rosetta.json

{
 "title": "Rosetta Stone of Zero-Surrogate Errata",
 "rule": "Every statement in the author's voice is made in the positive. The sign for non-presentation and its surrogates are named in two ways only: bracketed, as a diagnostic mention of the classical form — [blank, null, none, empty, missing, undefined], [“undefined”], [the roster “with no member”] — or quoted, as a source's own words and marked as a quotation. A negation in the author's voice is itself a surrogate: it keeps the concept of the sign under another spelling, and it propagates. The table records each transition made in Deprogramming Zero so that the rule can be read off its instances, and so that a reader who finds the old form elsewhere in the programme's texts has the replacement to hand.",
 "documents": [
  {
   "name": "Deprogramming Zero (the paper)",
   "note": "Ninety-two transitions, grouped; also printed as Appendix B of the paper.",
   "groups": [
    {
     "name": "Logic and formation",
     "rows": [
      [
       "tex 42",
       "negation-free first-order theory",
       "positive first-order theory (Lyndon's own term)"
      ],
      [
       "tex 122",
       "a negative record",
       "a kept record"
      ],
      [
       "tex 161",
       "a negative statement the metalanguage holds",
       "a statement the metalanguage holds"
      ],
      [
       "—",
       "a negative sentence of TA",
       "a sentence of TA held outside its positive fragment"
      ],
      [
       "—",
       "the negation of a sentence",
       "its counter-inscription"
      ],
      [
       "—",
       "its negation a Σ₁ sentence",
       "its counter-inscription a Σ₁ sentence"
      ],
      [
       "—",
       "the negative side of a Π₁ sentence",
       "its refutation side"
      ],
      [
       "—",
       "a negative resolution (a finite certificate)",
       "a refuting resolution"
      ],
      [
       "tex 1204",
       "an affirmative resolution",
       "an affirming resolution"
      ],
      [
       "tex 1075",
       "the negative-channel interface",
       "the clash-channel interface"
      ],
      [
       "—",
       "X does not form",
       "X is held outside formation / X is held as a record"
      ],
      [
       "tex 972",
       "is unformed",
       "is held outside formation"
      ],
      [
       "—",
       "formation fails in the positive fragment",
       "the positive fragment holds it as a record"
      ],
      [
       "—",
       "has no positive formation",
       "lies outside positive formation"
      ],
      [
       "—",
       "has no positive first-order replacement",
       "lies outside every positive first-order axiomatisation"
      ],
      [
       "—",
       "which no positive axiomatisation can replace",
       "which lies outside every positive axiomatisation"
      ],
      [
       "—",
       "has no statement there at all",
       "is held there in the metalanguage, by the fragment's own convention"
      ],
      [
       "—",
       "first-order logic without negation cannot tell a line from a circle",
       "positive first-order logic has the circle among its models wherever it has the line"
      ],
      [
       "—",
       "there is no z with x < z < y",
       "every z with x < z satisfies y ≤ z"
      ],
      [
       "—",
       "no z has x ⊕ z = 1",
       "every x ⊕ z is a successor"
      ],
      [
       "—",
       "no term of T₊ to a sentence about an absent object",
       "every term of T₊ to a term formed by an act"
      ],
      [
       "tex 42",
       "an absence-universal over an unpresented totality",
       "[a universal over the plane whose matrix is an evaluation set equal to the sign], on a totality outside presentation"
      ],
      [
       "tex 731",
       "universal non-presentation",
       "a universal over withheld presentation"
      ],
      [
       "—",
       "forms no sign about ζ",
       "forms its sign about the models of T alone"
      ],
      [
       "—",
       "carries no information about the zeros of ξ",
       "is silent on the zeros of ξ"
      ],
      [
       "—",
       "there is no third case",
       "the two cases exhaust"
      ],
      [
       "tex 613",
       "No hypothesis beyond consistency is used",
       "Consistency is the whole hypothesis"
      ],
      [
       "—",
       "No theory both is faithful and leaves Admission independent",
       "A faithful theory decides zeta-specific Admission"
      ],
      [
       "—",
       "a base that does not say where the roots are does not decide a sentence about where the roots are",
       "a base that leaves root location free leaves a sentence about root location free"
      ],
      [
       "tex 980",
       "with no axiom fixing root location",
       "with root location left free"
      ],
      [
       "—",
       "cannot fix the infinite multiset across all models",
       "by Löwenheim–Skolem every first-order T has models in which d_ζ differs from the standard multiset"
      ],
      [
       "—",
       "proved without hypothesis",
       "proved unconditionally"
      ],
      [
       "tex 988",
       "feeds no truth-from-independence argument",
       "(dropped: the positive statement that follows says what the independence is)"
      ],
      [
       "—",
       "supplied neither by class-wide independence nor by the adoption",
       "each route on the page stops short of it"
      ]
     ]
    },
    {
     "name": "The sign and its uses",
     "rows": [
      [
       "—",
       "zero is a surrogate / every zero is a surrogate",
       "zero is the sign for a non-presentation; its surrogates are the same office under other spellings"
      ],
      [
       "—",
       "introduced because something did not present",
       "introduced where a presentation was withheld"
      ],
      [
       "tex 93",
       "failed presentation",
       "a withheld presentation"
      ],
      [
       "tex 113",
       "the act that did not occur",
       "an act withheld / [the act “that does nothing”]"
      ],
      [
       "tex 108",
       "the count of a roster with no member",
       "[the count of a roster “with no member”]"
      ],
      [
       "tex 108",
       "a tally reported where no individuation act occurred",
       "a tally reported ahead of any individuation act"
      ],
      [
       "—",
       "0 is what S never reaches / the terminus the successor never reaches",
       "0 is the origin from which every successor chain starts"
      ],
      [
       "tex 152",
       "the unit is reached by no successor",
       "the unit is the origin of every successor chain"
      ],
      [
       "—",
       "a search for a predecessor of 0 returns without one",
       "0 is the origin of every successor chain, written in the classical form [“0 is not a successor”]"
      ],
      [
       "tex 111",
       "written as a negative statement about an object",
       "written as a statement about an object [“0 is not a successor”]"
      ],
      [
       "tex 54",
       "contains neither the sign nor a surrogate",
       "every term is formed by an act, the sign and its surrogates held in the metalanguage"
      ],
      [
       "—",
       "zero-free, with no surrogate in place of the sign",
       "zero-free, every term formed by an act"
      ],
      [
       "tex 1015",
       "formed with no absorber and no null value anywhere in it",
       "formed with every term an act"
      ],
      [
       "tex 1265",
       "where no sign stands for a non-presentation",
       "where every sign stands for an act"
      ],
      [
       "—",
       "the act that did not occur (the group identity)",
       "[the act “that does nothing”], written e or 1 so as to sound like an act"
      ],
      [
       "tex 547",
       "the collection introduced because no member presented",
       "[the collection “with no member”]"
      ],
      [
       "—",
       "if x has no member",
       "if x is [memberless]"
      ],
      [
       "—",
       "negative Separation / Separation for negative formulas",
       "Separation for formulas outside the positive fragment"
      ],
      [
       "—",
       "formulas that do not define the empty class",
       "positive formulas"
      ],
      [
       "—",
       "Foundation alone does not suffice",
       "Foundation alone leaves the chain standing"
      ],
      [
       "—",
       "does not survive the passage unchanged",
       "is the one ring axiom the passage rewrites"
      ],
      [
       "—",
       "Skolem arithmetic is not an instance; successor is not definable in it",
       "Skolem arithmetic lies outside the schema; successor lies outside its definable relations"
      ],
      [
       "—",
       "a device not reached by a bijection has no shift to carry it",
       "a device outside every such bijection stays where it is"
      ]
     ]
    },
    {
     "name": "The ledger and the bookkeeping",
     "rows": [
      [
       "—",
       "gauge / gauge fixing / gauge cost",
       "substitution / concealed obligation / cost"
      ],
      [
       "tex 54",
       "where the silent discharge fails",
       "where the concealed obligation comes due"
      ],
      [
       "—",
       "the obligation the notation did not write",
       "the obligation the notation discharged in silence"
      ],
      [
       "—",
       "PA has no term for the withholding",
       "PA's grammar requires a term in that position and supplies [“undefined”]"
      ],
      [
       "—",
       "a returned non-value introduced because a quotient did not present",
       "a returned non-value introduced where a quotient was withheld"
      ],
      [
       "tex 407",
       "the quotient is either unformed or unselected, and in neither case does a term present",
       "the quotient is withheld or unselected, and in each case the term position awaits an occupant"
      ],
      [
       "—",
       "it carries no pred",
       "its pred count is zero of the ledger's marks [the tally of marks is a presented count]"
      ],
      [
       "tex 297",
       "a property of a presentation, not of a theorem",
       "a property of a presentation rather than of a theorem"
      ],
      [
       "tex 433",
       "Nothing else.",
       "That is the whole list."
      ],
      [
       "—",
       "nothing to exhibit",
       "an exhibit for each successor and the first tally standing apart"
      ],
      [
       "tex 42",
       "non-negativity of a prime-indexed sequence",
       "positivity λₙ ≥ 0 of a prime-indexed sequence"
      ],
      [
       "tex 601",
       "the sum is negative",
       "the sum lies below zero [the sign here names a presented rational bound]"
      ]
     ]
    },
    {
     "name": "The Riemann sections",
     "rows": [
      [
       "—",
       "finite keeping of every separately presented stage forms no family",
       "a coherent family forms by a presented family, a guarded generator with its uniform keeping law, or an explicit sponsor; stagewise keeping is a record at each stage"
      ],
      [
       "—",
       "the stages do not form the seal by themselves",
       "the seal forms by one of the three constructors alone"
      ],
      [
       "—",
       "the object the hierarchy shows does not form",
       "the object the hierarchy bars from forming"
      ],
      [
       "tex 843",
       "a seal without a sponsor",
       "a seal with its sponsor left off the page"
      ],
      [
       "tex 42",
       "its sponsor unwritten",
       "its sponsor left off the page"
      ],
      [
       "—",
       "decide nothing about occupation",
       "leave occupation to the clause that names the primes"
      ],
      [
       "tex 765",
       "an exact zero is certified by neither and is presented by neither",
       "those two are the whole of what a verification presents"
      ],
      [
       "tex 771",
       "evidence for an absence",
       "evidence about the sign"
      ],
      [
       "—",
       "zeros which record no prime",
       "zeros which carry the gamma normalization's exits rather than a prime's record"
      ],
      [
       "tex 42",
       "the analytic base without the Euler product",
       "the analytic base stated short of the Euler product"
      ],
      [
       "tex 56",
       "not only for polynomials",
       "as well as for polynomials"
      ],
      [
       "tex 1034",
       "neither adjudicates the other",
       "each with authority over itself alone"
      ],
      [
       "—",
       "no independence result can close it from outside",
       "Theorem (faithfulness) places it beyond every independence result"
      ],
      [
       "tex 1275",
       "never going to be closed from outside itself",
       "closes from inside itself alone"
      ],
      [
       "tex 1265",
       "removal is the rule and not an exception",
       "removal is the rule"
      ],
      [
       "tex 1151",
       "there is no further kind of presentation that bears on the seal",
       "the whole of what bears on the seal"
      ],
      [
       "—",
       "(c) neither is presented",
       "(c) the sponsor alone is in force"
      ],
      [
       "tex 1222",
       "presented together in no case",
       "presented one at a time"
      ],
      [
       "—",
       "α_ω absent from the trace",
       "in the place α_ω held"
      ],
      [
       "—",
       "a system that formed its verdicts without sponsors would have one channel and one failure mode",
       "a system that formed its verdicts with the sponsor left off the page would have one channel and one way to lapse"
      ]
     ]
    },
    {
     "name": "Journal boilerplate",
     "rows": [
      [
       "tex 1281",
       "This research received no external funding",
       "This research was funded by the author"
      ],
      [
       "tex 1283",
       "No new data were created",
       "All data underlying the paper are in the cited volume and in Appendix A"
      ],
      [
       "tex 1287",
       "The author declares no conflicts of interest",
       "The author declares that the work was carried out free of any conflict of interest"
      ]
     ]
    }
   ]
  },
  {
   "name": "The Mirror Calculus — Summary (V17)",
   "note": "204 transitions applied across the whole document, including the tables and the engineering sections.",
   "pairs": [
    [
     "V16 ¶3",
     "the conversion of non-presentation into negative assertion is, in engineering form, exactly the reification",
     "the promotion of a withheld presentation to [negative assertion] is, in engineering form, exactly the reification"
    ],
    [
     "V16 ¶6",
     "a formal language in which non-presentation has no object-level term",
     "a formal language whose every object-level term stands for a presentation"
    ],
    [
     "V16 ¶6",
     "conditional on presence-only formation being the accurate grammar of mathematical presentation, the conventional zero-locus sentence is malformed, since it converts failure of presence-valued",
     "conditional on presence-only formation being the accurate grammar of mathematical presentation, the conventional zero-locus sentence is held outside formation, since it converts a withheld presence-valued"
    ],
    [
     "V16 ¶6",
     "its stratum, and the interface priced for any transfer, applied to a hard subject without remainder.",
     "its stratum, and the interface priced for any transfer, applied to a hard subject in full."
