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summary-title | Give the title of The Mirror Calculus — Summary (V17) exactly as printed. | The Mirror Calculus: A Presence-Only Mathematical Language —\
Formation, Descent, Geometry, and the Register-Typed\
Resolution of the Riemann Question | |
summary-author | Give the byline of The Mirror Calculus — Summary (V17) exactly as printed. | Parker Emmerson
Independent researcher | |
summary-date | Give the date line of The Mirror Calculus — Summary (V17) exactly as printed. | August 2026 | |
summary-001 | In The Mirror Calculus — Summary (V17), the opening, before the first section: give the first paragraph of this section. | Abstract | |
summary-002 | In The Mirror Calculus — Summary (V17), the opening, before the first section: give the paragraph that follows the passage ending “Abstract”. | Formation precedes assertion. This paper defends presence-only formation as the accurate grammar of mathematical presentation: an object-language expression may form only when sponsored by a positive witness, trace, relation, transformation, roster, pairing, or certificate, and every term has a sponsor, and a sponsor i... | |
summary-003 | In The Mirror Calculus — Summary (V17), the opening, before the first section: give the paragraph that follows the passage ending “…stems. The object language is the protagonist throughout; every classical appearance in the paper is an interpretation the interface prices.”. | © 2026 Parker M. D. Emmerson. All rights reserved. This summary, the programme texts it summarizes (The Mirror Calculus, Against Zero, Counting Back from Infinity, Deprogramming Zero), and their notation, plates, and source are the copyright of the author; reproduction or adaptation in any form requires written permiss... | |
summary-005 | In The Mirror Calculus — Summary (V17), the opening, before the first section: give the paragraph that follows the passage ending “… to a hard subject in full. And the surrogate-zero taxonomy with its engineering transfers, which a fully classical reader may adopt entire.”. | *What sponsors what.* Each result here is read off its sponsor. P† ⊢ RHₘ is a derivation. The relative independence of class-wide Admission from the base is a theorem with both sides exhibited by finite models. The interface equivalence I(Admζ) ⇔ RHᴄ is proved from the definition of the interface, in the classical meta... | |
summary-006 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…s constitutive of the object. The residue is named and located: faithful reference to the completed prime-fused descent.”, exactly as written. | # Formation and the argument against zero | |
summary-007 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the first paragraph of this section. | **Thesis.** Formation precedes assertion. This paper defends presence-only formation as the accurate grammar of mathematical presentation. An object-language expression may form only when sponsored by a positive witness, trace, relation, transformation, roster, pairing, or certificate. Every term has a sponsor, and a s... | |
summary-008 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…\] and related devices are its surrogates — the same office under other spellings — so all are analyzed as reifications of non-presentation.”. | Two claims must be distinguished at once, because conflating them would beg the question the paper takes seriously. The first is *foundational*: that presence-only formation is the accurate account of how mathematical content is actually presented — counting requires prior presentation and individuation; one is imposed... | |
summary-009 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…ond the grammar itself; the transcendental argument defends why the grammar should govern, and the theorems then say what governs within it.”. | The position has a lineage and a distinctness worth fixing. Constructive mathematics in the Bishop line \[1\] demands witnesses for existence claims, and type theory in the Martin-Löf line \[2\] makes inhabitation the meaning of a proposition; presence-only formation is downstream of both in spirit but orthogonal in ax... | |
summary-010 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…d false” and “not recorded” are engineering anticipations of the same insight, and the foundational generalization is this program's supply.”. | The critique proceeds from the observation that classical practice maintains \[a family of devices\] whose shared function is to convert a withheld presentation into a positively inscribed object: the numeral zero \[a count reported ahead of any individuated member\], \[the empty collection (a roster “with no members”)... | |
summary-011 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “… changes the costume and keeps the category. Table [1](#tab%3Asurrogates) collects the family with the presence-only replacement discipline.”. | The sign, its surrogates, and their replacements. | |
summary-012 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the table that follows the passage ending “The sign, its surrogates, and their replacements.”. | ------------------------------------------------------------------------------------------------------------------------------------------
the sign and its surrogates presence-only discipline
------------------------------------------ ----------------------------------------------------------------... | |
summary-013 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…} ------------------------------------------------------------------------------------------------------------------------------------------”. | The transcendental argument behind the table runs, in compressed form, as follows. Counting is an act performed on presented individuals: before a tally can begin, something must be given, and given *as* countable — individuated under a procedure that says where one individual ends and the next begins. “One” is therefo... | |
summary-014 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…he zero-based regime is a licensed formalism whose central device misdescribes the phenomenon of presentation it is supposed to systematize.”. | The misdescription propagates. \[Closed-world\] and \[negation-as-failure\] systems infer $\neg P$ upon the closing of the derivation of $P$ \[3\]; presence-only formation permits that inference exactly when a positive completeness or coverage certificate closes the relevant search domain — short of the certificate, th... | |
