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Numerical Information Object Theory NIOT-05 · Numerical index geometry (reference page) Neo.K (as signed)

Numerical Index Geometry: Addressing, Reindexing, Local Neighborhoods, and Identity Preservation

Defines a geometry of addresses and indices: typed indices, an address graph, reindexing, charts and an atlas, with holonomy as an 'index-curvature candidate'. An address is not a value; identity-preserving reindexing leaves canonical identity unchanged. The paper disclaims smooth-manifold, universal-atlas and curvature claims. About 290 vocabulary-style sections: a reference page.

Changing how an object is indexed should not change its canonical identity. This is a definition-level norm. 'The microscopic world of numbers is no longer a metaphor; it now has an engineerable local geometric skeleton' has no implementation behind it so far; 'Theorems 1–5' are one-line statements, and the proof of Theorem 2 is literally 'by definition'.

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This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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