ABC BRIDGE V1.1 RESULT RECORD
Cosmological Boundary Routing
Orientation-Sensitive A–B–C Comparison

STATUS

BRIDGE V1.1: COMPLETE
SHARED DIMENSIONLESS ROUTE COORDINATE: ACHIEVED
NORMALIZED SIGNED-FLOW COMPARISON: ACHIEVED
BRANCH-RESOLVED DATASET B SUMMARY: ACHIEVED

INPUT

ABC_orientation_sensitive_bridge_v1_1.csv

SOURCE TRAJECTORIES

Dataset A:
Classical Friedmann contraction toward the terminal small-a boundary.

Dataset B:
Effective LQC contraction, exact finite bounce, and expansion.

Dataset C:
Planck-anchored Lambda-CDM expansion away from the early small-a regime.

SHARED ROUTE COORDINATE

The coordinate is constructed from cumulative |Delta ln(a)|.

Dataset A:
-1 at the outer contraction endpoint
0 at the terminal endpoint

Dataset B:
-1 at the outer contraction endpoint
0 at the exact bounce
+1 at the outer expansion endpoint

Dataset C:
0 at the early small-a endpoint
+1 at the late expansion endpoint

This replaces the heterogeneous distance fields used in Bridge v1.0.

NORMALIZED SIGNED FLOWS

Each raw signed interval flow is normalized using its dataset-specific Q90 absolute scale:

normalized flow =
raw flow / (Q90(|raw flow|) + |raw flow|)

The normalized quantities are:

- dimensionless;
- sign-preserving;
- bounded within [-1,1];
- resistant to endpoint-scale domination.

DATASET A — TERMINAL APPROACH

Intervals:
4000

Route:
-1 to 0

Mean normalized signed Delta ln(a):
-0.499999999889

Mean normalized signed H flow:
-0.1007717104

Mean normalized signed density flow:
0.462723620322

Mean normalized signed curvature flow:
0.480637974312

Mean normalized signed margin flow:
-0.0927786021672

Margin-decreasing fraction:
0.538

Interpretation:

Dataset A contracts toward the terminal endpoint.

Its scale-factor flow is negative, while density and curvature flows are positive.

The provisional margin flow is negative.

The resulting route class is:

terminal_boundary_approach

DATASET C — BOUNDARY RECESSION

Intervals:
4000

Route:
0 to 1

Mean normalized signed Delta ln(a):
0.499999999889

Mean normalized signed H flow:
-0.1007717104

Mean normalized signed density flow:
-0.462723620322

Mean normalized signed curvature flow:
-0.480637974312

Mean normalized signed margin flow:
0.0927786021672

Margin-increasing fraction:
0.538

Interpretation:

Dataset C is the directional counterpart of Dataset A.

Its scale-factor flow is positive, density and curvature flows are negative, and provisional margin flow is positive.

The resulting route class is:

boundary_recession_expansion

A–C DIRECTIONAL SEPARATION

Dataset A and Dataset C are opposite orientations of the same magnitude geometry.

Their normalized route-flow signatures reverse sign:

A:
Delta ln(a) negative
density positive
curvature positive
margin negative

C:
Delta ln(a) positive
density negative
curvature negative
margin positive

The degeneracy present in sorted scalar ladders and magnitude-only alpha representations is therefore resolved.

DATASET B — BRANCH-RESOLVED RESULT

The full-path mean of Dataset B is not used as the primary interpretation because symmetric contraction and expansion cancel.

The accepted interpretation is branch resolved.

B PRE-BOUNCE APPROACH

Intervals:
1999

Route:
-1 to -2.22044604925e-16

Mean normalized signed Delta ln(a):
-0.304526787399

Mean normalized signed H flow:
0.0587747447951

Mean normalized signed density flow:
0.298770158107

Mean normalized signed curvature flow:
-7.539576704e-05

Mean normalized signed margin flow:
-0.100245896603

Margin-decreasing fraction:
0.0970485242621

Interpretation:

The contracting LQC branch approaches the finite turning surface.

