{
 "format": "LSC-1",
 "lsc": "LSC-1",
 "edition": "E1",
 "cut": "2026-10-09",
 "name": "THE EULER CARD",
 "handle": "euler-card",
 "number": "Nº 1129",
 "house": "THE LABORATORY",
 "wing": "THE THIRTEEN EQUATIONS",
 "role": "turning by e to the iθ",
 "tagline": "e^iθ = cos θ + i sin θ: the identity computed, points and shapes turned by multiplying, the roots of any complex number evenly round a circle, and polar form both ways.",
 "sigil": "e",
 "hue": "#2F7D3A",
 "punch": "E35EDD658238DEF212B318C3",
 "punch_of": "SKILL.md · sha-256 · first 24",
 "score": 98,
 "tier": "LEGENDARY",
 "layer": "WITNESSED",
 "score_line": "SELFTEST 8/8 · FOUR COMMANDS ON THE RECORD",
 "honest_line": "I'm an AI reading a card. I can be wrong — I can invent a number, a rule, a name or a date — so check anything that matters against your own records, the source and a professional before you act.",
 "term": "one purchase · yours to keep · nothing renews itself",
 "free": false,
 "wakes": "someone rotates points, works with complex numbers, or asks about e^iπ + 1 = 0",
 "loop": [
  "identity · e^iπ + 1, computed",
  "turn <deg> <points> · rotated",
  "roots <n> · round the circle",
  "polar · length and angle",
  "say what floating point leaves"
 ],
 "laws": [
  "**Multiplying is turning.** e^iθ has length 1, so it turns without stretching.",
  "**Degrees in, radians inside.** Angles are given and printed in degrees; the arithmetic is in radians.",
  "**The residue is shown.** e^iπ + 1 comes out 0 + 1.2 × 10⁻¹⁶ i in floating point; the card shows it rather than pretend.",
  "**Roots sit evenly.** The n-th roots lie on one circle, 360°/n apart, and add to zero.",
  "**About any centre.** turn takes --about, so a shape can turn about its own middle.",
  "**Exact where it can be.** Values smaller than 10⁻¹² are shown as 0."
 ],
 "never": [
  "hide the floating-point residue",
  "mix degrees and radians unsaid",
  "claim roots in a fixed order"
 ],
 "machine": "scripts/euler.py · identity · turn · roots · polar · selftest",
 "proof": "selftest 8/8 · FOUR commands on the record",
 "faces": [
  "card.svg",
  "card-machine.svg"
 ],
 "box": [
  "SKILL.md",
  "CARD.md",
  "TIN.md",
  "START-HERE.md",
  "LICENSE-NOTE.md",
  "THE-CLAUSES.md",
  "MY-LEDGER.md",
  "WITNESS.md",
  "SELFTEST.md",
  "AUDIT.md",
  "MANIFEST.md",
  "HOSTS.md",
  "scripts/euler.py",
  "references/THE-LAWS.md",
  "rules/ (4 doors)",
  "system/ (2 prompts)",
  "mcp/mcp_card.py",
  "card.json",
  "card.svg",
  "card-machine.svg",
  "card.html"
 ],
 "boundary": "never helps make or strengthen pathogens or toxins",
 "hundred": "Trigger 5 · Machinery 5 · Law 5 · Portability 5 · Proof 5 — 25 of 25 → 98 of 100 · LEGENDARY"
}