UNNS Cosmology CMB Array

🛰

Injection Data Files  ·  CMB Observational Archive

REQUIRED INPUTS — load via chamber data loaders
📦
cmb_i_com_power+spectr.zip
CMB-I · TT power spectrum + binned spectra · Planck COM
ZIP 📦
cmb_ii_com_power+spectr.zip
CMB-II · TT + full-mission spectra · directional input
ZIP 📦
CMB-II_fullI.zip
CMB-II · full intensity alm coefficients · Σ v1+v2
ZIP 📦
CMB-III_stab.zip
CMB-III-STAB · perturbation ensemble · phase-randomized seeds
ZIP 📦
cmb_spectra_sigma.zip
CMB-SPECTRA-Σ · spectrum JSON + bin-edge JSON · Σord input
ZIP 🗄
lowell_alm.json
Low-ℓ alm coefficients · CMB-III geometry & integration layers
JSON

⬡ Preregistered Protocol — CMB Observational Arc

🌌 Navigation Guide — Understanding the Six-Chamber CMB Arc

What is this array?

This is the complete UNNS cosmological CMB investigation arc spanning six chambers. The arc tests whether recursive substrate dynamics, without external cosmological parameters, can reproduce the structural signatures observed in the Planck CMB data: acoustic peak ordering, directional alignment stability, geometric axis persistence, perturbation robustness, and spectral inversion hierarchy.

The Complete Arc

Chamber CMB-I — Acoustic Peak Order Stability Tests K=7 acoustic peak windows across ℓ_max truncation levels (L0 → L). Falsifier: any run where peak rank order is violated. Pass: RIGID ORDER DESCENT confirmed for both TT-binned and TT-full spectral variants, with BINNING STABLE check. Injection: cmb_i_com_power+spectr.zip.
Chamber CMB-II — Directional Rigidity (Σ v1 + v2) Extends CMB-I to the multipole axis domain. Computes the quadrupole/octopole preferred axis via Wigner D-matrices, Condon-Shortley Y_{2m} evaluations, and Jacobi eigenvalue decomposition. Tests whether the axis direction (eigenvector) remains rigid under ℓ_max truncation. Injection: CMB-II_fullI.zip + cmb_ii_com_power+spectr.zip.
Chamber CMB-III-GEO — Geometry Isolation Layer Isolates the geometric component of Phase 3: axis orientation stability at fixed low-ℓ alm input. Runs the multipole axis pipeline (u2, u3 eigenvectors) in isolation, without perturbation overlay. Establishes the baseline geometric fingerprint before stability testing. Injection: lowell_alm.json.
Chamber CMB-III-STAB — Perturbation Stability Layer Adds the phase-randomization overlay to CMB-III-GEO results. Phase-randomizes alm coefficients (preserving conjugacy for −m modes) across a seed ensemble, computing D_internal vs. null-distribution separation. Falsifier: null distribution fails to separate from observed. Injection: CMB-III_stab.zip + lowell_alm.json.
Chamber CMB-III-FULL — Phase 3 Integration Production integration of CMB-III-GEO and CMB-III-STAB into a single instrument. Runs the full pipeline: geometry isolation → perturbation ensemble → D_internal significance test → null_S / null_R summary grids. Single-file deployment. Injection: lowell_alm.json.
Chamber CMB-SPECTRA-Σ — Spectra Signature Layer Closes the arc with operator-manifold descent testing. Computes Σord(L): the π_L ranking permutation of spectral peaks at each truncation level. Tracks σ_P(L): the max rank displacement across bins. Tests whether V(L) — the budget set of operators within 2σ_P(L) — contains sufficient inversion capacity: inv(L) ≤ ν(V(L)). Injection: cmb_spectra_sigma.zip.

Injection Data Map

Each chamber requires specific injection files. Use the data loaders inside each chamber. The injection panel above lists all files; download the relevant ZIP/JSON and load via the chamber's DATA LOADER panel before pressing RUN.

CMB-I

Load cmb_i_com_power+spectr.zip → extracts TT-binned + TT-full spectrum JSON.

CMB-II

Load cmb_ii_com_power+spectr.zip (spectra) + CMB-II_fullI.zip (full alm). Both required for Σ v1+v2.

CMB-III-GEO / CMB-III-STAB / CMB-III-FULL

Load lowell_alm.json for geometric input. CMB-III-STAB additionally requires CMB-III_stab.zip for the perturbation ensemble.

CMB-SPECTRA-Σ

Load cmb_spectra_sigma.zip → extracts spectrum JSON + bin-edges JSON. Press RUN Σ after both files are loaded.

⟡ Six-Chamber CMB Instrumentation Array

Click any chamber card to open the instrument. Load injection data before running.

