§1 CORPUS OVERVIEW — 3 DATASETS · 3/3 FULL_PERCOLATION · ZERO DIRECT PERCOLATION VIOLATIONS
3
TOTAL STRUC-PERC RUNS
3
FULL PERCOLATION
0
HARD / GIANT / TAIL
3
ROUTE CLASSES
7.5×
κ RATIO B / A,C
0.306
B MEAN PRESSURE ρ̄
0.0416
A,C MEAN PRESSURE ρ̄
98.83%
B ADMISSIBILITY PERSIST.
99.26%
A,C ADMISSIBILITY PERSIST.
0
BOUNCE-CROSSING UNSTABLE
FINDING §1.1
3 / 3 FULL_PERCOLATION — all three canonical direct ladder encodings reach full connectivity, with zero direct percolation violations
All three canonical direct ladder encodings — classical Friedmann contraction (A), post-bounce LQC expansion (B), and Planck-anchored ΛCDM (C) — return FULL_PERCOLATION with final giant ratio = 1.000 and isolated = 0. The result holds even for Dataset B, whose expansion ladder requires a connectivity threshold approximately 7.5 times larger than A or C to assemble. This is not a failure of B: it indicates that the selected post-bounce LQC expansion encoding carries a structurally broader gap hierarchy than the matched classical encodings. All three canonical direct encodings preserve A_κ = 1.000 across the tested STRUC-I κ range. The full Dataset B route also remains overwhelmingly admissible under α deformation (98.83% admissibility persistence), with all localized instability confined to symmetric near-bounce shells and none at the exact turning surface.
§2 DATASET ARCHITECTURE — ROLE, TRAJECTORY, AND ROUTE COORDINATE
THREE-DATASET DESIGN · COSMOLOGICAL BOUNDARY ROUTING PILOT CORPUS
Dataset
Physical Role
Source
Rows
Route Coord.
Route Class
Branch Convention
A — Classical Friedmann
Contraction toward a→0 terminal boundary
Synthetic · Planck 2018 params · H<0
4001
−1 → 0
terminal_boundary_approach
a = 1 → 10⁻⁸ · monotone
B — Effective LQC Bounce
Contraction → exact bounce (H=0) → expansion
Synthetic · effective LQC v2.2 · ρ_c = 0.41ρ_Pl
4001
−1 → 0 → +1
finite_turning_surface_route
2000 contraction + 1 bounce + 2000 expansion
C — Planck ΛCDM
Classical expansion compatible with CMB observations
Planck 2018 best-fit · PR3 TTTEEE+lowl+lowE
4001
0 → +1
boundary_recession_expansion
a = 10⁻⁸ → 1 · monotone
Route coordinate is cumulative |Δln(a)|, path-intrinsic, not a final metric distance on ℳ_adm · boundary_margin_candidate remains provisional · v2 normalization authoritative for alpha and bridge comparisons
PLANCK 2018 ANCHOR PARAMETERS · DATASET C + A BASELINE
Parameter
Best-Fit Value
Unit
H₀
67.3218
km s⁻¹ Mpc⁻¹
Ω_m
0.31580
dimensionless
Ω_Λ
0.68420
dimensionless
Ω_b h²
0.022377
dimensionless
Ω_c h²
0.12010
dimensionless
Likelihood tag
base_plikHM_TTTEEE_lowl_lowE · PR3 2018
T_CMB
2.7255
K
N_eff
3.046
—
DATASET B — LQC BOUNCE PARAMETERS · v2.2 VALIDATED
Property
Value
Effective equation
H² = H₀² · ρ_rel · (1 − ρ_rel / ρ_c_rel)
ρ_c
0.41 × ρ_Planck
a_bounce
2.468 × 10⁻³²
H at bounce
0 (exact)
ρ / ρ_c at bounce
1 (exact turning surface)
LQC correction at bounce
0
Branch time bounce → a=1
13.7989 Gyr
Planck age reference
13.7973 Gyr
Difference
0.00163 Gyr (<0.012%)
Bounce-safe coord.
q_B = asinh(H_signed / H₀)
ρ/ρ_c = 1 at bounce does not signal inadmissibility — it marks the finite turning locus in the provisional margin construction · branch time concordance with Planck reference confirms the intended post-bounce age calibration
§3 STRUC-PERC-I — DIRECT CONNECTIVITY GEOMETRY
STRUC-PERC-I RESULTS · v2.5.0 · 3 RUNS · ALL FULL_PERCOLATION
Dataset
Verdict
κ_connect
Giant Ratio
n
Tail Dom.
