Sources & Citations

Where the outside literature comes in.

SFT is built mostly from first-principles derivation, but it doesn't work in a vacuum — every postulate that leans on an established mathematical or physical result names that result here, and every claim the theory tests itself against a piece of outside literature (a no-go theorem, a counter-example, an observational bound) is sourced as well.

This page was compiled directly from the addenda archive: every external source cited anywhere in the theory's working record, standardized into one list. Where an addendum names a source informally, the full citation is given here; nothing on this page adds a claim the addenda don't already make.

Algebra & geometry — octonions, Clifford algebras, division algebras
  1. [1]

    J.F. Adams, "Vector Fields on Spheres," Annals of Mathematics 75(3), 603–632 (1962).

    The Hurwitz–Radon bound on anticommuting generators, completed by Adams — grounds Postulate 6's dimensional-floor argument.

  2. [2]

    J. Baez, "The Octonions," Bulletin of the American Mathematical Society 39, 145–205 (2002).

    Standard reference for Aut(𝕆) as the compact real form of G₂, used throughout Postulates 1, 7 and 8.

  3. [3]

    J.H. Conway & D.A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry (A K Peters, 2003), building on H.S.M. Coxeter's 1946 construction of the integral octonions.

    Source for the canonical maximal order in the octonions (Addendum FQ, Postulate 1's discretization thread).

  4. [4]

    J. Gallier & C. Kassel, "Clifford Algebras, Clifford Groups, and a Generalization of the Quaternions," arXiv:0805.0311.

    Explicit low-rank Clifford algebra table, cross-checked against the general mod-8 classification (Postulate 5, Postulate 8).

  5. [5]

    M. Fecko & D. Husemoller, general mod-8 periodicity table for real Clifford algebras, arXiv:1209.5665.

    Cross-check for Addendum AZ.9's Clifford-algebra table (Postulate 5/8 signature derivation).

Stability & network structure — Postulate 4
  1. [6]

    R.M. May, "Will a large complex system be stable?" Nature 238, 413–414 (1972).

    The stability criterion, combined with random matrix theory, that forces sparsity and bounded degree on the coupling structure — Postulate 4's entire foundation.

  2. [7]

    J. Cheeger, "A lower bound for the smallest eigenvalue of the Laplacian," in Problems in Analysis (Princeton University Press, 1970).

    Cheeger's inequality, used to establish that H.17's generic branch cannot support real-space coarse-graining (Addendum DU).

  3. [8]

    J. Friedman, "A proof of Alon's second eigenvalue conjecture and related problems," Memoirs of the American Mathematical Society 195 (2008).

    Spectral-gap result for random regular graphs, paired with Cheeger's inequality in the same argument.

Discrete geometry & growth — the H.17 adjacency-before-geometry thread
  1. [9]

    J. Milnor, "A note on curvature and fundamental group," Journal of Differential Geometry 2, 1–7 (1968); A.S. Švarc, 1955.

    The Milnor–Švarc lemma — lattices are quasi-isometric to their ambient Lie group — closing off non-compact split-octonion routes (Addendum AN).

  2. [10]

    M. Gromov, "Groups of polynomial growth and expanding maps," Publications Mathématiques de l'IHÉS 53, 53–78 (1981).

    Polynomial growth ⇔ virtually nilpotent — the theorem that ultimately points the H.17 thread toward nilpotent-group constructions.

  3. [11]

    D. Kleitman & B. Rothschild, "Asymptotic enumeration of partial orders on a finite set," Transactions of the AMS 205, 205–220 (1975).

    The counting result behind why most causal sets are not manifold-like — cited when checking whether causal set theory's manifoldlikeness problem bears on H.17 (Addendum GV).

  4. [12]

    B. Bollobás & W. Fernández de la Vega, "The diameter of random regular graphs," Combinatorica 2, 125–134 (1982).

    Classical random-regular-graph diameter result underlying H.17's log-diameter default.

  5. [13]

    G. Bianconi & C. Rahmede, "Network geometry with flavor: From complexity to quantum geometry," Phys. Rev. E 93, 032315 (2016), arXiv:1511.04739.

    Dimension-parametrized gluing construction generalized in Addendum DT.

  6. [14]

    A. Kaplan & M. Subils, "Parabolic nilradicals of Heisenberg type," arXiv:1608.02663 (2016); "Parabolic nilradicals of Heisenberg type, II," arXiv:1708.08981 (2017).

    The classification theorem Addendum HQ applies — every Heisenberg-type parabolic nilradical of a simple Lie algebra reduces to two families indexed by ℝ, ℂ, ℍ, 𝕆 — closing GR.24's algebraic exhaustiveness question.

