DATASET C — DIRECT PRELIMINARY STRUCTURAL RESULT
Cosmological Boundary Routing
Planck-Anchored Lambda-CDM
Date: 2026-06-08

STATUS

DIRECT PRELIMINARY DATASET C STAGE: COMPLETE

ENCODING

Source trajectory:
generated_trajectory/validated/planck_lcdm_trajectory_validated.csv

Scalar ladder:
q_C(a) = ln(E(a))

where:
E(a) = H(a) / H0

Direct ladder:
canonical/ladder/planck_lcdm_response_ladder_preliminary.csv

STRUC-I-compatible ladder:
canonical/ladder/planck_lcdm_response_ladder_preliminary_struc_i.csv

Ladder size:
4001 elements
4000 gaps

STRUC-PERC-I v2.5.0 — DIRECT RUN

Input:
planck_lcdm_response_ladder_preliminary.csv

Settings:
Domain adapter = Generic
kappa points = 17
kappa minimum = 0.01
kappa maximum = 1.0

Result:
Verdict = FULL_PERCOLATION
Giant ratio = 1.000000
Final chain size = 4000 / 4000 gaps
Isolated vertices = 0
kappa_connect = 0.0133352143
kappa_star = none
Outliers = 0
Tail dominance = 0
Run status = COMPLETE
Downsampling = no
Approximate mode = no

Interpretation:
The direct preliminary ln(E) ladder forms one fully connected vulnerability
structure across the tested kappa range. The percolation result is consistent
with admissibility but is not, by itself, a proof of admissibility.

STRUC-I v1.0.4 — FULL DIRECT RUN

Input:
planck_lcdm_response_ladder_preliminary_struc_i.csv

Settings:
Maximum ladder size = at least 5000
Monte Carlo runs = 2000
kappa steps = 40
kappa minimum = 0.01
kappa maximum = 1.0

Full-ladder status:
n = 4001
subsampled = false

Result:
Regime = Geometric Persistence
State = Stable Structure
mean A_kappa = 1.000000
minimum A_kappa = 1.000000
A_kappa at kappa = 1 = 1.000000
mean structural pressure rho = 0.041627
maximum structural pressure rho = 0.290517
rho at kappa = 1 = 0.290517

Interpretation:
Every tested Monte Carlo perturbation satisfied:

inv(P_epsilon; L) <= nu(V_epsilon(L))

at every one of the 40 tested kappa values.

The direct preliminary Dataset C ladder therefore remains admissible throughout
the tested perturbation range and occupies the Geometric Persistence / Stable
Structure regime under the present ln(E) encoding.

SUBSAMPLING ROBUSTNESS CHECK

Earlier surrogate:
n = 2000
subsampled = true
mean A_kappa = 1.000000
minimum A_kappa = 1.000000
mean rho = 0.041524
maximum rho = 0.289789
regime = Geometric Persistence
state = Stable Structure

Full ladder:
n = 4001
subsampled = false
mean A_kappa = 1.000000
minimum A_kappa = 1.000000
mean rho = 0.041627
maximum rho = 0.290517
regime = Geometric Persistence
state = Stable Structure

Conclusion:
The regime classification and pressure profile are stable against the earlier
2000-point stratified subsampling. The accepted result is the full 4001-point
run.

DIRECT PRELIMINARY CONCLUSION

For the preliminary response coordinate q_C(a) = ln(E(a)), the Planck-anchored
Lambda-CDM expansion ladder is:

- fully percolating in STRUC-PERC-I;
- admissible throughout the STRUC-I Monte Carlo test;
- classified as Geometric Persistence;
- classified as Stable Structure;
- well inside the structural-pressure boundary, with max rho approximately
  0.291.

INTERPRETIVE LIMIT

This is an encoding-specific direct result.

It does not yet establish:

- the final cosmological boundary-margin definition;
- alpha stability;
- equivalence between Datasets A, B, and C;
- cosmological boundary routing;
- singularity removal.

The result becomes part of the authoritative A/B/C comparison only after the
same scalar mapping, alpha operation, sampling convention, and chamber settings
are applied across all three datasets.

NEXT REQUIRED STEP

Apply the established project alpha operator to the same 4001-element direct
ladder without changing the sampling grid or point count.

Then rerun:

1. STRUC-PERC-I v2.5.0
2. STRUC-I v1.0.4

under settings identical to the direct run.

The direct-versus-alpha comparison must record:

- verdict;
- giant ratio;
- kappa_connect;
- isolated vertices;
- tail dominance;
- mean A_kappa;
- minimum A_kappa;
- mean rho;
- maximum rho;
- regime;
- state.

Do not define a new alpha formula specifically for Dataset C. The exact
established project alpha implementation must be reused so that the result is
comparable with the other UNNS structural-regime datasets.
