Appendix A. Table of statements

The volume counts 298 numbered statements. The main status is the first indicated; count of main statuses: Open site 4; F 56; L 115; P 17; Th 106. Count of all status mentions (a statement may carry two or three): Open site 5; F 60; L 177; P 17; Th 109.

No.	Statement	Status	Chapter
1.1	Regime I: for Z = 1 to 9, Z equals the total number of electrons (9 out of 9)	Th	1
1.2	Regime II: for Z = 11 to 18, the units digit equals the number of valence electrons (8 out of 8)	Th	1
1.3	The potassium frontier	Th, L	1
1.4	Regime III: for Z = 21 to 28, the tens digit carries the 4s shell and the units digit counts the 3d population (7 out of 8, plus one declared exception)	Th	1
1.5	The copper interface and the family of eight elements of sum 11	Th	1
1.6	Tally: 30 correspondences out of 30	Th	1
1.7	Representation theorem of the mirrors	Th	1
1.8	The anomalies of the table fall on reversed pairs	L, Chantier	1
1.9	Law of the Fold	Th	1
1.10	The chemistry of the fold: configurations answer each other across the axis	Th	1
1.11	Fractal reach of the fold	L	1
1.12	Cantor's alloy occupies a full cadastral window	F	1
1.13	The link between the full window and the single-phase stability of the alloy	L	1
1.14	Silicon and niobium	L	1
2.1	The three numbers of the trinity	Th	2
2.2	Three arrangements, three anomalies	Th	2
2.3	Carbon as elementary instance of the trinity	L	2
2.4	The identities of the 24 / 46 / 64 signature	Th	2
2.5	Karyotype and code occupy the same cadastral address	L	2
2.6	Theorem III.1 (the uniqueness of 24, 4 October 2026)	Th	2
2.7	Corollary III.1 bis (a single group does not close)	Th	2
2.8	The 24 is read from both sides at once	L	2
2.9	Remark III.2: the halves of 46 and 64 are mirrors	Th	2
2.10	The 32 of gadolinium is a half, not an obstacle	L	2
2.11	Theorem III.3 (the one-period mirror)	Th	2
3.1	Chlorophyll a counts 137 atoms	Th	3
3.2	The squares of the first seven digits of π sum to 137	Th	3
3.3	The light sensor carries the constant of light	L	3
3.4	137 − 29 = 108, the interior angle of the regular pentagon	Th	3
3.5	Identities of the pentagon, corrected	Th	3
3.6	Gilson's proposal is an approach to α, not a closure	L	3
3.7	The chlorophyll-haemoglobin interface	Th, L	3
3.8	1/37 carries cobalt	Th, F, L	3
3.9	Molybdenum, mirror of chromium	Th, L	3
3.10	The fundamental figure in three steps, and √2 as operator	Th	3
3.11	The structure (8) produces the form (5) that captures the energy (137)	L	3
3.12	Each node of the circuit of life carries a cadastral constant, and the circuit closes	L	3
4.1	The quanta of the mirror-sum	Th	4
4.2	The scale of the membrane	Th	4
4.3	Theorem of the deterministic descent	Th	4
4.4	The descent of light, from 945 to 3	Th	4
4.5	The descent of the perfect, from 496 to 4	Th	4
4.6	Zero common points, terminals of sum 7	Th	4
4.7	The layer of meanings	L	4
4.8	The switch from 101 to 11: from the wormhole to the interface	L	4
5.1	Refused: stability does not stop when DR(A) crosses 4.5	Th	5
5.2	Refused: the same statement on N − Z	Th	5
5.3	Refused: the magic numbers do not fall on the rails	Th	5
5.4	Refused: capacities and cumulative totals of the shell model	Th	5
5.5	Theorem XII.1 (a): the orbital mirror is ψ(l) = 8 − l, with axis l = 4	Th	5
5.6	Theorem XII.1 (b): the half-integer mirror is φ(k) = 9 − k, with axis k = 4.5	Th	5
5.7	Corollary XII.2 (a): the two mirrors are offset by exactly ½	Th	5
5.8	Corollary XII.2 (b): confinement on the 3-6-9 axis	Th	5
5.9	Corollary XII.2 (c): the two mirrors coincide on the single branch j = l + ½	Th	5
5.10	Corollary XII.2 (d): spin-orbit coupling separates the branches by an odd half	Th	5
5.11	The half-step and the octagon	L	5
