Prove what isn’t there
Ordinary archives prove a record is present; none can prove one is absent, because absence is a statement about everything not shown. AT-1 Complete seals the keyed column (receipt no., invoice id, sequence counter) as a sorted-Merkle commitment. A sortedcommitment turns absence into a positive statement: “these two neighbours are adjacent in the sealed order, and nothing sits between them.”
- exact gaps
- the precise missing receipt/invoice numbers, not just 'something is off'
- provably absent
- record X was never in this archive — bracketed by its two sealed neighbours
- 44× smaller
- a range proof discloses only the window, not the whole keyset
- verify-only
- any auditor re-checks from the committed root — no data, no account
Seal it, then prove the gaps
at1 complete seal receipts.csv --key receipt_no -o receipts.at1c # sealed 494 keys of column 'receipt_no' root=9652c565... commit=aff56af5... at1 complete prove-complete receipts.at1c --key receipt_no --range 1..500 # MISSING keys : [37, 111, 112, 288, 289, 290, 401, 499] # DUPLICATE keys: [150, 372] # duplicate sequence numbers, too # self-verify : PASS at1 complete prove-absent receipts.at1c --key receipt_no --value 111 # case=interior (110 < 111 < 113) # 111 was never in this archive # self-verify: PASS at1 complete verify p.json # any auditor, no data, no account # VERIFIED · commit aff56af5... (pin this to anchor the archive)
Exact gap list
Over any claimed range, get the precise missing keys and the duplicated sequence numbers — the fingerprint of deleted-transaction fraud — derived only from a keyset that reproduces the sealed root.
Succinct range proof
A proof over [a..b]discloses only the window of leaves around the range plus its two bracketing neighbours — keys outside stay hidden. Narrow queries are tens of times smaller than a full keyset dump, with identical soundness.
Honest scope
Feasible on keyed sequences, a wall in general.Absence is provable only over a column sealed as a total order (receipt/invoice/sequence/timestamp). Proving “no record matching P” over unkeyed data is a soundness limit, not a missing feature — the engine refuses it rather than fake it.
Certifies the sealed archive’s integrity — that every committed key is accounted for — not that reality was faithfully recorded at seal time. Pairs with the append-only Ledger (now gap-provable) and the Regulated Archive. “Secure” means integrity + third-party verifiability, not confidentiality.