Appendix A. Table of statements

249 statements: 72 Th, 43 F, 123 L, 6 P, 5 Open site.

No.	Statement	Status	Chapter
1.1	Thesis of the volume: the obstacle manufactured by language	L	1
1.2	Closure principle	L	1
1.3	Limit principle	F	1
1.4	Status principle	L	1
1.5	Name principle	L	1
1.6	Rank principle	L	1
1.7	Definition of the limit (Cauchy, 1821; Weierstrass)	F	1
1.8	Definition of the mixing of the finite and the infinite	L	1
1.9	Definition of the three marks	L	1
1.10	The address: n = 9k + DR(n)	Th	1
1.11	A single gesture under three faces	L	1
1.12	Main result of the transversal piece	L	1
2.1	Alogos, arrhetos, ratio	F	2
2.2	A ratio without ratio	L	2
2.3	Archimedes, Lambert, Lindemann	F	2
2.4	No common unit for the circumference and the diameter	Th	2
2.5	The word “ratio” denotes two objects (M1)	L	2
2.6	Every finite decimal writing of π is a ratio of integers	Th	2
2.7	The continued fraction of π and its convergents	Th	2
2.8	The “perfectly defined” number is a limit (M2)	L	2
2.9	The infinite is born between the circle and the line (M3)	L	2
2.10	Dalzell (1944): 22/7 − π is an area	Th	2
2.11	The gap bracketed without a decimal	Th	2
2.12	Lucas (2005): the next convergent has the same form	Th	2
2.13	The pair around the centre	Th	2
2.14	The gap between the count and the circumference is a finite area	L	2
2.15	“Ratio” cannot keep the same meaning from one sentence to the next	Th	2
2.16	π is a relation, not a position	L	2
2.17	Reading of π by the three marks	L	2
2.18	Author's thesis: the source of the mixing	L	2
2.19	The end as nothing, and the two zeros	L	2
2.20	What would refute the reading of π	L	2
3.1	Riemann's statement and its region	F	3
3.2	Euler (1737): no zero beyond 1	Th	3
3.3	The Dirichlet series diverges at every non-trivial zero	Th	3
3.4	No closure zero for a product of non-zero factors	Th	3
3.5	ζ in the strip is the limit of the gap between the sum and the area	Th	3
3.6	Impossibility theorem	Th	3
3.7	Abel's formula defines ζ in the strip	Th	3
3.8	The four gates: each advances on one side and withdraws on the other	Th	3
3.9	Hermite's formula, closed form of gate (i)	Th	3
3.10	Corollary of the zero	Th	3
3.11	The dilemma	Th	3
3.12	The explicit formula (Riemann, 1859; von Mangoldt, 1895)	F	3
3.13	Reading of ζ by the three marks	L	3
3.14	The difficulty lies in the transfer of status	L	3
3.15	The Mertens function and the Riemann hypothesis	F	3
3.16	The two counts and their gap	Th	3
3.17	The couple (A, B) is the complete object	L	3
3.18	The corpus's arithmetic target for Riemann	Chantier	3
3.19	What would refute the impossibility theorem and the dilemma	L	3
3.20	What would refute the reading of the gates	L	3
3.21	What would weaken the reading of the two counts	L	3
4.1	The gap from a position to its inverse vanishes only at 4.5	Th	4
4.2	A zero is not a position	L	4
4.3	The butter	L	4
4.4	The zeros of the strip are exactly the zeros of η	Th	4
4.5	The money for the butter: the folding and the accounting subtraction	L	4
4.6	The farmer's wife	L	4
4.7	The contradiction fits in a single function	L	4
4.8	The completed function is real on the line ½	Th	4
4.9	The fourth term: “no orbit of four”	L	4
4.10	Davenport and Heilbronn (1936): symmetry alone does not hold the zeros at the centre	F	4
4.11	The counter-test of the fable	L	4
4.12	The seal and the void under one sign	L	4
4.13	It is not the formula that is at issue, it is the gate	L	4
4.14	Lagarias's criterion (2002)	F	4