5.12	Law of torsion	L	5
5.13	Reach of Theorem XII.1	Th	5
5.14	The sign of the spin-orbit doublet is inverted between the atom and the nucleus	F	5
5.15	The magic numbers beyond 20 are produced by intruders j = l + ½	F	5
5.16	The four intruders are all coincidence states ψ(l) = φ(k)	Th	5
5.17	The complete family of aligned states runs through the cadastre once	Th, L	5
5.18	The relativistic mean field explains the sign by a pair of potentials	F	5
5.19	The core is a pair of echoes, the periphery a term	L	5
5.20	Corroboration by the Λ: the same grammar one floor lower	F, L	5
5.21	Synthesis: a weak quantity is the residue of two active contributions	L	5
5.22	C-XIII.1: derive from the figure why the core is a pair and the periphery a term	Chantier	5
5.23	P-XIII.1 (preregistered 25 August 2026): the spin-orbit splitting of the antiproton bound in ¹⁶O is less than 0.6 MeV	P	5
6.1	P-NA-1 (fixed 10 October 2026, 20:16 Eastern Time, UTC−4, before any reading of the literature on Na-Cr-Co oxides)	P	6
6.2	What is known before the prediction	F	6
6.3	The arithmetic foundation of P-NA-1	Th, L	6
6.4	State of the literature, read after fixing (10 October 2026)	F	6
6.5	P-XII.1 (reformulated with preregistration, Plan v6.4, 25 August 2026): in the Mauna Loa series, the slowing of δ¹³C precedes that of CO₂ by at least twelve months	P	6
7.1	Democritus's programme and its method	F, L	7
7.2	The cut is Agrippa's trilemma in an accelerator	L	7
7.3	Two ontologies: tearing versus unfolding	L	7
7.4	The figure is the whole atom	L	7
7.5	The ratio of the areas is ½	Th	7
7.6	Spin ½ as the projection ratio between the two circles of a single object	L	7
7.7	The complete network of the figure carries three exact signatures	Th	7
7.8	To cut is to sever edges	L	7
7.9	The inner cascade: the inscribed becomes its own circumscribed	Th	7
7.10	Two infinities, two natures	L	7
7.11	The pattern theorem	Th, L	7
7.12	The golden folding height: height over half-base = √Φ	Th	7
7.13	The triple convergence on Khufu	Th, F	7
7.14	The double inscription of the slope 14/11	Th	7
7.15	What is posited, and what is not	L	7
7.16	The three pieces of the figure were in Greek geometry	F	7
7.17	Statics: the square does not stand alone	F, L	7
7.18	Chronology: they had cut before isolating	F, L	7
7.19	Nature holds its crystals by the diagonals	F	7
7.20	The wrong triangle	L	7
7.21	Prediction 1 (physics): every new "fundamental particle" will be an additional fold of the same figure	P	7
7.22	Prediction 2 (history): independent pyramid traditions will inscribe slopes from the family of folding heights	P	7
8.1	The nine digits, the involution and the root	Th	8
8.2	Universal folding, corrected	Th	8
8.3	Full closure	Th	8
8.4	√2 opens, π circulates, Φ stabilises	Th, L	8
8.5	The square inverts, the circle conserves	L	8
8.6	The table of the 5/7 couple	Th	8
8.7	The walls that motion does not build	L	8
8.8	The full, the hollow and the cadastral spin 495	Th	8
8.9	Salt: 11 + 17 = 28	Th, L	8
8.10	The gradient 198 = 2 × 9 × 11 and its contexts	Th	8
8.11	Remark on the 3-6-9	L	8
8.12	Light and iron are born from the same pair	Th, L	8
8.13	The mirror-cost	Th	8
8.14	The iron triad sums to 81	Th	8
8.15	Involution and evolution	L	8
8.16	The ascent replays the genesis	Th, L	8
8.17	The two peaks of the nuclear background	F	8
8.18	The octet of stability 54 → 62	Th, L	8
8.19	The double terminus: 26 + 56 = 82, lead	Th, L	8
8.20	Salt separates light from iron	Th	8
8.21	Matter is sedimented light	L	8
8.22	Two factorisations of spin	Th	8
8.23	The common motionless axis 49.5	Th	8
8.24	Copper links the two axes	Th	8
8.25	The machine separates salt from copper	Th, L	8
