Core Framework — STRUC-PERC-I v2.5.0
Foundational Manuscript
Margin-Confinement Law
A structural invariance proof: once a system is represented inside the admissible region ℳadm, identity-preserving dynamics cannot cross the boundary m(Lt) = 0. Systems approach collapse asymptotically, generating the Forced Coherent Collapse (FCC) regime — trapped near the boundary, never through it.
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Genuine crossings
p < 3.0×10⁻⁴ at 99% CI
p < 3.0×10⁻⁴ at 99% CI
15,401
Evaluations
across 16 domains
across 16 domains
9/9
Δ-lifting recovery
100% RISC fragments → Full
100% RISC fragments → Full
34
FCC-like states in Δ-space
up from 5 raw (6.8×)
up from 5 raw (6.8×)
Boundary Monitor — Interactive
∂ℳadm
0.284
Min m(Lt)
1.000
Min GR
0.748
Max TD
2 / 5
FCC zone
0
Crossings
Forcing →
35%
Invariant Manifold
Non-Crossable
FCC Regime
Lyapunov Bounded
RISC Safe
Heliospheric Corpus
Voyager 1 |B|
[VGR1] CORPUS: 3,500 windows loaded
[VGR1] MAG_LADDER: admissibility scan ACTIVE
[VGR1] GIANT_RATIO: 0.974 — FULL
[VGR1] BOUNDARY_STATUS: ADMISSIBLE
97.4% Full percolation across a 7-year heliopause approach and crossing. First long-duration non-crossability trajectory. Zero HARD events.
Neutrino Detector Corpus
Stage 1 + 2
67
Ladders · 5 repr. groups
9/9
Δ-recovery rate · 100%
6
RISC matched pairs
0
USL violations
Δ-lifting (ΔL = |xi+1 − xi|) recovers Full percolation in all fragmented ladders. Continuity was not recreated — it was uncovered.
RISC Monitor
Repr.-Induced Collapse
The same source, genuinely in ℳadm, produces different classes depending on the observational chart. Key matched pairs:
TMVA HARD
→
deepL FULL
h_SigSB_2 · max
TMVA TAIL ×5
→
deepL FULL
hSigSB, significance
ANY HARD
→
Δ FULL
9/9 · 100%
Observational Collapse
Not Ontological
Chart-Dependent
Minimal Structural Principle
Corpus-Scoped
Admissible structures tend to preserve or recover relational continuity under identity-preserving evolution and locality-preserving representation transforms. Structural collapse, in the sense relevant to realizability geometry, is asymptotic rather than trans-boundary.
Theorem 1
Forbidden collapse — IPF flows cannot cross ∂ℳadm
Conjecture 1
Locality-preserving transforms preserve admissibility
FCC
Near-boundary asymptotic state — locally relational coherence
Framework Manuscripts
Four-Document Architecture
Central Theorem
The Margin-Confinement Law
Proves structural non-crossability in admissibility space via the background chain invariant and Lyapunov confinement functional. Introduces RISC, FCC, Δ-lifting, and representation-covariant admissibility. 15,401 evaluations · 0 crossings.
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Empirical Boundary Dynamics
Beyond Fragmentation
Establishes the empirical geometry of confinement across supernovae, Voyager heliosphere transport, nuclear seismic events, and detector corpora. Discovers FCC as a coherent near-boundary regime. The empirical precursor the Law explains.
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Percolative Foundation
Percolative Realizability Principle
Defines realizability through graph-theoretic connectivity and giant component persistence. Introduces Full, Giant, Tail, and Hard fragmentation classes via vulnerability graphs. The operational percolative layer underlying all admissibility evaluation.
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Foundational Constraint
Universal Structural Law v6
Establishes the foundational admissibility constraint governing all realizable ordered physical sequences. Defines ℳadm and the USL inequality inv(P;L) ≤ ν(V(L)). The root axiom from which all downstream confinement results derive.
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