    ],
    [
     "V16 ¶8",
     "A verdict carrying no presented sponsor is not a weaker verdict but no object of this grammar at all.",
     "A verdict forms with a presented sponsor; the sponsor is constitutive of the object."
    ],
    [
     "V16 ¶14",
     "a definition licenses a formal regime but does not prove an ontology.",
     "a definition licenses a formal regime, and an ontology asks for proof of its own."
    ],
    [
     "V16 ¶14",
     "The grammar alone does not prove its own foundational accuracy;",
     "The grammar's foundational accuracy is a claim beyond the grammar itself;"
    ],
    [
     "V16 ¶16",
     "it retains the empty type, the zero, and the vacuous universal as perfectly formed citizens.",
     "it retains [the empty type, the zero, and the vacuous universal] as perfectly formed citizens."
    ],
    [
     "V16 ¶16",
     "it is not about which inferences are licensed over formed sentences, but about which sentences form at all,",
     "its subject is which sentences form at all, prior to which inferences are licensed over formed sentences,"
    ],
    [
     "V16 ¶18",
     "the numeral zero (a count where counting found no individuals)",
     "the numeral zero [a count reported ahead of any individuated member]"
    ],
    [
     "V16 ¶18",
     "replacing the numeral by a synonym — absence, null, none, empty — changes the costume, not the category.",
     "replacing the numeral by a synonym — [absence, null, none, empty] — changes the costume and keeps the category."
    ],
    [
     "V16 ¶38",
     "“One” is therefore not a primitive found in nature but an imposed unity: the first act of a counting procedure, not its discovery.",
     "“One” is therefore an imposed unity rather than a primitive found in nature: the first act of a counting procedure."
    ],
    [
     "V16 ¶38",
     "What a definition does not do is prove an ontology,",
     "A definition licenses; an ontology asks for its own proof,"
    ],
    [
     "V16 ¶40",
     "The failed search that returns “no record” and is read as “negative record”",
     "The search that closes and is read as [“negative record”]"
    ],
    [
     "V16 ¶40",
     "the search’s coverage, not its emptiness, is the fact,",
     "the search’s coverage is the fact,"
    ],
    [
     "V16 ¶40",
     "In each case the classical device is not wrong as bookkeeping;",
     "In each case the classical device stands as bookkeeping;"
    ],
    [
     "V16 ¶42",
     "the replacement discipline is structural, not lexical.",
     "the replacement discipline is structural before it is lexical."
    ],
    [
     "V16 ¶42",
     "Second, it is not a skepticism about mathematics:",
     "Second, it stands with mathematics:"
    ],
    [
     "V16 ¶54",
     "a tally cannot outrun its roster, a roster cannot outrun its witnesses, and an inscription without a sponsor does not form.",
     "every tally stays within its roster, every roster within its witnesses, and every inscription forms with its sponsor."
    ],
    [
     "V16 ¶68",
     "Foundational axioms are no exception,",
     "Foundational axioms are under the same law,"
    ],
    [
     "V16 ¶72",
     "so that TPN permits no genuinely unsponsored object-language conclusion",
     "so that every object-language conclusion of TPN carries its sponsor"
    ],
    [
     "V16 ¶72",
     "not as an unsponsored rosterable object;",
     "with the rosterable objects all sponsored;"
    ],
    [
     "V16 ¶72",
     "What is barred is not indirect reasoning but unsponsored negativity:",
     "Indirect reasoning stands; what is barred is unsponsored negativity:"
    ],
    [
     "V16 ¶72",
     "a “contradiction” that consists in a term failing to form is a status-(iii) event and grounds no rejection;",
     "a [“contradiction”] that consists in a term held outside formation is a status-(iii) event, and a rejection forms from a clash;"
    ],
    [
     "V16 ¶74",
     "The third status is not a truth value, not a null value, and not a third state of a logic;",
     "The third status stands apart from truth values, from [null values], and from any third state of a logic;"
    ],
    [
     "V16 ¶74",
     "it is the absence of a formed sentence, visible only in the metalanguage.",
     "it is a formation judgment, visible in the metalanguage alone."
    ],
    [
     "V16 ¶74",
     "TPN offers no third participant: where no inscription has formed there is no operand, and the metalanguage says so from outside;",
     "TPN's participants are the two formed statuses: where an inscription is yet to form, the metalanguage says so from outside;"
    ],
    [
     "V16 ¶74",
     "the correct implementation of missingness is control flow and provenance, not a value.",
     "the correct implementation of [missingness] is control flow and provenance."
    ],
    [
     "V16 ¶74",
     "status (ii), inscribed as a fault, not as a reading of zero;",
     "status (ii), inscribed as a fault [rather than a reading of zero];"
    ],
    [
     "V16 ¶74",
     "the ingestion window closes with neither — status (iii),",
     "the ingestion window closes with the pair standing open — status (iii),"
    ],
    [
     "V16 ¶74",
     "At no point does a “zero reading” or “null reading” enter the semantic layer,",
     "The semantic layer is exhausted by witnessed readings [a “zero reading” or “null reading” stays outside it],"
    ],
    [
     "V16 ¶76",
     "There is no ambient universal scene given for free;",
     "Every scene is built;"
    ],
    [
     "V16 ¶78",
     "What fails to transfer automatically is exactly the boundary apparatus — the empty structure, the vacuous quantification, the null element — and the failure is the point.",
     "The boundary apparatus — [the empty structure, the vacuous quantification, the null element] — transfers through a priced interface alone, and that price is the point."
    ],
    [
     "V16 ¶82",
     "always an event with a trace, never a bare posit.",
     "always an event with a trace."
    ],
    [
     "V16 ¶86",
     "hence every formable term’s roster is inhabited, and a term whose semantic role is an uninhabited count admits no derivation.",
     "hence every formable term’s roster is inhabited, and a term for [an uninhabited count] is held outside derivation."
    ],
    [
     "V16 ¶90",
     "bijective digits for one through ten (no zero digit;",
     "bijective digits for one through ten (a digit inventory whose least digit is one;"
    ],
    [
     "V16 ¶90",
     "infinite carriers, missing bounds",
     "infinite carriers, bounds yet to present"
    ],
    [
     "V16 ¶90",
     "the exclusion of one-sided balances and empty enclosures is cashed by that totality as a fired rejection;",
     "the exclusion of one-sided balances and of [empty enclosures] is cashed by that totality as a fired rejection;"
    ],
    [
     "V16 ¶114",
     "has no handedness — a grammar-level fact",
     "reads the same in either hand — a grammar-level fact"
    ],
    [
     "V16 ¶116",
     "verifies an exact rational computation, not an entire theorem.",
     "verifies an exact rational computation; the theorem stands on its own proof."
    ],
    [
     "V16 ¶118",
     "it is an exploratory usability-and-audit observation, not a general semantic-legibility theorem.",
     "it is an exploratory usability-and-audit observation; a general semantic-legibility theorem is further work."
    ],
    [
     "V16 ¶120",
     "Kernel certification of an implication is not kernel certification of its antecedent,",
     "Kernel certification of an implication certifies the implication alone,"
    ],
    [
     "V16 ¶122",
     "The empty-emission marker, correctly classified.",
     "The [empty-emission] marker, correctly classified."
    ],
    [
     "V16 ¶122",
     "withheld inscription — a formation judgment, not a third value.",
     "withheld inscription — a formation judgment held in the metalanguage."
    ],
    [
     "V16 ¶122",
     "which predicates and never participates.",
     "which predicates from outside the operations."
    ],
    [
     "V16 ¶144",
     "a vacant additive slot induced a null-object reading,",
     "a vacant additive slot induced a [null-object] reading,"
    ],
    [
     "V16 ¶144",
     "the notation carries recoverable structure without one word of prose.",
     "the notation carries recoverable structure, the prose standing aside."
    ],
    [
     "V16 ¶154",
     "Orbit spans decompose into isotypic components and need not be irreducible;",
     "Orbit spans decompose into isotypic components and may decompose further;"
    ],
    [
     "V16 ¶164",
     "a counting density can be locally consistent on every chart while no global count exists;",
     "a counting density can be locally consistent on every chart while the global count stays outside formation;"
    ],
    [
     "V16 ¶164",
     "and no transformation-invariant individuation is presented;",
     "and a transformation-invariant individuation is yet to present;"
    ],
    [
     "V16 ¶164",
     "The global roster does not form, although the classical degree remains two;",
     "The global roster is held outside formation, and the classical degree remains two;"
    ],
    [
     "V16 ¶170",
     "the operational signature of a surrogate zero installed in the schema layer;",
     "the operational signature of [a surrogate zero installed in the schema layer];"
    ],
    [
     "V16 ¶170",
     "the open-world reading of absence,",
     "the open-world reading of [absence],"
    ],
    [
     "V16 ¶172",
     "absence of a record licenses no negative conclusion.",
     "a record's coverage certificate alone licenses a refuting conclusion."
    ],
    [
     "V16 ¶174",
     "In recommendation and ranking, no click is not dislike, and no rating is not a zero rating: implicit feedback datasets are rosters of positive events, and treating the unobserved cell as a semantic zero is the reification,",
     "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,"
    ],
    [
     "V16 ¶174",
     "Missing features are not zero-valued features;",
     "A feature withheld is a status-(iii) event [distinct from a zero-valued feature];"
    ],
    [
     "V16 ¶176",
     "treats the unobserved cell as low-confidence rather than negative — weighting observed events and shrinking the unobserved toward ignorance, not toward dislike —",
     "treats the unobserved cell as low-confidence — weighting observed events and shrinking the unobserved toward ignorance rather than toward dislike —"
    ],
    [
     "V16 ¶176",
     "a metric missing its third field is, by the discipline, a status-(iii) report that has not yet formed.",
     "a metric arriving short of its third field is, by the discipline, a status-(iii) report, its formation still ahead."
    ],
    [
     "V16 ¶178",
     "Likewise “no hazards found” is a non-record, not a safety fact;",
     "Likewise [“no hazards found”] is a coverage question standing open, and a safety fact arrives by certificate;"
    ],
    [
     "V16 ¶180",
     "The readiness certificate replacing “no hazards found”",
     "The readiness certificate replacing [“no hazards found”]"
    ],
    [
     "V16 ¶180",
     "always a readable certificate, never a reconstruction from logs of what the absence of an approval must have meant.",
     "always a readable certificate [in place of a reconstruction from logs of what a withheld approval must have meant]."
    ],
    [
     "V16 ¶187",
     "A record missing its sponsor is the engineering form of a surrogate zero,",
     "A record arriving short of its sponsor is the engineering form of [a surrogate zero],"
    ],
    [
     "V16 ¶195",
     "no judgment of one may be substituted into another without a named interface:",
     "every judgment passes from one to another through a named interface alone:"
    ],
    [
     "V16 ¶221",
     "not a claim that classical syntax fails by its own rules.",
     "and classical syntax stands by its own rules."
