Ageometrics / GSR

Measure what a representation preserves, what it erases, and what must be added back.

WORKING PAPERMeasurement research

The Problem

When a fuller system record is compressed into a declared geometric representation (embeddings, graphs, summaries, attractors, memory topologies), critical information is lost: provenance, contradiction history, continuity, causal sequence, and recovery information. We need to measure this loss.

The Approach

Ageometrics studies information loss during representation compression. GSR (Geometric Sufficiency Ratio) is a task-relative measure of the fraction of recoverable predictive/decision performance retained by a declared geometric representation. NGR, V-GSR, and a residue taxonomy (temporal, causal, provenance, contextual, algorithmic, semantic, identity, energetic) define what is not preserved. A minimal reproducible illustration seeds temporal residue outside a terminal geometric representation and recovers a GSR of approximately 0.21 with a bootstrap confidence interval [0.189, 0.231].

What Exists Today

✓Working research paper (v0.5)
✓GSR metric defined as task-relative and protocol-dependent
✓NGR, V-GSR, and residue taxonomy specified
✓Minimal reproducible illustration demonstrates the measurement concept

//What It Does Not Prove

What this project does not prove.

✗Working research paper only
✗Empirical validation, sensitivity analysis, and observer-envelope testing in progress
✗Not a commercial certification score
✗No production implementation
✗AI-memory application is research direction only

Evidence

GSR (Geometric Sufficiency Ratio) metric and Ageometrics framework for measuring information loss in representation compression (embeddings, graphs, summaries, attractors, memory topologies)

ageometrics

WORKING-PAPER

Artifact: Ageometrics and the Geometric Sufficiency Ratio

Version: v0.5

Environment: Research paper + minimal reproducible illustration

Date: 2026-08

Result:

Working paper defines GSR as a task-relative, protocol-dependent measure; specifies NGR, V-GSR, and a residue taxonomy. A minimal reproducible example seeds temporal residue outside a terminal geometric representation and recovers GSR ≈ 0.21 (bootstrap CI [0.189, 0.231]).

//Verification Boundary

Working research paper only. Minimal example is illustrative, not broad empirical validation. Sensitivity and observer-envelope testing in progress. Not a commercial certification score. No production implementation.

Anti-Illogical Audit Engine SymID SessionGlyph ExoMCP

Source Artifacts

📄Ageometrics and the Geometric Sufficiency Ratio (v0.5)
📄ageometrics_public_intro_v0_5