Compiled Companion Papers (17-22)¶

Jean-Paul Niko · Compiled Feb 2026

Six papers compiled with LaTeX, ~114 additional pages beyond the 14 discipline-specific companions.

#	Title	Pages	Refs	Status
17	Self-Foundation: Aczel's AFA as Axiom 0	13	5	Compiled
18	Yang-Mills Mass Gap from Spectral Geometry of \((S^2)^\infty\)	20	22	Compiled · needs arXiv endorsement
19	Gravity from RTSG (GRF 2026 essay)	10	14	Ready · deadline March 31
20	Gravity from Sheaf Gluing	—	—	Compiled · companion to #19
21	Riemann Hypothesis as Spectral Gap on \((S^2)^\mathbb{P}\)	18	13	Compiled
22	Complexity as Sheaf: Grothendieck Topology and Cohomological Consciousness	20	12	Compiled

Key Results by Paper¶

#17 (Axiom 0): Source space equation (Thm 4.1), three-space self-reference (Thm 4.2), exact self-model via bisimulation (Thm 4.3).

#18 (Yang-Mills): Mass gap from spectral gap \(\Delta=2\) on \(S^2\); CFN = three-space decomposition; confinement from compactness.

#19 (GRF): Equivalence principle from trivial stalk; Einstein-Hilbert from Chamseddine-Connes at \(\Lambda^2\) order.

#21 (Riemann): Arithmetic source space \((S^2)^\mathbb{P}\); functional equation as \(S^2\)-involution; spectral gap \(\approx 0.961\); RH conditional on self-adjointness.

#22 (Complexity Sheaf): Formal sheaf \(C\) over PS with 9 axioms; Grothendieck topology on substrate category; qualia as \(H^1\); emergence as positive curvature.

Cross-References Between Papers¶

Claim	Sources	Tier
CFN decomposition = three-space	Yang-Mills + master	B
Spectral gap \(\Delta=2\) \(\to\) mass gap \(\to\) confinement	Yang-Mills + master	B
Spectral action \(\to\) Einstein-Hilbert	GRF + master	B
Trivial stalk \(\to\) equivalence principle	GRF + Gravity-Gluing	B
Arithmetic Laplacian \(\to\) RH	Riemann + master	C
Sheaf \(C\) defines \(C_S\) formally	Complexity Sheaf + master	B
\(\sigma=1\) \(\to\) exact bisimulation	Axiom 0 + master	B