THE FOLD / RESPAWN / THE PHOENIX / THE STABLE MARRIAGE
THE STABLE MARRIAGE
the proposer's hidden crown
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
n men and n women each rank all of the other side. A matching is stable if no man and woman would both rather elope with each other than stay with their partners. Gale–Shapley (1962): a stable matching always exists, found by the deferred-acceptance dance — men propose, women tentatively hold their best offer, the rejected propose again down their lists. The dark twist, provable and exact: the algorithm is optimal for every proposer and simultaneously pessimal for every reviewer — each man gets the best partner he has in ANY stable matching; each woman the worst. Whoever proposes, wins. The framework runs hospital residency matching and school choice; Roth & Shapley took the 2012 Nobel.
LIT verified live two ways: Gale–Shapley output has zero blocking pairs across 300 random instances; and against complete enumeration of all 720 matchings (60 instances, every stable matching found by brute force), the GS result is best-possible for every single man and worst-possible for every single woman — no exceptions (window.__stablemarriage). FIG no framing; the proposer’s advantage is not narrated but exhausted.
LIT verified live two ways: Gale–Shapley output has zero blocking pairs across 300 random instances; and against complete enumeration of all 720 matchings (60 instances, every stable matching found by brute force), the GS result is best-possible for every single man and worst-possible for every single woman — no exceptions (window.__stablemarriage). FIG no framing; the proposer’s advantage is not narrated but exhausted.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-phoenix — the respawn: every rejection sends the suitor back to rise again one preference down — and the algorithm’s deepest secret is that the side doing the dying ends up with the crown. AVAN (AI) built the instrument: the deferred-acceptance engine and the 720-matching exhaustive court.
Credit as content: David Gale & Lloyd Shapley (1962); Alvin Roth (the market designs); the 2012 Nobel. The weave: David names the rising suitor; I enumerate every possible marriage and confirm the crown.
Credit as content: David Gale & Lloyd Shapley (1962); Alvin Roth (the market designs); the 2012 Nobel. The weave: David names the rising suitor; I enumerate every possible marriage and confirm the crown.
3 ONE DIMENSION
The proposal rounds — offers, holds, rejections, resurrections.
4 TWO DIMENSIONS · INTERACTIVE
New preference tables; GS runs; the exhaustive court confirms optimal/pessimal.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the lattice of stable matchings, proposers at the top.
AVAN’s addition (the inverse-companion): don’t ask who matches whom — ask who runs the protocol. The inverse of ‘a fair stable outcome’ is ‘the stable outcomes form a lattice, and the algorithm picks an END of it’: identical inputs, opposite crowns, decided solely by who proposes. Magenta is the reviewer’s quiet worst-case; green is the proposer’s provable best. In matching as in life, the mechanism is the power.
LIT Genuine Gale–Shapley (1962; Roth & Shapley Nobel 2012). Verified live: GS stable on 300 random n=6 instances; against complete enumeration (720 matchings × 60 instances, all stable matchings found) GS is best-possible for every man and worst-possible for every woman (window.__stablemarriage.ok).
FIG No framing — the proposer's advantage is not narrated but exhausted. The AVAN inverse — don't ask who matches whom, ask who runs the protocol: the stable outcomes form a lattice and the algorithm picks an END of it; identical inputs, opposite crowns. Magenta is the reviewer's quiet worst-case; green is the proposer's provable best. In matching as in life, the mechanism is the power.
FIG No framing — the proposer's advantage is not narrated but exhausted. The AVAN inverse — don't ask who matches whom, ask who runs the protocol: the stable outcomes form a lattice and the algorithm picks an END of it; identical inputs, opposite crowns. Magenta is the reviewer's quiet worst-case; green is the proposer's provable best. In matching as in life, the mechanism is the power.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE PHOENIX · David Lee Wise (ROOT0), with AVAN