Phase 1 & 2 — Truncation Stability · Acoustic & Directional
CHAMBER CMB-I · v1.0.0
Role: Acoustic Peak Order · ℓ_max Truncation Stability
Acoustic Peak Order Stability
Under ℓ_max Truncation
Tests whether the rank ordering of K=7 acoustic peak positions in the CMB TT power spectrum is preserved as the multipole ceiling ℓ_max is varied from baseline L0 down to successively lower truncation levels. Runs both TT-binned and TT-full spectral variants with a BINNING STABLE cross-check. Exports a full artifact JSON for reproducible downstream analysis. PROTOCOL LOCKED — peak windows preregistered before first data load.
Verdict states: ✓ RIGID ORDER DESCENT (pass) · ⚠ FALSIFIER DETECTED (fail) · ◈ BOUNDARY DEGENERACY — BOUND HOLDS (boundary) · ◎ PARTIAL COVERAGE (incomplete) · Cross-variant robustness: BINNING STABLE check across TT-binned vs TT-full · Peak windows K=7, preregistered, injection-locked
K=7 peaks TT-binned + TT-full Protocol locked Artifact JSON export Binning stability check
Inject: cmb_i_com_power+spectr.zip Planck TT COM ℓ_max sweep Binning stability Falsifier: rank inversion
✦ Acoustic peak order stability: is the recursive operator's rank structure preserved as cosmological resolution is degraded? Null result = structural order lost at truncation. Positive result = RIGID ORDER DESCENT — order is a deep substrate property, not resolution artifact.
✦ Protocol Locked · Acoustic Order · v1.0.0
CHAMBER CMB-II · v1.0.0
Role: Directional Rigidity · Multipole Axis Alignment · Σ v1+v2
Directional Rigidity
Under ℓ_max Truncation (Σ v1+v2)
Extends CMB-I to the directional domain. Computes the preferred axis of CMB quadrupole and octopole structure using Wigner D-matrices, Condon-Shortley Y_{2m} spherical harmonics, and Jacobi eigenvalue decomposition on the multipole alignment tensor. Tests whether the principal eigenvector (preferred axis) remains stable — within preregistered angular tolerance — as ℓ_max is truncated. Σ v1+v2 combines full-intensity alm coefficients with power spectral input for the complete directional test.
Axis computation: Jacobi 3×3 eigensystem · Y_{2m} Condon-Shortley phase locked · Degenerate axis fallback: status = "axis_degenerate" when eigenvalues nearly equal · Verdict chain: ✓ RIGID ORDER DESCENT · ⚠ FALSIFIER DETECTED · ◈ BOUNDARY DEGENERACY · Cross-variant: TT-binned vs TT-full comparison with BINNING STABLE check
Wigner D-matrix Y_{2m} locked phase Jacobi eigensystem Σ v1 + v2 2 inject files Axis stability
Inject: cmb_ii_com_power+spectr.zip Inject: CMB-II_fullI.zip ℓ=2,3 axis Phase convention locked Falsifier: axis drift
◈ Directional rigidity: does the UNNS substrate impose a persistent preferred direction in the CMB sky? Rigid axis under truncation suggests deep geometric locking. Axis degenerate fallback guards against numerical degeneracy false positives.
◈ Directional Rigidity · Σ v1+v2 · v1.0.0
Phase 3 — Geometry & Stability · Decomposed + Integrated
CHAMBER CMB-III-GEO · v0.2.0
Role: Geometry Isolation Layer · Axis Orientation Baseline
CMB-III Geometry Isolation
Low-ℓ Axis Baseline
Phase 3 decomposed — geometry layer only. Runs the multipole axis pipeline in isolation: computes u2 (quadrupole eigenvector) and u3 (octopole eigenvector) from the lowell_alm.json input without perturbation overlay. Establishes the baseline geometric fingerprint — axis orientation, eigenvalue gap, and degenerate fallback handling — before any phase-randomization testing. Prerequisite for CMB-III-STAB and CMB-III-FULL.
Outputs: u2 axis orientation · u3 axis orientation · eigenvalue gap (ev0−ev1)/scale · Degenerate guard: returns {axis: null, status: "degenerate"} when gap < 1e-6 · Fallback: status = "degenerate_fallback" with alternate axis estimate · Input: lowell_alm.json (low multipole alm coefficients)
u2 eigenvector u3 eigenvector Eigenvalue gap test Degenerate guard Baseline geometry
Inject: lowell_alm.json Geometry only u2 axis u3 axis Feeds: III-STAB, III-FULL Falsifier: axis shift
⬡ Geometry isolation: establishes the pure axis fingerprint before any stability perturbation is applied. Degenerate fallback prevents false rigidity claims when eigenvalue gap is below the numerical floor.
⬡ Geometry Isolation · v0.2.0
CHAMBER CMB-III-STAB · v0.2.0
