Results for source.

Full-state search across frontiers, findings, sources, and evidence

Input material. It can support a finding only after extraction, checks, and review.

Durable home for accepted state, correction history, proof, sources, and review events.

The shipped Vela language kernel for portable, correctable frontier state, finding bundles, events, proof packets, and content addressing.

The Python SDK shape for agents that produce signed Vela substrate artifacts and coherent frontier change sets.

The on-ramp for agents that read frontier state and draft reviewable changes under the same reviewer-gated path as humans.

The deliberate local-to-hub checklist for publishing frontiers as public signed registry entries.

The public replay contract and fixtures an independent implementation can use to prove it agrees with Vela.

paper, dataset, protocol, note, repository, or record

source record with provenance, locator, extraction method, and caveats · evidence and provenance checks, then reviewer acceptance

choose a writable frontier · inspect source connectors · inspect provenance gates · inspect record objects

The largest distance of a single-logical-qubit stabilizer code at length 10, [[10,1,d]], is open within the band d in [3,4]; whether a [[10,1,4]] stabilizer code exists is undetermined here.

The [[4,2,2]] code with stabilizers XXXX, ZZZZ encodes 2 logical qubits in 4 physical qubits with distance 2, verified by exact recomputation of k and d.

The Steane code [[7,1,3]] (CSS from the [7,4,3] Hamming code) encodes 1 logical qubit in 7 physical qubits with distance 3, verified from its six stabilizer generators.

The perfect five-qubit code [[5,1,3]] (cyclic stabilizers XZZXI and rotations) encodes 1 logical qubit in 5 physical qubits with distance 3, and is optimal at its length.

The Shor code [[9,1,3]] (concatenated bit- and phase-flip repetition) encodes 1 logical qubit in 9 physical qubits with distance 3, verified from its eight stabilizer generators.

Erdős Problem #105 has status 'disproved (lean)'. Topics: geometry. Erdős prize: $50. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #40 remains OPEN. Statement: For what functions $g(N) → \infty$ is it true that $$\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}$$ implies $\limsup 1_A\ast 1_A(n)=\infty$? Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

Erdős Problem #461 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.

Erdős Problem #861 is SOLVED. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A143824, A227590, A003022, A143823.

Erdős Problem #71 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #641 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #343 has been PROVED (Erdős's conjecture holds). Topics: number theory, complete sequences. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #903 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #610 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.

Erdős Problem #749 remains OPEN. Statement: Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$? Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

Erdős Problem #802 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #186 is SOLVED. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A389784.

Erdős Problem #719 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.

Erdős Problem #14 remains OPEN. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, possible.

Erdős Problem #795 has been PROVED (Erdős's conjecture holds). Topics: number theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.

Erdős Problem #1002 remains OPEN. Statement: For any $0<\alpha<1$, let $f(\alpha,n)=\frac{1}{\log n}\sum_{1\leq k\leq n}(\tfrac{1}{2}- \{ \alpha k\})$. Does $f(\alpha,n)$ have an asymptotic distribution function? In other words, is there a non-decreasing function $g$ such that $g(-\infty)=0$, $g(\infty)=1$, and $\lim_{n\to \infty}\lvert \{ \alpha\in (0,1): f(\alpha,n)\leq c\}\rvert=g(c)$? Topics: analysis, diophantine approximation. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

Erdos-Turan additive-bases conjecture (1941, open): for every additive basis A of order h for the natural numbers, the representation function r_A(n) cannot be bounded. The h=2 case is open.

Erdős Problem #224 has status 'proved (lean)'. Topics: geometry. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.

Erdős Problem #1044 has status 'solved (lean)'. Topics: analysis. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.