CMB-SPECTRA-Σ · Spectra Signature Layer

DATA INPUT

Planck Spectrum JSON *

minimal · {"ell":[…],"Dl":[…],"channel":"TT"} or table form — no file loaded —

Bin Edges JSON * (admissible interface)

{"edges":[b0,b1,…,bm]} — fixed before run — no file loaded —

Channel

L_min

L0 (baseline cutoff)

L_grid mode

PROTOCOL (FROZEN)

operatorT_L (ℓ ≤ L)

baseline cutoff—

eval range—

bin edges B—

feature q_j(L)mean f(ℓ) in bin j under cutoff

Σord(L)π_L ranking permutation

σ_P(L)max_j |q_j(L) − q_j(L0)|

Δ_kq_(k)(L0) − q_(k+1)(L0) baseline sorted

V(L){k: Δ_k ≤ 2σ_P(L)}

ν(V(L))path matching (no adjacent k)

inv(L)Kendall inversion count vs baseline

falsifierinv(L) > ν(V(L))

descentΣord constant on interval

tie_rulestable_index (frozen)

rank_scopecommon_items_only (frozen)

INVARIANT STATUS

INTERFACE — OPERATOR — BASELINE — FALSIFIER — BINNING-INDEP OFF

COMPUTATION LOG

Ready. Load spectrum JSON + bin edges JSON, then press RUN Σ.

Overall

—

awaiting run

Descent Status

—

Boundary Activations

—

ν(V(L)) > 0

Primary Falsifier

—

inv(L) > ν(V(L))

Σ PANEL — CURRENT L L = —

Run chamber to populate

DESCENT & STRATIFICATION

Run chamber to populate

BASELINE GAP SPECTRUM Δ_k

Run chamber to populate

RANK COMPARISON π_L vs π_L0

Run chamber to populate

CMB-SPECTRA-Σ · Spectra Signature Layer — Operator-Manifold Descent