hash jet — universal genesis jet
the one jet every algebra needs. Hemera (Poseidon2-Goldilocks) is the anchor — all algebras settle through F_p via hemera. hash is the only jet that crosses every instantiation boundary.
committed in genesis BBG state.
jet
| name | signature | exec cost | constraints | pure cost |
|---|---|---|---|---|
| hash | hash(x) → 4×F_p | 200 | ~736 | ~1,000 |
where hash is used
| context | frequency | purpose |
|---|---|---|
| content addressing | every particle | identity = H(content) |
| Fiat-Shamir | ~3 per proof | verifier challenges |
| domain separation | every commitment, nullifier, Merkle op | collision isolation |
| structural hash | every noun | H(cell) = H(H(left) ‖ H(right)) |
| cross-algebra boundary | every type transition | hemera commitment at algebra crossing |
hash is the most frequently executed jet in the system. without it, one Poseidon2 permutation = ~1,000 Layer 1 patterns. with it, 200 execution cost, ~736 STARK constraints.
the Hemera anchor
all algebras compute natively in their own field. all algebras settle through Goldilocks via Hemera:
- nox<F_p>: hash is native (200 budget cost)
- nox<F_p²>, nox<F_p³>, nox<F_p⁴>: hash operates on base field (native)
- nox<F₂>: hash deferred to settlement boundary (~736 constraints at boundary)
- nox<R_q>: hash operates on coefficient field F_p (native)
- nox<F_q>: hash deferred to settlement boundary (~736 constraints at boundary)
the hash jet is the same across all instantiations — the Hemera permutation over Goldilocks. what changes is when it executes (native vs deferred).
hardware mapping
hash → p2r (Poseidon2 round) on GFP
parameters
from hemera spec (frozen at genesis):
state: 16 field elements
rate: 8 elements
capacity: 8 elements
rounds: 8 full (4+4) + 16 partial = 24 total
full-round S-box: x^7
partial-round S-box: x^(-1) (field inversion, 0^(-1) = 0)
output: 4 field elements (32 bytes)