Slot Substrate Assessment

Cumulative |L_signed| as a function of cumulative mass across the 49,998-object LEO catalog. Eight real cutoffs computed from compiler/data/leverage_map_v2_full_results.csv at SHA 47f32fd6…. The 45° dashed line is what mass-proportional leverage would look like — the curve’s departure from it is the substrate’s discrimination.

Methodology

(1) L_signed(a) = ρ(a) · σ_mag(a) per-object substrate leverage (2) ⟨P_σ⟩_LEO = Σ_a L_signed(a) / Σ_a ρ(a) catalog-level Kessler-saddle observable (3) Δ⟨P_σ⟩(S) = ⟨P_σ⟩(C ∖ S) − ⟨P_σ⟩(C) closed-form intervention algebra over any subset S

The 28× concentration ratio is unpriced tail risk in every covariance matrix that assumes kinematic-distance independence. Per-asset Pc screening treats spatially distant satellites as failing independently. The substrate measures the topological coupling that assumption misses.

Definitions: ρ is per-object density on the momentum-aware conjunction graph; σ_mag is the character-graded coupling magnitude inherited from the rank-4 V₄ carrier of the prime hyper-radix; L_signed is their product. Equation (3) is closed-form arithmetic over the leverage map — no Monte Carlo, no propagator, no statistical sampling, reproducible bit-for-bit against the snapshot SHA.

What you receive

Top-K (K ≤ 5) cataloged objects coupling into your slot, ranked by L_signed = ρ·σ_mag, scoped to conjunction-graph adjacency in your operational shell.
Top-K (K ≤ 5) substrate-neutral safe harbors — algebraically minimal |σ_mag| residues — within station-keeping distance, with counterfactual Δ⟨P_σ⟩ at co-location.
Closed-form Δ⟨P_σ⟩ for any intervention you specify: subset removal, addition, or replacement. Floating-point precision.

Deliverable: an audit JSON pinned to the snapshot SHA, plus a rendered PDF. Same form as the public artifacts in the audit charter.

Selected data points

Rank cutoff	Cum. mass	Cum. \|L\|	Concentration ratio
top-1	0.01%	2.22%	356×
top-10	0.06%	14.30%	247×
top-100	1.50%	42.16%	28×
top-1,000	15.40%	65.52%	4.26×
top-5,000	47.20%	89.52%	1.90×
top-10,000	65.93%	96.07%	1.46×
top-25,000	84.51%	99.44%	1.18×
top-49,998	100.00%	100.00%	1.00×

Top-10 highest-|L| objects (named)

#	Name	COSPAR	Class	inc°	mass (kg)	L_signed
1	KH-8 (05171)	1971-033A	Payload	110.9	2,973	33,384
2	KH-8 (04492)	1970-061A	Payload	111.0	2,973	27,617
3	KH-8 (04874)	1971-005A	Payload	110.9	2,973	24,869
4	KH-8 (03984)	1969-050A	Payload	110.0	2,973	24,405
5	Firefly Alpha second stage	2023-202B	Rocket Body	140.0	909	20,739
6	KH-8 (03665)	1969-007A	Payload	106.2	2,973	18,950
7	KH-8 8 (Gambit-3 8 - OPS 4941)	1967-090A	Payload	106.1	3,650	18,469
8	KH-8 (03335)	1968-064A	Payload	110.0	2,973	16,468
9	KH-8 (06837)	1973-068A	Payload	110.5	2,973	16,341
10	KH-7 35 (Gambit-1 35 - OPS 1890)	1966-109A	Payload	104.6	2,190	13,536

Retrograde inclination (>90°) and low perigee dominate the upper leverage tail. KH-8 reconnaissance assets carry the highest-|L| signatures in the public catalog because their orbit class intersects prograde traffic at every node crossing.

Engagements are direct. Email with the asset, fleet, or jurisdiction you want assessed and a sample lands in your inbox within one day.

Engage by email →

tony@fancyland.net