Isolated
Ladder Used
A — Classical Friedmann
FULL
0.013335
1.000000
4001
0
0
ln(|H|/H₀) sorted · full 4001
B — Effective LQC Bounce
FULL
0.100000
1.000000 †
2000
0
0
Post-bounce expansion only · ln(E_lqc) ‡
C — Planck ΛCDM
FULL
0.013335
1.000000
4001
0
0
ln(|H|/H₀) sorted · full 4001
† A and C: GR at κ=0.01 = 0.97675 (77 components each), full connectivity at κ=0.013335 · B: GR at κ=0.01 = 0.53277 (22 components), full connectivity at κ=0.1000 · B direct ladder = post-bounce expansion only (2000 rows) · ‡ ln(E_lqc) undefined at exact bounce; contraction branch excluded from sorted direct ladder to avoid duplicate magnitudes
κ_CONNECT COMPARISON — ALL DATASETS
Linear scale · max = κ_connect(B) = 0.1000
A — Classical
0.013335
B — LQC Bounce
0.100000
C — Planck ΛCDM
0.013335
Ratio: κ_connect(B) / κ_connect(A,C) = 7.5×
A and C are degenerate in sorted magnitude geometry because one is the time-orientation reversal of the other · B requires a much larger vulnerability scale reflecting a broader gap hierarchy in the LQC expansion branch
INITIAL GIANT RATIO AT κ = 0.01 vs FINAL
GR scale 0 → 1.000
GR at κ = 0.01
A — Initial GR
0.97675
B — Initial GR
0.53277
C — Initial GR
0.97675
Final GR at κ_connect
A — Final GR
1.000
B — Final GR
1.000
C — Final GR
1.000
At κ=0.01: A has 77 components (GR=0.97675), C has 77 components (GR=0.97675), B has 22 components (GR=0.53277) · A and C are already giant-component dominated but not yet fully connected at κ=0.01 · all three reach GR=1.000 at their respective κ_connect thresholds
FINDING §3.1
B is fully connected but structurally broader — κ_connect 7.5× larger than A or C, reflecting the LQC expansion gap hierarchy
Dataset B's sorted expansion ladder requires κ_connect = 0.1000 to form a single connected structure, versus 0.013335 for both A and C. This 7.5-fold elevation is not an admissibility violation — it is a structural distinction. The selected post-bounce LQC expansion encoding carries a broader gap hierarchy than the matched classical encodings. This is consistent with, but does not by itself causally isolate, structural inheritance from the preceding bounce transition; the α analysis, not the direct ladder, localizes behavior around the quantum-transition shell. At the smallest tested vulnerability scale (κ = 0.01), A and C are already dominated by a giant component containing approximately 97.675% of the ladder (77 components each), while B's expansion branch is substantially more fragmented (GR = 0.53277, 22 components). Full connectivity for A and C is achieved at κ = 0.013335; Dataset B requires κ = 0.10000.
§4 STRUC-I — STRUCTURAL PRESSURE AND ADMISSIBILITY STATE
B max ρ = 0.636 · 2.2× A,C maximum · classified as Weak Persistence
A_κ = 1.000 at all κ for all three canonical direct ladder encodings — none cross the admissibility boundary under the direct STRUC-I operator · B classified Weak Persistence on structural pressure, not on A_κ failure · B full-path α analysis carries 98.83% admissibility persistence with localized near-bounce instability
FINDING §4.1
All three canonical direct ladder encodings preserve A_κ = 1.000 across the tested κ range — but B occupies a substantially more pressured admissible regime
The admissibility metric A_κ = 1.000 holds at every κ point for all three canonical direct encodings. No direct ladder enters a non-realizable structural state. However, Dataset B's mean structural pressure (ρ̄ = 0.306) exceeds A and C (ρ̄ ≈ 0.042) by a factor of approximately 7.4. Its maximum reaches 0.636 compared to 0.290 for A and C. The STRUC-I classification of Weak Persistence (versus Stable Structure for A and C) captures this: B remains admissible but lies closer to the structural boundary, operating under substantially higher internal deformation pressure. This elevated pressure is measured in the post-bounce LQC expansion ladder and reflects its broader sorted gap geometry. Note that B's direct STRUC-I uses only the 2000-row post-bounce expansion ladder; the near-bounce spatial localization belongs to the full-path α analysis.
