bbg proposals

design proposals for bbg authenticated state layer evolution. proposals compose with zheng-2 proof architecture and hemera-2 hash.

polynomial state

proposal	status	target
algebraic-nmt	draft	9 NMT trees → 1 polynomial, 30× fewer constraints per cyberlink
mutator-set-polynomial	draft	SWBF + MMR → polynomial, O(1) non-membership proofs
temporal-polynomial	draft	continuous time queries, time.root elimination
unified-polynomial-state	draft	13 sub-roots → 1 polynomial, LogUp eliminated

migration: algebraic-nmt → mutator-set-polynomial → unified-polynomial-state. each phase independently valuable. temporal-polynomial composes with any phase.

storage and replication

proposal	status	target
signal-first	draft	bbg state as materialized view over signal log, solves storage proofs
pi-weighted-replication	draft	replication ∝ π, storage budget follows attention
storage-proofs	draft	proving data retention at all 4 tiers

signal-first reframes storage-proofs: prove signal availability, derive everything else. π-weighted replication allocates resources by importance.

query

proposal	status	target
verifiable-query	draft	arbitrary CozoDB queries → polynomial opening proofs

implemented

proposal	status
valence	implemented — migrated to spec

combined targets (all proposals)

                        bbg-1 (current)         bbg-2 (all proposals)   improvement
per-cyberlink:          ~94K constraints        ~3K constraints         30×
non-membership proof:   128 KB witness + MMR    32 bytes + 1 opening    O(1)
historical query:       3 × O(log n) NMT walk  1 polynomial opening    O(1)
sub-root count:         13                      1                       13×
cross-index (LogUp):    ~1.5K constraints       0 (structural)         ∞
storage proof:          open problem            signal availability     solved
replication cost:       uniform                 ∝ π (power-law)        natural
query proofs:           namespace only          arbitrary CozoDB        general
light client witness:   ~416 bytes roots        32 bytes polynomial     13×

recommended sequence

phase 1: signal-first               reframe storage proofs
phase 2: algebraic-nmt              30× per-cyberlink (public indexes)
phase 3: mutator-set-polynomial     O(1) privacy proofs
phase 4: pi-weighted-replication    natural storage allocation
phase 5: temporal-polynomial        continuous time queries
phase 6: verifiable-query           arbitrary provable queries
phase 7: unified-polynomial-state   one polynomial for everything

cross-repo dependencies

zheng-2 proposal	bbg interaction
gravity-commitment	verification cost + replication + query routing all follow π
proof-carrying	fold nullifier updates into signal accumulator
universal-accumulator	checkpoint = 200 bytes, enables signal-first recovery
folding-first	multi-hop queries fold per hop
brakedown-pcs	updateable PCS enables incremental polynomial state

lifecycle

status	meaning
draft	idea captured, open for discussion
accepted	approved — ready to implement
rejected	decided against, kept for rationale
implemented	done — migrated to relevant spec file

Dimensions

trident/reference/props

Design Proposals Proposals for language and VM design changes. Not spec — these are desires documented for future consideration. Each proposal is a standalone markdown file. Status is tracked in the frontmatter. Status values | Status | Meaning | |--------|---------| | `draft` | Idea captured, open…

zheng/reference/props

zheng proposals design proposals for zheng proof system evolution. zheng-2 is the integrated architecture — all other proposals feed into it. architecture | proposal | status | target | |----------|--------|--------| | zheng-2 | draft | dual-algebra proof architecture: 2 PCS, 1 IOP, 1 hash, 14…

nox/reference/props

props

hemera/reference/props

hemera proposals design proposals for hemera hash function evolution. hemera-2 (pre-genesis upgrade) | proposal | status | target | |----------|--------|--------| | inversion-sbox | draft | x⁻¹ partial S-box + 16 rounds: 36% fewer constraints, 5.4× MPC depth, 2^1046 algebraic degree | |…

bbg/reference/props.md