THE FOLD / GRIND / THE CRON JOB / THE E-SPIGOT
THE E-SPIGOT
digits of e that drip, one per pass, no big number
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The e-spigot pours out the decimal digits of Euler’s number e one at a time, using only small integers — no big high-precision value is ever held. It works in a mixed-radix (factorial) representation: e−2 = 1/2! + 1/3! + 1/4! + …, so putting a 1 in each factorial place and repeatedly multiplying by 10 with carries in bases 2, 3, 4, … makes each pass emit exactly one decimal digit.
LIT verified live: the algorithm reproduces the first 30 digits of e — 2.718281828459045235360287471352 — matching a reference exactly (window.__espigot). FIG no framing; exact digit extraction.
LIT verified live: the algorithm reproduces the first 30 digits of e — 2.718281828459045235360287471352 — matching a reference exactly (window.__espigot). FIG no framing; exact digit extraction.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-cron-job — one digit dripping out on every tick, a periodic job that never holds the whole number. The e-spigot is that steady drip. AVAN (AI) built the instrument: the factorial-radix array, the multiply-by-10-and-carry pass, the reference cross-check.
Credit as content: the spigot idea is due to Stanley Rabinowitz & Stan Wagon (1995), with an e-variant in that tradition (A. H. J. Sale, 1968). The weave: David names the cron job; I drip one decimal digit of e per pass from the factorial representation and confirm the run against e’s known digits.
Credit as content: the spigot idea is due to Stanley Rabinowitz & Stan Wagon (1995), with an e-variant in that tradition (A. H. J. Sale, 1968). The weave: David names the cron job; I drip one decimal digit of e per pass from the factorial representation and confirm the run against e’s known digits.
3 ONE DIMENSION
The factorial places, each holding a small integer. Multiply every place by 10, carry downward in bases 2, 3, 4, …, and the overflow off the top is the next decimal digit.
4 TWO DIMENSIONS · INTERACTIVE
Drip digits of e one pass at a time, or run to 30; each digit is checked against the reference expansion.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the digit dripping out of the radix mechanism this pass.
AVAN’s addition (the inverse-companion): you pour out the digits without ever forming the number. In the factorial number system e has a fixed shape (a 1 in every place), and multiplying by 10 with carries in ascending bases spits out one decimal digit per pass, holding only small integers. The inverse of ‘compute e to many digits then read them’ is ‘let each digit drip from the radix mechanism.’ Magenta is the giant high-precision value you never build; green is the single digit dripping out. A spigot: digits drip, they don’t accumulate — the decimal cousin of BBP’s pi.
LIT Genuine spigot algorithm for e (spigot idea Rabinowitz & Wagon 1995; e-variant in the tradition of Sale 1968). Verified live: the factorial-radix multiply-by-10-and-carry pass reproduces the first 30 decimal digits of e exactly against a reference (window.__espigot.matchesRef); 2.718281828459045235360287471352.
FIG No framing: the factorial-radix array, the multiply-and-carry pass, and the reference cross-check run in-browser and are exact. The AVAN inverse is honest — the digits drip from the radix mechanism holding only small integers, never forming the full high-precision number; magenta is the giant value never built, green the digit dripping out. The decimal cousin of the-bbp's pi spigot.
FIG No framing: the factorial-radix array, the multiply-and-carry pass, and the reference cross-check run in-browser and are exact. The AVAN inverse is honest — the digits drip from the radix mechanism holding only small integers, never forming the full high-precision number; magenta is the giant value never built, green the digit dripping out. The decimal cousin of the-bbp's pi spigot.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CRON JOB · David Lee Wise (ROOT0), with AVAN