GaussBook
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 simulation
$0.00
Bank wire or cash custody
100%
Net Equity preserved (AR − AP)
Commercial Construction (5 Firms)
INTERACTIVE SIMULATION // GAUSSIAN EQUILIBRIUM (Ax = 0)
$365,000.00 Extinguished
2 Directed Loops (75.3% Cleared) • $0.00 Bank Cash
Participant A
General Contractor
−$65,000 Cleared
Participant B
Structural Steel Supplier
−$100,000 Cleared
Participant C
Ready-Mix Concrete
−$100,000 Cleared
Participant D
Electrical Subcontractor
−$65,000 Cleared
Participant E — Mechanical & HVAC −$35,000 Cleared
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
GUIDED PLATFORM WORKFLOW // JUMP DIRECTLY TO ANY CLEARINGHOUSE STAGE
HOW MULTILATERAL CLEARING WORKS

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 (Participant A → Participant B). Because isolated ERPs cannot see across private supply chains without exposing vendor lists, businesses borrow working capital at 14% APR to pay invoices that actually cancel out in a closed loop.

TRADITIONAL SETTLEMENT // BILATERAL CASH GRIDLOCK

Sequential bank wires & working-capital debt

A General Contractor (Participant A) owes its Structural Steel Supplier (Participant B) $85k, while waiting 60 days on an Electrical Subcontractor (Participant D) to pay $65k. Every firm waits on the next, 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
GAUSSBOOK CLEARING // MULTILATERAL NOVATION

Simultaneous balance-sheet compression (Ax = 0)

GaussBook blinds every tax ID via RFC 9497 OPRF, finds the closed 4-party and 3-party 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)
CLIENT-SIDE BLINDED INGESTION // QUICKBOOKS, XERO, NETSUITE & STRIPE CSV

Test an AP & AR aging export—blinded locally in your browser.

Drop a standard Accounts Payable / Receivable CSV export (or test with our 10-row sample ERP export below). Your browser strips non-trade operating expenses (payroll, legal, rent) on your device, hashes Tax IDs via WebCrypto SHA-256 + RFC 9497 OPRF before upload, and solves your clearable $0.00-cash loops in Microsoft Z3.

Download .CSV Template ↓
READ-ONLY OAUTH 2.0 LEDGER HANDSHAKE // ZERO BANK CUSTODY SCOPES
Or trigger a 1-click read-only ERP sandbox sync (RFC 9497 OPRF blinded before solver ingestion)
0 Bank Transfer Scopes Requested
LOCAL IN-BROWSER PRIVACY SCRUBBER TELEMETRY
Client-Side CSV Staging Buffer (Editable Before Blinding)
Rows marked PRIVATE_* (payroll, legal, rent) are stripped in your browser and never uploaded.
WebCrypto SHA-256
Ready to blind & solve
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

Unconnected Supplier Clearing

When an unconnected supplier connects read-only to close an open payable chain, every participating firm clears additional liabilities immediately.

Open Chain
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 counterparty identities revealed.

SUPPLY-CHAIN LIQUIDITY // MULTI-HOP CLEARING DEPTH

Why Supplier Participation Compounds Clearing Yield (pk)

To clear a k-party payable loop, all k businesses must participate in the clearing graph (P = pk). At 80% supplier participation across a regional industry cluster, 0.805 = 32.8% of 5-party loops clear automatically—compared to 0.032% in a fragmented 20% network (1,024× more multi-party payables cleared).

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 AP 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
CIRCUIT-PSI BILATERAL HANDSHAKE • LIVE GRAPH EDGE INJECTOR

Co-sign disputed invoices or inject a live payable edge.

Verify how Circuit-PSI bilateral attestation resolves disputed invoices (INV-DISPUTED-999) under ASC 405-20-40-1, or inject a new payable edge into the active graph and watch Tarjan’s SCC & Min-Cost Circulation solver clear the loop live.

Open 1.00% Fee & Savings Statement ↗
1. BILATERAL CIRCUIT-PSI INVOICE HANDSHAKE
Theorem #2 (ASC 405-20-40-1)

Reconcile an open or disputed invoice (INV-DISPUTED-999) down to the exact cent and record mutual Debtor + Creditor novation consent:

2. LIVE OPRF-BLINDED PAYABLE EDGE INJECTOR
Tarjan SCC + Min-Cost Flow

Inject a new B2B payable edge (Participant D → Participant C) into the active cluster and watch the cycle solver extinguish the newly formed loop:

3. ATOMIC MULTI-ERP WRITEBACK DISPATCHER & IDEMPOTENCY VERIFIER

Dispatch Ed25519-signed CreditMemo & JournalEntry payloads across QuickBooks Online, Xero, NetSuite, and Stripe with cryptographic idempotency-key deduplication (preventing any duplicate ledger deduction on replay).