8.26	Five constants form a closed circuit of subtractions	Th, L	8
8.27	The two descents	Th	8
8.28	The 1-18 machine and the nineteenth electron	F, L	8
8.29	The copper bridge	Th	8
8.30	Definition of the trinitarian subtraction	L	8
8.31	Every stage of nucleosynthesis is trinitarian	F, L	8
8.32	Lavoisier corrected	L	8
8.33	Validation under high pressure	F, L	8
8.34	The folding of Mendeleev on the interface	Th	8
8.35	The rails of the primes	Th	8
8.36	The synthesis of the sedimentary universe	L	8
8.37	Six falsification criteria of cosmic sedimentation	P	8
9.1	Completeness principle	L	9
9.2	The statement in seven registers	L	9
9.3	The P register as an unfolding trajectory	L	9
9.4	The identities of the register	Th	9
9.5	The cardinal nine as self-reference	L	9
9.6	The double historical amputation	F, L	9
9.7	The cascade operator	L	9
9.8	The table of the six constants, recalculated	Th	9
9.9	Correction: the factor 113 does not exist	Th	9
9.10	The reading of α⁻¹ as the couple (137, 36)	L	9
9.11	Reading-search and constrained derivation	L	9
9.12	The calculations of the neighbourhood test	Th	9
9.13	Withdrawal of the robustness test (Register of Errors, G.14)	L	9
9.14	√2 and √5 as founding operators	L	9
9.15	First register: E = Dc², the active cadastral density	L	9
9.16	Second register: the bridge between π and Φ	Th, L	9
9.17	Third register: Galilean invariance as a corollary of closure	L	9
9.18	The light-space couple (137, 163) and its three regimes	Th, L	9
9.19	Gravity at two scales: a resonance of units, not a derivation	L	9
9.20	Fourth register: the magnetic dipole as corollary	L	9
9.21	Fifth register: the anomalous moment of the muon as a closed ratio	Th, L	9
9.22	Sixth register: the lifetime of the neutron	L	9
9.23	Seventh register: the observed cosmic dipole	L	9
9.24	P1, anomalous moment and signed residues (v1.5 and v1.6)	P	9
9.25	P2, neutron and coupling dependence (v1.5)	P	9
9.26	P3, binding energy beyond iron (v1.5)	P	9
9.27	P4, cosmic dipole and organisation by tracer (v1.5 and v1.6)	P	9
9.28	P5, the ferromagnetic triad (v1.5 and v1.6)	P	9
9.29	P6, gravitational constancy and cosmic history (v1.5)	P	9
9.30	P7, signatures in the decimal tails (v1.5 and v1.6)	P	9
10.1	The perimeter is declared: no operational result is contested	L	10
10.2	The root apparatus	Th	10
10.3	The 9 conjugates with memory	L	10
10.4	Base ten is a window, not a source	Th	10
10.5	The two braided cycles	L	10
10.6	The Meno: the diagonal solves the doubling without a number	F	10
10.7	The roots of perfect squares are in {1, 4, 7, 9}: the 2 is not there	Th	10
10.8	Exact as a relation, infinite as a quantity	Th, L	10
10.9	The Hippasus-Stevin-Copenhagen cascade	F, L	10
10.10	The script does not exist; the code is total	L	10
10.11	Theorem of the structural residue (promoted in v1.2)	Th	10
10.12	Theorem of the non-deducible choice (by definition)	Th	10
10.13	Unpredictability is the projection of the embedded	L	10
10.14	Einstein rehabilitated	F, L	10
10.15	The encounter without a gaze: the first twin pair	Th	10
10.16	The three figures of the encounter and the +1 that completes	Th	10
10.17	The perfect deposit: the cycle of 1/7	Th	10
10.18	A single wheel	L	10
10.19	The positional folding of the four pairs	Th	10
10.20	Information is cooled encounter	L	10
10.21	Two zeros	L	10
10.22	No sequence without an archivist	L	10
10.23	The false zero: insertion at the head	F, L	10
10.24	The survival test of the two zeros	F, L	10
10.25	The calendar has no year zero	F, L	10
10.26	The word was born right	F	10
10.27	Boltzmann and Shannon have the same form	Th, F	10
10.28	The second law is the law of sedimentation	L	10
10.29	Von Neumann's recommendation to Shannon	F	10
