Reading and source map for the complete course

Edition 2.2, 1 October 2026. Read the notes’ calculations first. The sources below supply theorems, broader context, or the original gravitational construction; they do not replace missing steps in a calculation the course claims to derive.

The opening map retains the detailed rationale for Lectures 1–4. Source records and the indicated portions of available full texts were consulted during the redesign. This is a map of the active course, not a claim to have audited every result in every cited paper.

Finite models, field algebras, and the first geometric clock

Lectures	Source	What it supplies; what is calculated in the course
1–4, 7	Cleve, Gottesman, Lo, How to share a quantum secret	Secret-sharing context. The decoder, reference tests, and the weighted deformation are explicitly calculated in the notes. The deformation is a course example.
1, 4, 21	Harlow, The Ryu-Takayanagi Formula from Quantum Error Correction	Algebraic complementary recovery and the role of a center; finite entropy and modular identities are derived on the page.
2, 18–21	Almheiri, Dong, Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT	The code-subspace interpretation and its physical scope.
5	Casini, Huerta, Rosabal, Remarks on entanglement entropy for gauge fields	Context for regional algebra choices and centers. The four-qubit constrained system is independently specified and solved; it is not represented as a complete lattice gauge theory.
6	Pastawski, Yoshida, Harlow, Preskill, Holographic quantum error-correcting codes	Perfect tensors, isometries, and cut bounds; the notes calculate a particular six-leg state and a concatenated qutrit encoding. Full-text tensor/isometry discussion consulted.
8	Srednicki, Entropy and Area	The historical scalar-field oscillator calculation and the two-oscillator example. The note derives the reduced state from the wavefunction and from the covariance, and reproduces the lattice scaling numerically; the area law of a sphere is a research extension.
8	Casini, Huerta, Entanglement entropy in free quantum field theory; Peschel, Eisler, Reduced density matrices and entanglement entropy in free lattice models; Weedbrook et al., Gaussian Quantum Information; Audenaert, Eisert, Plenio, Werner, Entanglement Properties of the Harmonic Chain; Eisert, Cramer, Plenio, Area laws for the entanglement entropy - a review	The Gaussian-state formalism and the lattice results. Williamson’s normal form is proved in the note in the block-diagonal case; the general theorem is cited.
8	Peschel, Chung, Density Matrices for a Chain of Oscillators; Peschel, Kaulke, Legeza, Density-matrix spectra for integrable models	The corner-transfer-matrix spectrum of the half-chain, stated and checked numerically to six digits; the entropy per endpoint is derived from it in the note.
8	Casini, Huerta, Entanglement and alpha entropies for a massive scalar field in two dimensions	The infrared term of the small-mass interval entropy, stated only.
8, 10	Eisler, Di Giulio, Tonni, Peschel, Entanglement Hamiltonians for non-critical quantum chains; Di Giulio, Tonni, On entanglement hamiltonians of an interval in massless harmonic chains	Lattice modular Hamiltonians, for the research extensions. The lattice test of the coherent-state formula in Lecture 10 is computed independently.
3, 9–10	Witten, Notes on Some Entanglement Properties of Quantum Field Theory	Modular theory and relative entropy (Sections 2–4), the wedge and the accelerated observer (Section 5), algebra types and infinite products (Section 6), and factorized states (Section 7). Section headings checked against the arXiv text.
9	Sorce, Notes on the type classification of von Neumann algebras; Yngvason, The Role of Type III Factors in Quantum Field Theory; Summers, Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State	Type classification and the structure of local algebras. The modular spectra of the infinite products are computed in the note; the classification theorems are stated with references.
9	Fewster, The split property for quantum field theories in flat and curved spacetimes	Definition and sufficient-condition framework for split inclusions. The course proves only the elementary consequences used in its tensor-product discussion.
9	Hollands, Sanders, Entanglement measures and their properties in quantum field theory	Finite entanglement measures across a corridor, stated; the lattice mutual information of Lecture 8 is the elementary counterpart.
10	Crispino, Higuchi, Matsas, The Unruh effect and its applications	Review of the Unruh effect. The KMS property along the orbit, the detector rate and the Bogoliubov ratio are calculated in the note.
