lean rights.lean: claims_exactly_what_arises_without_formality — instruments.all (fun r => auto r == claim r) — decided by the Lean kernel over its whole finite domain, axiom-free

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 · lean_rights_claims_exactly_what_arises_without_formality
• content-address (receipt) · 9fe1d10f-1cdd-8cd6-85ef-e1e4735a79ee
• status · decidable, re-verified on every build — recomputes from src/
• entails · 0/7

lean_rights_claims_exactly_what_arises_without_formality

Rouschev, T. · Millennium Solutions — the ℤ/9 vortex framework · DOI 10.5281/zenodo.21819217

content-address 9fe1d10f-1cdd-8cd6-85ef-e1e4735a79ee

Theorem

Theorem (lean_rights_claims_exactly_what_arises_without_formality).

$$\forall r\in \mathrm{instruments},\mathrm{auto}\left(r\right)=\mathrm{claim}\left(r\right)$$

instruments.all (fun r => auto r == claim r)

LaTeX source

\forall r \in \mathrm{instruments},\; \mathrm{auto}\mathopen{}\left(r\right) = \mathrm{claim}\mathopen{}\left(r\right)

claims exactly what arises without formality — a closed identity, evaluated by the Lean 4 kernel. No domain is walked here — the proposition reduces, and the kernel confirms the reduction. It is checked, not exhausted, and it is not offered as the larger claim.

Statement (Lean):

instruments.all (fun r => auto r == claim r)

Statement (LaTeX):

\forall r \in \mathrm{instruments},\; \mathrm{auto}\mathopen{}\left(r\right) = \mathrm{claim}\mathopen{}\left(r\right)

Proof. by decide — by evaluation; no domain is walked. Checked sorry-free; #print axioms reports no axiom dependency. No Mathlib, no native_decide. □

Structure. The statement parses to a tree of 3 nodes across 2 levels, with 2 leaves. That parse is verified to read back symbol for symbol against the Lean source, so it is the proposition's own structure and not a rendering of it; the theorem's page draws the same tree in three dimensions, where height is depth in the parse, horizontal position is each symbol's in-order rank, and depth is the size of the subtree beneath it.

What this record establishes. A dated, public, citable deposit of this declaration and its machine-checked proof, recomputable from the sources attached to it. That is priority, and the record proves it on its own. It is a different proposition from "no one has proved this before", which only a search of the literature can settle, so the two are stated separately and neither is smuggled in under the other.

Prior art: NAMED AND CREDITED. This declaration restates or builds on work with an earlier author, recorded in src/proof/priorart.lean. No priority over that work is claimed here.

Verification. The proof needs one file, all attached: src/proof/rights.lean. Check it with lake env lean src/proof/rights.lean, or clone https://github.com/ceccec/millennium-solutions and run npm run lean. The content-address of this declaration is recorded as lean_rights_claims_exactly_what_arises_without_formality at https://ceccec.psg.bg/millennium-solutions/theorem/lean_rights_claims_exactly_what_arises_without_formality. A content-address proves integrity, not truth: it fixes which statement was checked, not that the statement is significant.

Funding. Independent research. No institutional grant and no funder registered with OpenAIRE or ROR, so no award is claimed in this record. Development is supported by direct contribution: https://revolut.me/ceccec

Scope, stated as plainly as the claim. The declaration is decided over a finite domain. It settles no Clay Millennium Problem, asserts no quantum speedup, and describes no physical system. 0/7.

The statement's parse tree: 3 nodes, 2 levels, 2 leaves. Height is depth in the parse, horizontal position is the symbol's in-order rank as the statement reads, and depth is the size of the subtree beneath each node. Colour is the node's grammatical kind. Nothing here is chosen for this theorem — the shape is the parse, and npm run latex-gate checks that this parse reads back symbol for symbol against the Lean source, for this statement and all others.

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 is a Lean 4 theorem, checked by the kernel over its whole domain — sorry-free and axiom-free, which scripts/lean.ts re-verifies per theorem on every run. That is a stronger thing than a passing test: a test reports that a computation agreed on the cases it ran, on one machine; the kernel checks the proposition itself. It was then receipted and chained append-only by scripts/seal-lean.ts, which seals only by decide theorems — algebra the kernel evaluates, never a declaration asserted by rfl.

The source: the Lean proofs · the standing theorems. Re-check them yourself with npm run lean-claims, or the whole layer with node scripts/lean.ts. A content-address proves integrity, not truth. entails → 0/7.