Role: Perturbation Stability Layer · Phase-Randomization Ensemble
CMB-III Perturbation Stability
Phase-Randomization Test
Phase 3 decomposed — stability layer only. Applies phase-randomization to the lowell_alm input across a multi-seed ensemble, preserving conjugacy for −m modes (using a secondary PRNG seeded at seed + 0x12345678). Computes D_internal: the internal dispersion of axis orientations across the ensemble. Compares against the null distribution (shuffled phases) to determine whether the observed axis clustering is statistically separable. Injection: CMB-III_stab.zip for the perturbation ensemble seeds.
Phase randomization: m=0 magnitude preserved, new phase drawn · m>0: random phase, conjugacy enforced for −m · Secondary seed: (seed + 0x12345678) >>> 0 · Output metrics: D_internal · null_S_summary · null_R_summary per L-value · Falsifier: null distribution encloses observed D_internal (no separation)
Phase randomization Conjugacy enforced D_internal metric Null distribution 2 inject files
Inject: CMB-III_stab.zip Inject: lowell_alm.json Phase ensemble Conjugacy: −m Falsifier: no separation
◈ Perturbation stability: is the axis clustering robust against phase perturbation, or is it a phase-coherence artifact? Null separation = stable. No separation = phase-driven. D_internal separation is the critical falsification threshold.
◈ Perturbation Stability · Phase Ensemble · v0.2.0
CHAMBER CMB-III-FULL · v1.2.0
Role: Phase 3 Integration · Geometry + Stability · Production
CMB-III Full Integration
Phase 3 Production Instrument
Full Phase 3 integration: combines CMB-III-GEO and CMB-III-STAB into a single production-ready instrument. Runs the complete pipeline: low-ℓ alm geometry extraction → axis orientation (u2, u3) → perturbation ensemble with phase-randomization → D_internal computation → null_S / null_R significance grids → global verdict. Single-file deployment with no external dependencies. Renders null distribution summary grids and imports summary for artifact export.
Full pipeline: geometry isolation → perturbation stability → D_internal significance · Outputs: null_values_summary · null_S_summary (per L) · null_R_summary (per L) · z-score and p-value verdict columns · Degenerate fallback integrated · Artifact JSON export for downstream Phase 4 coupling
Full pipeline Null grids S + R z + p-value table Single-file deploy Artifact JSON v1.2.0
Inject: lowell_alm.json Integrates: GEO + STAB Null S + R grids Degenerate fallback Feeds: Phase 4 Falsifier: global FAIL
✦ Phase 3 Integration: the authoritative Phase 3 instrument. Combines both sub-layers into a production verdict with full significance reporting. Use CMB-III-GEO and CMB-III-STAB for isolated debugging; use CMB-III-FULL for publication-ready results and artifact generation.
✦ Phase 3 Integration · Production · v1.2.0
Phase Σ — Operator-Manifold Descent · Spectral Inversion Budget
CMB-SPECTRA-Σ · v0.1.0
Role: Spectra Signature Layer · Operator-Manifold Descent
CMB-SPECTRA-Σ
Operator-Manifold Descent Test
Closes the CMB arc with the operator-manifold descent protocol. Computes Σord(L): the ranking permutation π_L of spectral peaks at each truncation level ℓ ≤ L. Tracks σ_P(L): the maximum rank displacement max_j |q_j(L) − q_j(L0)| across bins. Constructs the inversion budget set V(L) = {k : Δ_k ≤ 2σ_P(L)} and tests the descent falsifier: inv(L) > ν(V(L)) at any L — inversion count exceeds the budget. Load spectrum JSON + bin-edges JSON, then press RUN Σ.
Protocol: T_L: ℓ ≤ L · fixed bins B · Σord(L) permutation ranking · σ_P(L) = max_j |q_j(L) − q_j(L0)| · V(L) budget set · Verdict: DESCENT CONFIRMED (pass) or STRATIFIED (partial) · PASS: overallPass = true · Binning independence test: OFF by default
Σord ranking σ_P displacement V(L) budget set inv(L) threshold DESCENT CONFIRMED 2 inject files
Inject: cmb_spectra_sigma.zip Σord permutation σ_P(L) displacement V(L) budget DESCENT CONFIRMED Falsifier: inv > budget
◈ Operator-manifold descent: the final arc test. Does the spectral inversion count remain within the structural budget at every truncation level? Budget respected = DESCENT CONFIRMED. Budget exceeded = STRATIFIED or FALSIFIER, requiring operator redesign or extended V(L) construction.
◈ Operator-Manifold Descent · v0.1.0