summary-015 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…e the classical device stands as bookkeeping; it is wrong as semantics, because it installs an object where the ledger holds a withheld act.”. | The positive obligations are symmetric: positive contraries require independent witnesses. A rejection is its own inscribed act, with its own sponsor. The critique admits two clarifications that prevent misreadings. First, renaming leaves it in place: a language that bans the numeral \[“0”\] and retains an object calle... | |
summary-016 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…registers, of the most famous zero-normalized sentence in mathematics (Section [8](#the-register-typed-resolution-of-the-riemann-question)).”. | Two standing objections receive their replies here, since every reader raises them. *Objection: zero is algebraically indispensable* — additive identities, kernels, vanishing loci are the working grammar of modern mathematics. Reply: indispensable to the classical presentation, and recovered from the presence side thro... | |
summary-017 | In The Mirror Calculus — Summary (V17), section “Formation and the argument against zero”: give the paragraph that follows the passage ending “…of the sensitivity certificate that alone sponsors it — a distinction experimental practice already enforces under the name of upper limits.”. | *The source hierarchy, for orientation.* The program is a stack, and this paper summarizes it in stack order. *Against Zero* states the philosophical thesis and the surrogate-zero analysis; *Counting Back from Infinity* unifies it as a treatise; TPN (this section) is its formal notation; the Descent Calculus (Section [... | |
summary-018 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…tly one direction: the syntax implements the calculus, the calculus enacts the notation, the notation enacts the thesis.”, exactly as written. | # Transcendental Presence Notation | |
summary-019 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the first paragraph of this section. | TPN is the formal decision-language contribution: an inference discipline in which every inscription carries the positive procedure by which it formed. Its primitive sorts are: *witness* (a presented individual or event); *scene* (a presentation context); *trace* (the record of a procedure); *inscription* (a formed obj... | |
summary-020 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…e-form of contradiction); and *certificate* (a trace-bearing warrant that a procedure completed with stated coverage). The formation flow is”. | $$\text{positive witness} \rightarrow \text{inscription} \rightarrow \text{roster} \rightarrow \text{tally},$$ | |
summary-021 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “$$\text{positive witness} \rightarrow \text{inscription} \rightarrow \text{roster} \rightarrow \text{tally},$$”. | and every arrow is an act with a trace: every tally stays within its roster, every roster within its witnesses, and every inscription forms with its sponsor. | |
summary-022 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…s an act with a trace: every tally stays within its roster, every roster within its witnesses, and every inscription forms with its sponsor.”. | Four formation rules fix the discipline’s load-bearing joints, written as inference rules with the trace obligations explicit: | |
summary-023 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “Four formation rules fix the discipline’s load-bearing joints, written as inference rules with the trace obligations explicit:”. | $$\frac{Witness(w),Scene(\sigma),Trace\left( \pi:w\text{presented in}\sigma \right)}{Inscribe\left( ⌜w⌝;\pi \right)}$$ | |
summary-024 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “$$\frac{Witness(w),Scene(\sigma),Trace\left( \pi:w\text{presented in}\sigma \right)}{Inscribe\left( ⌜w⌝;\pi \right)}$$”. | $$\frac{Inscribe\left( t_{1};\pi_{1} \right)\cdots Inscribe\left( t_{k};\pi_{k} \right),Sep\left( t_{i},t_{j};\sigma_{ij} \right)_{i\text{<}j},k \geq 1}{Roster\left( \text{<}t_{1} \frown \cdots \frown t_{k}\text{>};\pi_{1}\text{*}\cdots\text{*}\pi_{k} \right)}$$ | |
summary-025 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…\right)_{i\text{<}j},k \geq 1}{Roster\left( \text{<}t_{1} \frown \cdots \frown t_{k}\text{>};\pi_{1}\text{*}\cdots\text{*}\pi_{k} \right)}$$”. | $$\frac{Roster(R;\pi)}{Tally(R) \geq 1}$$ | |
summary-026 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “$$\frac{Roster(R;\pi)}{Tally(R) \geq 1}$$”. | $$\frac{Inscribe(t;\pi),Inscribe(t\prime;\pi\prime),Clash(t,t\prime;\kappa)}{ClashRecord(t,t\prime;\pi,\pi\prime,\kappa)}$$ | |
summary-027 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “$$\frac{Inscribe(t;\pi),Inscribe(t\prime;\pi\prime),Clash(t,t\prime;\kappa)}{ClashRecord(t,t\prime;\pi,\pi\prime,\kappa)}$$”. | Natively the conclusion $Tally(R) \geq 1$ reads $Pres\left( Tally(R) \right)$ — the tally of a roster is presented by the formation that produced it — and the side condition $i\text{<}j$ reads $t_{i} \prec_{R}t_{j}$, precedence in the roster’s own genealogy. | |
summary-028 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…the formation that produced it — and the side condition $i\text{<}j$ reads $t_{i} \prec_{R}t_{j}$, precedence in the roster’s own genealogy.”. | The first rule is the whole philosophy in one line: an inscription forms from a witness in a scene, carrying the trace of its presentation \[22\]. Foundational axioms are under the same law, and the discipline’s honesty depends on saying so: an adopted law forms through an explicit sponsorship event, | |
summary-029 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…xioms are under the same law, and the discipline’s honesty depends on saying so: an adopted law forms through an explicit sponsorship event,”. | $$\frac{Sponsor(\alpha,\varphi)}{Assert(\varphi;\alpha)},$$ | |
summary-030 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “$$\frac{Sponsor(\alpha,\varphi)}{Assert(\varphi;\alpha)},$$”. | so that every object-language conclusion of TPN carries its sponsor — a foundational axiom forms through an adoption event recorded in the metalanguage, with $\alpha$ its named sponsor. The Plenum of Section [3](#the-descent-calculus) is accordingly classified as a foundational horizon — the ground sweeps act upon — wi... | |
summary-031 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…h coverage, $Cert\left( \text{proc};\text{scope};\text{traces} \right)$ — the only device by which the discipline licenses exclusion claims.”. | Three statuses must be kept distinct, and the third is the one classical habits collapse: (i) a *positively presented assertion*, sponsored by witness and trace; (ii) a *positively presented contrary or rejection*, sponsored by its own independent witness — a clash, a counterexample, a coverage-backed exclusion; and (i... | |
