digital root is the ring homomorphism onto ℤ/9 (casting out nines): for all a,b the digital root respects both operations — dr(a+b) = dr(dr(a)+dr(b)) and dr(a·b) = dr(dr(a)·dr(b)) — so dr is the canonical map ℤ→ℤ/9 with 9 representing the class of 0, exactly the classical "casting out nines" check. Verified by exhaustion over a bounded grid
ab3e7c0b-4a21-8c31-a6a2-23155325ebb2Type 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 ·
digital_root_is_the_ring_homomorphism_onto_z9 - content-address (receipt) ·
9db2de84-f5d5-8ac7-9eba-cf82cb1c2678 - 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.