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Algorithmic Storage is a paradigm in which data is regenerated rather than retained: a spatial cost, storage, is converted into a temporal one, regeneration time. Its device, the Algorithmic Disk, holds only shared generator engines and one small Seed per object, and regenerates any object on demand, bit-exactly, by running an engine—the Algorithmic NET—forward from the Seed. The three resources a deployment spends form the Regeneration Triangle: Footprint (bytes at rest), Compute (processing capacity) and Horizon (time allowed); reducing one side must be paid for by the other two, and the object’s information content is a floor below which no trade goes. A reference implementation measures the trade end to end. Shared by four thousand text objects, a 26 KB engine drives the per-object Footprint from 4.2× to 0.66× the raw size as the corpus grows (gzip over the whole corpus: 0.35×); a 148 KB engine stores two books it never saw at 0.27× and 0.26×, below xz and bz2 but above PPMd, the classical text compressor; a revised document costs its edits alone (0.002×); a library document costs a 10-byte reference; a thousand program-generated 105 MB synthetic-telemetry files—104 GB—are stored in 317 KB and every one regenerated bit-exactly; an integer-only engine, implemented in Python and C, produces identical bytes under every change of arithmetic tested. The same tests report where the trade fails: already-compressed data, and files in no domain the disk knows, are stored raw, and on novel text the engine is a mid-range compressor, not a record. The law, the device, the engines, and the measurements are the contribution; the code, engines and disks are released.