  7. [15]

    C.A. Trugenberger, "Combinatorial Quantum Gravity: Geometry from Random Bits," JHEP 09, 045 (2017), arXiv:1610.05934; C. Kelly, C.A. Trugenberger & F. Biancalana, "Self-assembly of geometric space from random graphs," Classical and Quantum Gravity 36, 125012 (2019).

    The combinatorial-quantum-gravity model mapped onto SFT's own dynamics at Addenda K–N and reconnected at Addenda EH–EL.

  8. [16]

    L. Bombelli, J. Henson & R. Sorkin, "Discreteness without symmetry breaking: a theorem," Modern Physics Letters A 24, 2579–2587 (2009).

    No-go theorem for discrete Lorentz invariance, checked against H.17's own fork in Addendum GV.

Random walks & heat kernels on nilpotent groups
  1. [17]

    B. Gaveau, "Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents," Acta Mathematica 139, 95–153 (1977).

    Heat-kernel formula for the Heisenberg group, tested as a Q=4 discriminator candidate (Addendum HO).

  2. [18]

    A. Hulanicki, "The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group," Studia Mathematica 56, 165–173 (1976).

    Companion result to Gaveau (1977) for the same heat-kernel formula.

  3. [19]

    N. Varopoulos, L. Saloff-Coste & T. Coulhon, Analysis and Geometry on Groups (Cambridge University Press, 1992).

    Standard reference for random-walk return-probability decay on groups of polynomial growth; G. Alexopoulos and W. Hebisch & L. Saloff-Coste supply the same result independently (Addendum HO).

  4. [20]

    A. Dvoretzky & P. Erdős, "Some problems on random walk in space," in Proc. Second Berkeley Symposium on Mathematical Statistics and Probability (1950); S.J. Taylor & P. Erdős, on random-walk self-intersections (1960).

    Random-walk self-intersection results, tested as a critical-dimension analogy for Q=4 and found not to transfer (Addendum HO).

  5. [21]

    T. Hara & G. Slade, on the lace expansion and the self-avoiding walk's upper critical dimension.

    Background for the same critical-dimension analogy above.

Quantum graphs & disorder — the overlap-admissibility question
  1. [22]

    T. Kottos & U. Smilansky, "Periodic orbit theory and spectral statistics for quantum graphs," Annals of Physics 274, 76–124 (1999).

    Bond-scattering-matrix quantization framework, built directly and validated in Addendum HP.

  2. [23]

    V. Kostrykin & R. Schrader, "The generalized star product and the factorization of scattering matrices on graphs," Journal of Mathematical Physics 42, 1563–1598 (2001).

    Self-adjoint vertex-condition classification for quantum graphs, underlying the Kirchhoff condition used in Addendum HP.

  3. [24]

    V.E. Kravtsov, B.L. Altshuler & L.B. Ioffe, "Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph," Annals of Physics 389, 148–191 (2018).

    Proposes the non-ergodic delocalized (NEE) phase tested against SFT's own measured disorder-to-hopping ratio (Addendum HP).

  4. [25]

    G. Biroli & M. Tarzia, "Delocalization and ergodicity of the Anderson model on Bethe lattices," arXiv:1810.07545 (2018).

    Retained in Addendum HP as secondary corroborating evidence for the large-N ergodicity-recovery result, distinct from the paper proposing the NEE phase above.

  5. [26]

    C. Vanoni, B.L. Altshuler, V.E. Kravtsov & A. Scardicchio, "Renormalization group analysis of the Anderson model on random regular graphs," PNAS 121, e2401955121 (2024).

    Precursor to the 2025 renormalization-group resolution below.

  6. [27]

    B.L. Altshuler, V.E. Kravtsov, A. Scardicchio, P. Sierant & C. Vanoni, "Renormalization group for Anderson localization on high-dimensional lattices," PNAS 122, e2423763122 (2025).

    Resolves the NEE-phase dispute in favor of a single transition — the finding Addendum HP checks SFT's own shortfall result against.

Holography & entanglement — Family D of the H.17 literature survey
  1. [28]

    M. Van Raamsdonk, "Building up spacetime with quantum entanglement," General Relativity and Gravitation 42, 2323–2329 (2010), arXiv:1005.3035.

    Read in full for Addendum HE's test of entanglement-derived adjacency.

  2. [29]

    B. Swingle, on entanglement renormalization and tensor-network holography, arXiv:1209.3304.

    The MERA/tensor-network line of literature referenced alongside Van Raamsdonk in Addendum HE.

