% =====================================================================
%  ch-08.additions.bib — Bibliography additions for
%  Chapter 8: The Vessel and The Real
%
%  Discovered during the missing-citation pass on the chapter prose.
%  Style: apalike. Title case-protection uses braces only where
%  apalike's lowercasing would damage a proper noun.
%
%  Keys already defined in ch-01.additions.bib or ch-02.additions.bib
%  (scholem1946, chittick1989, ibnarabi1980) are cited but NOT
%  redefined here, to avoid duplicate-key warnings at merge time.
% =====================================================================

% =====================================================================
%  EMPIRICAL ANCHOR — token-subspace stratification result
% =====================================================================

% --- The Robinson--Dey--Chiang result that the chapter takes as its
%     empirical hinge: token subspaces of LLMs are not manifolds. ---
@inproceedings{robinson2025token,
  author    = {Robinson, Michael and Dey, Sourya and Chiang, Tony},
  title     = {Token Embeddings Violate the Manifold Hypothesis},
  booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
  year      = {2025},
  note      = {Also available as arXiv:2504.01002}
}

% =====================================================================
%  MANIFOLD HYPOTHESIS — the position that Robinson et al. refute
% =====================================================================

@article{fefferman2016testing,
  author  = {Fefferman, Charles and Mitter, Sanjoy and Narayanan, Hariharan},
  title   = {Testing the Manifold Hypothesis},
  journal = {Journal of the American Mathematical Society},
  volume  = {29},
  number  = {4},
  pages   = {983--1049},
  year    = {2016}
}

@article{tenenbaum2000isomap,
  author  = {Tenenbaum, Joshua B. and de Silva, Vin and Langford, John C.},
  title   = {A Global Geometric Framework for Nonlinear Dimensionality Reduction},
  journal = {Science},
  volume  = {290},
  number  = {5500},
  pages   = {2319--2323},
  year    = {2000}
}

% =====================================================================
%  STRATIFIED SPACES — mathematical foundation behind Def. 8.1
% =====================================================================

% --- Mather's foundational notes on stratifications. ---
@article{mather2012notes,
  author  = {Mather, John},
  title   = {Notes on Topological Stability},
  journal = {Bulletin of the American Mathematical Society},
  volume  = {49},
  number  = {4},
  pages   = {475--506},
  year    = {2012},
  note    = {Originally circulated as Harvard preprint, 1970}
}

% --- Goresky--MacPherson: stratified Morse theory and intersection
%     homology, the canonical reference for stratified geometry. ---
@book{goresky1988stratified,
  author    = {Goresky, Mark and MacPherson, Robert},
  title     = {Stratified {Morse} Theory},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1988},
  series    = {Ergebnisse der Mathematik und ihrer Grenzgebiete},
  volume    = {14}
}

% =====================================================================
%  LURIANIC KABBALAH — tzimtzum, shevirat ha-kelim, tikkun, nitzotzot
% =====================================================================

% --- Idel's revisionist scholarship on Kabbalah, the standard
%     counter-Scholem reference. Cited alongside scholem1946 wherever
%     tzimtzum / shevira / tikkun are introduced. ---
@book{idel1988,
  author    = {Idel, Moshe},
  title     = {Kabbalah: New Perspectives},
  publisher = {Yale University Press},
  address   = {New Haven},
  year      = {1988}
}

% --- Fine's authoritative monograph on Isaac Luria, the Safed circle,
%     and the doctrine of tikkun. ---
@book{fine2003physician,
  author    = {Fine, Lawrence},
  title     = {Physician of the Soul, Healer of the Cosmos: {Isaac Luria} and His {Kabbalistic} Fellowship},
  publisher = {Stanford University Press},
  address   = {Stanford, CA},
  year      = {2003}
}

% --- Scholem's monograph on the Lurianic doctrine, more focused than
%     the broad 1946 survey. ---
@book{scholem1991mystical,
  author    = {Scholem, Gershom},
  title     = {On the Mystical Shape of the Godhead: Basic Concepts in the {Kabbalah}},
  publisher = {Schocken Books},
  address   = {New York},
  year      = {1991},
  note      = {Translated by Joachim Neugroschel}
}

% =====================================================================
%  IBN ʿARABI AND AKBARIAN SUFISM — tajallī, al-Ḥaqq, barzakh, maẓāhir
% =====================================================================

% --- Chittick's second major Ibn ʿArabi monograph, the canonical
%     reference for tajallī as ``self-disclosure'' rather than
%     ``manifestation.'' Complements chittick1989 (defined in
%     ch-01.additions.bib). ---
@book{chittick1998,
  author    = {Chittick, William C.},
  title     = {The Self-Disclosure of {God}: Principles of {Ibn al-`Arab{\=\i}}'s Cosmology},
  publisher = {State University of New York Press},
  address   = {Albany},
  year      = {1998}
}

% --- Schimmel's standard survey of Sufi metaphysics, used here for
%     maqāmāt / sulūk / ṭarīqa terminology. ---
@book{schimmel1975mystical,
  author    = {Schimmel, Annemarie},
  title     = {Mystical Dimensions of {Islam}},
  publisher = {University of North Carolina Press},
  address   = {Chapel Hill},
  year      = {1975}
}

% --- al-Jīlī's classical treatise: the locus classicus of
%     al-Insān al-Kāmil (the Perfect Human) used in Def. 8.16. ---
@book{jili1983,
  author    = {al-J{\=\i}l{\=\i}, {`Abd al-Kar{\=\i}m}},
  title     = {Universal {Man} ({al-Ins\={a}n al-K\={a}mil}): Extracts},
  publisher = {Beshara Publications},
  address   = {Sherborne, Gloucestershire},
  year      = {1983},
  note      = {Originally composed c.\ 1402. Translated with commentary by Titus Burckhardt; English rendering by Angela Culme-Seymour}
}

% --- Sells's anthology of early Sufi mystical writings, used for the
%     ``knowledge by presence'' (maʿrifa) tradition. ---
@book{sells1996early,
  author    = {Sells, Michael A.},
  title     = {Early {Islamic} Mysticism: {Sufi}, {Qur'an}, {Mi`raj}, Poetic and Theological Writings},
  publisher = {Paulist Press},
  address   = {New York},
  year      = {1996},
  series    = {Classics of Western Spirituality}
}