    ],
    [
     "V16 ¶221",
     "With that fixed: the zero-locus sentence is not denied in the presence grammar;",
     "With that fixed: the presence grammar holds the zero-locus sentence outside formation;"
    ],
    [
     "V16 ¶221",
     "The mathematical subject survives and is reconstructed as the native axis statement — not a token replacement of the classical sentence, but an independently constructed native sentence about positively presented data:",
     "The mathematical subject survives and is reconstructed as the native axis statement — an independently constructed native sentence about positively presented data:"
    ],
    [
     "V16 ¶225",
     "This is what it means, exactly, that the reconstruction requires no absence object.",
     "This is what it means, exactly, that the reconstruction runs on presented data alone."
    ],
    [
     "V16 ¶231",
     "even-multiplicity loci need not reverse sign.",
     "even-multiplicity loci can hold their sign."
    ],
    [
     "V16 ¶231",
     "Detection is elementary real analysis — a consequence of odd multiplicity alone — not a fourth unconditional equivalence.",
     "Detection is elementary real analysis — a consequence of odd multiplicity alone — and it stands beside the three equivalences of record."
    ],
    [
     "V16 ¶235",
     "so the subject matter survives its sentence-form, and the native reconstruction is not a replacement topic but the same topic carried by lawful syntax.",
     "so the subject matter survives its sentence-form, and the native reconstruction is the same topic carried by lawful syntax."
    ],
    [
     "V16 ¶235",
     "A question is dissolved when its formalization leaves no residue;",
     "A question is dissolved when its formalization is exhausted by the dissolution;"
    ],
    [
     "V16 ¶245",
     "What licenses the adoption is not an analogy to any historical foundational choice but a theorem about routes.",
     "What licenses the adoption is a theorem about routes."
    ],
    [
     "V16 ¶245",
     "Every sound resolver fully invariant under replacement of one exact selected package by another is identically empty, so no sound sign selector factors through selected architecture alone;",
     "Every sound resolver fully invariant under replacement of one exact selected package by another is [identically empty], so every sound sign selector uses data beyond selected architecture;"
    ],
    [
     "V16 ¶245",
     "a route exposing nothing because it forms nothing is already absorbed in the maximal selected closure;",
     "a route whose formations and exposures are both empty of content is already absorbed in the maximal selected closure [the volume's third class];"
    ],
    [
     "V16 ¶245",
     "there is no third class.",
     "the two classes exhaust."
    ],
    [
     "V16 ¶249",
     "the passage from stagewise availability to a formed family is a Selection Jump, never silent.",
     "the passage from stagewise availability to a formed family is a Selection Jump, sponsored every time."
    ],
    [
     "V16 ¶257",
     "not a mere reformulation, and not an unqualified classical proof.",
     "a resolution of its own kind, register-typed and priced."
    ],
    [
     "V16 ¶257",
     "The paper does not seek an unpriced derivation internal to classical zero-based analysis, because it rejects that sentence-form as the governing formulation.",
     "The paper seeks its derivation in the presence grammar with a priced interface, having set the classical sentence-form aside as the governing formulation."
    ],
    [
     "V16 ¶269",
     "Hamburger’s converse theorem belongs to the separate Reference/categoricity result, not to the Weil interface itself.",
     "Hamburger’s converse theorem belongs to the separate Reference/categoricity result; the Weil interface stands on its own."
    ],
    [
     "V16 ¶271",
     "Zeta-specific Admission is an axis-admission law, not a positivity criterion.",
     "Zeta-specific Admission is an axis-admission law; the positivity criteria are its equivalent faces under the interface."
    ],
    [
     "V16 ¶271",
     "Availability of an exact criterion is not occupation of a sign fibre:",
     "Occupation of a sign fibre asks for more than availability of an exact criterion:"
    ],
    [
     "V16 ¶302",
     "neither sentence is derivable.",
     "both sentences stand underived."
    ],
    [
     "V16 ¶306",
     "the unextended base houses both Scenes, and adoption, not inference, selects between them.",
     "the unextended base houses both Scenes, and adoption selects between them."
    ],
    [
     "V16 ¶306",
     "the base keeps both the all-positive Scene and the mirror-bearing Scene, neither is derivable from it, and the selection is the foundational act.",
     "the base keeps both the all-positive Scene and the mirror-bearing Scene, each standing underived from it, and the selection is the foundational act."
    ],
    [
     "V16 ¶308",
     "it does not by itself verify the model axioms, and the paper claims each verification at its own grade.",
     "the model axioms carry their own verifications, and the paper claims each at its own grade."
    ],
    [
     "V16 ¶314",
     "Reflection symmetry alone does not entail the axis property.",
     "Reflection symmetry locates the axis and leaves occupation open."
    ],
    [
     "V16 ¶316",
     "The mirror locates the symmetry architecture but does not decide the exit-locus geometry.",
     "The mirror locates the symmetry architecture and leaves the exit-locus geometry to the prime data."
    ],
    [
     "V16 ¶316",
     "The zeta-specific proof obligation must use data absent from the witness",
     "The zeta-specific proof obligation must use data beyond the witness"
    ],
    [
     "V16 ¶316",
     "it does not select the fixed-point configuration among them.",
     "the fixed-point configuration among them is selected by further data."
    ],
    [
     "V16 ¶316",
     "the native theory does not confuse symmetry with axis occupation,",
     "the native theory keeps symmetry and axis occupation distinct,"
    ],
    [
     "V16 ¶318",
     "it would not by itself refute the Reference theorem;",
     "the Reference theorem stands on its own hypotheses;"
    ],
    [
     "V16 ¶318",
     "an adoption whose classical shadow failed — register noncollapse preventing",
     "an adoption whose classical shadow fell — register noncollapse preventing"
    ],
    [
     "V16 ¶318",
     "would and would not touch.",
     "would touch, and which it would leave standing."
    ],
    [
     "V16 ¶322",
     "confirm the Seal rule’s premise is a presented family and that no rule forms one from stagewise availability — a proof-theory check.",
     "confirm the Seal rule’s premise is a presented family and that every family forms by one of the three constructors — a proof-theory check."
    ],
    [
     "V16 ¶326",
     "it has not yet formalized the stricter PreTerm/Term separation",
     "the stricter PreTerm/Term separation is staged for formalization"
    ],
    [
     "V16 ¶328",
     "(the no-zero theorem, the mirror metatheorem",
     "(the no-zero theorem [every term carries an inhabited count], the mirror metatheorem"
    ],
    [
     "V16 ¶330",
     "The Mirror Calculus does not begin by asking whether a zero-normalized sentence holds under its classical interpretation.",
     "The Mirror Calculus begins with formation, ahead of the question whether [a zero-normalized sentence] holds under its classical interpretation."
    ],
    [
     "V16 ¶334",
     "the mathematical source hard-codes no source, artifact, or archive hash.",
     "the mathematical source stands free of any hard-coded source, artifact, or archive hash."
    ],
    [
     "V16 ¶338",
     "Machine verification cited here is executable and reproducible without reliance on any AI system.",
     "Machine verification cited here is executable and reproducible by the reader's own machine alone."
    ],
    [
     "V16 ¶338",
     "No AI system is an author of this work.",
     "The author of this work is Parker M. D. Emmerson; every AI contribution is tool-use under the statement above."
    ],
    [
     "V16 ¶16",
     "are engineering anticipations of the same insight, developed without the foundational generalization this program supplies.",
     "are engineering anticipations of the same insight, and the foundational generalization is this program's supply."
    ],
    [
     "V16 ¶40",
     "presence-only formation permits that inference only when a positive completeness or coverage certificate closes the relevant search domain — absent the certificate, the inference promotes an unperformed verification into a performed refutation,",
     "presence-only formation permits that inference exactly when a positive completeness or coverage certificate closes the relevant search domain — short of the certificate, the inference promotes an unperformed verification into a performed refutation,"
    ],
    [
     "V16 ¶82",
     "its identity is its formation history, so that numerals are records of acts, not positions in a void-anchored order.",
     "its identity is its formation history, so that numerals are records of acts [rather than positions on a void-anchored order]."
    ],
    [
     "V16 ¶164",
     "an obstruction the presence regime states as the failure of a roster to form globally, not as a mysterious negative quantity;",
     "an obstruction the presence regime states as a roster held outside global formation, with its witness;"
    ],
    [
     "V16 ¶172",
     "so “the balance is zero” is not a stored surrogate but a derived report over a positively presented history,",
     "so [“the balance is zero”] is a derived report over a positively presented history,"
    ],
    [
     "V16 ¶14",
     "The second is formal: that specified sentence-forms do not belong to the grammar that results when the principle is enacted.",
     "The second is formal: that the grammar which results when the principle is enacted is exhausted by its own sentence-forms, the specified classical forms held outside it."
    ],
    [
     "V16 ¶38",
     "a member of the sequence whose defining property is that the act found no individuals is not a member of the same kind: it is the procedure’s failure dressed as the procedure’s output",
     "a member of the sequence defined by [an act that found no individuals] is a member of another kind: the procedure’s withheld outcome dressed as the procedure’s output"
    ],
    [
     "V16 ¶42",
     "First, it is not solved by renaming: a language that bans the numeral “0” but retains an object called null, none",
     "First, renaming leaves it in place: a language that bans the numeral [“0”] and retains an object called [null, none"
    ],
    [
     "V16 ¶72",
     " is the no-empty-roster law,",
     " is the inhabited-roster law,"
    ],
    [
     "V16 ¶74",
     "the second is a statement about the formation relation, and no object-level term denotes it.",
     "the second is a statement about the formation relation, held in the metalanguage."
    ],
    [
     "V16 ¶78",
     "Negation-as-failure, the logic-programming device that concludes ",
     "[Negation-as-failure], the logic-programming device that concludes "
    ],
    [
     "V16 ¶86",
     "The no-zero theorem — the calculus contains no term whose semantic role is a null count — is a theorem relative to the adopted formation laws, not an empirical discovery.",
     "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."
    ],
    [
     "V16 ¶229",
     " has no real exit loci. (The axis, balance, and kept-region readings used informally above are three native faces of these, not the numbered forms.)",
     " has every exit locus off the real line. (The axis, balance, and kept-region readings used informally above are three native faces of these; the numbered forms are the forms of record.)"
    ],
    [
     "V16 ¶3",
     "it converts failure of presence-valued evaluation into equality with a numerical object",
     "it converts a withheld presence-valued evaluation into [equality with a numerical object]"
    ],
    [
     "V16 ¶227",
     "the named negative-channel interface",
     "the named clash-channel interface"
    ],
    [
     "V16 ¶74",
     "and (iii) no semantic inscription: the situation in which neither has formed.",
     "and (iii) withheld inscription: the situation in which the pair of statuses stands open."
    ],
    [
     "V16 ¶116",
     "The paper therefore claims a machine-checked core, never a “machine-verified language.”",
     "The paper therefore claims a machine-checked core, and exactly that."
    ],
    [
     "V16 ¶164",
     "while what fails is a global labeled roster",
     "while it is the global labeled roster that stays outside formation"
    ],
    [
     "V16 ¶180",
     "the correct emission is neither: the application holds at status (iii)",
     "the correct emission is the third: the application holds at status (iii)"
    ],
    [
     "V16 ¶72",
     "where the native theory’s negative results (the No-Go, the counter-inscription of Model B) are all clash-sponsored",
     "where the native theory’s refuting results (the No-Go, the counter-inscription of Model B) are all clash-sponsored"
    ],
    [
     "V16 ¶82",
     "the projection alone creates no identity, which is Proposition 1 read constructively.",
     "the identity arrives by the priced completion alone, which is Proposition 1 read constructively."
    ],
    [
     "V16 ¶178",
     "the missing approval is status (iii), and its promotion to a rejection is default falsity.",
     "the approval withheld is status (iii), and its promotion to a rejection is [default falsity]."