§5 ALPHA-DEFORMATION — 5D STRUCTURAL VECTORS AND INSTABILITY LOCATION
A and C 5D vectors are degenerate under magnitude-only treatment — orientation is erased in sorted scalar ladders and recovered only in Bridge v1.1 · B uses full signed bounce path with Q90 regional normalization and response cap = 5
ADMISSIBILITY PERSISTENCE — ALL DATASETS
Scale 98% → 100%
A · v2.0.0
99.26%
B · v2.2.0
98.83%
C · v2.0.0
99.26%
All values in the range 98.8–99.3% · B 0.43pp below A,C · distinction is the location and nature of instability, not the global admissibility fraction
DATASET B — INSTABILITY LOCATION BY REGION
All 982 unstable rows confined to symmetric near-bounce shells
contraction_outer
0
contraction_near_bounce
491
bounce_crossing
0 ✓
expansion_near_bounce
491
expansion_outer
0
Instability shell: 0.03 ≤ ρ/ρ_c ≤ 0.82 · first onset at |α−1| = 0.05 (strict first-local-instability coordinate, not global collapse) · exact bounce crossing: 0 unstable rows
FINDING §5.1
The exact turning surface (bounce_crossing) is admissible across the full alpha grid — instability is confined to the surrounding quantum-transition shell
The 982 unstable rows in Dataset B are distributed symmetrically: 491 in the contraction near-bounce region and 491 in the expansion near-bounce region. Zero unstable rows occur at the exact bounce-crossing intervals. The outer contraction and outer expansion regions are entirely stable. This pattern identifies the quantum-transition shell (approximately 0.03 ≤ ρ/ρ_c ≤ 0.82) as a narrow deformation-sensitive region surrounding, but not including, the turning surface itself. The collapse onset radius of 0.05 is a strict first-local-instability coordinate: localized near-bounce sensitivity begins at a five-percent deformation, while 98.83% of the full grid remains admissible. The LQC bounce is not structurally forbidden — it is admissible at the exact turning point and broadly stable away from the transition region.
Why v1.1 was necessary. Under sorted magnitude geometry (direct ladders and magnitude-only alpha), Datasets A and C are nearly degenerate — their sorted ln(|H|/H₀) values are essentially the same sequence. The orientation distinction between contraction and expansion is erased. Bridge v1.1 restores signed Δln(a), signed H flow, signed density and curvature flows, signed provisional-margin flow, branch identity, and a shared cumulative route coordinate. This is what separates terminal boundary approach from boundary recession in the structural representation.
‡ B full-path signed means nearly cancel due to pre/post-bounce symmetry — this is the expected signature of route reversal, not absence of structure · branch-resolved interpretation is authoritative for B
BRANCH-RESOLVED PROFILE — DATASET B · FIVE PHASES · v1.1
Phase
n_intervals
Route Coord.