Scale factor decreases, density increases, and provisional margin decreases.

B TURNING SURFACE

Intervals:
2

Route neighborhood:
-2.22044604925e-16 to 1.95259924488e-16

Turning-crossing intervals:
2

Mean normalized signed Delta ln(a):
0

Mean normalized signed density flow:
0

Mean normalized signed margin flow:
0

Interpretation:

The trajectory reaches route coordinate zero at the exact finite bounce.

The turning surface joins the contracting and expanding branches without introducing an artificial epsilon or a terminal path break.

B POST-BOUNCE RECESSION

Intervals:
1999

Route:
1.95259924488e-16 to 1

Mean normalized signed Delta ln(a):
0.304526787399

Mean normalized signed H flow:
0.0587747447951

Mean normalized signed density flow:
-0.298770158107

Mean normalized signed curvature flow:
7.539576704e-05

Mean normalized signed margin flow:
0.100245896603

Margin-increasing fraction:
0.0970485242621

Interpretation:

The expanding LQC branch recedes from the finite turning surface.

Scale factor increases, density decreases, and provisional margin increases.

DATASET B ROUTING SYMMETRY

The pre-bounce and post-bounce route signatures have opposite signs and closely matched magnitudes.

This is the expected signature of:

approach
→ finite turning surface
→ recession

The near-zero full-path signed means are therefore cancellation signatures, not absence of structure.

ROUTE TOPOLOGY RESULT

Dataset A:
-1 to 0
terminal boundary approach

Dataset B:
-1 to 0 to +1
finite turning-surface routing

Dataset C:
0 to +1
boundary-recession expansion

PRINCIPAL FINDING

The classical contraction and expansion trajectories are opposite orientations of the same magnitude geometry.

The LQC trajectory has a different route topology.

It reaches a finite turning locus, preserves path continuity through the bounce, and continues onto the opposite branch.

This computationally distinguishes:

terminal boundary approach

from:

finite boundary routing

ROUTE-PROFILE DATASET

The route-profile dataset is:

ABC_orientation_sensitive_route_profile_v1_1.csv

It contains binned profiles for:

- A terminal approach;
- B pre-bounce approach;
- B turning surface;
- B post-bounce recession;
- C boundary recession.

Each ordinary phase is represented by up to 50 bins in the shared route coordinate.

The exact turning-surface intervals are retained as their own profile rather than blended into neighboring bins.

The profile reports:

- route-coordinate range;
- interval count;
- signed and absolute normalized flows;
- margin-increase and margin-decrease fractions;
- turning-surface crossing fraction;
- Dataset B rho/rho_c and x-bounce profiles.

PHASE SUMMARY DATASET

The branch-resolved phase summary is:

ABC_orientation_sensitive_phase_summary_v1_1.csv

This file preserves the Dataset B branches separately and should be used for interpretation instead of the cancelling full-path B means.

ACCEPTED STATUS

Bridge execution:
PASS

Shared route coordinate:
PASS

A/C directional separation:
PASS

Dataset B finite turning topology:
PASS

Normalized signed flows:
PASS

Branch-resolved B interpretation:
PASS

Route-profile export:
PASS

Universal physical metric distance:
NOT YET ACHIEVED

Final canonical UNNS margin:
NOT YET FROZEN

INTERPRETIVE LIMITS

The shared route coordinate is path intrinsic.

It is not yet a metric distance on the admissibility manifold.

The Q90 normalization is dataset specific.

The normalized values compare direction and relative within-path flow, not absolute physical amplitudes across different cosmological models.

boundary_margin_candidate remains provisional.

NEXT STEP

Use the accepted bridge result, phase summary, and route-profile dataset to construct the consolidated Cosmological Boundary Routing synthesis.

That synthesis should compare:

- terminal approach;
- finite route reversal;
- boundary recession;
- direct STRUC-PERC-I structure;
- direct STRUC-I pressure;
- alpha admissibility;
- orientation-sensitive route topology.