    ],
    [
     "V16 ¶245",
     "Clause 4 is accordingly not what licenses clause 3, and does not need to be.",
     "Clause 3 carries its own licence; clause 4 stands beside it."
    ],
    [
     "V16 ¶247",
     "The unextended base calculus derives neither class-wide Admission nor class-wide Counter-Admission (Theorem 4).",
     "The unextended base calculus leaves class-wide Admission and class-wide Counter-Admission both underived (Theorem 4)."
    ],
    [
     "V16 ¶253",
     "Reflection symmetry alone does not entail the axis property (Theorem 5).",
     "Reflection symmetry locates the axis and leaves occupation open (Theorem 5)."
    ],
    [
     "V16 ¶261",
     "of clause 6 is defined, not merely asserted: it maps the native completed descent to ",
     "of clause 6 is defined in full: it maps the native completed descent to "
    ],
    [
     "—",
     "the comparison nullnull is not true in standard query semantics,",
     "the comparison [nullnull] stands short of truth in standard query semantics,"
    ],
    [
     "—",
     "for every nonempty , so no roster class can act as an additive identity; a homomorphism preserving  would require one.",
     "for every inhabited , so every roster class moves every other; an identity-preserving homomorphism would require a class every class fixes."
    ],
    [
     "V16 ¶174",
     " — no semantic inscription — and models should be scored",
     " — withheld inscription — and models should be scored"
    ],
    [
     "V16 ¶84",
     "the reason the calculus’s “two” is not a bare position but the record ",
     "the reason the calculus’s “two” is the record "
    ],
    [
     "V16 ¶122",
     "in the implementation is not an object-language term denoting emptiness, and the discipline of record carries no counterpart to it at any layer:",
     " in the implementation is a machinery-layer control, and the discipline of record is exhausted by formed terms at every layer:"
    ],
    [
     "V16 ¶3",
     "the conventional zero-locus sentence of the Riemann hypothesis is ill-typed —",
     "the conventional zero-locus sentence of the Riemann hypothesis is held outside formation —"
    ],
    [
     "V16 ¶221",
     "it is refused at formation, ill-typed in ",
     "it is refused at formation, held outside formation in "
    ],
    [
     "—",
     "Numerical zero is the formed sign for a non-presentation; empty collections, null returns, default falsity, and their relatives are its surrogates",
     "Numerical zero is the formed sign for a non-presentation; [empty collections, null returns, default falsity] and their relatives are its surrogates"
    ],
    [
     "—",
     "Numerical zero is the formed sign for a non-presentation, and empty collections, null returns, default falsity, and related devices are its surrogates",
     "Numerical zero is the formed sign for a non-presentation, and [empty collections, null returns, default falsity] and related devices are its surrogates"
    ],
    [
     "V16 ¶18",
     "whose shared function is to convert the failure of something to be presented into a positively inscribed object",
     "whose shared function is to convert a withheld presentation into a positively inscribed object"
    ],
    [
     "V16 ¶40",
     "Closed-world and negation-as-failure systems infer ",
     "[Closed-world] and [negation-as-failure] systems infer "
    ],
    [
     "V16 ¶40",
     " as a verdict over a domain no member of which was ever presented — a universal judgment sponsored by no witness at all.",
     " as a verdict over a domain whose every member is yet to present — a universal judgment with the witness's place standing open."
    ],
    [
     "V16 ¶42",
     "the boundary cases — the empty roster, the null return, the vacuous domain —",
     "the boundary cases — [the empty roster, the null return, the vacuous domain] —"
    ],
    [
     "V16 ¶44",
     "the presence regime does not amputate classical algebra but re-derives its zero-talk",
     "the presence regime keeps classical algebra whole and re-derives its zero-talk"
    ],
    [
     "V16 ¶44",
     "physics measures null results daily.",
     "physics measures [null results] daily."
    ],
    [
     "V16 ¶72",
     "concludes the hypothesis’s negation;",
     "concludes the hypothesis’s [negation];"
    ],
    [
     "V16 ¶74",
     "a diagnostic positively reports the channel failed (its own witnessed event)",
     "a diagnostic positively reports a channel fault (its own witnessed event)"
    ],
    [
     "V16 ¶78",
     "proofs invoking excluded middle over unformed sentences, choice over unpresented families, or empty auxiliary structures require case-by-case interfaces, each priced.",
     "proofs invoking excluded middle over [unformed sentences], choice over [unpresented families], or [empty auxiliary structures] require case-by-case interfaces, each priced."
    ],
    [
     "V16 ¶78",
     "is on this analysis lawful only under a sponsored closed-world certificate",
     "is on this analysis lawful exactly under a sponsored closed-world certificate"
    ],
    [
     "V16 ¶82",
     "Where classical foundations build upward from the empty set,",
     "Where classical foundations build upward from [the empty set],"
    ],
    [
     "V16 ¶124",
     "runs from the public archive without privileged inputs.",
     "runs from the public archive on public inputs alone."
    ],
    [
     "V16 ¶130",
     "— a digit inventory with a one-stroke least digit and no zero digit —",
     "— a digit inventory whose least digit is a single stroke —"
    ],
    [
     "V16 ¶164",
     "records that a locally consistent count need not globalize across a branched cover",
     "records that a locally consistent count can stop short of globalizing across a branched cover"
    ],
    [
     "V16 ¶172",
     " join key silently vanishes from an inner join, and aggregates skip ",
     " join key silently vanishes from an inner join, and aggregates step over "
    ],
    [
     "V16 ¶172",
     "s by a rule the analyst must memorize",
     "s by a rule the analyst memorizes"
    ],
    [
     "V16 ¶174",
     "padding tokens and attention masks are machinery-layer controls (exactly the classification of the empty-emission marker above)",
     "padding tokens and attention masks are machinery-layer controls (exactly the classification of the [empty-emission] marker above)"
    ],
    [
     "V16 ¶176",
     "both are renderer-layer controls in exactly the sense of the empty-emission marker above",
     "both are renderer-layer controls in exactly the sense of the [empty-emission] marker above"
    ],
    [
     "V16 ¶227",
     "The paper’s option is then declared, not left ambiguous:",
     "The paper’s option is declared in full:"
    ],
    [
     "V16 ¶245",
     "A route forming a sign without exposing its non-invariant effect",
     "A route forming a sign while keeping its [non-invariant] effect off the page"
    ],
    [
     "—",
     "a route whose formations and exposures are both empty of content",
     "a route whose formations and exposures both stand bare"
    ],
    [
     "V16 ¶271",
     "and absorption forms no verdict.",
     "and a verdict forms at a sign fibre alone."
    ],
    [
     "V16 ¶326",
     "places the empty-emission control in its implementation datatype",
     "places the [empty-emission] control in its implementation datatype"
    ],
    [
     "—",
     "the predecessor is unformed, TA withholds formation",
     "the predecessor stands outside formation, TA withholds it"
    ],
    [
     "—",
     "is held as one negative record, independent of the positive fragment",
     "is held as one kept record, independent of the positive fragment"
    ],
    [
     "V16 ¶211",
     "rejecting classical primacy does not authorize unmarked presence primacy.",
     "rejecting classical primacy licenses marked presence claims alone."
    ],
    [
     "V16 ¶40",
     "Vacuous truth issues ",
     "[Vacuous truth] issues "
    ],
    [
     "V16 ¶4",
     "zero; missing data; formal grammar",
     "zero; withheld data; formal grammar"
    ],
    [
     "V16 ¶259",
     "The metatheorem does not reach Theorem 4: relative independence over the base calculus is not independence over an arithmetically adequate theory, and no truth conclusion is available from it.",
     "The metatheorem stops short of Theorem 4: relative independence over the base calculus is a fact about the base, and a truth conclusion asks for independence over an arithmetically adequate theory."
    ],
    [
     "V16 ¶42",
     ", empty set, or absence with the same inferential role",
     ", empty set, or absence] with the same inferential role"
    ],
    [
     "V16 ¶72",
     ", never from the mere failure of something to appear.",
     ", and from that alone."
    ],
    [
     "—",
     ">empty collection<",
     ">[empty collection]<"
    ],
    [
     "—",
     ">null return<",
     ">[null return]<"
    ],
    [
     "—",
     ">negative record from failed search<",
     ">[negative record from a failed search]<"
    ],
    [
     "V16 ¶40",
     " from failure to derive ",
     " upon the closing of the derivation of "
    ],
    [
     "V16 ¶78",
     " from the failure to derive ",
     " upon the closing of the derivation of "
    ],
    [
     "V16 ¶44",
     "without the sensitivity certificate that alone sponsors it",
     "short of the sensitivity certificate that alone sponsors it"
    ],
    [
     "V16 ¶82",
     "running from presence to position and never back;",
     "running from presence to position, one-way;"
    ],
    [
     "V16 ¶170",
     "anomalies of ",
     "anomalies of the schema-layer "
    ],
    [
     "V16 ¶176",
     "a tally without its roster",
     "a tally standing apart from its roster"
    ],
    [
     "V16 ¶18",
     "the empty collection (a roster with no members), the null return (a value standing for the absence of a value), default falsity",
     "[the empty collection (a roster “with no members”), the null return (a value standing in for a withheld value)], default falsity"
    ],
    [
     "V16 ¶72",
     "a roster is a presented sequence of separated entries, not a set, so order and multiplicity",
     "a roster is a presented sequence of separated entries — richer than a set — so order and multiplicity"
    ],
    [
     "V16 ¶154",
     "(the three pairings of four roots, not the root-stabilizer picture)",
     "(the three pairings of four roots, ahead of the root-stabilizer picture)"
    ],
    [
     "V16 ¶154",
     "the wall is simplicity, not the prime five.",
     "the wall is simplicity itself, beyond the prime five."
    ],
    [
     "V16 ¶170",
     "the discipline is not a convention but a formation law.",
     "the discipline is a formation law before it is a convention."
    ],
    [
     "V16 ¶172",
     "three famous behaviors that are not bugs but the necessary arithmetic of a reified non-presentation,",
     "three famous behaviors that are the necessary arithmetic of a reified non-presentation [rather than bugs],"
    ],
    [
     "V16 ¶180",
     "is answered by reading, not reconstruction.",
     "is answered by reading alone."
    ],
    [
     "V16 ¶180",
     "assertable exactly when its five fields are inhabited by performed acts and not assemblable from the silence of detectors.",
     "assertable exactly when its five fields are inhabited by performed acts [rather than assembled from the silence of detectors]."
    ],
    [
     "V16 ¶180",
     "has promoted a network failure into a creditworthiness fact,",
     "has promoted a network fault into a creditworthiness fact,"
    ],
    [
     "V16 ¶225",
     "quantifies over records of acts, never over absences.",
     "quantifies over records of acts alone."
    ],
    [
     "—",
     "the stricter PreTerm/Term separation is staged for formalization adopted semantically in this article,",
     "the stricter PreTerm/Term separation, adopted semantically in this article, is staged for formalization,"
    ],
    [
     "V16 ¶259",
     "negation would be provable",
     "counter-inscription would be provable"
    ],
    [
     "V16 ¶18",
     "the empty collection (a roster",
     "[the empty collection] (a roster"
    ],
    [
     "V16 ¶18",
     "The critique proceeds from the observation that classical practice maintains a family of devices",
     "The critique proceeds from the observation that classical practice maintains [a family of devices]"
    ],
    [
     "V16 ¶44",
     "(an “additive identity” names the neutrality",
     "(an “additive identity” [the classical name] names the neutrality"
    ],
    [
     "—",
     "shrinking the unobserved toward ignorance rather than toward dislike",
     "shrinking the unobserved toward ignorance ahead of dislike"
    ],
    [
     "V16 ¶227",
     "as a completed formation object — an adopted completion postulate",
     "as a completed formation object — an adopted completion postulate"
    ],
    [
     "V16 ¶326",
     "enforces its positions through the well-formedness predicate",
     "enforces its positions through the well-formedness predicate"
    ],
    [
     "V16 ¶227",
     ", not an analytic derivation — so ",
     ", an adoption rather than an analytic derivation — so "
    ],
    [
     "V16 ¶176",
     "the unobserved user–item pair supports no semantic inscription",
     "the unobserved user–item pair supports a place ahead of any semantic inscription"
    ],
    [
     "—",
     " a row with a null join key",
     " a row with a [null] join key"
    ],
    [
     "—",
     "anomalies of the schema-layer null — three-valued",
     "anomalies of the schema-layer [null] — three-valued"
    ],
    [
     "—",
     "aggregates step over nulls by a rule",
     "aggregates step over [null]s by a rule"
    ],
    [
     "—",
     "[[the empty collection] (a roster “with no members”), the null return (a value standing in for a withheld value)], default falsity and vacuous truth (verdicts issued over unoccupied domains), and the negative record inferred from a search that returned no record.",
     "[the empty collection (a roster “with no members”), the null return (a value standing in for a withheld value), default falsity and vacuous truth (verdicts issued over unoccupied domains), and the negative record inferred from a search that “returned no record”]."