mean Δln(a)
mean H flow
mean density flow
mean margin flow
m-dec frac
m-inc frac
A — terminal approach
4000
−1 → 0
−0.5000
−0.1008
+0.4627
−0.0928
0.538
0.000
B pre-bounce approach
1999
−1 → ≈ 0
−0.3045
+0.0588
+0.2988
−0.1002
0.0970
0.000
B turning surface
2
≈ 0
≈ 0
1.76×10⁻⁴
0
0
0.000
0.000
B post-bounce recession
1999
≈ 0 → +1
+0.3045
+0.0588
−0.2988
+0.1002
0.000
0.0970
C boundary recession
4000
0 → +1
+0.5000
−0.1008
−0.4627
+0.0928
0.000
0.538
Normalized flows dimensionless · sign-preserving · bounded [−1,+1] · Q90 dataset-specific normalization · compare direction and relative within-path flow only, not absolute physical amplitudes across models · turning surface H flow = 1.76×10⁻⁴ (near-zero, not identically zero; Δln(a), density, and margin flows are 0 by exact symmetry)
§7 ROUTE TOPOLOGY — THE DECISIVE STRUCTURAL DISTINCTION
ROUTE COORDINATE TOPOLOGY — THREE CLASSES IN ONE DIMENSIONLESS COORDINATE
Route coordinate is path-intrinsic · constructed from cumulative |Δln(a)| · not yet a universal metric distance on ℳ_adm · all three canonical direct encodings remain admissible across the tested STRUC-I κ range
A–C directional separation: Under sorted magnitude geometry, A and C are nearly degenerate (both use ln(|H|/H₀) sorted, both have n=4001, both have κ_connect = 0.013335 and admissibility persistence = 0.992619). Bridge v1.1 resolves this: A has mean signed Δln(a) = −0.500, C has +0.500; A has density flow +0.463, C has −0.463; A has margin flow −0.093, C has +0.093. They are not the same trajectory — they are opposite orientations of matched magnitude structure.
§8 PRINCIPAL FINDING — COSMOLOGICAL BOUNDARY ROUTING
PRINCIPAL FINDING
Classical singular approach, LQC route reversal, and Planck-compatible expansion are structurally distinguishable by route topology
The combined experiment produces one route topology result readable in a single dimensionless coordinate. Dataset A (classical Friedmann contraction) approaches a terminal boundary: scale factor decreases, density increases, provisional margin decreases, and the represented classical route terminates at coordinate zero, with no continuation included in Dataset A. Dataset C (Planck ΛCDM expansion) recedes from the corresponding early boundary regime: all signs are reversed relative to A. Dataset B (effective LQC) exhibits neither pattern — it approaches a finite turning locus at coordinate zero, preserves path continuity through the route change (zero unstable rows at the exact bounce crossing), and continues onto the opposite branch. The three route classes — terminal approach, finite route reversal, boundary recession — are computationally distinguishable within this controlled pilot corpus. Magnitude-only analysis cannot produce this distinction; orientation-sensitive route comparison is required.
FINDING §8.1
The cosmological pilot identifies a second boundary-routing morphology: finite turning-locus continuation
Stellar Boundary Dynamics identified branching routing: a catastrophic event generates internally admissible but mutually non-equivalent downstream regimes. All three stellar phases returned FULL_PERCOLATION, but the ABC bridge revealed A→B contact with C branching — demonstrating that internal admissibility is not cross-regime equivalence. The cosmological experiment identifies a complementary morphology: turning-locus routing, in which a continuous trajectory approaches a finite critical locus, reverses orientation, and remains admissible through the route change. The identity-preserving path is not broken; it is re-routed. Together, the two corpora support a broader Boundary Routing framework while retaining distinct topological signatures — branching downstream in the stellar case, continuous reversal in the cosmological case. The route topology changes while direct structural admissibility is preserved across all canonical encodings and full-path α admissibility remains overwhelmingly persistent; localized sensitivity is confined to the near-bounce shell rather than the exact turning locus.
§9 CONSOLIDATED COMPARISON — ACROSS ALL STRUCTURAL LAYERS
BOUNDARY ROUTING MORPHOLOGY — STELLAR vs COSMOLOGICAL
Admissible route continuation through finite turning locus (this corpus)
Both corpora support the broader principle: catastrophic transitions may preserve admissibility while changing route topology · the two morphologies are complementary, not interchangeable · together, the two corpora support a broader framework in which admissibility-preserving boundary events can produce distinct routing morphologies: downstream branching or continuous turning-locus reversal
FULL LAYER COMPARISON — A / B / C
Layer
A — Classical Friedmann
B — Effective LQC
C — Planck ΛCDM
Physical role
Classical contraction
LQC bounce
Planck expansion
Route coordinate
−1 → 0
−1 → 0 → +1
0 → +1
Route class
terminal_boundary_approach
finite_turning_surface
boundary_recession
Percolation verdict
FULL
FULL(post-bounce expansion ladder)
FULL
κ_connect
0.013335
0.100000
0.013335
Initial GR (κ=0.01)
0.97675 · 77 comp.
