SHD-CCP Geometric Computing BenchmarkStep-by-Step
Manifold → packet → codec → oracle → certifier → ε; routing ≫0 vs factoring ≤0
Flat / Euclidean — the objective IS the geometry, ε ≫ 0
Hyperbolic — hidden structure invisible, ε ≤ 0 (honest negative)
Synthesis · Foundations · Source
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Start Here · Bridges Both
The Benchmark
One page runs the whole architecture live and shows the contrast directly.
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Flat / Euclidean Geometry · ε ≫ 0
Where the geometry helps
Zero curvature — the golden Clifford torus is the canonical flat torus in S³; knots live in ℝ³, rotations are unit quaternions on S³. The measured Oracle Bias is strongly positive.
∞
Hyperbolic Geometry · ε ≤ 0
The oracle and its wall
Negative curvature — the Lorentz-hyperboloid attention kernel and the "hyperbolic oracle" aimed at factoring / ECDLP, where the hidden structure is invisible to the embedding and the √n wall stands.
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Synthesis & Substrate
Interface & motivation
Where the geometry becomes an interface, and the conceptual reason both curvatures matter.
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Network & Consensus · Polycentria Applied
Many certifiers, no center
The oracle+certifier cell scaled out: gossiping peers propose (Helix A), every node's exact validation processor decides (Helix B) — the seal & canon system off GitHub/Firebase and onto participant-hosted nodes.
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Foundations · Verified Proofs
The math under both tracks
The pump lab verifies the flat Clifford-torus winding and the hyperbolic sparsemax kernel in the same place — exact rational arithmetic, no hand-waving.
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Source Material · TTMPT
The crystallization pipeline
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Protocol Notes · SHD-CCP schema, crystallization, torsion flow
SHD-CCP Seed Schema — each engram is seeded by a 64-bit integer packed from bit fields
XOR Crystallization — text is tokenized character-by-character; each grid is XOR'd into an accumulator, building a topological fingerprint ("knot") for any sequence.
Torsion Flow J —
3-Packet Window — Alpha (oldest) ← Beta ← Gamma (active). On each utterance the window shifts and a new crystallized engram enters Gamma.
ST/PA/CO/FR/SP/AM, streamed through Mulberry32 into panmagic 8×8 boolean grids.XOR Crystallization — text is tokenized character-by-character; each grid is XOR'd into an accumulator, building a topological fingerprint ("knot") for any sequence.
Torsion Flow J —
(upper_triangle_sum − lower_triangle_sum)/32 from the active
Gamma packet. Positive → exploratory; negative → grounded; near-zero → balanced.3-Packet Window — Alpha (oldest) ← Beta ← Gamma (active). On each utterance the window shifts and a new crystallized engram enters Gamma.