Why Order the values F < U < T: AND is the lower, OR is the higher, NOT flips the order.

Term strong Kleene connectives

Cost Cheap and uniform, but unknown spreads through a formula quickly.

Here Three values give 9 cells per connective, all built from min and max.

Why When p is unknown, p or not-p is unknown: the law of excluded middle is lost.

Term K3, after Stephen Kleene

Cost You gain an honest unknown and lose some classical theorems.

Here A three-valued evaluator can return non liquet instead of guessing.

Why Classical logic is two-valued: each sentence gets exactly one of true or false.

Term bivalence, from Latin bis, twice

Cost It forces an answer even where the evidence is missing.

Here A plain if/else has no third branch; the usage experiments add one.

Why An argument is valid if, whenever the premises are designated, so is the conclusion.

Term designated values

Cost Change what is designated and you change which arguments are valid.

Here Our verdict holds is the designated one: only a holds supports the next step.

Why L3 sets U implies U to true, so p implies p stays a law; K3 leaves it unknown.

Term L3, Jan Lukasiewicz, 1920

Cost More classical laws survive, but the arrow is less uniform.

Here Choose the arrow before building the evaluator: it changes what a rule can conclude.

Why Flipping what you do not know tells you nothing new.

Term NOT U = U

Cost Unknown is a fixed point: negation cannot resolve it.

Here Denying a claim does not turn a non liquet into a holds.

Why Excluded middle: "p or not-p" is a theorem. Bivalence: every sentence is true or false. Supervaluationism keeps the first and drops the second.

Term LEM versus bivalence

Cost Keeping one without the other is subtle.

Here Say which one you are dropping when you add a third value.

Why LP adds "both" as a designated third value, so a contradiction does not explode.

Term paraconsistent logic; LP, Graham Priest

Cost You can reason about inconsistent data but lose disjunctive syllogism.

Here Two sessions can record opposite facts; keep both, delete neither.

Why From P and not-P, any Q follows.

Term ex falso quodlibet

Cost One inconsistency in the premises makes the whole system useless.

Here A log that may hold a contradiction needs a logic that survives it.

Why In classical logic it is a contradiction; in K3 it can be unknown; in LP it is both.

Term the Liar paradox

Cost Each repair changes what else you can say.

Here A record that describes its own reliability needs a rule for itself.

What would settle it Which logic you adopt; the sentence alone does not decide.

Why It means 'it is not clear': the Roman juror's verdict when the evidence does not settle the case.

Term non liquet, from liquere, to be clear

Cost A third verdict is honest but gives no ruling.

Here On our tiles, non liquet says what would settle it.

Why Aristotle's future contingents: the answer depends on the logic. Lukasiewicz built L3 to leave it open.

Term future contingents, De Interpretatione 9

Cost Leaving it open denies determinism; closing it asserts it.

Here A claim about next week's traffic is non liquet until the traffic arrives.

What would settle it A choice of logic and of a theory of time; the data cannot settle it.

Why Ambiguous grammars exist; the dangling else is the classic case.

Term ambiguous grammar

Cost Fixing it costs extra rules or a convention.

Here A precedence table is a convention that settles ambiguity.

Why The lexer groups characters into words of the language: numbers, names, symbols.

Term lexical analysis

Cost A separate pass is simple but cannot see grammar context.

Here It is where the character + becomes the token ADD.

Why It is independent of ZFC: Goedel (1940) showed it cannot be refuted, Cohen (1963) that it cannot be proved.

Term CH, Cantor, 1878

Cost Settling it means adding axioms, which is a choice, not a discovery.

Here Some questions are non liquet by proof, not by lack of effort.

What would settle it Only a new axiom, accepted by the field.

Why That is lexical scope. Dynamic scope looks up the call stack.

Term lexical versus dynamic scope

Cost Lexical is predictable; dynamic is flexible but hard to reason about.

Here A Tris-Trik lane copies its globals, so its names cannot reach sideways.