summary-032 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…$ for the metalanguage judgment that emission is withheld; the second is a statement about the formation relation, held in the metalanguage.”. | Scenes themselves compose, and the composition law is where the notation earns the word “transcendental”: a scene is a presentation context — an instrument, a procedure, an epoch of observation — and two scenes compose exactly where a presented pairing identifies witnesses across them, with the pairing’s trace recordin... | |
summary-033 | In The Mirror Calculus — Summary (V17), section “Transcendental Presence Notation”: give the paragraph that follows the passage ending “…r — a metric quoted outside its cohort, a reading quoted outside its calibration — is barred at the same joint that bars the surrogate zero.”. | The primitive sorts carry a small algebra, and stating it shows the discipline is generative rather than merely restrictive. Rosters compose by concatenation of presented members with traces composing alongside ($R_{1}\text{*}R_{2}$, defined whenever both operands formed); tallies are monotone under roster extension an... | |
summary-034 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…l exactly under a sponsored closed-world certificate, which is precisely the condition its careful users already impose.”, exactly as written. | # The Descent Calculus | |
summary-035 | In The Mirror Calculus — Summary (V17), section “The Descent Calculus”: give the first paragraph of this section. | Where classical foundations build upward from \[the empty set\], the Descent Calculus begins from the *plenum* — undifferentiated total presence — and obtains mathematical objects by differentiation downward. Its formation laws, which are adopted foundational stipulations and are labeled as such, are summarized here at... | |
summary-036 | In The Mirror Calculus — Summary (V17), section “The Descent Calculus”: give the paragraph that follows the passage ending “… geometric semantics in which the strict syntax of Section [4](#the-mirror-grammar-and-its-assurance) can be drawn, and drawn symmetrically.”. | Two consequences deserve their exact status. A worked pair of formations fixes the machinery. At degree one, a single sweep across the plenum precipitates a residue wherever its support concentrates: call one such residue $r$, with genealogical numeral recording (degree 1; sweep $\sigma_{1}$; site). At degree two, a se... | |
summary-037 | In The Mirror Calculus — Summary (V17), section “The Descent Calculus”: give the paragraph that follows the passage ending “… and both agree with classical arithmetic under the genealogy-forgetting projection — an interpretation-labeled fact, checked wherever used.”. | The no-zero theorem — every term of the calculus carries an inhabited count \[a term for a “null count” is held outside formation\] — is a theorem relative to the adopted formation laws. The proof is a closure induction: every formation rule’s conclusion carries at least the witnesses of its premises; the base rules re... | |
summary-038 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…bridge over which the classical realizations of Section [6](#geometry-and-representative-classical-realizations) travel.”, exactly as written. | # The Mirror grammar and its assurance | |
summary-039 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the first paragraph of this section. | The Mirror Calculus is the strict syntax that makes the foregoing checkable. Its alphabet is a closed inventory of atoms, each with a left–right symmetric stroke construction: bijective digits for one through ten (a digit inventory whose least digit is one; numeration is bijective base ten, so a value has exactly one c... | |
summary-040 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…s and of \[empty enclosures\] is cashed by that totality as a fired rejection; the syntactic enforcement of the marker classification below.”. | Constructor inventory (condensed). | |
summary-041 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the table that follows the passage ending “Constructor inventory (condensed).”. | --------------------------------------------------------------------------------------------------------
constructor layout reflection action
----------------------- -------------------------------------------------------- -----------------------
$$R... | |
summary-042 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…xt{Frac}$$ vinculum stack pointwise --------------------------------------------------------------------------------------------------------”. | A numeral example shows WF3 and WF5 at work: thirty-two is a two-digit cluster — a rank-marked three-bars digit and a chevron — order-free by commutativity, canonical by WF5; reflection swaps the cluster’s arguments and fixes each digit’s symmetric stroke form, so the reflected numeral is the same numeral. In this arit... | |
summary-043 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…ber, unlike its classical decimal carrier, reads the same in either hand — a grammar-level fact the checker confirms on every numeral plate.”. | The central metatheorem is reflection equivariance: the mirror involution $\mu$ — argument-reversing on $Row$, $Jux$, and $Bal$, so that $\mu\left( Bal(l,r) \right)\text{=}Bal(\mu r,\mu l)$; pointwise on the remaining constructors; and fixing strict object atoms, with auxiliary implementation codes permitted to occur i... | |
summary-044 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…ies an exact rational computation; the theorem stands on its own proof. The paper therefore claims a machine-checked core, and exactly that.”. | One exploratory observation deserves record at its exact evidential weight. The volume’s figures were subjected to a caption-blind trial: the full glyph corpus, stripped of every caption, label, and word, was staged to a caption-blind language model run in a fresh context ($n\text{=}1$; confidence figures self-reported... | |
summary-045 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…t observation; a general semantic-legibility theorem is further work. Full transcripts and staging protocol are in the source volume \[21\].”. | The Transport lemma’s dictionary hypothesis, since its conditionality is load-bearing for scope: the lemma transports interface structure along a presented atlas *given* that the stagewise dictionaries agree on overlaps as its hypothesis clause states; the kernel certifies the implication, and the hypothesis is dischar... | |
summary-046 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “… presented. Kernel certification of an implication certifies the implication alone, and the paper’s assurance claims observe the difference.”. | *The \[empty-emission\] marker, correctly classified.* The founding text prohibits any object-language sign whose purpose is to represent non-presentation, and the assertion of record follows it. The marker written $Blank$ in the implementation is a machinery-layer control, and the discipline of record is exhausted by ... | |