10	Longo, Entropy of Coherent Excitations; Casini, Grillo, Pontello, Relative entropy for coherent states from Araki formula; Ciolli, Longo, Ruzzi, The information in a wave	The rigorous coherent-state relative entropy of the wedge and its null-translated form. The note derives the formula from the unitary-excitation identity of Lecture 9 and tests it on the lattice.
10	Casini, Relative entropy and the Bekenstein bound	The relative-entropy form of the Bekenstein bound.
10–11	Casini, Teste, Torroba, Modular Hamiltonians on the null plane and the Markov property of the vacuum state; Faulkner, Leigh, Parrikar, Wang, Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition	Null-plane modular Hamiltonians, used in the research extensions.
11	Casini, Huerta, Myers, Towards a derivation of holographic entanglement entropy	The vacuum-ball conformal thermal construction. The note constructs the wedge-to-diamond map and the map to hyperbolic space, integrates the modular flow and the energy kernel, and checks them symbolically.
11	Brunetti, Guido, Longo, Modular Structure and Duality in Conformal Quantum Field Theory	Geometric modular flows of double cones in conformal nets, stated; the conjugation of the wedge theorem is sketched in the note.
11	Blanco, Casini, Hung, Myers, Relative Entropy and Holography; Bhattacharya, Nozaki, Takayanagi, Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States; Wong, Klich, Pando Zayas, Vaman, Entanglement Temperature and Entanglement Entropy of Excited States	The first law as stationarity of relative entropy, and its holographic and field-theory checks. The note proves the finite-dimensional law and computes the exact two-dimensional thermal relative entropy.
11, 22	Lashkari, McDermott, Van Raamsdonk, Gravitational Dynamics From Entanglement “Thermodynamics”	From the first law to the linearized Einstein equations, developed in Lecture 22.
11	Cardy, Tonni, Entanglement hamiltonians in two-dimensional conformal field theory; Casini, Huerta, Reduced density matrix and internal dynamics for multicomponent regions; Rosenhaus, Smolkin, Entanglement Entropy: A Perturbative Calculation	Modular Hamiltonians beyond the ball and entropy under shape deformations, for the research extensions.

CFT, bulk fields, and recoverability

Lectures	Source	Role and scope
12	Rychkov, EPFL Lectures on Conformal Field Theory in D >= 3 Dimensions	Radial quantization, representation positivity, and OPE. The scalar descendant norms are derived and symbolically checked in the course.
12	Simmons-Duffin, TASI Lectures on the Conformal Bootstrap; Ginsparg, Applied Conformal Field Theory	The conformal algebra, correlators and crossing; the two-dimensional material. The note derives the conformal Killing vectors, the correlator constraints, the Virasoro central term, the Schwarzian on the cylinder and Cardy’s formula.
12	Osborn, Petkou, Implications of Conformal Invariance in Field Theories for General Dimensions; Pappadopulo, Rychkov, Espin, Rattazzi, OPE Convergence in Conformal Field Theory	The stress-tensor two-point function, stated with its normalization, and the convergence of the OPE.
12	Rattazzi, Rychkov, Tonni, Vichi, Bounding scalar operator dimensions in 4D CFT; Poland, Rychkov, Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications; Hartman, Keller, Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit	Historical context for the bootstrap, and the sparseness condition that extends Cardy’s formula at large central charge; research extension only.
13–15, 19	Harlow, TASI Lectures on the Emergence of the Bulk in AdS/CFT	Global scalar modes, the gapped large-$N$ regime, and reconstruction. Relevant full-text sections consulted; broad existence claims remain conditional on their hypotheses.
13–14	Aharony, Gubser, Maldacena, Ooguri, Oz, Large N Field Theories, String Theory and Gravity	AdS geometry, the large-$N$ expansion and the parameters of the AdS${}_5\times S^5$ example. The note derives the conformal compactification, the Poincaré isometries and $L^3/G_5=2N^2/\pi$.
13	Balasubramanian, Kraus, Lawrence, Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime; Ishibashi, Wald, Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime	Normal modes and their boundary interpretation; boundary conditions as self-adjoint extensions. The spectrum $\omega =\Delta +2n+\ell$ and its degeneracies are derived in the note.
