-front geometry
square / center gate  -> local conservation cell
colored crossing arcs -> competing diffusion / radiation / material modes
12 / 28 bands         -> occupancy or angular bins for survivor routes

That means the drawing is strongest as a routing receipt, not as a literal stellar surface model. The physical lane adds the equations needed for the receipt to stop being only geometric and become testable against shock-front physics.

Next Work

Add PhysicalShockEigenAxis as a receipt surface.
Build fixture cases for buried shock, breakout gate, and missing conservation.
Add the public underwater shock benchmark as a non-operational historical modeling lane: shock-front arrival, attenuation, bubble-pulse eigenmode, boundary reflection, and residual.
Re-run the eigen remapper and require the Detonics & Shock Physics entries to move from strength 0.000000 to a declared nonzero support lane before promotion.

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