summary-047 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…forcing itself against its own implementation, and it is why this paper’s classification is stricter than the implementation’s variant name.”. | Reproduction of the assurance stack is a fixed five-step sequence, and stating it makes the implementation facts checkable rather than testimonial: verify the edition hash by zeroing the stamp field of the source and hashing; compile the source twice; run the reference checker over the plate corpus; compile the two Lea... | |
summary-048 | In The Mirror Calculus — Summary (V17), section “The Mirror grammar and its assurance”: give the paragraph that follows the passage ending “…-the-riemann-question). Each step exercises one assurance grade, and the whole sequence runs from the public archive on public inputs alone.”. | *Claim kinds.* Throughout, four kinds are distinguished: *stipulation* (adopted formation law), *implementation fact* (a property of the shipped artifacts), *theorem* (derived under stated laws), and *interpretation* (a reading across an interface). The source volume additionally versions its assertions — assertion of ... | |
summary-049 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…ertion of record, register reassigned, superseded, historical exhibit — and this paper states only assertions of record.”, exactly as written. | # The language on the page | |
summary-050 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the first paragraph of this section. | The preceding sections state the grammar; this one shows it. The strict atoms are strokes: the tally marks that carry the bijective numerals — a digit inventory whose least digit is a single stroke — the balance bar that asserts, the vinculum that divides, the enclosures that keep, the lens that binds. Every glyph is k... | |
summary-051 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give paragraph 2 of this section, which holds image 1 of the Summary, as written. | {width="3.1979166666666665in" height="0.7604166666666666in"} | |
summary-052 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the paragraph that follows the passage ending “{width="3.1979166666666665in" height="0.7604166666666666in"}”. | squares and ten roots balance thirty-nine. | |
summary-053 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the paragraph that follows the passage ending “squares and ten roots balance thirty-nine.”. | The first specimen is al-Khwārizmī’s equation — squares and ten roots balance thirty-nine — carried whole into the strict notation: every mark is a presence, the balance is the assertion, and the numerals are bijective throughout. The reflection $\rho$ acts on such terms with $\rho(\rho t)\text{=}t$, and the renderer i... | |
summary-054 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give paragraph 5 of this section, which holds image 2 of the Summary, as written. | {width="2.6979166666666665in" height="2.4583333333333335in"} | |
summary-055 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the paragraph that follows the passage ending “{width="2.6979166666666665in" height="2.4583333333333335in"}”. | nested accumulation and its mirror, evaluated as twenty-one over four in the displayed finite example. General interchange still requires the applicable Tonelli or Fubini hypotheses. | |
summary-056 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the paragraph that follows the passage ending “…ted as twenty-one over four in the displayed finite example. General interchange still requires the applicable Tonelli or Fubini hypotheses.”. | The second specimen sets a nested accumulation beside its own page-mirror: one term, one reflection, both readings kept. | |
summary-057 | In The Mirror Calculus — Summary (V17), section “The language on the page”: give the paragraph that follows the passage ending “The second specimen sets a nested accumulation beside its own page-mirror: one term, one reflection, both readings kept.”. | The exploratory evidence that the strokes carry their own reference is the caption-blind decoding audit reported in full in the volume. A language-model session ($n\text{=}1$) received plates with every caption withheld, under a staged prompt protocol, and recovered from the strokes alone: the bijective numeration and ... | |
summary-058 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…he prose standing aside. In the volume’s own words: reference travels in the strokes; the keeping, as ever, is the cell.”, exactly as written. | # Geometry and representative classical realizations | |
summary-059 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the first paragraph of this section. | The presence-only regime recovers standard mathematics where standard mathematics is positively formed. Two samples are given at assertion-of-record strength. | |
summary-060 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “…regime recovers standard mathematics where standard mathematics is positively formed. Two samples are given at assertion-of-record strength.”. | *Invariant carriers.* For a reading surface $\Sigma$ with symmetry group $G$, lawful scalar carriers are the $G$-fixed functions, equivalently functions on the quotient $\Sigma\text{/}G$; for the polynomial actions used in the source volume \[5\], | |
summary-061 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “…e $G$-fixed functions, equivalently functions on the quotient $\Sigma\text{/}G$; for the polynomial actions used in the source volume \[5\],”. | $${\mathbb{R}}\lbrack x,y)^{{\mathbb{Z}}\text{/}2}\text{=}{\mathbb{R}}\left\lbrack x^{2},y \right),{\mathbb{R}}\lbrack x,y)^{C_{3v}}\text{=}{\mathbb{R}}\left\lbrack r^{2},\text{Re}\left( z^{3} \right) \right),{\mathbb{R}}\lbrack x,y)^{O(2)}\text{=}{\mathbb{R}}\left\lbrack r^{2} \right).$$ | |
summary-062 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “…R}}\left\lbrack r^{2},\text{Re}\left( z^{3} \right) \right),{\mathbb{R}}\lbrack x,y)^{O(2)}\text{=}{\mathbb{R}}\left\lbrack r^{2} \right).$$”. | Orbit spans decompose into isotypic components and may decompose further; the tent, corner, and cone are geometric realizations of the actions (an interpretation, so labeled), and the folding/root correspondences of the volume are labeled theorem or interpretation per the taxonomy above. Two of those correspondences ar... | |
summary-063 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “…prime five. The calculus’s right-folding family realizes exactly the $2$- and $3$-torsion tower, which is why the quintic stands outside it.”. | *Counting by presence.* The calculus’s counting constructions realize classical residue counting \[7\]: for a counting density $N$ on a region $\Omega$, | |