14	Di Francesco, Ginsparg, Zinn-Justin, 2D Gravity and Random Matrices	The genus expansion of matrix integrals. The Gaussian moments and the cumulants of a single-trace operator are computed exactly in the note.
14	Heemskerk, Penedones, Polchinski, Sully, Holography from Conformal Field Theory; El-Showk, Papadodimas, Emergent Spacetime and Holographic CFTs; Camanho, Edelstein, Maldacena, Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling	The gap condition for a local bulk, stated with its sources.
15	Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity; Gubser, Klebanov, Polyakov, Gauge Theory Correlators from Non-Critical String Theory; Witten, Anti De Sitter Space and Holography	The correspondence and the source prescription, stated in §1 as the holographic input. The boundary-value problem, counterterms, one-point relation and two-point normalization are derived in the note and checked in the model script.
15	Freedman, Mathur, Matusis, Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence	The Ward-identity comparison that fixed the factor $2\Delta -d$, and the three-point integrals of the research extension. The mismatch by $(2\Delta -d)/\Delta$ and the Dirichlet problem at $z=ϵ$ were checked in the full text on 2026-09-29; the note derives the factor by two independent routes.
15	Klebanov, Witten, AdS/CFT Correspondence and Symmetry Breaking	Alternate quantization and the Legendre transform. The alternate two-point coefficient and its sign change at $\nu =1$ are derived in the note.
15	de Haro, Skenderis, Solodukhin, Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence; Skenderis, Lecture Notes on Holographic Renormalization; Henningson, Skenderis, The Holographic Weyl anomaly; Balasubramanian, Kraus, A Stress Tensor for Anti-de Sitter Gravity	General counterterm framework and its gravitational origin. The scalar counterterms for $0<\nu <2$ are derived directly with the course’s action normalization and outward normal; the logarithmic case and the metric are cited.
15	Penedones, TASI lectures on AdS/CFT	Pedagogical companion for the dictionary.
15, 18	Banks, Douglas, Horowitz, Martinec, AdS Dynamics from Conformal Field Theory; Harlow, Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT	The extrapolate dictionary and its equivalence with the source prescription. The note derives the normalization $(2\Delta -d)\mathcal{N}{L}^{d-1}$ from the bulk propagator; the general equivalence is stated.
15	Son, Starinets, Minkowski-space correlators in AdS/CFT correspondence: recipe and applications; Skenderis, van Rees, Real-time gauge/gravity duality	Lorentzian response, used only in the research extension.
15	Witten, Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence; Klebanov, Polyakov, AdS Dual of the Critical O(N) Vector Model; Hartman, Rastelli, Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT	Double-trace flows and the vector-model pair; context for §4 and the research extension.
15	Susskind, Witten, The Holographic Bound in Anti-de Sitter Space	The relation between depth and resolution read from the propagator in §6; its use as a general renormalization-scale identification is labeled heuristic.
16	Ryu, Takayanagi, Holographic Derivation of Entanglement Entropy from AdS/CFT and Aspects of Holographic Entanglement Entropy	The classical static prescription. The Poincaré and BTZ geodesics and their regulated lengths are calculated in the note.
16	Calabrese, Cardy, Entanglement Entropy and Quantum Field Theory; Holzhey, Larsen, Wilczek, Geometric and Renormalized Entropy in Conformal Field Theory	The replica trick and twist fields. The twist dimension, the interval entropy and its thermal and finite-size forms are derived in the note from the Schwarzian of Lecture 12.
16	Rangamani, Takayanagi, Holographic Entanglement Entropy; Nishioka, Ryu, Takayanagi, Holographic Entanglement Entropy: An Overview	Reviews of the prescription and its checks.
16	Hubeny, Rangamani, Takayanagi, A Covariant Holographic Entanglement Entropy Proposal; Headrick, Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy; Hubeny, Maxfield, Rangamani, Tonni, Holographic entanglement plateaux	The covariant prescription, strong subadditivity and the plateau. The plateau condition and its critical length are derived in the note.
16, 27	Lewkowycz, Maldacena, Generalized gravitational entropy	The replica derivation of the prescription, sketched in Lecture 16 and developed in Lecture 27.