WEEKLY ATOMIC CLEARING WINDOW // EPOCH-2026-W45-FRI-1700EST

Enroll in the next Friday Batch Clearing Window.

Register your supply-chain role and ERP system to receive a blinded RFC 9497 OPRF token, a custom supplier/customer invite link, and the 5-part CFO & CPA Executive Audit Packet.

PRIVATE MULTI-COMPANY CLEARING ROOM // /room/room_pilot_demo_2026
Want to pool blinded AP/AR aging ledgers across your own supplier & subcontractor cohort?

Provision an isolated, tokenized clearing room where multiple participating companies can upload blinded CSV schedules or connect read-only QuickBooks/Xero/NetSuite/Stripe OAuth and mint a private Ed25519-signed ASC 405-20-40-1 Audit Packet.

Download 1-Page CFO Brief (.PDF) ↓
INSTITUTIONAL DUE DILIGENCE // CFO, CONTROLLER & EXTERNAL CPA FAQ

Answers for your Finance Team, General Counsel, and CPA Auditors.

Every accounting, regulatory, privacy, and ERP integration question answered from first principles. Need the full printable compliance binder? Open the 5-Part CFO & CPA Executive Audit Packet or visit our Security & Trust Center.

1. How can GaussBook clear Accounts Payable with $0.00 of bank cash under U.S. GAAP? + −

U.S. GAAP ASC 210-20-45-1 restricts unilateral balance-sheet presentation offsetting to two-party bilateral relationships. GaussBook never performs unilateral offsetting. Instead, when a closed loop (A owes B → B owes C → C owes A) is discovered, all participants execute a binding Multilateral Contractual Release and Novation Agreement under ASC 405-20-40-1b (Extinguishments of Liabilities) and UCC § 9-406, reducing each firm’s AP and AR by the exact cycle bottleneck Δ_C while leaving Net Equity (AR − AP) 100.00% unchanged.

2. Does GaussBook ever touch our bank account or require FinCEN money transmitter licensing? + −

No ($0.00 principal custody). GaussBook never requests bank wire or ACH debit scopes, never holds escrow accounts, and never transmits currency or funds. Pursuant to FinCEN 31 CFR § 1010.100(ff)(5)(ii), GaussBook operates strictly as a non-custodial clearing and bookkeeping message processor that posts balanced CreditMemo and JournalEntry records directly into your ERP.

3. Can competitors or other participants see our vendor list, customer list, or margins? + −

Never. Non-trade operating expenses (PRIVATE_PAYROLL, PRIVATE_LEGAL, PRIVATE_RENT) are stripped locally in your browser before upload. Tax IDs (EINs) are blinded with a 256-bit key via RFC 9497 OPRF, and each participant receives a 2-Edge SHA-256 Merkle Boundary Proof that proves its own incoming receivable and outgoing payable with 0 non-adjacent counterparty identities revealed. See our Privacy Policy.

4. What happens if an invoice is disputed or an ERP writeback is replayed twice? + −

Microsoft Z3 Theorem #2 automatically blocks any disputed or unconsented invoice from entering a clearing cycle until both Debtor and Creditor co-sign a reconciled integer-cent amount via bilateral Circuit-PSI handshake. During ERP writeback, every CreditMemo and JournalEntry carries a deterministic SHA-256 idempotency key so replaying a dispatch results in 0 duplicate deductions.

5. How does the 1.00% (100 bps) clearing fee work if $0.00 of principal cash moves? + −

There are $0 subscription fees and $0 discovery fees. When a verified cycle extinguishes your Accounts Payable with $0.00 of bank cash, GaussBook bills a separate 1.00% (100 bps) success fee on the extinguished amount. Because clearing a 60-day payable avoids ~2.00% in working-capital credit line interest (at 12%–14% APR), your treasury nets +1.00% in immediate interest savings while keeping 99.00% of the cash in your bank account.

6. How do our external CPA auditors verify a GaussBook clearing cycle during our audit? + −

Every cleared cycle generates a 5-Part CFO & CPA Executive Audit Packet, a printable Multilateral Novation Agreement, and an Ed25519 signature + SHA-256 Merkle root that your CPA can independently verify in the CPA Cryptographic Verifier.