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@@ -273,3 +273,30 @@ The graphic is a checked-in SVG so it displays in the AsciiDoc README without
 JavaScript or a diagram service. Its editable source is
 link:images/type-connections.dot[type-connections.dot]. Rebuild it with
 `just type-map` (Graphviz required).
+
+
+== Additions 2026-10-12
+
+Registered this day, pending merge into the tables above.
+
+[cols="1,3",options="header"]
+|===
+| Member | What it establishes
+| https://github.com/hyperpolymath/resource-algebra[Resource Algebra] (kernel module) | The parametric grade algebra: alternatives an idempotent commutative monoid, sequence a monoid; order, dioid and annihilation as layers. Instances: echo Loss (min-plus), tropical MaxPlus, HWM (occupancy). Loss and cost have opposite induced orders (checked).
+| https://github.com/hyperpolymath/occupancy-types[Occupancy Types] | High-water-mark occupancy; reclamation at a cut; occupancy ≤ cost with equality iff nothing is reclaimed; independent threads have order-dependent peaks invisible locally.
+| https://github.com/hyperpolymath/katagoria[Katagoria] (incubator, not a family) | Graduation rule to be written: an idea leaves only when a family repo holds its kernel-checked core theorem.
+|===
+
+[cols="1,2,2",options="header"]
+|===
+| Connection | Status | Established
+| Resource Algebra → Choreographic | PROVEN (fragment) | K-CUT-LOSS parametric; needs only ⊕-idempotence and ⊗-left-unit.
+| Epistemic → Choreographic | PROVEN (fragment) | K-CUT-WARRANT bound and transport; Kripke frame over consistent cuts; SoundWarrant instantiated.
+| Tropical → Choreographic | PROVEN via MaxPlus instance | Lean provenance bridge (M-2) a review obligation.
+| Echo → Choreographic | PROVEN via Loss instance | RoleGraded base case recovered; import direction (L-2) open.
+| Occupancy → Choreographic | PROVEN (A-3) | Two-thread diamond: projections swap, occupancy does not.
+| Residual → Epistemic | DECIDED: family | Dependence is not a function of the candidate set.
+| Secret → (none yet) | OPEN | TINI proved; the Echo reading of noninterference is a conjecture.
+|===
+
+Decision record: link:decisions/D-2026-10-12-proof-kernel-ruling.adoc[] (proof kernel for the family).
diff --git a/docs/decisions/D-2026-10-12-proof-kernel-ruling.adoc b/docs/decisions/D-2026-10-12-proof-kernel-ruling.adoc
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+// SPDX-License-Identifier: MPL-2.0
+= D-2026-10-12 — Proof kernel for the type family
+:revdate: 2026-10-12
+
+== Status
+
+Ruled by the owner, 2026-10-12, after a comparison recorded in the
+accompanying session. Supersedes per-repo prover choice for the family.
+
+== Decision
+
+. *Agda `--safe --without-K` is the proof kernel of the type family*
+  (echo-types, epistemic-types, residual-evidence-types, choreographic-types,
+  secret-types, resource-algebra; absolute-zero's active CNO/OND/EchoBridge
+  stack).
+. *Idris2 is the ABI/runtime layer*, not a kernel candidate (QTT linearity is
+  the right tool there; `believe_me`/`assert_total` make it the wrong one for
+  theorems).
+. *Lean 4 is provenance*: jtv keeps its existing proof layer; tropical-types'
+  Lean and Isabelle developments remain as the Mathlib/AFP-facing record and
+  are *ported*, not imported, into Agda where the family needs them.
+. *Isabelle/HOL only for AFP submissions.* Coq, Mizar: archived (absolute-zero
+  ruling 2026-10-10 stands).
+
+== Evidence weighed
+
+* Investment: the comparison reported ≈47.7k lines of Agda across the
+  family; ≈6.4k active Lean; 7.1k Isabelle (tropical only); Idris2 almost
+  entirely RSR ABI scaffolding. These estimates are not a safe-check receipt.
+* Postulate inventory: at echo-types commit
+  `e38fd465c4269ab9e9940802525630d7aae1e848`, three `postulate` blocks
+  declare *six* assumptions:
+** https://github.com/hyperpolymath/echo-types/blob/e38fd465c4269ab9e9940802525630d7aae1e848/proofs/agda/EchoImageFactorizationPropPostulated.agda[EchoImageFactorizationPropPostulated.agda]:
+   `Trunc-pos`, `∣_∣-pos`, `is-prop-pos`, and `rec-pos` (one block).
+** https://github.com/hyperpolymath/echo-types/blob/e38fd465c4269ab9e9940802525630d7aae1e848/proofs/agda/Ordinal/Buchholz/Fidelity.agda[Ordinal/Buchholz/Fidelity.agda]:
+   `denotation` and `ordinal-upper-bound` (two blocks).
++
+Both modules use `--without-K` only, are excluded from `All.agda` and
+`Smoke.agda`, and are exempted by Echo's foundation guardrail. They are
+outside the `--safe --without-K` checks; `--safe` rejects these postulates.
+This is not a family-wide total: choreographic-types also contains the
+https://github.com/hyperpolymath/choreographic-types/blob/a0f647531a8cacad10294703ade2b6c8cec3255c/applications/rapidnj-two-thread.agda[standalone RapidNJ interface/conjecture sketch],
+with postulates and no safe-check flags, outside its repository build.
+The earlier “3 postulates total” and “every file” claims are withdrawn.
+The link:../TYPE-CONNECTIONS.adoc[existing proof receipts] cover bounded
+checks; the complete constituent suites were not rerun for this record.
+* K: the equivalence-as-identity programme needs a kernel without UIP. Lean's
+  Prop proof-irrelevance gives K by construction; Idris2 has no without-K
+  mode; Agda has `--without-K` and `--cubical`.
+* Discipline: `--safe --without-K` is required for the selected proof kernel.
+  This requirement does not establish uniform compliance across exploratory
+  files or constitute an estate-wide verification result.
+* Cost: consolidating on Idris2 or Lean would mean re-proving the Agda
+  corpus; not viable this quarter.
+
+== Falsifier
+
+resource-algebra (the first repo written under the ruling) had to reach a
+postulate-free `ResourceAlgebra` record with three instances under the flags
+within a week. It did on day one (`just check`, Agda 2.6.3), so the ruling
+stands; it is revisited if a family theorem is later found unstateable under
+`--without-K`.
+
+== Consequences
+
+* absolute-zero `LANGUAGE-POLICY.adoc` v1.6.0 ("Idris2 is the only
+  formal-verification language") needs an exception record (see T1); the
+  constitution's change procedure applies.
+* katagoria's Idris2 research sketches remain the incubator's prototypes;
+  graduation into a family repo means an Agda formalisation.
+* Creusot and SPARK are implementation-verification questions for januskey's
+  and jtv's Rust surfaces, outside this ruling.