Why Each operator pulls on its neighbours with a number; the stronger pull wins.

Term top-down operator precedence, Vaughan Pratt, 1973

Cost Compact, but harder to read than a grammar.

Here Crafting Interpreters builds one in a few dozen lines.

Why It drops the punctuation and keeps the structure; the concrete tree keeps it all.

Term AST versus concrete syntax tree

Cost Dropping punctuation loses formatting, so a pretty-printer needs it back.

Here The house compiler converts a fixed six-node workflow, not free text.

Why A function plus the environment it was born in.

Term closure

Cost Captured variables live as long as the closure does.

Here The Arbitorium page functions close over the game state.

Why Operands wait on a stack; each instruction takes its inputs from the top.

Term stack VM, bytecode

Cost Compact code, but more instructions than a register machine.

Here Tris-Trik's VOTE pops three trits and pushes one.

Why Studies disagree, and they mix up language, team and task.

Term static versus dynamic typing

Cost Each side has strong stories and thin evidence.

Here The Python tools here lean on tests, not types.

What would settle it A controlled study across comparable teams and tasks.

Why Compile it once with some other compiler; afterwards it compiles itself.

Term bootstrapping, self-hosting

Cost The chain of trust starts at the first compiler (Thompson's Trusting Trust).

Here The first build of anything here is put on the record with a hash.

Why The house ternary language answers a claim with one of three values, not two.

Term Tris-Trik

Cost Every consumer of an answer must handle the third value.

Here The usage experiments return the same three.

Why Turing (1936): no general procedure decides halting.

Term the halting problem

Cost So program analyses are approximate: they say maybe.

Here Maybe is exactly the non liquet a sound analyser must be allowed to return.

Why Whatever the other does, defecting pays you more.

Term dominant strategy

Cost Both defecting leaves both worse off than both cooperating.

Here A shared GPU with no gate invites every job to grab it.

Why Tests show a bug's presence, never its absence (Dijkstra). Only a proof against a specification would settle it.

Term program correctness

Cost A proof usually costs more than the program.

Here Every build here reports 'N tests pass, 25 reruns', never 'no bugs'.

What would settle it A proof against a written specification.

Why It depends on the allocation pattern, the collector and the hardware.

Term garbage collection versus manual management

Cost Throughput against predictable pauses.

Here The Python tools here are collected; the C side is manual. Neither is ruled better.

What would settle it A benchmark on the real workload, which settles it for that workload only.

Why Moves form a tree; a strategy is a plan for every node you could reach.

Term extensive form, game tree

Cost Trees grow explosively with every extra branch.

Here The Arbitorium is a game tree: your path is a strategy, the held branches are moves not made.

Why In the prisoner's dilemma the equilibrium is worse for both than cooperation.

Term Pareto efficiency

Cost Equilibrium is stable, not good.

Here A fail-closed rule can be stable and still inconvenient.

Why Nash (1950): a set of strategies where nobody gains by changing alone.

Term Nash equilibrium

Cost It exists, but may be hard to find, and there may be many.

Here The one-branch rule has a best reply at every fork.

Why Computational irreducibility is believed (Wolfram) but unproven.

Term Rule 30, cellular automaton

Cost If true there is no shortcut; if false a shortcut exists.

Here Rule 30 is among the house's math files.

What would settle it A proof or a shortcut.

Why Sandpile models show it can; whether it is the general cause is debated.

Term SOC, Bak, Tang and Wiesenfeld, 1987

Cost A strong idea that is hard to test on real data.

Here Heavy-tailed usage would not by itself prove it.

What would settle it Direct tests on each specific system, one at a time.

Why Start at the last move, decide it, then step back.

Term Zermelo, Kuhn; subgame perfection, Selten

Cost It assumes everyone is rational and knows that everyone is.

Here Work back from the end of a path to decide the fork.

Why Open since 1971 (Cook); a proof either way would settle it.