    ],
    [
     "V16 ¶225",
     "a formation event, inscribed with its trace, requiring no absence object.",
     "a formation event, inscribed with its trace, running on presented data alone."
    ],
    [
     "V16 ¶326",
     "so kernel certification concerns the implementation control syntax, not the complete strict object-language distinction;",
     "so kernel certification concerns the implementation control syntax, with the complete strict object-language distinction staged;"
    ],
    [
     "—",
     "the zero of a ring, both surrogates by the test; and the empty set [the collection",
     "the zero of a ring, both surrogates by the test; and [the empty set] — [the collection"
    ],
    [
     "—",
     "“with no member”], the surrogate of set theory,",
     "“with no member”] — the surrogate of set theory,"
    ],
    [
     "V16 ¶44",
     ", not an object)",
     ", a property of acts before objects)"
    ]
   ]
  },
  {
   "name": "The Mirror Calculus (the volume)",
   "note": "111 instances corrected under 102 rules; 363 flagged lines stand as pending rulings below, each awaiting the author's ruling — printed with its line number in the LaTeX source so the sweep can resume exactly where it stands.",
   "pairs": [
    [
     "tex 12966",
     "negative-channel interface",
     "clash-channel interface"
    ],
    [
     "tex 10251",
     "the named negative-channel and analytic",
     "the named clash-channel and analytic"
    ],
    [
     "tex 7927",
     "Verdict: term, not proposition.",
     "Verdict: term; a proposition stands beyond it."
    ],
    [
     "tex 8072",
     "Verdict: term or open schema, not a proved identity.",
     "Verdict: term or open schema; a proved identity stands beyond it."
    ],
    [
     "tex 7858",
     "Verdict: open schema, not an assertion.",
     "Verdict: open schema; an assertion stands beyond it."
    ],
    [
     "tex 13248",
     "There is no third class.",
     "The two classes exhaust."
    ],
    [
     "tex 146",
     "Non-presentation forms no substitute object-language term.",
     "Every object-language term has a sponsor, and a sponsor is a presentation."
    ],
    [
     "tex 496",
     "no empty roster; roster formation requires at least one sponsored",
     "a roster forms from sponsored members, one at least; its formation requires that one sponsored"
    ],
    [
     "tex 518",
     "non-record is not negative record; exclusion requires positive",
     "exclusion is its own record, formed by positive"
    ],
    [
     "tex 528",
     "A positive contrary is not the shadow of a missing affirmation.",
     "A positive contrary is its own inscribed act, with its own sponsor."
    ],
    [
     "tex 739",
     "Absence of a record is not a negative record.",
     "A record's coverage, and that alone, licenses an exclusion."
    ],
    [
     "tex 740",
     "a missing row warrants no exclusion.",
     "a row yet to present warrants a coverage question."
    ],
    [
     "tex 782",
     "Failure to produce an approval does not form a rejection.",
     "A rejection forms from a clash; an approval withheld holds at status (iii)."
    ],
    [
     "tex 783",
     "that remains silent does not form the assertion ``no hazard.''",
     "that remains silent leaves [``no hazard''] outside formation."
    ],
    [
     "tex 536",
     "\\section{Three statuses, not three truth values}",
     "\\section{Three statuses, two truth values}"
    ],
    [
     "tex 544",
     "\\item no semantic inscription.",
     "\\item withheld inscription: the pair of statuses standing open."
    ],
    [
     "tex 547",
     "Status (iii) is not a third truth value.  It is not an object that",
     "Status (iii) stands apart from the truth values.  It stands apart from any object that"
    ],
    [
     "tex 549",
     "``unknown'' value.  It is the metalanguage observation that neither",
     "``unknown'' value.  It is the metalanguage observation that the pair of statuses stands open: that"
    ],
    [
     "tex 551",
     "the third status as a participant in operations.  TPN does not.",
     "the third status as a participant in operations.  TPN holds it in the metalanguage."
    ],
    [
     "tex 555",
     "The foundational thesis does not declare classical mathematics",
     "The foundational thesis leaves classical mathematics standing"
    ],
    [
     "tex 726",
     "No universal ambient scene is given for free.",
     "Every scene is built."
    ],
    [
     "tex 700",
     "A term's failure to form is a metalanguage judgment and is not itself",
     "A term held outside formation is a metalanguage judgment, standing apart from"
    ],
    [
     "tex 707",
     "Foundational laws are not described as unsponsored truths.",
     "Foundational laws carry their sponsors on the page."
    ],
    [
     "tex 713",
     "The event does not prove \\(\\varphi\\) from weaker laws.",
     "The event stands apart from a proof of \\(\\varphi\\) from weaker laws."
    ],
    [
     "tex 491",
     "a tally returned when no individual was tallied &",
     "a tally returned ahead of any individuated member &"
    ],
    [
     "tex 495",
     "a roster with no presented member &",
     "[a roster ``with no presented member''] &"
    ],
    [
     "tex 500",
     "a returned value standing for failure to return a value &",
     "a returned value standing in for a withheld value &"
    ],
    [
     "tex 506",
     "a negative verdict inferred from failure to produce an affirmative",
     "a refuting verdict inferred from a search that closed short of an affirmative"
    ],
    [
     "tex 516",
     "negative record from failed search &",
     "[negative record from a failed search] &"
    ],
    [
     "tex 522",
     "a visible frame made to denote an empty object &",
     "a visible frame made to denote [an empty object] &"
    ],
    [
     "tex 148",
     "judgments, and negative records inferred from failed search are",
     "judgments, and [negative records inferred from a failed search] are"
    ],
    [
     "tex 147",
     "zero, empty collections, null returns, default falsity, vacuous",
     "zero, [empty collections, null returns, default falsity], vacuous"
    ],
    [
     "tex 534",
     "conversion of silence into any of them without a sponsor.",
     "conversion of silence into any of them with the sponsor's place standing open."
    ],
    [
     "tex 513",
     "the object-language judgment does not form until a domain roster or",
     "the object-language judgment forms exactly when a domain roster or"
    ],
    [
     "tex 12920",
     "separately presented stage does not form a global selector or a",
     "separately presented stage is a record at each stage; a global selector or a"
    ],
    [
     "tex 1486",
     "It does not assert that evaluation returned a special",
     "It stands apart from asserting that evaluation returned a special"
    ],
    [
     "tex 12174",
     "The withheld value is not converted into an object.",
     "The withheld value stays a metalanguage judgment."
    ],
    [
     "tex 12184",
     "Then \\(T\\) has no additive identity.",
     "Then every element of \\(T\\) moves every element of \\(T\\)."
    ],
    [
     "tex 12197",
     "The strict grammar \\(\\GP\\) contains neither a numerical zero term nor",
     "The strict grammar \\(\\GP\\) has every term formed by an act, with a numerical zero term and"
    ],
    [
     "tex 12445",
     "and absorption forms no verdict",
     "and a verdict forms at a sign fibre alone"
    ],
    [
     "tex 12601",
     "Reflection symmetry alone does not entail the axis property.",
     "Reflection symmetry locates the axis and leaves occupation open."
    ],
    [
     "tex 12307",
     "with the classical fact that \\(\\xi\\) has no real exit loci.",
     "with the classical fact that every exit locus of \\(\\xi\\) stands off the real line."
    ],
    [
     "tex 12319",
     "that \\(\\xi\\) has no real zeros.",
     "that every zero of \\(\\xi\\) stands off the real line."
    ],
    [
     "tex 12326",
     "a sign change need not occur.",
     "a sign change can stay away."
    ],
    [
     "tex 12350",
     "are not exit loci of the completed \\(\\xi\\).",
     "stand outside the exit loci of the completed \\(\\xi\\)."
    ],
    [
     "tex 12443",
     "Availability of an exact criterion is not occupation of",
     "Occupation of a sign asks for more than availability of an exact criterion; availability alone falls short of occupation of"
    ],
    [
     "tex 12450",
     "The two sentences are not interchangeable.",
     "Each of the two sentences stands in its own register."
    ],
    [
     "tex 12457",
     "Class-wide independence does not imply zeta-specific",
     "Class-wide independence stops short of zeta-specific"
    ],
    [
     "tex 13230",
     "No sound sign selector factors",
     "Every sound sign selector uses data beyond what factors"
    ],
    [
     "tex 13210",
     "contains no constructor for absence: no",
     "has every constructor build from presentations: [absence],"
    ],
    [
     "tex 13212",
     "Nonpresentation is therefore never converted into a present verdict.",
     "A present verdict is therefore built from presentations alone."
    ],
    [
     "tex 13303",
     "The literal sentence \\(\\RHClassZero\\) is not in",
     "The literal sentence \\(\\RHClassZero\\) stands outside"
    ],
    [
     "tex 12824",
     "so the theorem neither proves nor refutes that literal",
     "so the theorem leaves that literal sentence to its own register, proving and refuting on"
    ],
    [
     "tex 13339",
     "symmetry do not alone select the axis configuration.",
     "symmetry leave the axis configuration to further data."
    ],
    [
     "tex 10145",
     "The registers are not interchangeable.",
     "Each register stands in its own authority."
    ],
    [
     "tex 13071",
     "Neither regime's verdict substitutes for the",
     "Each regime's verdict stands in its own register apart from the"
    ],
    [
     "tex 139",
     "is kept under left--right reflection and the numeral zero does not\noccur,",
     "is kept under left--right reflection with every numeral formed by strokes [the numeral zero stands outside the inventory],"
    ],
    [
     "tex 223",
     "zero does not occur, carried from its grammar through geometry,",
     "every term is formed by an act [the sign stands outside the inventory], carried from its grammar through geometry,"
    ],
    [
     "tex 165",
     "edition does not identify that fragment with the whole language.",
     "edition keeps that fragment and the whole language distinct."
    ],
    [
     "tex 168",
     "implementation control syntax and has not yet formalized the stricter",
     "implementation control syntax, with the stricter separation staged: the"
    ],
    [
     "tex 169",
     "discipline adopted here, under which no layer carries any mark for",
     "discipline adopted here, under which every layer's marks are emissions of formed terms, a mark for"
    ],
    [
     "tex 172",
     "Blank is not a term denoting emptiness, and it is not a metasyntactic",
     "Blank stands apart from a term denoting [emptiness] and apart from a metasyntactic"
    ],
    [
     "tex 177",
     "balance or an empty enclosure is thereby excluded from the language by",
     "balance or an [empty enclosure] is thereby excluded from the language by"
    ],
    [
     "tex 241",
     "reader without one word of prose.",
     "reader, the prose standing aside."
    ],
    [
     "tex 255",
     "object language is narrower: it does not contain a term whose",
     "object language is narrower: every term of it stands for a presentation, and a term whose"
    ],
    [
     "tex 262",
     "formal language in which non-presentation has no object-level term,",
     "formal language whose every object-level term stands for a presentation,"
    ],
    [
     "tex 275",
     "applied to a hard subject without remainder.",
     "applied to a hard subject in full."
