Cosmological Boundary Routing — STRUC-PERC-I v2.5.0 · Bridge v1.1 · α-Deformation v2.2
Pilot Corpus · 2026
Cosmological
Boundary Routing DASHBOARD
Structural Classification of Terminal Approach, Finite Bounce, and Cosmological Recession
A three-dataset structural study of cosmological model trajectories processed through the UNNS boundary-routing framework. Classical Friedmann contraction, the direct post-bounce LQC encoding, and Planck-anchored ΛCDM expansion each return Full-percolation, while the full LQC bounce path is analyzed through α-deformation and Bridge v1.1 — identifying three distinct route-topology classes and establishing that singularity avoidance is not fully characterized by bounded curvature alone, but by the replacement of terminal route topology with admissible turning topology.
3/3
Full-percolation
zero Hard/Giant/Tail
zero Hard/Giant/Tail
7.5×
κconn ratio
B / A,C
B / A,C
0.306
B mean pressure ρ̄
Weak Persistence
Weak Persistence
98.83%
B α-admissibility
persistence
persistence
0
Unstable rows
exact bounce crossing
exact bounce crossing
Route Topology — Shared Coordinate
Bridge v1.1
Route coord. s ∈ [−1,+1]
Signed flow
Path-intrinsic
Dataset Architecture
All Full
A
Classical Friedmann Contraction
Synthetic · Planck 2018 params · H < 0 · 4001 rows
a = 1 → 10−8 · route coordinate −1 → 0
a = 1 → 10−8 · route coordinate −1 → 0
κ = 0.01334
GRinit = 0.977
FULL
GRinit = 0.977
FULL
B
Effective LQC Bounce
Synthetic · eff. LQC v2.2 · ρc = 0.41 ρPl · 4001 rows total
contraction + bounce (H=0) + expansion · route −1 → 0 → +1
Direct κ/GR: post-bounce expansion ladder · n = 2000
Full 4001-row path → α-deformation + Bridge v1.1
contraction + bounce (H=0) + expansion · route −1 → 0 → +1
Direct κ/GR: post-bounce expansion ladder · n = 2000
Full 4001-row path → α-deformation + Bridge v1.1
κ = 0.10000
GRinit = 0.533
FULL
GRinit = 0.533
FULL
C
Planck 2018 ΛCDM Expansion
Planck 2018 best-fit · PR3 TTTEEE+lowl+lowE · 4001 rows
H0 = 67.32 km/s/Mpc · route coordinate 0 → +1
H0 = 67.32 km/s/Mpc · route coordinate 0 → +1
κ = 0.01334
GRinit = 0.977
FULL
GRinit = 0.977
FULL
STRUC-PERC-I · STRUC-I Log
v2.5.0 / v1.0.4
[A] classical_friedmann → FULL_PERCOLATION
[A] κ_conn = 0.013335 · GR_init = 0.97675
[A] n_comp_init = 77 · GR_final = 1.000
[A] STRUC-I: Stable Structure
[A] mean_rho = 0.04157 · max_rho = 0.290
[B] lqc_bounce_expansion → FULL_PERCOLATION
[B] κ_conn = 0.100000 · GR_init = 0.53277
[B] n_comp_init = 22 · GR_final = 1.000
[B] STRUC-I: Weak Persistence
[B] mean_rho = 0.30605 · max_rho = 0.636
[B] rho@kappa=1 = 0.451
[C] planck_lcdm → FULL_PERCOLATION
[C] κ_conn = 0.013335 · GR_init = 0.97675
[C] STRUC-I: Stable Structure
[C] mean_rho = 0.04163
[★] κ_conn ratio B/A,C = 7.50
[★] pressure ratio B/A,C = 7.36
0
Hard · Giant · Tail
7.5×
κconn ratio B/A,C
Connectivity & Structural Pressure
κ-threshold · ρ̄
κ_connect (max = B = 0.1000)
Mean structural pressure ρ̄ (max = B = 0.306)
B: Weak Persistence · A,C: Stable Structure
All A_κ = 1.000 throughout · admissibility distinct from depth
All A_κ = 1.000 throughout · admissibility distinct from depth
α-Deformation · Instability Localization
v2.2 · 84 000 rows
α-Admissibility Persistence — scale 98% → 100%
Dataset B — Instability by Region
Measured: symmetric turning-shell localization (491 / 0 / 491).