10.30	Calibration: the law is inherited, the gloss corrected	L	10
10.31	The code is creative by filtering, not by benevolence	L	10
10.32	Nowhere in the grammar is there an operation of annihilation	Th, L	10
10.33	Calibration: evil is real and sterile	L	10
10.34	The guarantee of non-closure	L	10
10.35	Retrograde legibility: ten trades at zero	L	10
10.36	The living archive is retroactive	L	10
10.37	The closing of an old file reorganises the present measurably	P	10
10.38	Two rules of method	L	10
10.39	Annexation: space ingests, time archives	Th, L	10
10.40	P-CAL-1 (preregistered 7 July 2026, result to be published whatever it is): no generating zero in the living count of independent systems	P	10
11.1	Perimeter	L	11
11.2	Thermodynamics was born in the mine	F	11
11.3	Only one of the two books was inscribed	L	11
11.4	The two books are coupled: no deposit without dissipation	Th, L	11
11.5	Coldness as the cause of the missing book	L	11
11.6	Wright's law (1936)	F, Th	11
11.7	Wright is the register of D kept by the factory	L	11
11.8	Rewarded, not reimbursed (correction of 7 July 2026)	L	11
11.9	Same equation, inverted verdict	L	11
11.10	Signature of convergence	L	11
11.11	Carnot-theorem: holds	Th, F	11
11.12	Carnot-vocabulary: falls	L	11
11.13	Kelvin-jurisdiction: falls	F, L	11
11.14	The only way to exceed Carnot is to deposit	F, L	11
11.15	η is a fraction	Th	11
11.16	The + that overflows belongs to the family of fusion	L	11
11.17	D is what S becomes when the observer and the user are returned to the system	Chantier	11
12.1	There is no dissipation	L	12
12.2	Five pieces in one, on eleven positions	L	12
12.3	Information is physical	F	12
12.4	The two faces of the bit	L	12
12.5	G.27: the twin of information is entropy, and E = TS (31 August 2026)	Th, L	12
12.6	The theorem of the fibres of the sum	Th	12
12.7	The bell curve is the portrait of forgetting	L	12
12.8	The same gesture as the confusion 9 ≡ 0	L	12
12.9	Entropy is relational (correction accepted)	L	12
12.10	No object has heat	F	12
12.11	Heat is the relation without an address; work, the relation with an address	L	12
12.12	To perspire, to expire, to express	L	12
12.13	Life as the holding of the difference	F, L	12
12.14	The word the language knew	L	12
12.15	Prigogine: dissipation makes structure	F	12
12.16	The lost heat of one is the inscription of the other	L	12
12.17	G.28: expressed order returns enriched (31 August 2026)	L	12
12.18	The same logic on eleven positions (Reading of method, that of the whole corpus)	L	12
12.19	No signal travels faster than light	F	12
12.20	The information that supports light has no speed	L	12
13.1	Fire is the only object that leaves no remains	F, L	13
13.2	The structural opposite of fire is air, not water	L	13
13.3	Fire creates neither light nor heat: it releases them	L	13
13.4	Combustion and digestion are the same operation	L	13
13.5	The operative trinity, by reference	Th	13
13.6	Combustion performs exactly the trinitarian subtraction	L	13
13.7	The three states	L	13
13.8	For comparable cage structures, the combustion energy per broken bond is approximately constant, and its deviations read as differences of folding	P	13
14.1	The acceleration of time is a relation between two cycles	F, L	14
14.2	Lived time is the count of inscriptions	F, L	14
14.3	Law of accessibility: lived duration is proportional to the path that must be travelled to reach the information	L	14
14.4	The counterweight, heart of the law: accessibility compresses acquisition, not inscription	L	14
14.5	Love, state of least tension, is the only variable that reverses the charge	L	14
14.6	Passion is short to live and long in memory; boredom, the reverse	F, L	14