17	Lin, Marcolli, Ooguri, Stoica, Tomography from Entanglement; Lashkari, Van Raamsdonk, Canonical Energy is Quantum Fisher Information; Asplund, Bernamonti, Galli, Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches	Positivity of relative entropy for small balls as a consequence of bulk energy positivity, its second-order form as the canonical energy, and the entropy of heavy states, stated for the research extensions. The note computes the first-order variation of the BTZ geodesic in two gauges and shows that it equals the modular energy of the thermal interval, point by point in Fefferman–Graham gauge. Almheiri–Dong–Harlow, Blanco–Casini–Hung–Myers and Casini–Huerta–Myers are its primary reading, and Harlow’s two papers and Cleve–Gottesman–Lo its secondary reading; all are listed with Lectures 1, 2, 4, 11 and 18–21.
18	Hamilton, Kabat, Lifschytz, Lowe, Local bulk operators in AdS/CFT: a boundary view of horizons and locality and Holographic representation of local bulk operators	Semiclassical operator reconstruction. The note derives the Poincaré AdS${}_2$ kernel for every $\Delta$ and checks it on the normalizable modes; the higher-dimensional and complexified kernels are stated.
18	Bena, On the construction of local fields in the bulk of AdS_5 and other spaces; Kabat, Lifschytz, Lowe, Constructing local bulk observables in interacting AdS/CFT	Early explicit reconstruction in AdS${}_5$, and the interacting corrections fixed by bulk microcausality; stated, with the first correction as a research extension.
18	Morrison, Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography; Leichenauer, Rosenhaus, AdS black holes, the bulk-boundary dictionary, and smearing functions; Heemskerk, Marolf, Polchinski, Sully, Bulk and Transhorizon Measurements in AdS/CFT	Lorentzian causal-wedge kernels, the obstruction to smearing functions in black-hole backgrounds, and measurements behind horizons; stated only.
18	Donnelly, Giddings, Diffeomorphism-invariant observables and their nonlocal algebra; Kabat, Lifschytz, Decoding the hologram: Scalar fields interacting with gravity; Hamilton, Kabat, Lifschytz, Lowe, Local bulk operators in AdS/CFT: A holographic description of the black hole interior	Gravitational dressing and interior reconstruction, for context and research reading.
19	Headrick, Hubeny, Lawrence, Rangamani, Causality & holographic entanglement entropy; Wall, Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy	The entanglement wedge and its inclusion of the causal wedge under the null energy condition, sketched. The strict inclusion for two intervals is computed exactly in the note.
19	Czech, Karczmarek, Nogueira, Van Raamsdonk, The Gravity Dual of a Density Matrix; Hubeny, Rangamani, Causal Holographic Information	The proposals for the bulk region dual to a density matrix and for the information in the causal wedge.
19	Headrick, Entanglement Renyi entropies in holographic theories; Hartman, Entanglement Entropy at Large Central Charge; Faulkner, The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT	The two-interval problem and the large-$c$ justification of the minimum formula, stated; the classical transition is computed in the note.
19, 21	Faulkner, Lewkowycz, Maldacena, Quantum corrections to holographic entanglement entropy; Engelhardt, Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime	The generalized entropy and the quantum extremal surface, stated; Lecture 19 computes the shift of the transition at order $1/c$.
19–21	Dong, Harlow, Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality; Cotler, Hayden, Penington, Salton, Swingle, Walter, Entanglement Wedge Reconstruction via Universal Recovery Channels	Entanglement-wedge reconstruction from the relative-entropy identity, exact and approximate; stated, with the finite ingredients proved in Lectures 20 and 21.
20	Junge, Renner, Sutter, Wilde, Winter, Universal recovery maps and approximate sufficiency of quantum relative entropy	Approximate recovery theorem, stated and checked on the erasure channel, where it is saturated at the ends. The notes distinguish its recovery channel from an unsupported universal bound for the unrotated Petz map.
20	Petz, Monotonicity of quantum relative entropy revisited; Hayden, Jozsa, Petz, Winter, Structure of states which satisfy strong subadditivity of quantum entropy with equality	The equality theorem through relative modular operators. The note proves data processing and the equality theorem in finite dimensions and checks every step numerically.
