DETERMINISTIC AUDIO DSP, 3D KIRCHHOFF BIOPHYSICAL SCALING & PROOF-CHAIN RESEARCH PLATFORM

Sovereign DSP & Biophysical Scaling Platform

Forward FFT & Parabolic Peak Interpolation • Distance-Weighted Kirchhoff Contact Laplacian (N=1,040, R²=0.8048) • Alan Phipps (ORCID 0009-0003-9289-854X, alan.phipps@pqr.info)

CERT = TRUE (SOV-BIOPHYS-N1040-RC2) dw-GNM R² = 0.8048 (CV 0.8039 | OOS 0.8612) VocalImaging v3.4 ↗

01 // Interactive Deterministic Forward FFT & Parabolic Peak Interpolation Engine (/api/v1/dsp/analyze)

Fundamental f0 (Hz)

Harmonics (1..12)

Sample Rate (Hz)

Executing live spectral analysis...

Harmonic	Target Freq (Hz)	DFT Bin Index	Parabolic Interpolated (Hz)	Sub-Bin Error (Hz)	Magnitude	dBFS

06 // Distance-Weighted Kirchhoff Contact Laplacian (dw-GNM) Scaling Law & Modulo-2 Scale-Erasure Proof (/api/v1/dsp/kirchhoff-scaling)

Governing Law (N = 1,040 Non-Redundant PDB Structures, 16–3,654 Residues):
ν₁(THz) = 0.42338 × (⟨z⟩ / (R_g / R₀))^1.1194 • R₀ ≡ 1.0 Å • R² = 0.8048 • 10-Fold CV R² = 0.8039 • Cross-Kingdom OOS R² = 0.8612 • Modulo-2 Folded Control R² = 0.0006 (1,341× Variance Collapse)

Mean Contact Coordination ⟨z⟩ (R_c=7.5 Å)

Radius of Gyration R_g (Å)

Loading dw-GNM Kirchhoff scaling telemetry...

Conformation-Paired Hinge Controls (N = 12 Apo/Open vs. Holo/Closed Pairs • Wilcoxon p = 4.88 × 10^-4 • R² = 0.8842)

Pair ID	Protein System	Apo / Open PDB	Holo / Closed PDB	Δ(⟨z⟩/R_g)	Observed Δν₁	Predicted Δν₁	Concordance

02 // Certified Proof-Chains (REP-CORP-2026-0001, PCD-001..003, SOV-BIOPHYS-N1040-RC2)

Domain / Protocol ID	Title	Initial Result	Adversarial Audit	Remediation	Final Epistemic State
SOV-BIOPHYS-N1040-RC2	Closed-Form Vibrational Scaling of Protein Contact Networks (N=1,040)	1D MW Fold (R²=0.06%)	1,341× Scale-Erasure Proven	3D dw-GNM Law (R²=0.8048, OOS=0.8612)	CERTIFIED (SK)
REP-CORP-2026-0001	First Certified Proof-Chain (v0.3.1-replication)	Outcome A	Rejected (Dead-End Preserved)	Completed & Anchored	CERTIFIED (SK)
PCD-001	48kHz RTP Audio Telemetry & Spectral Peak Invariant	UU → PK	Survived Wave 3 Challenge	Bit-Exact Verified	CERTIFIED (SK)
PCD-002	Distributed W3C Trace Context Propagation	UU → PK	Survived Span-Drop Challenge	100% Trace Continuity	CERTIFIED (SK)
PCD-003	Receipt-Driven Governance Enforcement (9-Seat Ed25519)	Static Flags → KU	Survived 8/8 Adversarial Vectors	9/9 Ed25519 Receipts Verified	CERTIFIED (SK)

03 // Deterministic DSP & Biophysical Research Experiments (/api/v1/dsp/experiments)

Experiment ID	Research Domain	Title	Epistemic Stage	Verified Metric	Status

04 // Cryptographic Artifact Hash Ledger (artifact_hashes.md — Live from /api/v1/dsp/ledger)

#	Artifact Path	SHA-256 Cryptographic Digest	Forensic Integrity

05 // Knowledge Court, KD Gate & RULE-VI-26 / RULE-VI-27 / RULE-VI-28 Governance

KNOWLEDGE DEBT (KD) & DUAL-TRACK GOVERNANCE

{
  "knowledge_debt_score": 0.0,
  "rule_vi_26_delta_ceiling": 1e-12,
  "rule_vi_27_dual_track": "ENFORCED",
  "rule_vi_28_claim_ceiling": "LAYER_4_HYPOTHESIS",
  "modulo_2_variance_collapse": "1,341x (80.48% -> 0.06%)"
}

EPISTEMIC STATE MACHINE & AUTHORITY LADDER

UU → KU → KK → PK → KD → CPK → OPK → CERT → SK → UU

Claim < Report < Execution < Artifact < Hash < ForensicVerification

Connected to https://vi.pqr.info and https://task.predator.run for 5-Gate Court of Admissibility and 9-seat Ed25519 council receipt inspection.