Paper 2 — The Informational Identity Boundary: Algebraic Foundations and Physical Conjectures

Based on the algebraic threshold between octonions (A₃) and sedenions (A₄) — where the Born Rule, multiplicative norm, alternativity, and zero-divisor freeness are simultaneously lost — we develop the Informational Identity Boundary (IIB) programme in four conjectures.

IIB-I (Conjecture). The transition A₃ → A₄ is the unique point in the Cayley–Dickson hierarchy at which standard quantum-probabilistic structure cannot be maintained. The algebras ℝ, ℂ, ℍ, 𝕆 are exactly those admitting a canonical Born-rule probability assignment.

IIB-II (Conjecture). The quadratic norm N — the unique structure preserved by every doubling step — is the algebraic correlate of gravity. Gauge forces are level-specific; gravity is level-universal.

IIB-III (Conjecture). Degrees of freedom in A₄ \ A₃ are gauge-invisible (Born Rule failure) and gravitationally active (universality of N), constituting a dark sector whose darkness is algebraic rather than dynamical.

IIB-IV (Speculation). Within Penrose's Conformal Cyclic Cosmology, Hawking evaporation leaves a structured sedenionic residue that crosses the conformal boundary and constitutes the dark matter of the succeeding aeon. Structural prediction: successive aeons have monotonically decreasing dark-matter fractions.

This version incorporates results from the full four-paper series: the orbit classification {2, 14, 84, 336} via S(z) ⊆ PG(2,𝔽₂), the Fano filtration ZD(n) = ℱ₄ ⊔ ··· ⊔ ℱₙ and its physical reading as the aeon tower, and the GL(3,𝔽₂)-equivariant Fano bijection. Experimental verification of the GHZ–Mermin contextuality witness and the Steane [[7,1,3]] stabilizer structure on IBM Quantum hardware (ibm_kingston, ibm_marrakesh, May 2026) is documented. All algebraic results are cited from the companion papers. Every physical statement is labelled [Theorem], [Conjecture], or [Speculation] throughout. No physical claim follows from the algebra without explicit statement of the additional physical assumptions required.