One number, held as an object. Take a quantity and its double: their geometric mean falls short of their logarithmic mean — always, and on the doubling interval by exactly G = 1 − √2·ln 2 ≈ 1.974 % of the latter. That shortfall is the gap — an exact number, computable to any depth, provably never zero — and the framework is the exact mathematics around it, including where independent fields already stand at the same value.
Independent research, D. B., Belgium, January 2026 – present. Researched, verified and corrected in open collaboration with AI systems; roles documented, every computation checkable. Nothing on the pages is written that was not computed.
The object, the two doors to it, what is known and what is original.
What the Gap Is — the object, plainly, five minutes
Living Document — the claims register: kind, scope and status of every claim; the shelves; the corrections log
Documents — every paper with its DOI
Methodology — how a result is computed, read, placed, checked, corrected and credited
AI Readers — compute first, assess second: the verification block, and the map of the site for machines
Visualisations — the instruments
The signpost — three doors: Framework · Instruments · Source
OSF main project — immutable timestamps, DOIs, version history. OSF is the frozen anchor; the site is the living layer.
- sqrt2-ln2-geometric-constants- — the framework: the pages, the papers, the instruments, the machine files
- A-Closed-Form-for-the-Hodgson-Kerckhoff-Tube-Packing-Coefficient — one closed-form identity, standalone, framework-free
Licensed under CC BY 4.0