summary-064 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “… presence.* The calculus’s counting constructions realize classical residue counting \[7\]: for a counting density $N$ on a region $\Omega$,”. | $$E\text{=}\frac{1}{2\pi i}\oint_{\partial\Omega}^{}N(z)dz,$$ | |
summary-065 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “$$E\text{=}\frac{1}{2\pi i}\oint_{\partial\Omega}^{}N(z)dz,$$”. | with the degree-$m$ cyclic factorization | |
summary-066 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “with the degree-$m$ cyclic factorization”. | $$n^{m} - l^{m}\text{=}\prod_{j\text{=}1}^{m}\left( n - \zeta_{m}^{j}l \right),n_{j\text{+}1}\text{=}\zeta_{m}n_{j}$$ | |
summary-067 | In The Mirror Calculus — Summary (V17), section “Geometry and representative classical realizations”: give the paragraph that follows the passage ending “$$n^{m} - l^{m}\text{=}\prod_{j\text{=}1}^{m}\left( n - \zeta_{m}^{j}l \right),n_{j\text{+}1}\text{=}\zeta_{m}n_{j}$$”. | exhibiting the deck orbit of the $m$-fold cover on which the count lives; tail subtraction is performed against the digamma comb $\psi(\rho - z)$, whose poles at $z\text{=}\rho,\rho\text{+}1,\rho\text{+}2,\ldots$ carry unit residues — the reference density of the shifted integer roster — so that a finite region’s count... | |
summary-068 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…$n$-wave realization generalizes. Detailed verifications and the full formula apparatus are in the supplementary volume.”, exactly as written. | # Intelligent decision systems: three concrete transfers | |
summary-069 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the first paragraph of this section. | The engineering thesis is the mathematical thesis verbatim: every judgment in an intelligent decision system names its sponsor — a completion certificate, an exclusion, a rejection, or a coverage record. | |
summary-070 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…ry judgment in an intelligent decision system names its sponsor — a completion certificate, an exclusion, a rejection, or a coverage record.”. | *A. Databases.* The presence discipline models a domain by positive event and relation records: the schema’s inventory is its emitted events and relations, and the unrecorded cell has status (iii). The long-documented anomalies of the schema-layer [\[null\]]{.smallcaps} — three-valued comparisons, vanishing rows, aggre... | |
summary-071 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…of presence-only formation, and the calculus supplies them a semantics in which the discipline is a formation law before it is a convention.”. | Concretely \[12, 13\]: the comparison \[nullnull\] stands short of truth in standard query semantics,$\text{=}$ a row with a [\[null\]]{.smallcaps} join key silently vanishes from an inner join, and aggregates step over [\[null\]]{.smallcaps}s by a rule the analyst memorizes — three famous behaviors that are the necess... | |
summary-072 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…e balance is zero”\] is a derived report over a positively presented history, and an auditor replays the acts rather than trusting the slot.”. | *B. AI and sparse data.* In recommendation and ranking, the unclicked cell holds status (iii) \[a click withheld is distinct from dislike, a rating withheld from a zero rating\]: implicit feedback datasets are rosters of positive events, and treating the unobserved cell as \[a semantic zero\] is the reification, with m... | |
summary-073 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…presence-notation) — withheld inscription — and models should be scored on positively witnessed events plus explicitly sponsored exclusions.”. | The implicit-feedback literature \[15\] already treats the unobserved cell as low-confidence — weighting observed events and shrinking the unobserved toward ignorance ahead of dislike — and the presence analysis says why that is the correct shape and where to hold the line: the unobserved user–item pair supports *a pla... | |
summary-074 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…rtificate} \right)$, and a metric arriving short of its third field is, by the discipline, a status-(iii) report, its formation still ahead.”. | *C. Decisions and safety.* A decision pipeline should emit positively witnessed branches — $Approved(\ldots)$, $Rejected(\ldots)$, $ReviewScheduled(\ldots)$ — each carrying its sponsor, and a rejection is a recorded $Rejected$ event — the judgment and its sponsor are the same record; the approval withheld is status (ii... | |
summary-075 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…redentials, and a coverage record — a certificate in exactly the TPN sense, and auditable because every field is a trace of a performed act.”. | The safety case generalizes to a design rule for the audit trail itself. Every branch emission carries its sponsor inline — $Approved\left( \text{req};\text{policy};\text{approver};\text{trace} \right)$, $Rejected\left( \text{req};\text{clash};\text{trace} \right)$, $ReviewScheduled\left( \text{req};\text{trigger};\tex... | |
summary-076 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the quotation that follows the passage ending “…st have meant\]. For system builders the discipline condenses to an assertion-record schema, stated once: every consequential record carries”. | > ⟨ statement ; register (the judgment form under which it holds) ;\
> sponsor (witness, clash, or certificate) ; trace ;\
> stratum (of record, superseded, historical) ;\
> edition (a recomputable hash binding the record to a source state) ⟩ | |
summary-077 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the paragraph that follows the passage ending “…tificate) ; trace ;\ > stratum (of record, superseded, historical) ;\ > edition (a recomputable hash binding the record to a source state) ⟩”. | — six fields, each exhibited doing real work in this paper: the register field in Section [8](#the-register-typed-resolution-of-the-riemann-question), the sponsor and trace fields throughout Section [2](#transcendental-presence-notation), the stratum field in the source volume’s self-corrections, and the edition field ... | |
summary-078 | In The Mirror Calculus — Summary (V17), section “Intelligent decision systems: three concrete transfers”: give the quotation that follows the passage ending “…l rather than discoverable at the postmortem. The general principle, displayed once because everything in this section is an instance of it:”. | > Every judgment names its sponsor: a completion certificate, an exclusion, a rejection, or a coverage record. | |