14.7	The exception is not granted, it is maintained	L	14
14.8	Each age bears the name of what it lacks and dies of the abundance of what it pursues	L	14
14.9	Artificial intelligence is the summit of the information age	L	14
14.10	The why was an information to be delivered	L	14
14.11	Socrates aimed at the wrong target	F, L	14
14.12	Scarcity migrates towards what does not deliver itself	L	14
14.13	The scarce good is the receipt	L	14
14.14	Information will no longer progress, it will densify	F, L	14
14.15	Isolated information costs	F, L	14
14.16	The more one accesses, the less one inscribes, the more one searches	L	14
14.17	A single mechanism: the speed of arrival exceeding the speed of processing	L	14
14.18	Fall clause to be formulated and dated	Chantier	14
14.19	The closing figure: the position that has no place	Th, L	14
14.20	Speed prevents walking: two regimes, not two degrees (Definitional lecture)	L	14
14.21	The relation is the first scarcity that does not deliver itself	L	14
15.1	Base pairing is an involution without a fixed point	F, Th	15
15.2	Pairing is the local manifestation of φ	L	15
15.3	Purines and pyrimidines: the signature (2, 1)	F, L	15
15.4	Two and three hydrogen bonds: the signature (2, 3)	F, L	15
15.5	The four bases as mirror of the four inversion pairs	L	15
15.6	64 = 4³ = 8²	Th	15
15.7	The derivation by the eight alignments of the 3 × 3 grid is not verifiable as it stands	L	15
15.8	The redundancy of the standard code, verified	F, Th	15
15.9	The multiplicities inscribe the cadastral positions	L	15
15.10	Twenty amino acids and the 19 + 1 signature	Th, L	15
15.11	The mechanism 4-5 → 9 → +1 gives 46 and 64	Th	15
15.12	The +1 is the passage from cycle to cycle	L	15
15.13	The Krebs cycle in eight steps	F, L	15
15.14	The carriers as inverse pairs	F, L	15
15.15	Glycolysis in ten steps and photosynthesis	F, L	15
15.16	DNA methylation as envelope inscription	F, L	15
15.17	The histone code and the signature 8	F, L	15
15.18	Non-coding RNAs	F, L	15
15.19	Mitosis is the identity involution	F, L	15
15.20	Meiosis applies k_arc to the karyotype	Th, L	15
15.21	Crossing-over	F, L	15
15.22	Consciousness = capacity of a system to operate its own cadastre	L	15
15.23	The three levels of the brain	F, L	15
15.24	Altered states as deregulations	L	15
15.25	Convergence with integrated information theory	Chantier	15
15.26	Apoptosis is involutive at the tissue level	F, L	15
15.27	Senescence as slow sedimentation	F, L	15
15.28	Telomeres: the reading of the absent cytosine is fragile	L	15
15.29	Four falsifiable protocols, to be quantified	P	15
15.30	Biology without reductionism	L	15
17.1	The 8-9-1 triplets	Th	17
17.2	The four ferromagnetics	F	17
17.3	The magic numbers of protons	F	17
17.4	The closed electron shells	F	17
17.5	The mirror keeps the place	Th	17
17.6	The two mirror anomalies	L	17
17.7	Why the motif repeats, and where it stops	Th	17
17.8	The 198 marks the places of closure and cohesion in the table	L	17
17.9	The sum of each triplet is 27 × k	Th	17
17.10	Three sums that speak the 198	Th, L	17
17.11	Copper closes the shell, zinc closes everything	F	17
17.12	The interface: 110	Th	17
17.13	The 29 touches the interface, the 30 releases the 3	L	17
17.14	The line is alive	F	17
17.15	Adding 29 to each sum	Th	17
17.16	Iron, the limit of stability, the interface, light	F, L	17
17.17	The two elements that follow each triplet	Th	17
17.18	What the interface and the release carry	F, L	17

Chapter 16. Where the rule goes wrong: the twenty exceptions of the periodic table (piece entered word for word). The statuses are those the piece itself carries, section by section; no statement has been renumbered.