{
 "format": "LSC-1",
 "lsc": "LSC-1",
 "edition": "E1",
 "cut": "2026-10-09",
 "name": "THE ZETA CARD",
 "handle": "zeta-card",
 "number": "Nº 1139",
 "house": "THE LABORATORY",
 "wing": "THE THIRTEEN EQUATIONS",
 "role": "the zeta function and the primes",
 "tagline": "ζ(s) = Σ 1/nˢ: its value for any real s (ζ(2) = π²/6), its first zeros on the critical line, the primes up to x beside li(x), and the count of zeros up to a height — the hypothesis still open since 1859.",
 "sigil": "ζ",
 "hue": "#2F7D3A",
 "punch": "A998AEE7339A445E7BCDB9B4",
 "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 asks about the primes, the zeta function, or the Riemann hypothesis",
 "loop": [
  "value <s> · ζ(s)",
  "zeros <n> · on the critical line",
  "primes <x> · counted, beside li(x)",
  "count <height> · the zeros below",
  "say the hypothesis is unproved"
 ],
 "laws": [
  "**Real s above zero.** ζ(s) for s > 0, s ≠ 1, by an accelerated alternating series; the pole at 1 is named.",
  "**Zeros to about 0.01.** By the classical asymptotic formula on the critical line; the first ten are checked against the published values.",
  "**Primes counted exactly.** π(x) by a sieve up to twenty million.",
  "**li(x) wins.** The logarithmic integral is a far better guess than x / ln x; the zeros correct what is left.",
  "**Open since 1859.** That every non-trivial zero lies on the critical line is unproved; the card never says otherwise.",
  "**Small numbers, honest digits.** Zeros are printed to three decimals."
 ],
 "never": [
  "claim the hypothesis proved or false",
  "give zeros past the tenth as exact",
  "evaluate at the pole, s = 1"
 ],
 "machine": "scripts/zeta.py · value · zeros · primes · count · 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/zeta.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"
}