summary-080 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “# The register-typed resolution of the Riemann question”, exactly as written. | ## Registers, compressed | |
summary-081 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Registers, compressed”: give the first paragraph of this section. | Five registers govern the section’s verdicts, and the register theorem of the source volume states that every judgment passes from one to another through a named interface alone: ${Reg}_{Gra}$ (formation in the presence grammar $G_{P}$); ${Reg}_{Obj}$ (derivability in the adopted native theory); ${Reg}_{\omega}$ (omega... | |
summary-082 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Registers, compressed”: give the table that follows the passage ending “…independence over the base calculus); and ${Reg}_{Cla}$ (classical analytic interpretation). In compressed tabular form:”. | ---------------------------------------------------------------------------------------------
register judgment form
----------------------------------- ---------------------------------------------------------
$${Reg}_{Gra}$$ formation in the presence grammar $G_{... | |
summary-083 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Registers, compressed”: give the paragraph that follows the passage ending “…_{Cla}$$ classical analytic interpretation $I$ ----------------------------------------------------------------------------------... | One caution binds the paper’s own side: rejecting classical primacy licenses marked presence claims alone. “Ill-typed” is a grammar-register judgment; the transcendental argument of Section [1](#formation-and-the-argument-against-zero) separately defends why that grammar should govern. | |
summary-084 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…tal argument of Section [1](#formation-and-the-argument-against-zero) separately defends why that grammar should govern.”, exactly as written. | ## Nontranslation and formation | |
summary-085 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the first paragraph of this section. | []{#thm%3Anontranslation .anchor}**Proposition 1** (Every tally moves every tally). *Let* $T$ *be the set of pairing classes of nonempty finite rosters, with addition* $\oplus$ *induced by disjoint concatenation. Then* $T$ *is moved by every one of its elements. Consequently an identity-preserving homomorphism* $\left(... | |
summary-086 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…, \oplus )$ *sending classical numerals directly to presence tallies would require a tally that every element fixes, and e... | *Proof.* $|R \oplus S)\text{=}|R)\text{+}|S)\text{>}|R)$ for every inhabited , so every roster class moves every other; an identity-preserving homomorphism would require a class every class fixes.$S$$0$ ◻ | |
summary-087 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the quotation that follows the passage ending “…ry inhabited , so every roster class moves every other; an identity-preserving homomorphism would require a class every cl... | > *Corollary.* The literal zero-normalized formula $\xi(s)\text{=}0$ is translated into the tally grammar through a priced interface alone. Relational encodings, partial-evaluation semantics, or completion constructions remain possible — but only as explicitly priced interfaces, which is what clause 6 of Theorem [3](#t... | |
summary-088 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…constructions remain possible — but only as explicitly priced interfaces, which is what clause 6 of Theorem [3](#thm%3Ares... | The conventional zero-locus sentence of the Riemann hypothesis is an instance. One statement of exactness first, so the foundational disagreement is located precisely rather than appearing factual: in classical semantics $\xi$ is $\mathbb{C}$-valued and $\xi(s)\text{=}0$ is a perfectly formed equality. The presence int... | |
summary-090 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “$${RH}_{C}^{(0)} \notin Sent\left( G_{P} \right),{RH}_{M} \in Sent\left( G_{P} \right).$$”. | (Classical background on $\xi$ and its zeros: \[17\].) Here ${RH}_{M}$ reads: *every exit locus of the completed prime-fused descent is fixed by the mirror-axis involution*, where an *exit locus* is a positively presented parameter at which presence-valued evaluation ceases to form under the native partial semantics — ... | |
summary-091 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…mar-robust rather than dissolved: refused in one sentence-form, reconstructed and answered in another, with the correspond... | Clause 5 of the theorem below references the completion apparatus, stated here since the clause carries real weight. A coherent omega-kept family is a *presented* object $K\text{=}\left( k_{n} \right)_{n \in {\mathbb{N}}}$ with $Keep\left( n,k_{n} \right)$ and $k_{n} \preccurlyeq k_{n\text{+}1}$; the *Omega-Seal rule* ... | |
summary-092 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…channel interface, under which an off-axis exit record yields an accepted finite address that the sponsored family’s cover... | Alongside the native sentence, three forms carried by the source volume’s assertion of record are proved classically equivalent to the classical hypothesis, anchoring the reformulation on the classical side as well: R1, all roots of $\Xi(t)$ are real; R2, every exit locus of $\xi$ is fixed by $s \mapsto 1 - \overline{s... | |
summary-093 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…three native faces of these; the numbered forms are the forms of record.) A former fourth form is retained at exactly its ... | **Proposition 2** (Odd-multiplicity detection). *An exit locus on the real parameter axis of odd multiplicity — in particular a simple one — is detected by a sign reversal of the real completed function; even-multiplicity loci can hold their sign. Detection is elementary real analysis — a consequence of odd multiplicit... | |
summary-094 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…n. Detection is elementary real analysis — a consequence of odd multiplicity alone — and it stands beside the three equiva... | The conditionalization is itself a stratum event of the source volume’s taxonomy: the unconditional form is superseded, its successor is the assertion of record, and the equivalence theorem is titled for three forms. | |
summary-095 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “Nontranslation and formation”: give the paragraph that follows the passage ending “…nomy: the unconditional form is superseded, its successor is the assertion of record, and the equivalence theorem is title... | One more sentence on why the question is grammar-robust rather than dissolved, since dissolution is the standard fate of questions declared ill-formed. When a positivist declares a metaphysical sentence meaningless, the sentence’s subject matter ends there; the presence analysis does the opposite work. The zero-locus s... | |
