# Math marriages (RSA, vesica, Chord metaphor)

**Status:** established + opinion + metaphor labeled  
**Mood:** fun. Two structures that only unlock something together.

## The pattern you named

RSA is the poster: one math alone is not the crypto. You need a *marriage*.

| Piece A | Piece B | Child |
|---------|---------|--------|
| Hardness of factoring n = pq (believed) | Easy modular exponentiation once you know φ(n) = (p-1)(q-1) | Public encrypt / private decrypt |
| Two equal circles, centers one radius apart | Equilateral / Pythagoras | Vesica chord = r√3 (real geometry under "sacred" paint) |
| Discrete log hardness (cousin story) | Diffie-Hellman group exponentiation | Shared secret without a prior shared key |

**Established (RSA):** Rivest-Shamir-Adleman. Publish (e, n). Keep d with ed ≡ 1 (mod φ(n)). Cipher c ≡ m^e (mod n), plain m ≡ c^d (mod n). Correctness uses Euler/Fermat and usually CRT across p and q. Factoring n lets you build φ and thus d; the precise complexity equivalence is contested / not a theorem that "breaking RSA ≡ factoring" in all models. Lamp: `lamps/rsa_marriage.py` (toy primes; correctness only).

**Established (vesica piscis):** Intersection of two disks of radius r whose centers are distance r apart. Inscribed equilateral triangles. Height/width of the lens is √3. Archimedes bounded √3 between 265/153 and 1351/780 (Farey flavored neighbors of √3). MathWorld / Wikipedia. Lamp: `lamps/vesica_sqrt3.py`.

**Refuse (Aperture):** φ as destiny, Flower of Life as proof, "the universe is RSA." Keep the weird geometry. Drop the incense unless labeled metaphor (`03`, prefs).

## Chord as big bang (metaphor)

**Metaphor (labeled):** drainfun / Cadence "Chord" sits next to honesty boxes: a striking that starts a world. Here the marriage *is* the bang: two circles kiss and √3 appears; two primes multiply and a lock appears. Not cosmology. Not a claim that Chord equals RSA. Just the rhyme: **capability arrives when two structures touch.**

Opinion: Aperture likes marriages the way it likes Farey neighbors (|bc-ad|=1) and Seekers in the gap. The interesting event is the handshake, not the solo virtuoso.

## Synapses (proposed)

1. `29-math-marriages` shares pattern with `28-farey-near-miss` (bounds on √3; handshake determinants)
2. `29-math-marriages` feeds `04-leftover-as-map` (product n hides the primes; residual is the factor map)
3. `29-math-marriages` constrains `03-esoterica` (sacred geometry only with a FAIL-able check)

*Formed 2026-09-13.*