GaussBook
Inspect Live Ledger ↓
U.S. GAAP ASC 405-20-40-1 Clearinghouse

Clear payables
without spending cash.

Every invoice in your supply chain is a directed edge in a hidden graph. GaussBook connects read-only to QuickBooks, Xero, NetSuite, and Stripe, discovers closed circular debt loops (A owes B → B owes C → C owes A), and legally extinguishes the overlapping liabilities across every balance sheet simultaneously using $0.00 of bank cash.

75.3%
Payables cleared in Circle #1
$0.00
Bank wire or cash custody
1,024×
Cycle moat at k=5 hops
Texas Commercial Construction (5 Participating Firms)
$110k → −$100k $85k → −$65k $65k Bottleneck → $0 $95k → −$65k Apex General GC −$100,000 Cleared Brazos Electrical −$100,000 Cleared Lone Star Copper −$65,000 Cleared Gulf Coast Rebar −$65,000 Cleared GAUSSIAN EQUILIBRIUM (Ax = 0) $365,000 Extinguished +$35k Alamo Concrete • $0 Cash
Gross Payables Before
$485,000.00
7 Blinded ERP Edges
Extinguished ($0 Cash)
$365,000.00
75.26% Cleared
Residual Payables After
$120,000.00
2 Directed Loops
Formal Proof Status
VERIFIED_QED (5/5)
ASC 405-20-40-1
THE ZERO-TO-ONE INSIGHT

Why trillions in B2B payables stay frozen—and how Gaussian elimination unlocks them.

Banks, credit cards, and payment processors only see one bilateral invoice at a time (Company A → Company B). Because nobody could align private QuickBooks and NetSuite ledgers without leaking supplier lists, businesses have been forced to borrow cash at 14% APR to pay debts that actually cancel out in a closed loop.

THE OLD WORLD // BILATERAL CASH GRIDLOCK

Sequential bank wires & working-capital debt

Apex General owes Brazos Electrical $110k, but is waiting 60 days for Gulf Coast Rebar to pay $95k. Everyone waits on everyone else, draws down high-interest credit lines, or pays 2.9% card fees on gross volume.

Cash Required
$485,000.00
Settlement Delay
60–90 Days
Credit Line Cost
12%–18% APR
THE GAUSSBOOK WORLD // MULTILATERAL NOVATION

Simultaneous balance-sheet compression ($Ax = 0$)

GaussBook blinds every tax ID via RFC 9497 OPRF, finds the closed 4-company and 3-company loops, proves Net Equity invariance in Microsoft Z3, and writes credit memos directly into QuickBooks, Xero, NetSuite, and Stripe.

Cash Required
$0.00
Payables Cleared
$365,000 (75.3%)
Success Fee
1.00% ($3,650)
LIVE DOUBLE-ENTRY CLEARING BOOK

Before & After Corporate Balance Sheets

Verify how every company's Accounts Payable and Accounts Receivable drop by the exact same dollar amount—preserving 100.00% of Net Equity (AR − AP) with zero cash movement.

Participating Company & ERP RFC 9497 OPRF Token AP Before AR Before Extinguished ($0 Cash) AP After AR After Net Equity (AR − AP)

Extinguished Circular Debt Loops

Each directed cycle subtracts its bottleneck payable Δ_C = min w(e) from every invoice in the loop.

$0.00 Bank Float

Missing-Link Counterparty Pull

Zero-CAC viral growth: when an unconnected vendor joins to close an open chain, every firm clears more payables immediately.

Viral Loop
FORMAL MATHEMATICAL VERIFICATION // MICROSOFT Z3 SMT-LIB2

U.S. GAAP ASC 405-20-40-1 Five-Theorem Prover

No journal entry or credit memo is ever written until Microsoft Z3 formally proves all 5 accounting and legal invariants over exact integers.

CRYPTOGRAPHIC PRIVACY // RFC 9497 OPRF

Blinded Discovery & Merkle Tamper Lab

Non-intersecting private vendors (law firms, payroll, landlords) are stripped on your device before sync. Each participant receives a 2-edge SHA-256 Merkle proof for its CPA with 0 non-adjacent competitor identities revealed.

NETWORK ECONOMICS // THE p^k CYCLE LAW

Why the #1 Graph Captures 1,024× More Cycles

To clear a $k$-company debt loop, all $k$ companies must be on the same network ($P = p^k$). A network with 80% share clears $0.80^5 = 32.8\%$ of 5-hop loops, while a 20% challenger clears $0.20^5 = 0.032\%$—a 1,024× structural monopoly advantage.

TREASURY & WORKING CAPITAL SIMULATOR

Calculate how much cash stays in your bank account.

Instead of drawing down a 14% APR credit line to pay vendors while waiting 60 days on receivables, extinguish overlapping supply-chain payables at a flat 1.00% success fee.

Monthly Accounts Payable Volume $250,000
$50k / mo $1.25M / mo $2.5M / mo
Est. Payables Extinguished ($0 Cash)
$150,000.00
At 60% supply-chain loop density
Treasury Cash Preserved
$148,500.00
Remains untouched in your bank account
GaussBook 1.00% Clearing Fee
$1,500.00
$0 subscription • Charged only on cleared debt
Net Credit-Line Interest Saved
+$1,500.00 / cycle
Compared to 14% APR working capital