PROOF SELFTEST 8/8 · witnessed in Claude 2026-10-11 · Edition 1.
THE SEAL 98 of 100 · LEGENDARY · WITNESSED · Trigger 5 · Machinery 5 · Law 5 · Portability 5 · Proof 5
IT CAN BE WRONG an AI reading a text file: it can be wrong and can invent a number, a rule, a name or a date; check what matters against your own records and the source; the risk is yours. THE-CLAUSES.md rides in the packet and is part of the licence.
THE PUNCH · SHA-256 OF SKILL.MD · E35EDD658238DEF212B318C3
CITE THIS CARDTHE EULER CARD, Edition 1. Lund Studio LLC, Westminster, Colorado. https://lundr.tech/?view=euler-card. Punch E35EDD658238DEF212B318C3. Retrieved 2026-10-11.
What it is.
Works with Euler's formula, e^iθ = cos θ + i sin θ, where multiplying by e^iθ turns a point by θ: identity computes e^iπ + 1 in floating point and shows (1 + 1/n)^n arriving at e; turn rotates a list of points about the origin or any centre; roots gives the n-th roots of any complex number, evenly spaced and adding to zero; polar moves between a + bi and length and angle.
It carries a machine that shows its working: identity — e^iπ + 1, and e arriving; turn — points turned; roots — the roots, round the circle; polar — length and angle — 8 checks in its selftest, every command on the record. It will never hide the floating-point residue; never mix degrees and radians unsaid; never claim roots in a fixed order. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
Six laws, written into the card.
They are in the card itself, so the AI follows them.
MULTIPLYING IS TURNINGe^iθ has length 1, so it turns without stretching.
DEGREES IN, RADIANS INSIDEAngles are given and printed in degrees; the arithmetic is in radians.
THE RESIDUE IS SHOWNe^iπ + 1 comes out 0 + 1.2 × 10⁻¹⁶ i in floating point; the card shows it rather than pretend.
ROOTS SIT EVENLYThe n-th roots lie on one circle, 360°/n apart, and add to zero.
ABOUT ANY CENTREturn takes --about, so a shape can turn about its own middle.
EXACT WHERE IT CAN BEValues smaller than 10⁻¹² are shown as 0.
What rides in the card.
In the card’s own voice, with a machine that shows its working.
THE GUIDEreferences/THE-LAWS.md
THE MACHINEeuler.py · four commandsidentity — e^iπ + 1, and e arriving; turn — points turned; roots — the roots, round the circle; polar — length and angle. Every command prints its working and refuses a bad input; 8 checks in its selftest, every command on the record.
What it does once your AI has it.
identity E^iπ + 1, and e arriving
turn Points turned
roots The roots, round the circle
polar Length and angle
On the record e^iπ + 1 computed with its residue; points and a square turned; the sixth roots of 1 round the circle, adding to zero; 3 + 4i as 5 at 53.13°.
What it will never do.
It will never hide the floating-point residue; never mix degrees and radians unsaid; never claim roots in a fixed order. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
Plain floating point, about sixteen digits; no symbolic algebra. It is an AI reading a text file: it can be wrong, so check what matters against your own records and the source.
What’s in the buy.
CARD.md — the whole card: who it is, its laws, when it says no, what it carries · SKILL.md — the door your AI reads first · START-HERE.md — the first five minutes, for you
THE-LAWS.md — the guide in references/, in the card's own voice
scripts/euler.py — the machine: identity · turn · roots · polar, standard library only, selftest 8/8
WITNESS.md + SELFTEST.md — every command on the record, as it printed · MANIFEST.md, every file hashed · AUDIT.md, the twelve checks
MY-LEDGER.md — the card's memory, on your own machine · TIN.md · LICENSE-NOTE.md · THE-CLAUSES.md · HOSTS.md
card.svg + card-machine.svg + card.json · card.html, the card as one offline file · the doors for ChatGPT, Gemini, Cursor, Claude Code and MCP hosts (rules/, system/, mcp/)
PROOF · SELFTEST 8/8 · 4 COMMANDS ON THE RECORD · WITNESSED IN CLAUDE 2026-10-11 · EDITION 1 · PUNCH E35EDD658238DEF212B318C3
ON EVERY DOOR · A CARD FOR YOUR AI, A FILE FOR YOUR COMPUTER
In Claude: turn on code execution under Settings › Capabilities, then Customize › Skills › + › Create skill, and upload the zip as it is — START-HERE.md in the box walks you through it, and tells you how to keep the ledger. In ChatGPT, Gemini and the rest: a Project, a GPT or a Gem with the card’s files attached and the short door in the box pasted as its instructions. The words run anywhere an AI reads Markdown; the machines run wherever the host runs Python. Witnessed in Claude only. The host marks →
Take it.
Nº 1129 PROPOSED — LAUNCHING SOON
Sold as is under the term printed. A card instructs an AI you operate; results depend on your model, your files and your judgement. Not medical, legal, tax or financial advice, never the person’s boss, and not a licence to practise. The terms →
One payment. The file is yours to keep and keeps working at its edition; new editions issued in the year after you buy reach you by email as replacement files. Tax is added at checkout where it applies. Nothing auto-renews.
A TERM, NOT A SUBSCRIPTION: NOTHING RENEWS ITSELF AND NOBODY IS CHARGED AGAIN. WHEN A TERM ENDS THE FILES STAY ON YOUR COMPUTER AND STAY READABLE — FREEZE, NOT LOSS.
THE MACHINE · IN THE OPEN · FROM THE WITNESSED RUN OF 2026-10-11
euler.py, every command showing its working.
A small Python program, standard library only. Your AI runs it; you can too. Every block below is pasted from the card’s own WITNESS.md, as printed.
identity
e^iπ + 1, and e arriving
turn
points turned
roots
the roots, round the circle
polar
length and angle
selftest
8 checks that prove the machine; it must print 8/8
identity · E^IΠ + 1, AND E ARRIVING
$ python3 scripts/euler.py identity
e^iπ + 1 = 0.0 + 1.22e-16 i · the real part is exactly 0; the imaginary part is sin π as floating point holds it
(1 + 1/n)^n at n = 1: 2.0000000000
(1 + 1/n)^n at n = 10: 2.5937424601
(1 + 1/n)^n at n = 100: 2.7048138294
(1 + 1/n)^n at n = 10,000: 2.7181459268
(1 + 1/n)^n at n = 1,000,000: 2.7182804691
e = 2.7182818285
THE NUMBERS, NAMES AND DATES IN THESE RUNS ARE THE STUDIO’S OWN EXAMPLES, INVENTED FOR THE RECORD; NO REAL COMPANY, PERSON OR PROPERTY IS NAMED.
QUESTIONS AT THE TABLE
Asked before the wire.
What does it need from me?
Identity · e^iπ + 1, computed. It asks first for an angle in degrees and the points, or n and a number, or a complex number.
Does it send anything anywhere?
No. The machine is a standard-library Python program that runs on your own computer and sends nothing anywhere; the words run wherever an AI reads Markdown. No server, no account, no key.
What is on the record?
The self-test (8/8) and every command run on real example inputs, pasted into WITNESS.md as they printed; the punch on the face is the SHA-256 of SKILL.md, so a downloaded copy can be checked against this room.
Can it be wrong?
Yes — it is an AI reading a text file. Plain floating point, about sixteen digits; no symbolic algebra.
What will it never do?
It will never hide the floating-point residue; never mix degrees and radians unsaid; never claim roots in a fixed order. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