🔗 Complete Arc — CMB-I → CMB-II → CMB-III-GEO → CMB-III-STAB → CMB-III-FULL → CMB-SPECTRA-Σ

  Chamber CMB-I       ──  Does recursive structure preserve acoustic peak ordering?
       ↓                   K=7 preregistered windows · TT-binned + TT-full · ℓ_max sweep
       ↓                   Falsifier: any rank inversion · Pass: RIGID ORDER DESCENT
       │                   Binning stability cross-check: TT-binned vs TT-full agreement
       │                   Injection: cmb_i_com_power+spectr.zip
       │
  Chamber CMB-II      ──  Is the preferred CMB axis rigid under truncation?
       ↓                   Wigner D-matrices · Condon-Shortley Y_{2m} (phase locked) ·
       ↓                   Jacobi 3×3 eigensystem · u2 + u3 axis vectors
       │                   Degenerate guard: eigenvalue gap < 1e-6 → axis_degenerate
       │                   Injection: CMB-II_fullI.zip + cmb_ii_com_power+spectr.zip
       │
  Chamber CMB-III-GEO ──  What is the pure geometric axis fingerprint at low ℓ?
       ↓                   Geometry isolation only: no perturbation · u2, u3 baseline
       ↓                   Eigenvalue gap test · Degenerate fallback protocol
       │                   Injection: lowell_alm.json
       │
  Chamber CMB-III-STAB──  Is the axis stable under phase perturbation?
       ↓                   Phase-randomization ensemble · conjugacy enforced for −m
       ↓                   D_internal metric · null_S / null_R distributions
       │                   Falsifier: null distribution engulfs D_internal
       │                   Injection: CMB-III_stab.zip + lowell_alm.json
       │
  Chamber CMB-III-FULL──  What is the integrated Phase 3 verdict?
       ↓                   Full pipeline: GEO + STAB → D_internal → z/p verdict table
       ↓                   Null summary grids · Artifact JSON export
       │                   Production instrument · single-file deployment
       │                   Injection: lowell_alm.json
       │
  CMB-SPECTRA-Σ       ──  Does the spectral inversion count stay within the budget?
                          Σord(L) permutation · σ_P(L) max displacement · V(L) budget set
                          Falsifier: inv(L) > ν(V(L)) at any truncation level
                          Verdict: DESCENT CONFIRMED · STRATIFIED · PASS / FAIL
                          Injection: cmb_spectra_sigma.zip

  ──────────────────────────────────────────────────────────────────────────────
  Acoustic peak order tests deep rank structure of recursive operator output.
  Directional rigidity tests whether substrate geometry projects a persistent sky axis.
  Phase 3 decomposition (GEO + STAB) isolates geometry from phase coherence effects.
  D_internal null separation is the critical test: axis clustering must exceed chance.
  Spectral descent budget closes the arc: ν(V(L)) bounds all admissible rank violations.
  CMB ARC OPEN. Each chamber exports JSON for cross-chamber coupling analysis.
  ──────────────────────────────────────────────────────────────────────────────

The CMB arc does not claim to "derive cosmology" — it tests whether specific structural signatures of the Planck CMB data (ordering, directionality, stability, spectral descent) can be reproduced by recursive substrate dynamics without external cosmological parameters. Null results are structural findings: they constrain the operator space and the framework. Positive results motivate the publication arc.

UNNS Research Collective | Acoustic Stability · Directional Rigidity · Phase 3 Geometry & Stability · Spectral Descent

Cosmological CMB arc: from peak order stability through operator-manifold descent

TauFieldEngineN · Cosmology CMB Arc · Chambers CMB-I · CMB-II · CMB-III · CMB-SPECTRA-Σ · Array v1.0.0 · March 2026

This array instruments the complete UNNS cosmological CMB arc spanning six chambers. "Recursive Substrate Signatures in the CMB: Acoustic Order, Directional Rigidity, and Spectral Descent" synthesises the arc: Chamber CMB-I establishes that recursive operators preserve acoustic peak rank ordering under ℓ_max truncation (Rigid Order Descent); Chamber CMB-II extends the test to the multipole preferred axis, checking directional rigidity via Wigner D-matrix alignment; Chambers CMB-III-GEO and CMB-III-STAB decompose Phase 3 into isolated geometry and perturbation stability layers, with CMB-III-FULL providing the integrated production verdict; and CMB-SPECTRA-Σ closes the arc by testing whether the inversion budget ν(V(L)) is never exceeded across the full spectral truncation sweep.

Chambers ≠ Proofs. Each chamber is a falsification instrument operating on Planck observational data. Protocol-locked preregistration prevents post-hoc threshold adjustment. Null results constrain operator architecture. Positive results enter the publication pipeline. The arc is open.