4.15	The inequality holds from 2 to 100 000	Th	4
4.16	A law of relation written without infinity	L	4
4.17	If the hypothesis can never be decided, it is true	Th	4
4.18	The author's “never” implies the “true”	L	4
4.19	Riemann, pupil of Gauss	F	4
4.20	The 1859 memoir starts from Euler	F	4
4.21	The second proof of the symmetry is made of squares	F	4
4.22	Jacobi's relation and Riemann's gate check out	Th	4
4.23	Doubling and squaring coincide only at 4; the square does not distinguish the inverse	Th	4
4.24	Riemann saw the exchange; he did not see the void	L	4
4.25	The pupil of the Euler who counts would have sealed it	L	4
4.26	The fable in full	L	4
4.27	OpenAI's manuscript on Riemann (made public on 6 October 2026)	F	4
4.28	The manuscript itself writes the three pieces of the paradox	F	4
4.29	With squares and the bell, one brings walls closer	L	4
5.1	Euler's product (1737)	F	5
5.2	Unique factorisation, proved in Gauss	F	5
5.3	Each factor counts the uses of a prime; each integer comes out once	Th	5
5.4	The number of uses of a prime is its number of turns	L	5
5.5	Euler's product is the inverse gesture of the folding of 1801	L	5
5.6	The queue and the relation are the same object	L	5
5.7	Removing the factor of 3 is removing the axis; the two rails remain	Th	5
5.8	The factors 2 and 3 removed together leave the 6k ± 1 grid	Th	5
5.9	The composites of the grid are four families	Th	5
5.10	Euler's product is the grid written in multiplication	L	5
5.11	A sieve that crosses nothing out	L	5
5.12	The cadastre cuts ζ into nine Hurwitz rails	Th	5
5.13	The product is the closure; a single rail is a cut pair	L	5
5.14	ζ has no real zero between 0 and 1	Th	5
5.15	The ARC form of the Riemann hypothesis	L	5
5.16	The bricks 2 and 3 generate everything from 1 to 30, except 1 and 4	Th	5
5.17	An orbit of four would be a folded brick, not a relation	L	5
5.18	The fourth term has a place only in the continuum	L	5
5.19	Closed in the language of the corpus, open in that of the host	L	5
6.1	π and the zeros of ζ both bear the marks M1 and M2	Th	6
6.2	The third mark, and a single gesture	L	6
6.3	A single word covers what is counted and what is traversed	L	6
6.4	Author's thesis: if the two extremes bear the mixing, the whole in-between bears it	L	6
6.5	Huygens measures motion without the limit	F	6
6.6	The gesture is not necessary, and it is dated	L	6
6.7	One hundred and fifty entries, a single view from one hundred and fifty angles	L	6
6.8	The address closes without a limit	L	6
6.9	The map can be refuted line by line	L	6
6.10	Main result: one same error, proved at both extremes and dated in the in-between	L	6
7.1	The frontier has an address: two against three	F	7
7.2	The double and the square coincide only at n = 2	Th	7
7.3	No two-term object; the third pays	L	7
7.4	The pre-image of the AND gate is not a class (March 2026, kept)	Th	7
7.5	Irreducibility of 3 in (ℤ/2ℤ)ⁿ (March 2026, kept)	Th	7
7.6	Definition: the amorphous pre-image	L	7
7.7	An amorphous pre-image does not imply a hard search	Th	7
7.8	Razborov and Smolensky (1987): counting by 3 escapes circuits that count by 2	F	7
7.9	Each separation was paid for by a third	F	7
7.10	Schaefer's dichotomy (1978)	F	7
7.11	Schaefer read as the frontier between structure and amorphism (March 2026, kept as a Reading)	L	7
7.12	Reservation: the frontier is not arity alone	F	7
7.13	The third that costs	L	7
7.14	Fitting 3 into 2 demands a third paid from outside	L	7