Interpretation: Turning-Locus Shielding Hypothesis 9.1 — pending replication.
Interpretation: Turning-Locus Shielding Hypothesis 9.1 — pending replication.
Empirical Phase-Sign Vectors & Signed Flows
Bridge v1.1 · Q90 normalized
A — terminal
Σ̄ = (−, +, +, −)
route: −1 → 0
B pre-bounce
Σ̄ = (−, +, ≈0, −)
route: −1 → ≈0
B turning surface
Σ̄ ≈ (0, 0, 0, 0) · H̄ = 1.76×10⁻⁴
s ≈ 0 · 2 intervals
B post-bounce
Σ̄ = (+, −, ≈0, +)
route: ≈0 → +1
C — recession
Σ̄ = (+, −, −, +)
route: 0 → +1
Phase-mean signed flows (normalized) · bar scale ±0.5
A — Terminal approach
Δln a
−0.500
density
+0.463
margin
−0.093
C — Boundary recession
Δln a
+0.500
density
−0.463
margin
+0.093
B pre-bounce
Δln a
−0.305
density
+0.299
margin
−0.100
B post-bounce ≈ −pre
Δln a
+0.305
density
−0.299
margin
+0.100
LQC Bounce Parameters
Dataset B · v2.2
Equation: H² = H₀² ρrel(1 − ρrel/ρc,rel)
ρc: 0.41 × ρPlanck
abounce: 2.468 × 10⁻³²
H at bounce: 0 (exact)
ρ/ρc at bounce: 1 (exact turning surface)
Branch time → a=1: 13.799 Gyr
Planck age ref.: 13.797 Gyr
Age diff.: < 0.01%
ρ/ρc=1 at the bounce marks the route-reversal coordinate,
not structural failure. The trajectory is tested-admissible at the turning locus
under all applied α-deformations.
Formal Layer — Key Results
Definitions · Propositions
Singularity avoidance is not fully characterized by bounded curvature alone. Structurally, it is the replacement of terminal route topology with admissible turning topology.
Prop. 9.1 — Full(A) ∧ Full(B) ∧ Full(C) ⇏ A ≡route B ≡route C
Prop. 9.2 — A,C magnitude-degenerate; B magnitude-distinct
Prop. 9.3 — Pilot-corpus verified result (3-layer)
Conj. 9.1 — Boundary routing for non-singular cosmologies
Hyp. 9.1 — Turning-locus shielding pattern
Conj. 9.2 — Phase-sign reversal as turning signature
Hyp. 17.1 — Perturbation continuation
Hyp. 17.2 — Route-localized spectral modification
Hyp. 17.3 — Background-symmetry transfer test
Open Problem 14.1: canonical boundary metric dℳ
— nonnegative on represented routes; zero only at a verified terminal boundary;
strictly positive at an admissible turning locus.
Cross-Model Route-Topology Taxonomy
Boundary Routing Framework
Model Family
Expected Route Topology
Status
Classical singular Friedmann contraction
Represented terminal approach (−1 → 0)
Realized · A
Effective LQC bounce
Finite turning-locus routing (−1 → 0 → +1) · phase-sign reversal
Realized · B
Planck-anchored expanding ΛCDM
Boundary recession (0 → +1) · ⟨fm⟩ > 0
Realized · C
Ekpyrotic nonsingular bounce
Turning-locus routing · possibly asymmetric pre/post Σ̄P
Prediction
Matter-bounce models
Turning-locus routing · different ρ̄ and ronset profile
Prediction
Modified-gravity bounce (f(R), Galileon)
Model-dependent turning; different κconn, ρ̄ than LQC
Prediction
Cyclic bounce models
Repeated turning-locus routing; multiple route-zero loci
Prediction
Emergent-universe models
Quasi-stationary corridor followed by boundary recession
Open
Conformal Cyclic Cosmology
Cross-chart continuation or conformal junction — requires extended chart
Open
Unifying question:
terminal obstruction
|
admissible turning
|
boundary recession
|
cross-chart continuation
— Route topology, not equations alone.