summary-096 | In The Mirror Calculus — Summary (V17), give the heading that comes after the passage ending “…malization is exhausted by the dissolution; this one leaves, on the account given here, its entire mathematical content.”, exactly as written. | ## The consolidated resolution | |
summary-097 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “The consolidated resolution”: give the first paragraph of this section. | []{#thm%3Aresolution .anchor}**Theorem 3** (Register-Typed Resolution of the Riemann Question). *Let* ${RH}_{C}^{(0)}$ *be the conventional zero-locus sentence and* ${RH}_{M}$ *the native axis sentence.* | |
summary-098 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “The consolidated resolution”: give the list item that follows the passage ending “…lution of the Riemann Question). *Let* ${RH}_{C}^{(0)}$ *be the conventional zero-locus sentence and* ${RH}_{M}$ *the nativ... | 1. ${RH}_{C}^{(0)} \notin Sent\left( G_{P} \right)$*.* | |
summary-099 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “The consolidated resolution”: give the list item that follows the passage ending “1. ${RH}_{C}^{(0)} \notin Sent\left( G_{P} \right)$*.*”. | 1. ${RH}_{M} \in Sent\left( G_{P} \right)$*.* | |
summary-101 | In The Mirror Calculus — Summary (V17), section “The register-typed resolution of the Riemann question”, section “The consolidated resolution”: give the list item that follows the passage ending “…aximal selected closure \[the volume's third class\]; the two classes exhaust. Clause 3 carries its own licence; clause 4 s... | 3. *The unextended base calculus leaves class-wide Admission and class-wide Counter-Admission both underived (Theorem 4).* |
End of preview. Expand in Data Studio
The Mirror Calculus — LLM Training Dataset, revision 2
Author: Parker Emmerson (Yaohushuason), Independent Researcher, ORCID 0009-0007-1288-3292, Parkeremmerson@icloud.com
This dataset carries the whole of The Mirror Calculus: A Presence-Only Mathematical Language — the edition of record deposited at doi:10.5281/zenodo.22002856 — in the forms a training run learns from. The edition of record contains, in order: the Summary of the volume (V17), the volume itself, the companion paper Deprogramming Zero, and the Rosetta Stone of Zero-Surrogate Errata. The two verification notebooks of the deposit and the text of the printed edition of 18 August 2026 (its PDF and JATS XML) are included as well.
Every answer is the book's own text. Nothing is summarized, paraphrased or written in the author's place; the questions (the user turns) only say which part of the book is wanted and where it sits.
Sources
| Source file | What it holds | How it enters the dataset |
|---|---|---|
mirror-calculus.tex |
The volume (10 parts, 27 chapters, 3 appendices, 305 plate drawings in TikZ) | Verbatim LaTeX, cut at blank lines into 1563 units |
deprogramming-zero.tex |
The companion paper | Verbatim LaTeX, 135 units |
Summary_V17.docx |
The Summary (V17), with 242 equations and 2 images | Converted once to Markdown with TeX math; images kept as files |
rosetta.json |
The errata: 458 transition rows and 363 pending-ruling lines | Every string verbatim, grouped as in the file |
verify_independence.ipynb, verify_symmetry_nogo.ipynb |
Two Jupyter notebooks | Every cell, with every printed output after its code |
mirror-calculus.xml, mirror-calculus.pdf |
The printed edition of 18 August 2026 | Its passages whose wording the LaTeX lacks (the wording before the 111 corrections), its keywords, front matter and figure entries, the printed table of contents and the printed statement numbers |
rosetta.pdf |
The errata as printed | Its title block, table headings and footer |
Questions name the part of the book by its printed numbers (Part IV, Chapter 7, Section 5.3, Theorem 3.7) as LaTeX typesets them from the source.
Files
All data files are JSON Lines. Every file is split into train and validation; the two parts of each file have no
record in common, and every record belongs to exactly one of them.
| Configuration | Content | Train records | Validation records |
|---|---|---|---|
openai_chat |
Question-and-answer examples, OpenAI chat format | 2064 | 96 |
sharegpt |
Question-and-answer examples, ShareGPT format | 2064 | 96 |
alpaca |
Question-and-answer examples, Alpaca format | 2064 | 96 |
prompt_completion |
Question-and-answer examples, prompt/completion format | 2064 | 96 |
pretraining |
Pretraining corpus in reading order | 87 | 6 |
vision_llava |
Image examples, LLaVA format | 297 | 10 |
vision_openai |
Image examples, OpenAI vision format | 297 | 10 |
plate_numbers_chat |
Plate drawing numbers, chat format | 295 | 10 |
plate_numbers_pretraining |
Plate drawing numbers, pretraining format | 295 | 10 |
plate_coordinates |
Plate drawing numbers, structured | 295 | 10 |
source_units |
Every source unit with its location | 2037 | 96 |
Images: images/The_Mirror_Calculus_plate_001.png … images/The_Mirror_Calculus_plate_305.png (the 305 plate drawings rendered from their TikZ
source at 450 dots per inch) and images/The_Mirror_Calculus_summary_image_1.png, images/The_Mirror_Calculus_summary_image_2.png (the two images of
the Summary, as stored in the Word file).
The_Mirror_Calculus_manifest.json lists every file with its size in bytes and its SHA-256 checksum (the manifest itself excepted).
Record shapes
openai_chat:{"messages": [{"role": "user", ...}, {"role": "assistant", ...}]}sharegpt:{"id", "conversations": [{"from": "human", ...}, {"from": "gpt", ...}]}alpaca:{"id", "instruction", "input", "output"}prompt_completion:{"prompt", "completion"}pretraining,plate_numbers_pretraining:{"text", ...}vision_llava:{"id", "image", "conversations"}with the image path relative to the dataset foldervision_openai: chat messages with the image as a base64data:URLplate_coordinates: the stored numbers of every drawing statement, by type (line, circle, rectangle, arc)source_units: every unit with its file, line range or cell, heading path and full text
The four question-and-answer files hold the same examples in the same order, so line n of each is the same example.
How long passages are handled
No passage is dropped for its length. A unit longer than 6,000 characters is cut into consecutive pieces — prose after a sentence, LaTeX code and tables after a line end, errata rows between rows. The first piece is asked for with the unit's question; each later piece is asked for with that question plus the last 200 characters of the piece before it. The pieces put back together reproduce the unit exactly (8 units are cut this way).