  3. [30]

    P. Chen, D. Wu & D. Yeom, on a counter-example to the ER=EPR conjecture, arXiv:1608.08695.

    Read as the "skeptical counterpoint" to ER=EPR in Addendum HE; found to identify a narrow technical exception rather than a general refutation.

  4. [31]

    S. Ryu & T. Takayanagi, "Holographic Derivation of Entanglement Entropy from AdS/CFT," Physical Review Letters 96, 181602 (2006).

    The minimum-cut scaling test applied to SFT's own substrate in Addendum FS, with a clean negative result.

  5. [32]

    F. Pastawski, B. Yoshida, D. Harlow & J. Preskill, "Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence," JHEP 06, 149 (2015).

    The HaPPY code, the {3,Q}-triangulation reference construction behind Addendum FS's vertex-valence-capped consistent core.

Emergent symmetry & cosmology — Family C of the H.17 literature survey
  1. [33]

    J.B. Jiménez & S. Tsujikawa, "Isotropic Universes with a Preferred Direction," arXiv:2608.02458.

    Read in full for Addendum HF's structural closure of the on-shell-symmetry escape route.

Field theory & particle physics foundations
  1. [34]

    T. Banks, W. Fischler, S.H. Shenker & L. Susskind, "M Theory As A Matrix Model: A Conjecture," Physical Review D 55, 5112 (1997).

    BFSS Matrix Theory, tested as a candidate resolution to H.17 in Addendum HB.

  2. [35]

    M.R. Douglas, D. Kabat, P. Pouliot & S.H. Shenker, "D-branes and Short Distances in String Theory," Nuclear Physics B 485, 85 (1997).

    The "no-force" result underlying BFSS's off-diagonal brane suppression, referenced in the same addendum.

  3. [36]

    H.B. Nielsen & M. Ninomiya, "Absence of Neutrinos on a Lattice," Nuclear Physics B 185, 20 (1981).

    Fermion-doubling obstruction that the overlap/Ginsparg–Wilson fermion sector is built to avoid (Part IV, effective action).

  4. [37]

    E.H. Lieb & D.W. Robinson, "The finite group velocity of quantum spin systems," Communications in Mathematical Physics 28, 251–257 (1972).

    Lieb–Robinson bound, the original tool choice for overlap-fermion admissibility, revisited and found not the most direct route in Addendum EX.

  5. [38]

    P. Hernández, K. Jansen & M. Lüscher, "Locality properties of Neuberger's lattice Dirac operator," Nuclear Physics B 552, 363 (1999).

    The theorem the overlap-fermion decision is actually based on — needs only bounded degree and a spectral gap, no volume-growth condition (Addendum EX).

  6. [39]

    S. Coleman & E. Weinberg, "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking," Physical Review D 7, 1888 (1973).

    Checked and found inapplicable as a route to forcing AZ.13's tachyonic-mass sign, since SFT's own algorithmic scale carries no genuine renormalization-group content (Addendum CS).

  7. [40]

    E. Witten, "Global Aspects of Current Algebra," Nuclear Physics B 223, 422 (1983).

    The SU(2)⊂SU(3) hedgehog soliton embedding tested as a fermion-generating mechanism in Addendum CP.

  8. [41]

    D. Finkelstein & J. Rubinstein, "Connection between spin, statistics, and kinks," Journal of Mathematical Physics 9, 1762 (1968); T.H.R. Skyrme, "A unified field theory of mesons and baryons," Nuclear Physics 31, 556 (1962).

    The Skyrme mechanism for fermionic statistics from solitons, the route tested and closed negative in Addendum CP.

  9. [42]

    G.H. Derrick, "Comments on Nonlinear Wave Equations as Models for Elementary Particles," Journal of Mathematical Physics 5, 1252 (1964).

    Derrick's instability theorem, the exact failure mode found for the hedgehog soliton in Addendum CP.

Observational data — falsifiable predictions
  1. [43]

    LIGO Scientific Collaboration and Virgo Collaboration, "GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral," Physical Review Letters 119, 161101 (2017).

    Multimessenger bound used to exclude the original theory's multiple-limiting-speeds problem (Part I, Defect 3).

  2. [44]

    Fermi Gamma-ray Burst Monitor and Large Area Telescope observations of GRB 090510 and GRB 221009A.

    Gamma-ray-burst timing data the quadratic Lorentz-invariance-violation prediction is checked against (Part IV, falsifiable predictions).

Every citation above traces back to a specific addendum. The Full Record links to the complete, addendum-by-addendum derivation work these sources appear in.

See the Full Record →