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 · 5CC287D0B4DC7F3E155C7F0D
CITE THIS CARDTHE LEAST ACTION CARD, Edition 1. Lund Studio LLC, Westminster, Colorado. https://lundr.tech/?view=least-action-card. Punch 5CC287D0B4DC7F3E155C7F0D. Retrieved 2026-10-11.
What it is.
Shows the principle of least action in numbers: throw takes a ball thrown up and caught and works out the action, motion energy minus height energy summed over the flight, for the true path and for paths bent away from it, so the true one is seen to cost least; fastest races a bead down a straight ramp, a circle arc and the cycloid between the same two points and shows the cycloid wins; chain gives the curve a chain hangs in between two posts and its sag, the shape of least height energy and, upside down, of an arch.
It carries a machine that shows its working: throw — the action of the true path and of bent ones; fastest — ramp, arc and cycloid timed; chain — the hanging curve and its sag — 8 checks in its selftest, every command on the record. It will never call the shortest path the fastest; never claim least without showing the comparison; never hang a chain shorter than its span. 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.
SHOWN, NOT ASSERTEDThe true path's action is printed beside the bent paths', so the least is seen.
STATIONARY, STRICTLYThe true path is where the action stops changing; for these cases that is its least, and the card says so.
THE CYCLOID WINSDropping steeply first buys speed; the straight ramp is shortest and slowest.
THE CHAIN'S CURVEy = a cosh(x/a), solved for the length given, with its depth in the middle.
NO FRICTIONEvery slide is frictionless and says so.
REFUSED, NOT GUESSEDA chain shorter than its span, or a slide with no drop, is refused.
What rides in the card.
In the card’s own voice, with a machine that shows its working.
THE GUIDEreferences/THE-LAWS.md
THE MACHINEaction.py · three commandsthrow — the action of the true path and of bent ones; fastest — ramp, arc and cycloid timed; chain — the hanging curve and its sag. 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.
throw The action of the true path and of bent ones
fastest Ramp, arc and cycloid timed
chain The hanging curve and its sag
On the record A ball in the air 2 s: the true path's action is least and every bent path costs more; across 2 m and down 1 m the cycloid (0.806 s) beats the arc and the ramp (1.010 s); a 12 m chain between posts 10 m apart hangs 2.92 m deep.
What it will never do.
It will never call the shortest path the fastest; never claim least without showing the comparison; never hang a chain shorter than its span. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
Ideal cases: a uniform field of gravity, no friction, no air, a perfectly flexible chain. The action is summed numerically, closely enough to compare paths. 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/action.py — the machine: throw · fastest · chain, 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 · 3 COMMANDS ON THE RECORD · WITNESSED IN CLAUDE 2026-10-11 · EDITION 1 · PUNCH 5CC287D0B4DC7F3E155C7F0D
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 1142 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
action.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.
throw
the action of the true path and of bent ones
fastest
ramp, arc and cycloid timed
chain
the hanging curve and its sag
selftest
8 checks that prove the machine; it must print 8/8
throw · THE ACTION OF THE TRUE PATH AND OF BENT ONES
$ python3 scripts/action.py throw 2
a 1 kg ball thrown up and caught 2 s later · it rises 4.903 m
the true path action -32.0568 J s
bent by +0.5 m action -31.7484 J s (+0.3084 more)
bent by +0.2 m action -32.0075 J s (+0.04935 more)
bent by -0.2 m action -32.0075 J s (+0.04935 more)
the path the ball takes is the one whose action is least; every other path between the same two moments costs more
fastest · RAMP, ARC AND CYCLOID TIMED
$ python3 scripts/action.py fastest 2 1
a bead from rest, 2 m across and 1 m down, without friction:
straight ramp 1.0098 s
circle arc 0.8288 s
cycloid 0.8057 s (rolling circle of radius 0.5172 m)
the cycloid is fastest: it drops steeply first to gain speed, then runs; the straight line is the shortest path, not the quickest
chain · THE HANGING CURVE AND ITS SAG
$ python3 scripts/action.py chain 10 12
a 12 m chain between posts 10 m apart hangs as y = 4.6954 cosh(x / 4.6954), 2.923 m deep in the middle
the curve of least height energy for its length; turned upside down, the arch that stands in pure compression
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?
Throw <seconds> · true path vs bent. It asks first for how long the ball is in the air; or how far across and down the slide goes; or the span and the chain's length.
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 cases: a uniform field of gravity, no friction, no air, a perfectly flexible chain. The action is summed numerically, closely enough to compare paths.
What will it never do?
It will never call the shortest path the fastest; never claim least without showing the comparison; never hang a chain shorter than its span. It never helps design, make, grow, enhance or spread a pathogen or toxin, or plan work meant to harm.
