Anagh's Law

Definition

If you know an object clears a space, you also know that any object contained within its spatial envelope clears that space in the same admissible placement.

If one object’s spatial envelope contains another’s, any placement that clears the containing envelope also clears the contained envelope, provided that placement is admissible for both.

The underlying mathematics is elementary and is not new. Anagh's Law names a practical heuristic grounded in the transitivity of geometric containment.

The bus–tunnel corollary

If a bus can clear a tunnel, any vehicle geometrically contained within the bus's relevant clearance envelope can also clear it under the same admissible conditions.

This is a simplified, straight tunnel with a rectangular opening. The demo tests width and height at a fixed orientation, with zero extra safety margin. Real routes also require checks along the entire path.

Geometric containment

A spatial envelope is the region occupied by an object, or a conservative boundary enclosing it. Geometrically contained means every point of the smaller envelope lies inside the containing envelope after the permitted alignment.

Lower volume, mass, or one shorter dimension is not enough. A narrow, tall vehicle can occupy less volume than a bus and still strike the tunnel roof.

You can use a conservative bounding box. If that box clears, everything inside it clears. If it fails, the actual object might still fit; an oversized bound cannot certify failure.

Applications

The useful saving comes when containment is easier to establish than repeating the full clearance check for every variant.

Limitations

Less volume ≠ contained

A long, thin rod may have less volume than a box and still extend beyond it.

A placement ≠ a path

Fitting at the entrance does not prove passage around a bend. Containment must hold at every point along an admissible motion.

Geometry ≠ vehicle dynamics

Steering limits, turning radius, ground clearance, suspension, and support can prevent a vehicle from following the same path.

Passing ≠ a universal guarantee

Load limits, structural strength, deformation, tolerances, and required safety margins need their own checks. This law concerns geometric clearance only.

Mathematical basis

Let A be a containing envelope, B a contained envelope, and S the available space. If B ⊆ A and an admissible placement T satisfies T(A) ⊆ S, then:

Applying the same transformation preserves containment. Transitivity then gives T(B) ⊆ S. The placement T must be allowed for B as well as A.

For motion, apply the argument at every time t along a path Tₜ, provided that entire path is admissible for both envelopes.

Set inclusion forms a partial order on envelopes in a common coordinate system. Geometric clearance is downward closed under that order: once a containing envelope passes, its contained envelopes pass too.

That familiar mathematical property is the basis of the heuristic. The contribution here is the name, formulation, and communication experiment.

Origin and naming

I'm Anagh Kanungo. On 10 October 2026, inspired by the bus-and-tunnel observation, I coined “Anagh's Law” and the line “Clear the maximum, clear the rest.”

This page is the canonical public formulation. The experiment is to give an elementary observation a memorable name, document its origin, and see whether other people find it useful enough to repeat.

The interesting milestones are discoverability, accurate attribution, and eventually independent use. Multiple pages published by me establish a record; they do not establish independent adoption.

Naming and formulation: Anagh Kanungo, 10 October 2026. Original formulation, version 1.0. This is a personal project. No claim of new mathematics, peer review, or institutional endorsement is made.

Citation

This citation refers to the webpage. The explanatory note is archived on Zenodo as a technical note under CC BY 4.0, DOI 10.5281/zenodo.23285520. It has not been peer reviewed.