Algebraic accounting — books that are provably correct, by mathematics, not trust.
For five centuries, accounting has run on trust. Laoh replaces it with proof. Everyone — your AI agent, your junior bookkeeper, your outside firm — can work on the books safely, because the mathematics decides what is allowed to happen to them. Here is how.
Act I
Built for AI agents
Accounting infrastructure for the agent era. Agents connect through the platform via MCP — in Claude Cowork, Cursor, and similar tools. They draft and reconcile at machine speed; Laoh's isolated drafts and mathematical checks keep errors away from the official books, preserve history, and make correctness provable.
Connect via MCP
Claude Cowork, Cursor, and other agents drive the books through the platform's MCP tools — draft, reconcile, and propose without touching live history.
Errors stay isolated
Math rejects invalid or unbalanced work. Other mistakes remain in draft for human review before they can reach the official ledger.
Corrections leave a trail
Nothing is silently rewritten. Fixes become new activity you can review, seal, and prove — history only grows.
The claim is not that agents never err — it is that a bad post cannot silently rewrite closed truth.
Act II
Safe drafts for the books
Give people and agents room to work without handing them the live ledger. Every AI agent, junior bookkeeper, or outside firm works in a safe draft. You review the changes, then approve only what belongs in the official books.
Draft
Work happens away from the live ledger.
Review
You see the proposed changes before they count.
Approve
Only balanced, approved work reaches the official books.
Delegation becomes safe because no one edits the books directly.
Act III
What makes it algebraic
Safe drafts are only possible because of what sits underneath them: five layers of proof, each earning the next. Together they are the category — accounting where correctness is mathematics, not trust.
Approved draft + official ledger = still balanced (Thm 6.4)
01
Immutable algebraic ledger
Your ledger is a vector; every transaction is a balanced delta. Posting is vector addition, so the books sum to zero by construction — not because software checked, but because the algebra permits nothing else.
Every entry is chained to its evidence — the invoice, the bank line, the contract — by cryptographic hash. Change one byte anywhere in history and the entire chain announces it.
cₖ = SHA-256(cₖ₋₁ ‖ hₖ ‖ metaₖ)
Kills: backdated entries, evidence that quietly disappears.
03
Merkle period roots
Every period close is compressed into a single Merkle root. Any individual entry can be proven to belong to a closed period in milliseconds, without exposing the rest of the book.
root = Merkle(c₁ … cₙ)
Kills: "re-run the report and hope it matches" reconciliation.
04
Public anchoring
Signed period heads are lodged outside the system. Once a close is anchored, nobody can rewrite it — not an administrator, not a vendor, not us.
anchor(sign(rootₚ)) → external notary
Kills: retroactive restatement without a trace.
05
Auditor verification bundle
One bundle contains everything needed to independently rebuild the books from raw evidence: document hashes, commit metadata, posting-rule versions, Merkle proofs, signed heads. The auditor recomputes — and either the math agrees or it does not.
reconstruct(evidence, rules) ≡ L
Kills: trust-me audits, sampling in place of certainty.
The difference
Traditional systems vs. Laoh
Property
Traditional systems
Laoh
Records can be silently edited
Yes
Never
Books balance
Checked at runtime
By construction
Every entry chained to evidence
No
Yes
Closed periods provably sealed
Policy only
Anchored proof
Draft → review → approve workflow
No
Yes ★
AI agents via MCP (Claude, Cursor, …)
Hope the model is careful
Draft + math + seal
Agent errors reach the official books
Possible
Isolated for review
Independent audit reconstruction
Weeks of sampling
One bundle
See it on your books.
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