0.53277 · 22 comp.
0.97675 · 77 comp.
STRUC-I state
STABLE STRUCTURE
WEAK PERSISTENCE
STABLE STRUCTURE
Mean structural pressure ρ̄
0.04157
0.306052
0.04163
Max structural pressure ρ
0.29026
0.636336
0.29052
Admissibility persistence
99.26%
98.83%
99.26%
Collapse onset radius
0.45
0.05 (near-bounce)
0.45
Exact turning point
none
admissible
none
mean Δln(a) signed
−0.500
≈ 0 (cancellation)
+0.500
mean density flow signed
+0.463
≈ 0 (cancellation)
−0.463
mean margin flow signed
−0.093
≈ 0 (cancellation)
+0.093
5D vector status
preliminary
preliminary
preliminary
A–C degeneracy in sorted scalar?
YES — A and C are degenerate in the sorted scalar representation; Bridge v1.1 resolves their opposite orientations.
§10 WHAT IS AND IS NOT ESTABLISHED IN THIS PILOT CORPUS
COMPUTATIONALLY ESTABLISHED · WITHIN SELECTED MODELS AND CONVENTIONS
✓ A and C are directionally distinct despite magnitude degeneracy
✓ Dataset B contains a finite exact bounce: H=0, ρ/ρ_c=1
✓ The exact bounce is admissible across the full alpha grid
✓ Dataset B post-bounce expansion ladder returns FULL_PERCOLATION
✓ Dataset B carries higher structural pressure than A and C
✓ Dataset B exhibits a symmetric near-bounce sensitivity shell
✓ Bridge v1.1 separates terminal approach, finite reversal, and boundary recession in one shared route coordinate
✓ Branch-resolved B profiles preserve non-cancelling pre/post structure
✓ Post-bounce branch time concordant with Planck age reference (<0.012%)
✓ 3/3 canonical cosmological ladder encodings returned FULL_PERCOLATION — zero Hard, Giant, or Tail direct verdicts
NOT YET ESTABLISHED · OPEN ITEMS
○ That LQC is the correct theory of the early universe
○ That a cosmological bounce occurred in nature
○ Direct observational confirmation of singularity removal
○ A universal metric distance on ℳ_adm
○ A final canonical UNNS boundary margin (frozen)
○ Deformation normalization independent of Q90 and response cap
○ That all non-singular cosmologies route through the same structural mechanism
○ Observational test of bounce-generated perturbation spectrum vs CMB / BAO / Pantheon+
○ Extension beyond this effective LQC construction to other singularity-removal models
Interpretive limits: The shared route coordinate is path-intrinsic (constructed from cumulative |Δln(a)|), not a final physical metric distance on ℳ_adm. Q90 normalization is dataset-specific — normalized values compare direction and relative within-path flow, not absolute physical amplitudes across different cosmological models. The collapse_onset_radius = 0.05 for Dataset B is a strict first-local-instability coordinate; it does not indicate global trajectory collapse under five-percent deformation. boundary_margin_candidate remains diagnostic-only. All three 5D vectors carry preliminary status pending canonical margin freeze.
§11 PROGRAM STATUS — COSMOLOGICAL BOUNDARY ROUTING PILOT
STAGE COMPLETION CHECKLIST
✓ COMPLETE — Dataset A trajectory (classical Friedmann, 4001 rows)
✓ COMPLETE — Dataset A direct structural analysis (STRUC-PERC-I + STRUC-I)
✓ COMPLETE — Dataset A alpha application (v2.0.0)
✓ COMPLETE — Dataset B trajectory (LQC v2.2, validated bounce)
✓ COMPLETE — Dataset B direct structural analysis (expansion branch)
✓ COMPLETE — Dataset B alpha application (v2.2.0, five-region Q90)
✓ COMPLETE — Dataset C trajectory (Planck 2018, 4001 rows)
All 5D vectors carry preliminary status · canonical UNNS boundary margin not yet frozen · route coordinate is path-intrinsic, not a final metric distance on ℳ_adm