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 · A63E15BA6C6F905CD4788628
CITE THIS CARDTHE ENTROPY CARD, Edition 1. Lund Studio LLC, Westminster, Colorado. https://lundr.tech/?view=entropy-card. Punch A63E15BA6C6F905CD4788628. Retrieved 2026-10-11.
What it is.
Works out entropy as Boltzmann wrote it in 1877, S = k ln W, the count of ways a thing can be arranged: count gives W and S for coins, dice or particles in two states and shows why the even split wins; erase gives the least energy erasing information can cost at a temperature, kT ln 2 a bit; speed gives a gas's molecular speeds from the same counting; arrow gives the odds of a mixed thing un-mixing on its own.
It carries a machine that shows its working: count — the ways and the entropy; erase — the least cost of erasing; speed — molecular speeds; arrow — the odds of un-mixing — 8 checks in its selftest, every command on the record. It will never call entropy disorder and stop there; never say a chip runs at the erasure floor; never round odds to impossible. 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.
COUNTINGW is the number of arrangements that look the same from outside; S is k times its logarithm.
BIG NUMBERS IN LOGARITHMSCounts too large for a computer are worked as logarithms and said in powers of ten.
THE ERASURE FLOORErasing one bit at temperature T costs at least kT ln 2; real chips spend far more.
SPEEDS FROM THE SAME COUNTThe most likely, the mean and the root-mean-square speeds of a gas.
THE ARROWMixed states vastly outnumber unmixed ones, so mixing runs one way.
EIGHT GASESHydrogen, helium, nitrogen, oxygen, argon, carbon dioxide, water vapour and air, or any mass in u.
What rides in the card.
In the card’s own voice, with a machine that shows its working.
THE GUIDEreferences/THE-LAWS.md
THE MACHINEboltzmann.py · four commandscount — the ways and the entropy; erase — the least cost of erasing; speed — molecular speeds; arrow — the odds of un-mixing. 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.
count The ways and the entropy
erase The least cost of erasing
speed Molecular speeds
arrow The odds of un-mixing
On the record 100 coins: 10²⁹ ways to land half heads, seven times the ways for 40; a terabyte's erasure floor at room temperature; nitrogen's molecules near 500 m/s; a room's air never un-mixes on its own.
What it will never do.
It will never call entropy disorder and stop there; never say a chip runs at the erasure floor; never round odds to impossible. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
Ideal gases and independent coins; real systems with interactions need statistical mechanics beyond counting. 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/boltzmann.py — the machine: count · erase · speed · arrow, 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 A63E15BA6C6F905CD4788628
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 1136 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
boltzmann.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.
count
the ways and the entropy
erase
the least cost of erasing
speed
molecular speeds
arrow
the odds of un-mixing
selftest
8 checks that prove the machine; it must print 8/8
count · THE WAYS AND THE ENTROPY
$ python3 scripts/boltzmann.py count 100
100 coins, 50 heads: W = 1.009 × 10^29 ways · S = k ln W = 9.221 × 10^-22 J/K · 7.96% of all 1.268 × 10^30 outcomes
count · THE WAYS AND THE ENTROPY
$ python3 scripts/boltzmann.py count 100 --heads 40
100 coins, 40 heads: W = 1.375 × 10^28 ways · S = k ln W = 8.945 × 10^-22 J/K · 1.08% of all 1.268 × 10^30 outcomes
erase · THE LEAST COST OF ERASING
$ python3 scripts/boltzmann.py erase 300 --bits 8e12
erasing 8e+12 bits at 300 K costs at least 2.297 × 10^-8 J (0.01792 eV a bit)
speed · MOLECULAR SPEEDS
$ python3 scripts/boltzmann.py speed 300 n2
n2 at 300 K: most likely 422 m/s · mean 476 m/s · root-mean-square 517 m/s
arrow · THE ODDS OF UN-MIXING
$ python3 scripts/boltzmann.py arrow 1e23
1e+23 particles all in one half of their box, on their own: odds 1 in 10^(3.010 × 10^22)
the reverse never happens because there are so many more ways to be mixed: that count is the arrow of time
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?
Count <n> · the ways, and S. It asks first for a count of coins or particles; a temperature and a number of bits; or a temperature and a gas.
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. Ideal gases and independent coins; real systems with interactions need statistical mechanics beyond counting.
What will it never do?
It will never call entropy disorder and stop there; never say a chip runs at the erasure floor; never round odds to impossible. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
