The vocabulary of this programme, defined once. Each entry has its own address, so a term may be cited directly.
Mirror Calculus
A mathematical notation in which every mark is kept under left–right reflection and every numeral is formed by strokes [the numeral zero stands outside the inventory]. Its strict grammar has exactly twelve object constructors — Bal, Row, Jux, Stk, Up, Dn, Lk, Ovl, Adh, Box, OBox, Frac — over an atom set every member of which is fixed by reflection. Reflection is proved involutive, well-formedness preserving, and renderer equivariant.
presence-only formation
The rule that an object-language inscription forms only through a positive event: a witness, trace, relation, transformation, nonempty roster, pairing, certificate, or explicit sponsorship. Every term has a sponsor, and a sponsor is a presentation. Formation precedes assertion.
surrogate zero
Any device that makes non-presentation participate as an object, value or verdict. Seven are analysed: the numeral zero and its surrogates — [the empty collection, the null return, default falsity, the vacuous judgment, a negative record inferred from failed search, and an enclosure drawn to denote an empty object. Each is given a presence-only replacement.
register-typed assertion
The discipline by which every claim is typed by the register in which it is made — grammatical, native object, omega, relative, or classical — and never migrates between them silently. A transfer names its interface, and the interface prices it.
plenary emission (WF6)
The well-formedness clause stating that every drawn mark is the emission of a formed term, and every constructor position in a drawn layout is occupied by the emission of its formed immediate subterm. Stated as a positive totality rather than as a prohibition.
the Balance
In THE WINDOW, the verdict reached when the three columns divide short of a majority for either seat. It is recorded under its own name and counted apart from wins and losses. Some of the rarest awards in the game are paid only for a Balance.
cost is weight, on the face
In THE WINDOW a certificate is built free. The number in a card’s ring is its weight at reckoning: its contribution to Substance, its ransom, the debt Spend-Covering reckons, a coordinate for Primeladder, and what Genealogy doubles. A heavy certificate is prize and exposure at once.
Admission (Adm)
The native law admitting an exit-locus record to the mirror axis. Class-wide Admission is independent of the declared base theory — both it and its counter-inscription are witnessed by finite models in exact rationals — while the zeta-specific law Adm_ζ enters by explicit sponsorship and is equivalent, under the named interface, to the classical Riemann hypothesis.
exit-locus record
A positively presented parameter together with a certificate that the declared completed evaluation procedure ran to completion at that parameter. Both parts are positive data; the withheld value stays a metalanguage judgment. This is what replaces the classical zero-locus in the presence grammar.
reading group
The symmetry group of a reading surface: ℤ/2 on the page, C₂ᵥ on the tent, C₃ᵥ on the corner, O(2) on the cone. Content expressible ahead of any orientation choice is the fixed component of the group’s action, and the group determines which operators the carrier can lawfully write.
the two lawful carriers of asymmetry
By the 1D Collapse Theorem, a one-line string can express only commutative operations and symmetric relations, so the notation is necessarily two-dimensional — and the plane offers exactly two lawful places to carry asymmetric content: the vertical axis, and adhesion.
Counterfoil
A free browser strategy card game implementing THE WINDOW (Contra-Zero Certificates): two seats, forty-three certificates, thirty strokes kept at every transition, and three scoring columns compared one against one. Cards are serial-numbered prints from fixed, published runs, and the census is public.