Term P versus NP, a Clay Millennium Problem

Cost Most believe they differ; nobody has proved it.

Here It is the reason some searches here are bounded.

What would settle it A proof.

Why Big-O describes growth and ignores constants; for small n the quadratic can win.

Term asymptotic notation

Cost Ignoring constants hides real cost.

Here The pinecone has 89 scales: small enough that clarity beats cleverness.

Why For P(x) ~ x^-a, the mean is finite only for a above 2, the variance only for a above 3.

Term heavy tail, Pareto

Cost The average then misleads; use medians and quantiles.

Here Our latency numbers are percentiles for that reason.

Why The second-price (Vickrey) auction does it.

Term mechanism design; Hurwicz, Maskin, Myerson

Cost There are impossibility results: you cannot have everything.

Here The usage log records what happened, so honesty is the cheap path.

Why It is the most irrational turn, so a seed never lands on an earlier seed's ray.

Term phyllotaxis; golden angle = 360 / phi squared

Cost Real plants vary; the model is an ideal.

Here The minecone puts scale m at angle m times 137.5 degrees.

Why A positive Lyapunov exponent means sensitive dependence on initial conditions.

Term chaos, Lorenz, 1963

Cost Long-range prediction fails even with a perfect rule.

Here A hash behaves this way on purpose: change one byte, change everything.

Why Fail-closed denies; fail-open allows.

Term fail-closed versus fail-open

Cost Outages lock people out.

Here The backend refuses everything if its session secret is missing.

Why A part that cannot do harm cannot be made to.

Term principle of least privilege

Cost More accounts and grants to manage.

Here The guardrail worker has no delete route, and holds no token that could delete.

Why Security is relative to a threat model: an attacker, a goal, a capability.

Term threat model

Cost Writing it down shows what you did not defend.

Here The house design names the API as the main attack vector.

Why Possession is authority: the secret is the permission.

Term capability security

Cost If it leaks, so does the power.

Here The y in xx-y-zz is a secret of this kind.

Why A nonce plus an expiry makes each approval good for one use.

Term nonce, replay protection

Cost The receiver has to keep state.

Here The passkey challenge spec binds one approval to one intent.

Why Each link hashes the one before it, so an edit shows downstream.

Term hash chain; Merkle trees are the branching cousin

Cost It detects change; it does not prevent it.

Here The usage log and the recall anchors are chained and checked.

Why Side channels leak through time, power and sound, not through the maths.

Term side channel

Cost Constant-time code is harder to write.

Here Our key comparisons are constant-time for this reason.

Why A wrong guess gets a believable answer, so the attacker cannot tell.

Term honey encryption, Juels and Ristenpart, 2014

Cost It needs a model of what plausible data looks like.

Here The house honey module generates decoys on the fly instead of storing them.

Why Kerckhoffs: assume the attacker knows the system; only the key is secret.

Term Kerckhoffs's principle, 1883

Cost Public scrutiny finds flaws you would miss.

Here The honey module's code can be public; only its key matters.

Why You cannot prove a negative about what you have not found.

Term unknown unknowns

Cost Time and review lower the risk but never close it.

Here Every report here says what was searched and what was not.

What would settle it Nothing finite; only more review lowers the risk.

Why Least privilege applied to delegation.

Term scoped grant, delegation

Cost More machinery to issue and check grants.

Here The house design has the AI hold a signed Grant, not the token.

Why No complete defence is known; an attacker can rephrase.

Term prompt injection

Cost Filters catch the known and miss the new.

Here The house treats untrusted text as data, never as instructions.

What would settle it A proof of a complete defence, or a demonstrated attack that breaks any given one.

Why Many eyes help only if the eyes look: Heartbleed sat in open code for years.

Term open source and security

Cost Both sides have strong examples.

Here The ternary public copy is scrubbed before it is published.

What would settle it Careful measurements per project, not a general ruling.