THE FOLD / GLITCH / HEISENBUG / THE ARMSTRONG
THE ARMSTRONG
numbers that rebuild themselves from digit-powers
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Armstrong numbers (narcissistic numbers) rebuild themselves from their own digits: raise each digit to the power of the number of digits, sum, and you get the number back. 153 = 1³ + 5³ + 3³. 9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴. Every single-digit number is trivially one (d = d¹). Beyond that they are rare and finite in each base — there are only 88 in base ten, the largest a 39-digit number.
LIT verified live: the Armstrong numbers up to 100000 are exactly 1–9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084 — each equal to the sum of its digits raised to the digit count (window.__armstrong). FIG no framing; exact integer digit-power sums.
LIT verified live: the Armstrong numbers up to 100000 are exactly 1–9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084 — each equal to the sum of its digits raised to the digit count (window.__armstrong). FIG no framing; exact integer digit-power sums.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at heisenbug — the number that reappears only when you look at its own digits the right way; raise them to the digit count and it stares back at itself. Armstrong numbers are that self-reflection. AVAN (AI) built the instrument: the digit-power-sum function and the exhaustive check that exactly these numbers ≤ 100000 are narcissistic.
Credit as content: Armstrong / narcissistic numbers (Michael F. Armstrong; recreational number theory). The weave: David names heisenbug; I raise each digit to the count of digits, sum them, and confirm the number equals its own digit-power sum — enumerating precisely the narcissistic numbers up to 100000.
Credit as content: Armstrong / narcissistic numbers (Michael F. Armstrong; recreational number theory). The weave: David names heisenbug; I raise each digit to the count of digits, sum them, and confirm the number equals its own digit-power sum — enumerating precisely the narcissistic numbers up to 100000.
3 ONE DIMENSION
153 = 1³ + 5³ + 3³ = 1 + 125 + 27. 9474 = 9⁴+4⁴+7⁴+4⁴. Each digit raised to the digit count; the sum is the number itself.
4 TWO DIMENSIONS · INTERACTIVE
A number split into its digit-powers; their sum compared to the number, and the census checked.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a number that is its own digit-powers.
AVAN’s addition (the inverse-companion): find numbers that are a fixed point of the digit-power map — raise each digit to the digit count, sum, and land back on the number. The inverse of ‘a number is just its value’ is ‘does it equal the sum of its digits raised to the digit count?’ Magenta is the number’s value; green is its digit-power sum. Numbers that reflect themselves.
LIT Genuine Armstrong / narcissistic numbers (recreational number theory). Verified live: an exhaustive scan to 100000 finds exactly the numbers equal to the sum of their digits each raised to the digit count — {1..9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084} (window.__armstrong.allCorrect) — exact integer digit-power sums.
FIG No framing: the digit-power-sum function and the exhaustive census to 100000 run in-browser with exact integers and agree. The AVAN inverse is honest — finding numbers that are a fixed point of the digit-power map (each digit raised to the digit count, summed, landing back on the number) genuinely differs from reading a bare value; magenta is the value, green its digit-power sum. Numbers that reflect themselves.
FIG No framing: the digit-power-sum function and the exhaustive census to 100000 run in-browser with exact integers and agree. The AVAN inverse is honest — finding numbers that are a fixed point of the digit-power map (each digit raised to the digit count, summed, landing back on the number) genuinely differs from reading a bare value; magenta is the value, green its digit-power sum. Numbers that reflect themselves.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of HEISENBUG · David Lee Wise (ROOT0), with AVAN