Algebra of Contexts

Where the algebra of spaces (path, refinement, plural, derivation, secret audience) lives in the v4.2.1 TypeScript source, which test proves each part, and what npm this.me 4.2.1 returns. Concept: Algebra of Contexts (also Syntax: Algebra first). Theory: Digital Space Algebra, Encrypted Audiences.

Map

Concept	Source (v4.2.1)	Test (v4.2.1)
Space ⊇ subspace: a path is a list of segments	proxy.ts createProxy L256–303, core.ts readPath L289–393	dsl.contract L37–45
Selected subspace x[pred]	core-read.ts evaluateFilterPath L247–272	dsl.contract L223–236
Plural x[] (count) and x[].f (sum)	aggregate.ts evaluateAggregate L110–197	aggregate-path.test.ts
Derivation = over members [i]	derivation.ts registerDerivation L577–608	derivation-wave.test.ts
Secret scope: readable audience {self}	secret-context.ts resolveBranchScope L232–265, me.ts as L1581–1589	axioms.test.ts A0/A2
Explain with masked secret inputs	derivation.ts explain L140–251, mask L214–215	dsl.contract L325–348
Deriving from a secret: no keyless leak	same plus core-write.ts postulate L983–1101	derived-from-secret.test.ts L185–216
Audiences: OR / AND coalitions, minus, reseal	audience.ts canonicalize L86–89, minus L101–107, sealAudience L207–226, openAudience L229–247	audience-algebra.test.ts L77–207
Namespace: me://handle.space[selector]/path	me-uri.ts parseMeUri L284–332	me-uri.test.ts

Outputs on npm 4.2.1

node against the npm this.me 4.2.1 dist, 2026-10-14.

import ME, { parseMeUri } from "this.me";
const me = new ME();

me.profile.contact.email("abella@neurons.me");
me("profile.contact.email");          // "abella@neurons.me"

me.friends[1].age(17); me.friends[2].age(34); me.friends[3].age(21);
me("friends[age > 18].age");          // { "2": 34, "3": 21 }
me("friends[]");                      // 3
me("friends[].age");                  // 72

me.friends["[i]"]["="]("adult", "age >= 18");
me("friends[1].adult");               // false
me.friends[1].age(19);
me("friends[1].adult");               // true
me.explain("friends.1.adult").meta.k; // 1

me.wallet["_"]("vault-key");
me.wallet.hidden.note("private");
me("wallet");                         // undefined
me("wallet.hidden.note");             // "private"
me.as(null)("wallet.hidden.note");    // undefined  (guest)

me.wallet.balance(500);
me["="]("budget", "wallet.balance * 0.1");
me.explain("budget").value;           // 50
me.explain("budget").derivation.inputs;
// [{ path: "wallet.balance", value: "●●●●", origin: "stealth", masked: true, … }]

parseMeUri("me://suign.neurons.me[macbook]/profile.name");
// { href: "me://suign.neurons.me[surface:macbook]/profile.name",
//   handle: "suign", space: "neurons.me",
//   selector: { kind: "surface", value: "surface:macbook" },
//   path: "profile.name", segments: ["profile", "name"] }

Test runs on 4.2.1

Test (v4.2.1)	Runs against	Result
tests/contracts/dsl.contract.test.mjs	npm 4.2.1 dist	Phase 6 contract suite passed
tests/aggregate-path.test.ts	npm 4.2.1 dist	165 passed, 0 failed
tests/derivation-wave.test.ts	npm 4.2.1 dist	all wave cases passed
tests/Security/derived-from-secret.test.ts	npm 4.2.1 dist	11 passed, 0 failed
tests/me-uri.test.ts	v4.2.1 src/me-uri.ts	passed
tests/Security/audience-algebra.test.ts	v4.2.1 src/audience.ts	16 passed, 0 failed (laws L1–L9 plus AND/OR cases)

audience.ts is in the v4.2.1 source but not exported by the npm 4.2.1 package, so audiences are only reachable from source.

Derived-from-secret, the cases that matter here:

✅ 5. GUARANTEE: a keyless party declaring a derivation over the secret gets nothing computed from it
✅ 6. GUARANTEE: mixing the secret with a public value (price * fuel) reveals nothing to a keyless party
✅ 8. GUARANTEE: an owner-declared derivation produces no new secret-derived values once the key is gone

Related

Algebra of Contexts (concept) · Digital Space Algebra · Proxy calls · Axioms: TypeScript validation · Kernel Core · Plurality Is Grammar · Syntax · me.explain(path)