Pretraining records follow the edition's reading order (Summary, volume, Deprogramming Zero, errata, notebooks, printed edition) and are at most 14,000 characters. Each record opens with the heading path of its first passage; a record that begins partway through a cut unit first repeats the end of the piece before it.
Plate drawings
Each of the 305 plates is a TikZ drawing. Its numbers are written out as training text in their own files
(plate_numbers_chat, plate_numbers_pretraining, gzip-compressed) so a trainer can weight them separately. Every
drawing statement is one line, in the order of the source; coordinates are TeX points; every number is the shortest
decimal that reads back to the same 64-bit value, in Wolfram notation (0., 19.8, -4.62). Example:
draw [line width 0.84, line cap round] line {{-4.62,6.6},{0.,19.8}}
fill circle {{-18.18,22.08},2.24}
draw [line width 0.84] arc {shift {-60.,3.96,3.96}, point {-22.14,0.99}, start angle -60., delta angle 300., radii {3.96,3.96}}
Each question names the drawing's place in the book and the command that drew it (\begin{tikzpicture}[baseline=-2pt]
and its source line). No number in these files is computed by a tool; all are stored in the book.
The vision examples pair each rendered plate with its place in the book, its printed caption and its TikZ source. The plates carry no typeset letters: every mark is a drawn glyph of the Mirror codex. The two images of the Summary reproduce plates 10 and 20 of the volume and are paired with the Summary's captions.
Text left out
- The author's location, printed in three places of the sources (the Summary's byline, the JATS XML's publisher and affiliation lines) and once in the Word file's document properties. It appears nowhere in this dataset.
README-zenodo.md, the deposit's instructions for updating the Zenodo record, which is not part of the book.
Bylines inside the book's text stay as the sources print them. Place names inside bibliography entries (publisher cities) are part of the citations and are kept.
Verification
| Check | Result |
|---|---|
| Whole book (characters, spacing ignored) | 829,421 |
| Characters left out of every answer, as written | 4,001 — all in the Summary, where the Word file's equations and styling are written as Markdown and TeX |
| Characters left out of every answer, compared in a notation-neutral view (Markdown markers removed, TeX math turned into its Unicode symbols) | 0 |
| Share of the whole book left out | 0.0000% |
| LaTeX units reproduced exactly, slice for slice | yes |
| Cut units that reassemble exactly | all 8 |
| Plate numbers read back bit for bit | 21,430 numbers in 305 drawings, 0 mismatches; a one-digit change is caught: yes |
| Second, independent decoding of the drawing numbers against the coordinate files | 21,430 numbers, 0 mismatches |
| Longest answer piece / longest pretraining record | 5,997 / 13,999 characters |
| Records shared between train and validation | 0 in every file |
Files loading with the Hugging Face datasets library |
all |
The deposited PDFs of Deprogramming Zero and the Summary match, word for word, PDFs typeset again from their source files. The deposited volume PDF differs from the current LaTeX by the 111 corrections; its wording is carried by the printed-edition records. Read by the same text extractor, 67 short stretches of the deposited volume PDF match neither the retypeset PDF nor the answers word for word: 43 are two or three pieces of answer text joined by page layout (paragraph and cell boundaries), and the other 24 come from words broken by line-end hyphens, mathematical symbols the extractor spells out as letters, and table cells read across columns.
Changes from the previous revision
This is the first revision; there is no earlier revision of this dataset.
Citation
@misc{emmerson_mirror_calculus_dataset_rev1,
author = {Parker Emmerson (Yaohushuason)},
title = {The Mirror Calculus — LLM Training Dataset, revision 1},
year = {2026},
note = {Built from the edition of record, doi:10.5281/zenodo.22002856}
}
Copyright
© 2026 Parker Emmerson (Yaohushuason). All rights reserved, as stated in the book.
Changes from The_Mirror_Calculus_LLM_Training_Dataset_rev1: every file reachable by the Parquet conversion
The_Mirror_Calculus_LLM_Training_Dataset_rev2 is The_Mirror_Calculus_LLM_Training_Dataset_rev1 with files added and the card's configs extended, so that the Hugging Face Parquet converter (the "parquet-converter" bot, which builds the dataset viewer and the refs/convert/parquet branch from the configurations a card declares) reaches every piece of content in the repository. No file of The_Mirror_Calculus_LLM_Training_Dataset_rev1 was removed or changed. Upload the folder of The_Mirror_Calculus_LLM_Training_Dataset_rev1 and this folder into the same repository; this README replaces the previous one.
What was added:
imagesconfiguration: the 307 pictures underimages/are now an image dataset (the pictures themselves become an image column in the Parquet conversion), withimages/metadata.jsonlgiving each picture's vision questions and answers.filesconfiguration: the manifest as a table — every file of the revision with its size and SHA-256.
New files:
| File | What it holds |
|---|---|
images/metadata.jsonl |
one row per picture (307): file name, the vision examples asked about it (questions and answers), and the earlier metadata columns where the folder had them |
The_Mirror_Calculus_LLM_Training_Dataset_rev2_files.jsonl |
every file of the revision (331 carried from The_Mirror_Calculus_LLM_Training_Dataset_rev1, 1 new) with its size and SHA-256, as rows |
What the bot still does not read, and why it is no loss: the manifest (its rows are in files). The pictures are converted through the images configuration.
Built 2026-10-30; every new configuration was loaded with the Hugging Face datasets library before this card was written (see the check table).
Loading check of the new configurations
| Configuration | Split | Result | Rows | Columns |
|---|---|---|---|---|
images |
train | loads | 307 | 5 |
files |
train | loads | 332 | 4 |
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