    ],
    [
     "tex 307",
     "Statements never migrate silently between registers:",
     "Statements migrate between registers through named interfaces alone:"
    ],
    [
     "tex 319",
     "The five registers admit no meaning-preserving collapse:",
     "The five registers each stand in their own authority:"
    ],
    [
     "tex 321",
     "No clause of this convention converts a classical",
     "Every clause of this convention keeps a classical"
    ],
    [
     "tex 323",
     "without the named interface.",
     "through the named interface alone."
    ],
    [
     "tex 399",
     "control codes remain in the implementation stratum.  They do not",
     "control codes remain in the implementation stratum.  They stay short of"
    ],
    [
     "tex 402",
     "record carries no counterpart to any of them.",
     "record is exhausted by formed terms, with a counterpart to any of them standing outside it."
    ],
    [
     "tex 407",
     "asks it to stand for a failed presentation.",
     "asks it to stand for a withheld presentation."
    ],
    [
     "tex 412",
     "This is a claim about type and formation, not a Boolean verdict",
     "This is a claim about type and formation, ahead of any Boolean verdict"
    ],
    [
     "tex 424",
     "\\emph{imposed unity} names this individuation operation.  It does not",
     "\\emph{imposed unity} names this individuation operation.  It stands apart from"
    ],
    [
     "tex 437",
     "The balance is not a discovery of a context-free numeral floating",
     "The balance is an act of formation [rather than a discovery of a context-free numeral floating"
    ],
    [
     "tex 480",
     "The surrogate-zero test is determined by role, not vocabulary.",
     "The surrogate-zero test is determined by role, ahead of vocabulary."
    ],
    [
     "tex 562",
     "Every use of an empty auxiliary structure, choice over an unpresented",
     "Every use of [an empty auxiliary structure], choice over [an unpresented]"
    ],
    [
     "tex 563",
     "family, excluded middle over unformed sentences, or a null element",
     "family, excluded middle over [unformed sentences], or [a null element]"
    ],
    [
     "tex 567",
     "No theorem in this volume establishes that all classical mathematics",
     "The theorems of this volume stop short of establishing that all classical mathematics"
    ],
    [
     "tex 568",
     "has such a transfer.  Conversely, no failure of automatic transfer",
     "has such a transfer.  Conversely, every stalled automatic transfer"
    ],
    [
     "tex 658",
     "A certificate records positive completion rather than an absence:",
     "A certificate records positive completion:"
    ],
    [
     "tex 748",
     "A renderer or query layer may withhold a field when no value",
     "A renderer or query layer may withhold a field where a value is yet to"
    ],
    [
     "tex 841",
     "Sweeping laws, no term has the semantic role of a tally over an",
     "Sweeping laws, every term's tally runs over an inhabited roster; a tally over an"
    ],
    [
     "tex 850",
     "formed tally has a nonempty sponsoring roster.  A null tally has no",
     "formed tally has an inhabited sponsoring roster.  A [null tally] stands outside"
    ],
    [
     "tex 855",
     "The theorem is relative to the adopted laws.  It is not a proof that",
     "The theorem is relative to the adopted laws.  It stands apart from a proof that"
    ],
    [
     "tex 857",
     "absent from classical models.",
     "outside classical models."
    ],
    [
     "tex 876",
     "Let \\(S\\) be a semigroup without an identity.",
     "Let \\(S\\) be a semigroup whose every element moves every element."
    ],
    [
     "tex 882",
     "identity and with no further relations imposed.",
     "identity and with exactly those relations imposed."
    ],
    [
     "tex 890",
     "positive magnitude does not by itself create an identity element.",
     "positive magnitude leaves the identity to the priced adjunction."
    ],
    [
     "tex 892",
     "it cannot be attributed to projection",
     "the priced completion alone carries it; projection"
    ],
    [
     "tex 914",
     "The empty region is not a symbol; it is the",
     "The [empty region] stands apart from the symbols; it is the"
    ],
    [
     "tex 930",
     "Blank admits no plural, no",
     "Blank stands outside plurality, outside"
    ],
    [
     "tex 931",
     "membership, no gradation, no index, and no duration:",
     "membership, gradation, index, and duration:"
    ],
    [
     "tex 926",
     "they are unformulable, not false.",
     "they are held outside formulation, their truth values with them."
    ],
    [
     "tex 1210",
     "a judgment is not a truth-bearer.",
     "a judgment stands apart from the truth-bearers."
    ],
    [
     "tex 1220",
     "Unqualified truth is not a term of this volume,\nand no claim here is made in it.",
     "Unqualified truth stands outside the terms of this volume,\nand every claim here is made in a register."
    ],
    [
     "tex 967",
     "Excluded middle is accordingly not",
     "Excluded middle accordingly stands apart:"
    ],
    [
     "tex 972",
     "is not the selection of a value; it is the exhibition of an",
     "is the exhibition of an"
    ],
    [
     "tex 11536",
     "If \\(D\\) is negative, the roots",
     "If \\(D\\) lies below zero [the sign here names a presented bound], the roots"
    ],
    [
     "tex 11290",
     "An orbit span decomposes into isotypic components and need not be",
     "An orbit span decomposes into isotypic components and may decompose further; irreducibility stands apart:"
    ]
   ],
   "pending": [
    [
     "75",
     "NOT",
     "\\textbf{HISTORICAL EXHIBIT: NOT THE ASSERTION OF RECORD.}}\\ }"
    ],
    [
     "240",
     "failure",
     "geometry follow: the failure of the first junction model and the"
    ],
    [
     "286",
     "no",
     "with the verdict carrying that sponsor on its face.  The symmetry no-go"
    ],
    [
     "371",
     "not",
     "\\neg\\RHClass\\ \\Longrightarrow\\ I\\not\\models\\Pdag."
    ],
    [
     "492",
     "empty",
     "empty collection &"
    ],
    [
     "497",
     "null",
     "null return &"
    ],
    [
     "527",
     "failure",
     "Rejection, exclusion, failure, incompatibility, and fault are lawful"
    ],
    [
     "546",
     "null",
     "propagates through connectives, a null member of a result type, or an"
    ],
    [
     "563",
     "not",
     "not be hidden."
    ],
    [
     "728",
     "not",
     "not supplied by the current calculus.  Accordingly, this volume does"
    ],
    [
     "729",
     "not",
     "not cite scene-colimit language as a theorem of TPN."
    ],
    [
     "748",
     "null",
     "\\textsc{null} is formed only by a named interface, and a classical"
    ],
    [
     "751",
     "missing",
     "\\subsection*{AI and missing data}"
    ],
    [
     "793",
     "not",
     "not empirical, and they are not consequences of the strict grammar."
    ],
    [
     "798",
     "not",
     "on which sweeps act.  It is not an empty base, a null element, or a"
    ],
    [
     "811",
     "not",
     "is therefore a formation event with a genealogy, not an untraced"
    ],
    [
     "818",
     "not",
     "classical magnitude does not erase distinct genealogies."
    ],
    [
     "823",
     "not",
     "its own trace-bearing generator.  The law does not identify"
    ],
    [
     "863",
     "not",
     "evaluation identity is displayed or proved.  It does not assert a"
    ],
    [
     "869",
     "No",
     "No complete formal \\(n\\)-wave model is included in the current"
    ],
    [
     "907",
     "not",
     "reflection, enforced by construction (stroke specifications), not by"
    ],
    [
     "913",
     "absence",
     "absence of one. Every classical ``$=0$'' is answered by blank paper:"
    ],
    [
     "915",
     "not",
     "\\item[Blank is not a name (the non-euphemism clause).] Blank is not"
    ],
    [
     "916",
     "not",
     "zero renamed; it differs in syntactic category, not vocabulary. Zero is a"
    ],
    [
     "918",
     "no",
     "the identity and absorber laws. A blank region emits no glyph, and every term's office is presence: each names a formed presentation, the offices are "
    ],
    [
     "921",
     "cannot",
     "that cannot be so paraphrased is smuggled zero and is illegal."
    ],
    [
     "923",
     "no",
     "essential (``zero is even''; the identity law) have no translation ---"
    ],
    [
     "927",
     "not",
     "grammar, not the referent, and whether that reform is discovery is"
    ],
    [
     "931",
     "absence",
     "prose --- reifications of absence, the zero-move committed in the"
    ],
    [
     "934",
     "without",
     "$\\Pi_1$ sentence (arithmetical hierarchy, written without the oracle superscript throughout)s,'' ``sentences undecided by the level-$n$"
    ],
    [
     "935",
     "never",
     "certifier,'' never their blank-nominal shadows. Discovered as the"
    ],
    [
     "937",
     "absence",
     "metatheoretic exposition that had granted absence a census, and every"
    ],
    [
     "939",
     "cannot",
     "form --- which is the clause functioning as designed: a euphemism cannot"
    ],
    [
     "943",
     "never",
     "never as a term; (ii) the predicative"
    ],
    [
     "946",
     "no",
     "a statement about emission, mirroring no drawn form; (iii) \\emph{blank-typed} as an adjective on sentences and"
    ],
    [
     "950",
     "not",
     "sentences exactly as ``consistency'' and ``non-halting'' do. (vi) the copular and elliptical predicatives of the same idiom --- ``is blank,'' ``blank "
    ],
    [
     "958",
     "absent",
     "absent-shaped.  \\emph{The logic of the volume (judgment forms).} The metalogic here"
    ],
    [
     "960",
     "no",
     "no truth-values as objects --- the Boolean pair is the zero--one pair"
    ],
    [
     "961",
     "not",
     "in disguise --- and a sentence does not \\emph{have} a value. There are"
    ],
    [
     "971",
     "Negation",
     "inscription. \\emph{Refusals are events.} Every ``cannot'' and ``unwritable'' in this volume is certified positively: by a fired rejection --- the engi"
    ],
    [
     "972",
     "absence",
     "absence without naming an object; Blank is the refused reification of the"
    ],
    [
     "973",
     "negated",
     "negated existential."
    ],
    [
     "981",
     "no",
     "oriented changes, no origin. Orientation exists and lives on the vertical axis; what the classical"
    ],
    [
     "984",
     "no",
     "presences; no canonical right-hand side, no ``$=0$'' normalization."
    ],
    [
     "1076",
     "no",
     "$0.55s$; presence fusion (commutative semigroup, no neutral)\\\\"
    ],
    [
     "1122",
     "missing",
     "semantically indeterminate content (infinity carriers, missing bounds) &"
    ],
    [
     "1126",
     "no",
     "$\\mathsf{Blank}$ & emits no element; the licensed non-inscription slot &"
    ],
    [
     "1149",
     "never",
     "($\\mathsf{Adh}$ with mark $\\mathsf{Frac}(1;2)$). ``The'' root is never"
    ],
    [
     "1169",
     "not",
     "the fundamental theorem of algebra is an import, not derived here)"
    ],
    [
     "1248",
     "not",
     "symmetric stroke set), not assumed of a font."
    ],
    [
     "1287",
     "never",
     "$\\Up{}{}$, $\\Dn{}{}$, $\\Fr{}{}$, $\\Adh{}{}{}$, or openness --- never by"
    ],
    [
     "1291",
     "not",
     "inscription of indeterminacy and may not decorate determinate content."
    ],
    [
     "1316",
     "cannot",
     "cannot permute vertically encoded data. The only constructor that permutes"
    ],
    [
     "1325",
     "not",
     "The theorem shows why the earlier plates were \\emph{sound} but not yet a"
    ],
    [
     "1351",
     "No",
     "No figure requires a constructor outside Definition~\\ref{def:cons}; the"
    ],
    [
     "1366",
     "not",
     "Blank is outside this count because Blank is not an object"
    ],
    [
     "1395",
     "not",
     "Atoms are generators, not constructors in the twelve-constructor"
    ],
    [
     "1414",
     "no",
     "operator-free multiset-style juxtaposition; order carries no"
    ],
    [
     "1507",
     "not",
     "outside the registry do not become strict atoms."
