Context engineering

The context sheaf, live

Most agents concatenate retrieved text and hope it is consistent. G6 treats context as a sheaf: evidence is restricted along exact maps into a strict belief layer F, and disagreement between independent sources on a shared key is a measured, localised obstruction — not a yes/no opinion. The scorecards below are produced live by the real context_engine block.

Architecture — evidence to tokens

flowchart LR
  E["E — evidence cosheaf
(append-only observations)"] -->|colimit / belief select| F["F — strict sheaf
(typed claims, exact restriction maps)"]
  F -->|presentation| P["P — rendered context
(lossy, defect measured)"]
  P -->|budgeted| T["Tokens → agent"]
  F -.consistency.-> S["consistency scorecard
radius · obstructions · gluable · edge residuals · λ₊"]

Obstructed packet

gluable = False

Two independently-sourced governance claims disagree on deploy_target (planner = production, approval = staging). The sheaf refuses to glue them and says exactly where.

consistency radius: 1.0
obstruction count: 1
gluable: False
coverage ratio: 1.0

edge residuals (where they disagree)

planner~approval1.0

Gluable packet

gluable = True

The same two sources now agree on deploy_target = staging. The packet glues into a single global section — radius zero, no obstructions.

consistency radius: 0.0
obstruction count: 0
gluable: True
coverage ratio: 1.0

edge residuals

none — all shared projections agree

Uncorroborated packet

coverage = 0.0

Two claims from different sources that never share a key (db_engine from planner, cache_ttl from retriever). Nothing contradicts — so it is gluable — but nothing was cross-checked either. Coverage tells these apart from a confirmed packet, so "gluable" is never mistaken for "verified true".

gluable: True
coverage ratio: 0.0
corroborated keys: 0
uncorroborated keys: 2

Consistency energy

E(x) = ‖δ⁰x‖² = ⟨x, Lx⟩ with the sheaf Laplacian L = (δ⁰)ᵀδ⁰ (Hansen–Ghrist). E = 0 iff every shared projection agrees — a global section.

Stability, honestly

dist(x, H⁰) ≤ ‖δ⁰x‖ / √λ₊. When the spectral gap λ₊ ≈ 0 no certificate is issued (the bound returns None) — a low residual is never over-read.

Cohomology honesty

δ⁰x is itself a coboundary, so its class is zero. We report a combinatorial nerve H⁰ and an obstruction count — never a fake non-zero H¹.

These scorecards are computed on the strict sheaf F (exact restriction-derived, independently-sourced claims) — not on summarised text. The consistency layer is gated by G6_CONTEXT_SHEAF and is byte-identical to the prior engine when off.