casting out nines is blind to digit transpositions but casting out elevens catches them: the digit-sum check (mod 9) is order-independent, so swapping two digits never changes it — every transposition slips through; the alternating-digit-sum check (mod 11) changes by twice the digit difference, which is ≢ 0 mod 11 for distinct digits, so it catches every adjacent transposition of distinct digits. Two checks with complementary blind spots, each a floor. Decidable by exhaustion over the 3-digit range

Interact — recompute a content-address:→ ab3e7c0b-4a21-8c31-a6a2-23155325ebb2

Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.

• theorem key · nines_are_blind_to_transpositions_but_elevens_catch_them
• content-address (receipt) · ffc2d3c5-5821-879e-898f-d5d6de44bce2
• status · decidable, re-verified on every build — recomputes from src/

The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.

How it was achieved

This theorem was computed by exhaustion over a finite domain in scripts/discover.ts — a test: () => boolean that runs to completion, holding by full enumeration. It was gate-checked (its name and content hold the honesty floor — no over-reach), receipted and chained append-only, and it is re-verified on every build: if it ever stopped holding, the build would fail, not production. That is what achieved means here — not asserted, but recomputable.

One leaf of the chained ledger: all theorems · computed results · the guide · the source formula. The repo and the site cross-link both ways — this hero page points back to the formula that recomputes it. Verify by cloning and running npm run lean-claims. A content-address proves integrity, not truth. entails → 0/7.