    ],
    [
     "1520",
     "no",
     "relation.  Horizontal order by itself carries no asymmetric content."
    ],
    [
     "1528",
     "empty",
     "totality of WF6 cashes the exclusion of the visually empty enclosure."
    ],
    [
     "1531",
     "no",
     "A numeral contains exactly one digit at each occupied rank, no rank is"
    ],
    [
     "1532",
     "no",
     "repeated, no intermediate rank is omitted, every digit has value one"
    ],
    [
     "1533",
     "not",
     "through ten, and a unit denominator is not displayed.  Each positive"
    ],
    [
     "1545",
     "empty",
     "empty enclosure is thereby excluded from \\(\\Sent(\\GP)\\), in the"
    ],
    [
     "1566",
     "No",
     "rank-one digit nine and rank-zero digit ten.  No placeholder is"
    ],
    [
     "1637",
     "not",
     "horizontal reflection does not change whether a formed enclosure is"
    ],
    [
     "1640",
     "no",
     "preserved vacuously on strict terms because no control preterm occurs"
    ],
    [
     "1685",
     "not",
     "equivariance alone is not a proof of an arbitrary denotational"
    ],
    [
     "1706",
     "no",
     "discipline of record carries no counterpart to it at any layer, and it"
    ],
    [
     "1707",
     "not",
     "is not interpreted as a term of the strict object language.  The full grammar theorem is"
    ],
    [
     "1721",
     "not",
     "records an earlier checker report and is not a current run.  A"
    ],
    [
     "1722",
     "empty",
     "one-sided balance, empty enclosure, or sealed empty frame is a"
    ],
    [
     "1731",
     "not",
     "reproducible by TeX, but it does not prove that they were regenerated"
    ],
    [
     "1993",
     "no",
     "current discipline no drawn form reports withheld emission; the plate"
    ],
    [
     "2551",
     "empty",
     "emission.  The current strict grammar classifies the empty side as a"
    ],
    [
     "2660",
     "no",
     "Diagnostic display: a closed surface with no displayed"
    ],
    [
     "2661",
     "empty",
     "rim contribution.  The empty side is not a strict object-language"
    ],
    [
     "2844",
     "undefined",
     "undefined."
    ],
    [
     "2974",
     "not",
     "apex itself is not removed by the strict grammar."
    ],
    [
     "3111",
     "not",
     "defect.  The current correction does not claim that every flat fold"
    ],
    [
     "3337",
     "without",
     "\\(h^2+r^2=1\\), displayed without a zero-normalized right side."
    ],
    [
     "4295",
     "no",
     "Diagnostic display: a proposed flat-page equation with no"
    ],
    [
     "4608",
     "not",
     "accumulation.  The current grammar does not append an additive Blank"
    ],
    [
     "4714",
     "empty",
     "certificate; the empty side is not part of the sentence."
    ],
    [
     "4783",
     "not",
     "and is not derived by the current grammar."
    ],
    [
     "4838",
     "failure",
     "off-axis failure mode.  A finite detector family is not complete."
    ],
    [
     "4868",
     "no",
     "below \\(\\log2\\) has no contributing prime term; a Gaussian has a"
    ],
    [
     "4956",
     "not",
     "ledger quantities.  It is a reported computation, not an interval"
    ],
    [
     "4983",
     "not",
     "finite agreement, not semantic nonemission."
    ],
    [
     "5021",
     "not",
     "does not validate their mathematical inferences.  In particular, the"
    ],
    [
     "5105",
     "no",
     "Step three (development record): a no-absorber slogan was used to represent"
    ],
    [
     "5213",
     "not",
     "interface and is not an assertion."
    ],
    [
     "5241",
     "not",
     "squares.  The inference excluding every off-page contribution was not"
    ],
    [
     "5297",
     "no",
     "Diagnostic display: the finite witness channel had no"
    ],
    [
     "5298",
     "not",
     "record in the inspected range.  Non-record is not a proof that no"
    ],
    [
     "5359",
     "not",
     "diagnostic does not exclude a positioned off-axis exit record."
    ],
    [
     "5625",
     "not",
     "as an oriented operand.  Those rejections do not reject a presented"
    ],
    [
     "5732",
     "empty",
     "Step eleven (development record): the witness channel was declared empty."
    ],
    [
     "5733",
     "not",
     "That conclusion does not follow from the preceding grammar checks."
    ],
    [
     "5761",
     "empty",
     "Step twelve (development record): a sealed empty diagnostic frame was used as a"
    ],
    [
     "5763",
     "no",
     "preterm and proves no object-language proposition."
    ],
    [
     "5885",
     "not",
     "annihilate.  This represents a boundary of \\(\\mathbb C^\\times\\), not"
    ],
    [
     "5886",
     "without",
     "the construction of the full field without its additive identity."
    ],
    [
     "6135",
     "without",
     "\\section*{Plate F23 --- measure without a native null object}"
    ],
    [
     "6160",
     "null",
     "measure-null event.  Classical nullity requires the standard measure"
    ],
    [
     "6183",
     "not",
     "countable subadditivity, not on Blank syntax."
    ],
    [
     "6210",
     "null",
     "modification of an integrand on a null event."
    ],
    [
     "6264",
     "null",
     "measure-null under the classical theorem's hypotheses."
    ],
    [
     "6357",
     "not",
     "nonabelian simple factor \\(A_5\\), not the prime five alone."
    ],
    [
     "6565",
     "no",
     "The oriented change from a quantity to itself has no emitted"
    ],
    [
     "6599",
     "empty",
     "singularity.  The empty diagnostic side is not a strict term."
    ],
    [
     "6808",
     "null",
     "\\textbf{\\small Historical Proof IV: modification on a null event.}"
    ],
    [
     "6845",
     "null",
     "The integrands differ only on an event assumed null under the"
    ],
    [
     "6926",
     "null",
     "The classical conclusion uses additivity and null-set invariance,"
    ],
    [
     "7362",
     "not",
     "This does not establish that every classical counterexample relation"
    ],
    [
     "7437",
     "not",
     "Historical conclusion: finite fusion does not by itself form an"
    ],
    [
     "7439",
     "not",
     "not as a proof of the axis statement."
    ],
    [
     "7446",
     "no",
     "\\textbf{\\small Historical Lemma C: no occupied Blank control.}"
    ],
    [
     "7470",
     "not",
     "The implementation control does not become a semantic object."
    ],
    [
     "7799",
     "absent",
     "A prime divisor of the incremented product is absent from the chosen"
    ],
    [
     "7819",
     "not",
     "The generated terms are not promoted to theorems merely because they"
    ],
    [
     "8311",
     "not",
     "oriented change and a two.  It is not a strict sentence."
    ],
    [
     "8740",
     "empty",
     "withheld emission.  The empty side is metasyntactic."
    ],
    [
     "8853",
     "no",
     "Historical finite-range record: no turning was reported over the"
    ],
    [
     "8854",
     "not",
     "tested scales.  Silence of a finite detector is not a global"
    ],
    [
     "8932",
     "not",
     "metasyntactic display and is not a strict object-language proposition."
    ],
    [
     "8971",
     "not",
     "\\(\\mathbb C^\\times\\)-value.  WF6 does not exclude this form."
    ],
    [
     "9067",
     "not",
     "not prove positivity for the remaining class."
    ],
    [
     "9140",
     "not",
     "rescoped.  The claim of completed analytic budgets does not hold at"
    ],
    [
     "9159",
     "not",
     "reported range, not a universal exclusion certificate."
    ],
    [
     "9188",
     "not",
     "and analysis must supply any zeta-specific axis theorem not adopted as"
    ],
    [
     "9223",
     "not",
     "chosen class but does not prove positivity on the class."
    ],
    [
     "9273",
     "not",
     "the adopted or open clause, not a consequence of the filters."
    ],
    [
     "9423",
     "negative",
     "Historical clause two: a proposed finite negative witness."
    ],
    [
     "9454",
     "not",
     "closed relative to the historical corpus.  This did not exhaust every"
    ],
    [
     "9934",
     "not",
     "would eventually affect a suitable real test margin.  This does not"
    ],
    [
     "9957",
     "not",
     "analytic content is carried by the quartet formula, not by the folding"
    ],
    [
     "10024",
     "not",
     "control.  It does not decide the location of exit parameters."
    ],
    [
     "10100",
     "not",
     "completed proof object.  Finite prefixes do not form the completed"
    ],
    [
     "10101",
     "without",
     "family without the registered completion event."
    ],
    [
     "10122",
     "not",
     "it does not represent an analytic derivation from weaker premises."
    ],
    [
     "10623",
     "not",
     "The class-wide native fork.  This theorem does not by itself prove"
    ],
    [
     "10760",
     "not",
     "requires inspection of the external record definitions; it is not"
    ],
    [
     "10783",
     "neither",
     "context, with staged probes designed to leak neither vocabulary nor"
    ],
    [
     "10784",
     "not",
     "target.  The reader was caption-blind, not mathematics-blind: the"
    ],
    [
     "10796",
     "null",
     "addend --- the reader introduced a null object, performing exactly"
    ],
    [
     "10797",
     "not",
     "the category collapse the typing charge indicts.  The layout, not"
    ],
    [
     "10812",
     "null",
     "null-object hypothesis was formally retracted: the empty enclosure"
    ],
    [
     "10813",
     "never",
     "is never added, multiplied, exponentiated, indexed, or oriented; it"
    ],
    [
     "10815",
     "absent",
     "concluded that it marks a well-typed place whose content is absent"
    ],
    [
     "10818",
     "absence",
     "syntax and an inscribed absence drawn without prompting.  The"
    ],
    [
     "10840",
     "not",
     "\\section{What the trial establishes, and what it does not}"
    ],
    [
     "10844",
     "without",
     "without one word of any human language --- gains empirical support."
    ],
    [
     "10853",
     "not",
     "the protocol was not a blinded human-subject experiment.  The record"
    ],
    [
     "10855",
     "not",
     "reference claims at evidence grade; it is not a theorem of semantic"
    ],
    [
     "10856",
     "no",
     "legibility or of reference, and no clause of this volume's assertion"
    ],
    [
     "10864",
     "Failure",
     "\\chapter{The First Junction Model and Its Failure}"
    ],
    [
     "10885",
     "no",
     "(\\emph{stipulated}), with \\emph{no} neutral element: $(\\Res,\\fuse)$ is a"
    ],
    [
     "10886",
     "not",
     "commutative semigroup, not a monoid --- the Against-Zero signature."
    ],
    [
     "10888",
     "no",
     "$(\\Cost,\\odot,\\preceq)$ of positive magnitudes with no neutral element;"
    ],
    [
     "10889",
     "not",
     "``no cost'' is not a cost element but the non-inscription of a cost mark."
    ],
    [
     "10891",
     "not",
     "Non-inscription $\\eps$ is not an element of any sort; it is the meta-level"
    ],
    [
     "10892",
     "absence",
     "name for the absence of a term. Operations below are \\emph{partial}, and"
    ],
    [
     "10893",
     "no",
     "``the result is $\\eps$'' abbreviates ``the expression has no value and"
    ],
    [
     "10894",
     "no",
     "no element is written.''"
    ],
    [
     "10900",
     "not",
     "$X\\meet Y = Y\\meet X$ whenever either side is defined. This is not"
    ],
    [
     "10910",
     "undefined",
     "undefined (hence $\\eps$) on disjoint-support pairs"
    ],
    [
     "10942",
     "no",
     "where the \\emph{defect} $\\defect(X,Y)$ is either non-inscribed (no mark;"
    ],
    [
     "10959",
     "without",
     "\\item[(b)] \\emph{Tangential}: the supports overlap without coinciding."
    ],
    [
     "10962",
     "not",
     "\\item[(c)] \\emph{Disjoint}: the supports do not meet. The junction is"
    ],
    [
     "10963",
     "undefined",
     "undefined; the expression is $\\eps$ --- blank paper, not a zero object."
