AI Mathematics Conjecture Explorer & Knot Invariant Analyzer

Topological Space & Invariants

DIM: $\mathbb{R}^3 \to S^3$

SELECT KNOT EMBEDDING:

DRAG: Orbit 3D Manifold $\theta$: 0.42 rad, $\phi$: 1.15 rad

Hyperbolic Volume Slice ($Vol$) 2.03

Chern-Simons Perturbation ($\Delta$) 0.18

Knot Identity

Trefoil Knot (3_1)

Crossing Number

Polynomial Signature (Alexander-Conway)

t^-1 - t + t^2

Verification & Conjecture Engine

Lean 4 / Coq Prover

NEURAL CONJECTURE CANDIDATE Active Formulation

Hidden unknotting number correlation found in signature coefficients

Pattern: Unseen signature symmetry detected at degree 2

Polymath Community Swarm Feed 42 Contributors

@gowers_fan: Check signature jump at root of unity $t = e^{2\pi i / 3}$.

@topologist_99: Verified: Seifert matrix skew-symmetry aligns with AI hypothesis.

@lean_bot: Lemma 4.1 instantiated in Lean 4 with 0 sorry instances.

[0.00s] Initializing Lean 4 kernel with mathlib topology bounds...

[0.15s] Searching combinatorial bridge: hyperbolic volume $\leftrightarrow$ signature...

[0.32s] Conjecture formulated: slope bounding conjecture instantiated.

[0.55s] Tactics dispatched: `ring`, `linarith`, `apply seifert_form_bound`.

[0.68s] QED: Formal proof verified. 0 unverified axioms remain.

142

Tactics Proved

8,192

Knots Scanned

0.68s

Solve Time