Filipe Bastos
Architecture of Relational Coherence
« Rien n'est demandé au lecteur sauf de vérifier. Les preuves, pas les paroles. »
The ARC corpus (Architecture of Relational Coherence) rereads mathematics, physics, the living world and the city from a single figure, two circles and a square, and from the constant ½ it imposes; the operation 1 ⊕ 1 = 3 and the cadastre of nine positions follow from it, down to the delfine, the composite of the 6k ± 1 grid read as a descendant and not as a reject. It is published in twelve volumes. Every statement carries its status: Theorem (verified finite computation or proof), Reading (interpretation declared as such), Prediction (falsifiable, with its criterion), Fact, or Open site (open question). The calculations are shown, and the reader is invited to redo them.
Start with Volume 0, The Threshold Go to the essential: Volume 1, The Foundation
Volume 0
Preface, method, statuses, Lexicon and map of the ARC corpus
The entrance to the ARC corpus (Architecture of Relational Coherence). This volume proves almost nothing by itself: it states where the work comes from, how it was done and under which rules. It opens with two texts by…
Volume 1
The Genesis, restored logic and the metaphysics of relation
The essential volume of the ARC corpus. From a single operation, 1 ⊕ 1 = 3 (two terms that meet make three, because the relation counts), it shows how the cadastre of nine positions unfolds without any choice up to the…
Volume 2
Two circles and a square: geometry, the forgotten operations and the convergences of the half
Everything the ARC corpus says about its root figure: two concentric circles with a square between them. The area of the small circle is exactly half that of the large one, the diagonal of the square is the diameter of…
Volume 3
What can be redone in pencil, and what the system exposes in established science
Three parts. The Code: two pages anyone can redo with the 1 to 9 multiplication table, the arithmetic core by pencil, the corpus auditing itself, and twelve worked exercises; each proof is given in four steps (the…
Volume 4
The primes never hidden, numbers in motion, and the numbers that remember
The whole number theory of the ARC corpus in one book. The position of primes on the self-generating 6k ± 1 grid, and the delfine: the corpus's name for a composite of the grid, a descendant rather than a reject,…
Volume 5
Riemann, P versus NP, Navier-Stokes, Yang-Mills: what they lack
What the ARC corpus has written on four Millennium Prize problems: the Riemann hypothesis, P versus NP, Navier-Stokes regularity and the Yang-Mills mass gap. One thesis: in these problems the obstacle is not in the…
Volume 6
The trial, the lineage of zero, the two Eulers, Gauss's drawer and the undecidable why
What the ARC corpus says about proof: what it is, what it forgot, how it was received, who showed their proofs and who kept them in a drawer, and why the question of why never receives an answer. The volume follows the…
Volume 7
Measurement as projection: Tsirelson without Hilbert, the wave, the quantum, the proton and the strings
What the ARC corpus says about physics, in one sentence: measurement is projection. A complete state is read by an instrument that keeps only part of it, and what is called randomness, indeterminacy or collapse is the…
Volume 8
The atomic number as blueprint, sedimented light, and nothing dissipates
What the ARC corpus says about matter, the cosmos and their thermodynamics, from the smallest to the largest. The digits of the atomic number read as the plan of electron shells, the 4-6 trinity and the uniqueness of…
Volume 9
Identity, life, consciousness; evolution reread; death as fiction
What the ARC corpus says about life, from a thesis set out in May 2026: identity, life and consciousness are not three phenomena to be linked by a theory of emergence, but three names of a single operation seen from…
Volume 10
Consciousness, automatism, the unconscious; panic and shame; grief as the loss of hope
Six pieces of the ARC corpus devoted to the mind, gathered into one book. A single operation, differentiation, yields three regimes: completed, it is consciousness; carried forward without being redone, it is…
Volume 11
The relation is the identifier: power, democracy, heritage, confession, the gaze and empathy
What the ARC corpus says about common life and meaning. One thesis runs through the volume: what identifies a being is not a substance it would contain but the position it holds in a fabric of relations; cutting the…