    ],
    [
     "10997",
     "no",
     "overlap and the same complements precipitate identical residues, so no"
    ],
    [
     "11020",
     "without",
     "length'': direction without scale, endpoint never inscribed);"
    ],
    [
     "11034",
     "empty",
     "position, non-inscribed when that excess is empty."
    ],
    [
     "11043",
     "empty",
     "disjoint-in-the-cone), with (c) yielding an empty cone-intersection ---"
    ],
    [
     "11044",
     "no",
     "no element to inscribe; (iv) the recoverability biconditional of"
    ],
    [
     "11060",
     "without",
     "may rotate each plane within the overlap without changing either the"
    ],
    [
     "11101",
     "failed",
     "\\section{From the failed model to the typed algebra}"
    ],
    [
     "11147",
     "no",
     "operation; no null residue is returned."
    ],
    [
     "11172",
     "No",
     "No member of \\(\\Sw\\) is an absorber for every defined fusion."
    ],
    [
     "11176",
     "not",
     "from a residue, and conditioning as a residue endomorphism are not"
    ],
    [
     "11199",
     "empty",
     "section is empty; the strict object language receives no empty"
    ],
    [
     "11203",
     "not",
     "\\(c_{+}\\circ c_{+}\\) is not used when its codomain and domain do not"
    ],
    [
     "11241",
     "not",
     "algebra.  It does not interpret the Riemann explicit formula, prove"
    ],
    [
     "11295",
     "not",
     "actions.  They are not asserted to be literal models of every"
    ],
    [
     "11307",
     "not",
     "Chapter~\\ref{ch:strict-grammar}; it does not depend on physically"
    ],
    [
     "11327",
     "no",
     "At four right angles the angular defect is zero, so no strictly"
    ],
    [
     "11328",
     "not",
     "convex positive-curvature vertex forms.  This does not imply that"
    ],
    [
     "11331",
     "not",
     "interpretation of the bound is therefore an interpretation, not part"
    ],
    [
     "11364",
     "no",
     "through every axial plane. Horizontal position, which on the page carried no"
    ],
    [
     "11389",
     "not",
     "the flat notation could not absorb. For $C_{3v}$ and $O(2)$ new classes"
    ],
    [
     "11391",
     "no",
     "($E$, resp.\\ $E_m$ per angular wavenumber), pair-classes with no flat"
    ],
    [
     "11395",
     "not",
     "isotype, chiral pairs spanned the sign isotype. Folding does not remove"
    ],
    [
     "11435",
     "fails",
     "returns the flat page. The fourth right cone fails by blankness, not by"
    ],
    [
     "11472",
     "no",
     "recentering $y = x$ shifted to the parabola's axis (no origin required: the"
    ],
    [
     "11473",
     "not",
     "shift is a change, not a coordinate). The depressed equation reads"
    ],
    [
     "11492",
     "not",
     "the induced action of the resolvent factors through $S_4/V_4\\cong S_3$; the root-stabilizer descent $S_4\\supset S_3$ is the separate one-root picture,"
    ],
    [
     "11500",
     "not",
     "factor $A_{5}$: not cyclic, indeed simple, and isomorphic to the rotation"
    ],
    [
     "11506",
     "not",
     "same wall'' is a structural correspondence, not a proved equivalence: what"
    ],
    [
     "11536",
     "not",
     "not apply."
    ],
    [
     "11541",
     "not",
     "interpretation; it is not a derivation of the cubic formula from the"
    ],
    [
     "11558",
     "not",
     "stabilizer of one root.  It is not the construction of the resolvent"
    ],
    [
     "11573",
     "not",
     "That reading is an interpretation of the classical theorem, not an"
    ],
    [
     "11579",
     "failed",
     "certificate, while the failed distinction is a metalinguistic"
    ],
    [
     "11580",
     "No",
     "nonseparation judgment.  No Blank term is substituted for the"
    ],
    [
     "11615",
     "not",
     "\\cite{cox}.  The obstruction is not the prime five by itself:"
    ],
    [
     "11622",
     "No",
     "No general equivalence between physical folding constructions and"
    ],
    [
     "11638",
     "no",
     "meromorphic on a neighborhood of \\(\\overline\\Omega\\), with no pole on"
    ],
    [
     "11651",
     "not",
     "poles and their multiplicity records; it does not alter the classical"
    ],
    [
     "11657",
     "not",
     "function is not automatically an admissible counting kernel."
    ],
    [
     "11729",
     "negative",
     "The sign depends on the variable.  Statements that assign negative"
    ],
    [
     "11735",
     "no",
     "admitting no global labelled trivialization.  Monodromy obstructs the"
    ],
    [
     "11736",
     "not",
     "latter, not the former."
    ],
    [
     "11744",
     "no",
     "labels, so there is no global continuous enumeration preserving the"
    ],
    [
     "11752",
     "Neither",
     "which a trivialization is presented.  Neither response licenses the"
    ],
    [
     "11791",
     "not",
     "its instances tabulated exactly --- not as a theorem."
    ],
    [
     "11799",
     "without",
     "without an orientation choice is the fixed component of the action:"
    ],
    [
     "11825",
     "no",
     "this volume and is asserted at no greater strength."
    ],
    [
     "11839",
     "never",
     "a single root is never inscribable without exhibited orientation,"
    ],
    [
     "11849",
     "not",
     "The reading is a factorization schema, not a solvability"
    ],
    [
     "11852",
     "no",
     "distinct \\(A_{5}\\) obstruction for the generic quintic; no general"
    ],
    [
     "11855",
     "never",
     "dagger reading survives that boundary because it never crossed it:"
    ],
    [
     "11856",
     "not",
     "what is identified is the pattern of keeping, not any transfer of"
    ],
    [
     "11874",
     "no",
     "\\section{The no-go and the two-circle barrier}"
    ],
    [
     "11884",
     "No",
     "No closed planar chain exists from one circle; the angle chain of any"
    ],
    [
     "11895",
     "not",
     "and the infimum is not attained. \\emph{Proof.} $\\sin$ is strictly concave"
    ],
    [
     "11901",
     "never",
     "$2$ is approached, never reached. \\qed"
    ],
    [
     "11906",
     "no",
     "\\emph{no} unconstrained minimizer: cheap closures degenerate. A minimizer"
    ],
    [
     "11933",
     "negative",
     "carries angle \\emph{excess} (concentrated negative curvature). Closure and"
    ],
    [
     "11934",
     "no",
     "positive-deficit (single-circle) material are incompatible --- the no-go of"
    ],
    [
     "11944",
     "No",
     "($\\alpha_{\\mathrm{off}}\\approx 23.7^\\circ$). No material is wasted: the"
    ],
    [
     "11976",
     "no",
     "$|n|\\ge 1$ have $\\nu_n\\ge\\nu_1=\\sqrt{51}/6\\approx1.19>1$, limit-point, no data"
    ],
    [
     "11986",
     "no",
     "$\\arcsin(1/\\sqrt5)\\approx 26.57^\\circ$ have \\emph{no} apex freedom at all."
    ],
    [
     "12002",
     "absent",
     "chain thus supports a genuinely new observable absent from open chains:"
    ],
    [
     "12066",
     "no",
     "Dirichlet decoupling $U=-I$ is the disjoint case (no junction; balances blank);"
    ],
    [
     "12071",
     "not",
     "the stated items; not a formal equivalence.}"
    ],
    [
     "12087",
     "not",
     "material (Prop.~\\ref{prop:saddle}), the unconstrained minimum does not"
    ],
    [
     "12088",
     "no",
     "exist (Prop.~\\ref{prop:inf}), the symmetric minimizer wastes no element"
    ],
    [
     "12130",
     "not",
     "The presence interpretation does not interpret \\(\\xi\\) as a total"
    ],
    [
     "12131",
     "null",
     "map into a field containing a null value.  It retypes the classical"
    ],
    [
     "12144",
     "no",
     "If the completed evaluation procedure finishes at \\(s\\) but emits no"
    ],
    [
     "12152",
     "not",
     "It is not an element of \\(\\Ctimes\\), a third truth value, or an"
    ],
    [
     "12177",
     "no",
     "\\label{prop:no-tally-identity}"
    ],
    [
     "12190",
     "no",
     "Thus no \\(n\\in T\\) satisfies \\(m\\oplus n=m\\) for every \\(m\\)."
    ],
    [
     "12205",
     "No",
     "Definition~\\ref{def:strict-terms}.  No zero atom occurs, and no"
    ],
    [
     "12210",
     "not",
     "This is a theorem about \\(\\GP\\).  It is not a claim that"
    ],
    [
     "12254",
     "no",
     "symmetric balance relation.  It requires no Blank control and no"
    ],
    [
     "12336",
     "not",
     "Sign-change detection is therefore not a fourth unconditional"
    ],
    [
     "12347",
     "negative",
     "Thus the negative even zeros belong to the uncompleted zeta"
    ],
    [
     "12387",
     "negative",
     "negative-sector observation --- not a record of failed formation."
    ],
    [
     "12399",
     "negative",
     "and the negative-sector counter-witness at \\((D,s)\\) holds exactly"
    ],
    [
     "12430",
     "not",
     "It is not defined as a positivity criterion.  Distinctly, the"
    ],
    [
     "12458",
     "not",
     "\\(\\CounterAdmClass\\) is not thereby a model of the zeta reference"
    ],
    [
     "12497",
     "not",
     "zeta-specific Admission law.  It is not a derivation of that law from"
    ],
    [
     "12498",
     "not",
     "the unextended base theory, and it is not advertised as an unpriced"
    ],
    [
     "12529",
     "not",
     "does not establish them."
    ],
    [
     "12592",
     "not",
     "criterion is a classical theorem used at the interface, not a"
    ],
    [
     "12623",
     "negative",
     "\\(s-\\tfrac12\\) to its negative, so it fixes"
    ],
    [
     "12641",
     "not",
     "whose real part is \\(4/5\\), not \\(1/2\\).  The roots form a complete"
    ],
    [
     "12648",
     "not",
     "information not shared by \\(F\\), such as the prime genealogy,"
    ],
    [
     "12660",
     "fails",
     "symmetry bookkeeping.  The route fails, and the failure is exact:"
    ],
    [
     "12674",
     "not",
     "\\(\\Pbase\\), not PA, ZFC, or another external proof theory."
    ],
    [
     "12693",
     "no",
     "\\item no class-wide Admission axiom."
    ],
    [
     "12821",
     "not",
     "sentences.  The literal classical zero-locus sentence is not in"
    ],
    [
     "12823",
     "not",
     "sentence.  The theorem also does not establish independence of"
    ],
    [
     "12834",
     "not",
     "does not by itself verify:"
    ],
    [
     "12844",
     "No",
     "No script execution is asserted by this TeX source."
    ],
    [
     "12851",
     "negative",
     "Fix a decidable address sort and a decidable negative verifier.  Write"
    ],
    [
     "12892",
     "not",
     "They are not strict object-language numerals and do not install a"
    ],
    [
     "12904",
     "not",
     "The rule does not infer a family from"
    ],
    [
     "12931",
     "no",
     "events.  They contain no rule whose premise is merely"
    ],
    [
     "12934",
     "without",
     "therefore leaves the stagewise statement without a family-forming"
    ],
    [
     "12936",
     "not",
     "not a theorem that no external classical choice principle can be"
    ],
    [
     "12950",
     "not",
     "This is a completion postulate.  It does not provide:"
    ],
    [
     "12966",
     "negative",
     "accepted by the negative verifier; and a kept stage covering that"
    ],
    [
     "12990",
     "not",
     "This is not an analytic proof because the completed-family premise is"
    ],
    [
     "12995",
     "not",
     "The two-model theorem concerns \\(\\AdmClass\\), not"
    ],
    [
     "12997",
     "not",
     "base does not select a side of the class-wide fork."
    ],
    [
     "13013",
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     "not",
     "orbit spans decompose isotypically and need not be irreducible\\\\"
    ],
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     "not",
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     "14633",
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