7.15	The lemma of the partition into powers of 2	Th	7
7.16	Affine characterisation	Th	7
7.17	Undoing is not inverting (Bennett)	L	7
7.18	Boolean poverty	Th	7
7.19	Cadastral richness	Th	7
7.20	The simulation gap (downgraded)	L	7
7.21	The cadastral hierarchy of compressions	L	7
7.22	The sedimentation of consecutive products	Th	7
7.23	Multiplication by neighbours is a sedimentation	L	7
7.24	The chessboard principle: determinism creates freedom	L	7
7.25	The parallel with Yang-Mills (March 2026)	L	7
7.26	C-1: lifting Smolensky beyond bounded depth	Chantier	7
7.27	C-2: Schaefer's frontier read from the orphans	Chantier	7
7.28	P-1 (10 September 2026): the separations of the decade will go through a third	P	7
7.29	P-2 (10 September 2026): if the bare problem is solved, it will be P ≠ NP	P	7
8.1	The AND gate on n bits	Th	8
8.2	The natural proofs wall (Razborov and Rudich, 1997)	F	8
8.3	The wall's hypothesis already contains the separation	Th	8
8.4	The bits of the fold are the writing of the count of turns	Th	8
8.5	Pseudo-randomness is a determined sequence whose count one does not have (M3)	L	8
8.6	Information, register and reconstruction	Chantier	8
8.7	Shannon's count (1949) and the explicit bound (2022)	F	8
8.8	The method that founded the field is the one that prevents it from concluding	L	8
8.9	The count of three bits: the carry and the digit	Th	8
8.10	Schaefer's closures, and their extension	F	8
8.11	The count of two bits	Th	8
8.12	All of Schaefer's closures are digits of one count	L	8
8.13	The census of relations without poles	Th	8
8.14	Frontier theorem	Th	8
8.15	Three does not fit into two because 3 = 2 · 1 + 1	L	8
8.16	The count says how many, not who	Th	8
8.17	1-in-3 SAT is NP-complete	F	8
8.18	The difficulty lies entirely in the address	L	8
8.19	Resolution width	F	8
8.20	Width is the count of carries held together	L	8
8.21	Lifting width out of the resolution model	Chantier	8
8.22	Pairs and trios (König, 1931; Karp, 1972)	F	8
8.23	Three trios: the integrality gap, and its closing by a sacrifice	Th	8
8.24	Odd rings	Th	8
8.25	The NP certificate is the address of who pays	L	8
8.26	Author's thesis: the price is dual	L	8
8.27	The chessboard is the only square whose edge is the number of its links	Th	8
8.28	The frame is the addressed price	L	8
8.29	The language assumes what it seeks, then forbids itself to read it	L	8
8.30	What would refute the statements of this chapter	L	8
9.1	The equations and the prize statement	F	9
9.2	The stretching term: present in three dimensions, absent in two	F	9
9.3	The proof of 8 September 2026	F	9
9.4	What remains open: the free fluid	F	9
9.5	The stretching term is physical	L	9
9.6	The stretching term is bounded by no universal constant	L	9
9.7	Tao (2016) and the 2026 proof point the same way	L	9
9.8	The Sobolev gap of ½	Th	9
9.9	The circularity of the bootstrap in three dimensions	L	9
9.10	Ninety years of results	F	9
9.11	The missing half does not forbid the breaking, it houses it	L	9
9.12	The Navier-Stokes scaling law: t ↦ λ²t	Th	9
9.13	The heat kernel follows the same law	Th	9
9.14	In the fluid, time is worth two lengths	L	9
9.15	The pivot theorem: closure requires p = 4.5	Th	9
9.16	The universal fold in multiplication tables	Th	9
9.17	The constant ½ does not depend on the base; the choice of 10 is not a convention	L	9
9.18	The seven convergences towards ½, and the projection formulas	L	9
9.19	The fluid does not violate Navier-Stokes; it fulfils it	L	9