Boundary Routing Morphologies
Two Corpora
Stellar — Branching Routing
Pre-collapse → light curves → spectral series.
All 10/10 FULL · ABC bridge: dAB=0.401 weak · dBC=1.287 strong · A→B contact, C branches.
Catastrophe ≠ structural destruction.
Route: identity-preserving path broken; multiple admissible downstream regimes.
All 10/10 FULL · ABC bridge: dAB=0.401 weak · dBC=1.287 strong · A→B contact, C branches.
Catastrophe ≠ structural destruction.
Route: identity-preserving path broken; multiple admissible downstream regimes.
Cosmological — Turning-Locus Routing
Contraction → bounce → expansion.
3/3 FULL · Bridge v1.1: Σ̄post ≈ −Σ̄pre · route reversal at finite admissible locus.
Singularity avoidance = route-topology replacement.
Route: identity-preserving path continuous; reversed orientation through a finite tested-admissible locus.
3/3 FULL · Bridge v1.1: Σ̄post ≈ −Σ̄pre · route reversal at finite admissible locus.
Singularity avoidance = route-topology replacement.
Route: identity-preserving path continuous; reversed orientation through a finite tested-admissible locus.
Γ₁ ≡route Γ₂ ⇏ Pℛ,1(k) = Pℛ,2(k)
Primary Resources
Cosmological Corpus
📄 Manuscript PDF
Admissible Boundary Routing
Structural Classification of Terminal Approach, Finite Bounce, and Cosmological Recession · 34 pages · 7 figures · formal definitions · pilot-corpus propositions · cross-model taxonomy
unns.tech/media/unns/cosmological_boundary_routing/Admissible Boundary Routing.pdf
📊 Analytics Dashboard
Corpus Analytics
Full numerical results · STRUC-PERC-I / STRUC-I / α tables · route-topology diagram · signed-flow profiles · instability localization · Open Problem roadmap
unns.tech/media/unns/stellar_boundary_dynamics/cosmological_boundary_routing_analytics.html
↓ Corpus Archive
Cosmological Boundary Routing Corpus ZIP
Datasets A / B / C · STRUC-PERC-I canonical ladders · α-deformation grids · Bridge v1.1 route profiles · phase summary CSVs · synthesis report
unns.tech/media/unns/cosmological_boundary_routing/cosmological_boundary_routing.zip
Secondary Resources
Stellar Corpus
📄 Companion Manuscript
Stellar Boundary Dynamics I
Catastrophic Transition as Routing Between Admissible Structural Regimes · 10/10 FULL · A→B contact with C branching · first morphology: branching routing
unns.tech/media/unns/stellar_boundary_dynamics/Stellar Boundary Dynamics.pdf
📊 Stellar Analytics
Stellar Corpus Analytics
Phase-level structural profiles · ABC tri-domain bridge · κ escalation · object archetypes · SN1993J (BI=0.504) · SN2012aw (BI=1.470) · driver orthogonality
unns.tech/media/unns/stellar_boundary_dynamics/stellar_boundary_dynamics_analytics.html
↓ Stellar Corpus Archive
Stellar Boundary Dynamics Corpus ZIP
Phase A MESA profiles · Phase B light curves · Phase C WISeREP spectra · AB / BC / ABC bridge · v2 normalization vectors · reproducibility scripts
unns.tech/media/unns/stellar_boundary_dynamics/stellar_boundary_dynamics.zip