Postulates P1–P5

The postulates are the five axioms on which the Broken-Born program builds its results. Physics lives on phase space, the space of positions and momenta together (P1); of its structures only the symplectic form, which encodes the constancy of Planck’s constant, is fixed in advance (P2′); the laws are unchanged by the quarter-turn that exchanges position and momentum (P3); ordinary matter is organized around position and conjugate matter around momentum, with only gravity acting between them (P4); and the vacuum selects one of the two organizations (P5). The first version of the second axiom fixed one structure too many, and the program’s geometry showed that this reduced it to general relativity plus one model of self-interacting dark matter; the corrected axiom, P2′, replaced it. Since checkpoint v2.2 the toy models qualify P2′ and P5: the polarization is a continuous angle, and fixing it needs an added potential.

Stands: P1, the nontriviality theorem, P2′, P3, P4, P5 · Superseded: the original P2; P1’s v0.1 form, with η · Died: nothing yet · Open: no page of its own here; folded sections on the extra structure P2′ needs, why position rather than momentum and what a derived selection still lacks; P4’s open end, forced locality and the P4 lock, is an Open page under spontaneous breaking of reciprocity

Map#

Checkpoint #11 states the postulates in §4 and records in §5 why the second one changed. Every page here is the program’s own: the five postulates are tagged [P], the nontriviality theorem is [D], and the strict reading of P4 is in force by decision rather than derivation. The structures they name are established mathematics, defined in Born geometry. The pages run in #11’s order, with the original P2 and the theorem that removed it placed just before P2′.

  • P1: the phase-space arena comes first because every other postulate refers to its structures: phase space with a symplectic form ω and a positive generalized metric H. The page explains both, the complex structure I = ω⁻¹H built from them, and what H can be with η fixed or free. It keeps the lab notebook’s v0.1 arena, which also listed the neutral metric η, as a superseded section.
  • Original P2: both structures rigid (superseded) is the lab notebook’s first rigidity axiom, which fixed both ω and η. The page records its “triple duty”, the compatibility theorem that froze H into diag(g, g⁻¹), the reduced theory it left (“Branch R”: general relativity plus one bespoke self-interacting dark-matter model), and the fate of each duty: one reversed, one surviving from ω alone, one open.
  • The nontriviality theorem is the argument that rejected it, set out step by step: with η fixed, the Maslov circle and the dark-energy field τ are gone (on the source’s word “discrete” for the remaining polarizations, see flag 1 in review/wiki-build-flags.md), and the geometric action depends on the spacetime metric alone; with η emergent, all of these return. It is a structural argument [D] on top of a machine-checked literature result.
  • P2′: only the symplectic form is rigid is the corrected axiom: ω rigid as the constancy of ℏ, and η = HJ chosen by the vacuum as the order parameter. The page covers the space of vacua Λ(d), the metastring precedent, and the v2.2 refinement from the toy models: a Goldstone angle [D][V], a ρ-preserving potential that adds “a rigid, unordered pair of axes”, and the twisted element that makes the breaking physical only through matter.
  • P3: a reciprocity-invariant action is the symmetry axiom. It explains why the program needs a symmetry of an action rather than the change of description that ρ is in ordinary quantum mechanics, how the referees turned that into acceptance criterion 1, how the coset toy model meets it, and where the program uses the symmetry.
  • P4: polarized matter and strict sector separation places ordinary matter and conjugate matter in opposite polarizations with gravity in common. The page traces the strict reading of v2.1 (no kinetic mixing beyond what gravity induces, ε ≲ 10⁻¹³) through the review record to round-3 Decision 1, flags the unresolved reading of that bound, and shows P4’s second role in the toy models as the lock that ties matter’s locality to the vacuum.
  • P5: the vacuum selects a polarization closes the list with the breaking: ours is the x-tilted vacuum, organized around position, and the mirror vacuum is equally lawful. The page gives the Freidel–Leigh–Minic credit, the toy models’ finding that the choice is an angle that orders in 1+1 dimensions only with a potential (the frozen-H Monte Carlo), and the one-loop lead on why position rather than momentum.

Boundaries#