9.20	Respecting the structure is the path to the breaking	L	9
9.21	The singularity proved is that of the forcing	L	9
9.22	P-NS-1 (27 September 2026): the free fluid slides	P	9
9.23	The slope of the spectrum near dissipation: k^{−(ln 2 + 2)} ≈ k^{−2.693}	P	9
9.24	The experimental context, as the source reports it	F	9
9.25	Kolmogorov and the projection are complementary	L	9
9.26	The laminar-turbulent transition as a discrete event	L	9
9.27	The objection of open orbits	L	9
9.28	The boundary layer	L	9
9.29	The March epistemological note, held as a quotation	L	9
10.1	The prize statement (Jaffe and Witten, 2000)	F	10
10.2	Scope declaration: the corpus does not construct the theory in Wightman's sense	L	10
10.3	Wick rotation and reconstruction	F	10
10.4	Under t = iτ, the difference becomes a sum	Th	10
10.5	The word “dimension” denotes two objects (M1)	L	10
10.6	Author's thesis: dimensions are not lived	L	10
10.7	Inversion pairs and projection pairs	L	10
10.8	The four exact relations of 3 and 8	Th	10
10.9	The inscribed circle and the circumscribed circle	L	10
10.10	Non-closure theorem for SU(n)	Th	10
10.11	Reading: the mass gap is the cost of non-closure	L	10
10.12	SO(n) and Sp(n): the sum equals 9 exactly when DR(n) = 8	Th	10
10.13	SO(8) and triality	F	10
10.14	SO(8) on the lattice	P	10
10.15	The five exceptional groups do not reach 9	Th	10
10.16	E₈ × E₈ and the perfect number	L	10
10.17	The arithmetic classification into three regimes	Th	10
10.18	Tripartite reading: deficit, closure, excess	L	10
10.19	The case of U(1)	L	10
10.20	The cadastral closure of the Standard Model	Th	10
10.21	The uniqueness test: eleven triples out of eighty-four	Th	10
10.22	The Standard Model as a minimal system	L	10
10.23	The number of Higgs components equals the deficit of SU(2)	Th	10
10.24	The Higgs as sedimentation of the deficit	L	10
10.25	The gluon is the 8 deprived of its 1	L	10
10.26	Asymptotic freedom (Gross, Wilczek, Politzer, 1973)	F	10
10.27	A single tension read at four distances from the centre	L	10
10.28	Level 1 and level 2	L	10
10.29	Confinement and NP-hardness share a root	L	10
10.30	All the known difficulty lies in the construction, not in the gap	L	10
10.31	The fall criteria of the gap reading	P	10
10.32	What would refute the arithmetic and the reading of time	L	10
11.1	The refutation criterion (Popper, 1934)	F	11
11.2	The corpus took this criterion for itself	F	11
11.3	The bottomless swamp	F	11
11.4	Popper kept the fall and threw away the getting up	L	11
11.5	If the count could fall, refutation would fall with it	L	11
11.6	Three complete counts	Th	11
11.7	The closed domain is obtained when the structure closes	L	11
11.8	In a finite domain, crossings are forced	Th	11
11.9	Two exact paths meet without knowing each other	Th	11
11.10	The crossing is written in the code	L	11
11.11	Error has two directions, which form an inverse pair	L	11
11.12	Part II of the Register and the corollary of R11	F	11
11.13	The statuses of the corpus separate the two domains	L	11
11.14	A count that cannot fall is not a dogma	L	11
11.15	Goldbach verified up to 4 × 10¹⁸	F	11
11.16	Goldbach and Collatz remain Chantiers	L	11
11.17	The register of what remains open after this volume	L	11
11.18	The fall is legible only against what does not fall	L	11

Chapter 12. Three void questions: Riemann, Collatz, Goldbach (piece entered word for word). The statuses are those the piece itself carries, section by section; no statement has been renumbered.