20	Barnum, Knill, Reversing quantum dynamics with near-optimal quantum and classical fidelity; Fawzi, Renner, Quantum conditional mutual information and approximate Markov chains; Wilde, From Classical to Quantum Shannon Theory	The transpose channel, approximate Markov chains, and a textbook account of recoverability.
20	Müller-Hermes, Reeb, Monotonicity of the Quantum Relative Entropy Under Positive Maps	Data processing for positive trace-preserving maps, by an argument other than the Kadison–Schwarz route of the note, stated as the answer to the checkpoint on complete positivity.
21	Jafferis, Lewkowycz, Maldacena, Suh, Relative entropy equals bulk relative entropy	Semiclassical modular and relative-entropy matching, sketched from the quantum-corrected formula. The sector-code identities and the implication from a central-area formula to relative-entropy equality are proved in the note.
21	Bény, Kempf, Kribs, Generalization of Quantum Error Correction via the Heisenberg Picture and Quantum Error Correction of Observables	Operator-algebra error correction in the Heisenberg picture, the theorem that supplies the representatives on $A$ in the step from relative-entropy equality to reconstruction, stated.
21	Kang, Kolchmeyer, Holographic Relative Entropy in Infinite-dimensional Hilbert Spaces; Lashkari, Van Raamsdonk, Canonical Energy is Quantum Fisher Information	The infinite-dimensional extension of Harlow’s equivalence and the second-order relative entropy as canonical energy, for the research extensions of Lectures 21 and 22.
22	Faulkner, Guica, Hartman, Myers, Van Raamsdonk, Gravitation from Entanglement in Holographic CFTs	The covariant derivation of the linearized equations from all balls, stated. The note carries out the static AdS${}_3$ case completely: the one-form, the integrated identity and an elementary injectivity argument.
22	Iyer, Wald, Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy; Wald, Black Hole Entropy is Noether Charge	The Noether charge and the fundamental identity, sketched; the AdS${}_3$ one-form of the note is a special case.
22	Jacobson, Thermodynamics of Spacetime: The Einstein Equation of State and Entanglement Equilibrium and the Einstein Equation; Swingle, Van Raamsdonk, Universality of Gravity from Entanglement; Faulkner et al., Nonlinear Gravity from Entanglement in Conformal Field Theories	The thermodynamic precursor, the sourced linearized equations, and the second-order extension; stated only.

Thermal systems, islands, and the algebraic closing route

Lectures	Source	Role and scope
23	Maldacena, Eternal Black Holes in AdS	The duality between the eternal black hole and the thermofield double, and the late-time version of the information problem, stated. The note computes the modular operator of the thermofield double, the Kruskal form of BTZ and the time average of a correlator in a system with discrete spectrum.
23	Witten, Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories	The Hawking–Page transition as deconfinement, stated with the Polyakov-loop criterion. The note derives the Euclidean action of AdS–Schwarzschild in every dimension by volume subtraction, with the boundary terms, and from it the mass, the entropy and the transition temperature.
23	Bañados, Teitelboim, Zanelli, The Black Hole in Three Dimensional Space Time; Bañados, Henneaux, Teitelboim, Zanelli, Geometry of the 2+1 Black Hole; Strominger, Black Hole Entropy from Near-Horizon Microstates	The BTZ black hole, its maximal extension and the Cardy match. The note derives the exchange of the two saddles by a modular transformation and the Cardy entropy from the action; the universality of Hartman, Keller and Stoica is stated.
23	Horowitz, Hubeny, Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium; Birmingham, Sachs, Solodukhin, Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes; Barbón, Rabinovici, Very Long Time Scales and Black Hole Thermal Equilibrium; Cotler et al., Black Holes and Random Matrices	Quasinormal decay and its conformal-field-theory match, the time-averaged bound and the spectral form factor, stated for the research extensions. The thermal correlator of a two-dimensional conformal field theory is derived in the note.
23	Van Raamsdonk, Building up spacetime with quantum entanglement; Hartman, Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors; Gao, Jafferis, Wall, Traversable Wormholes via a Double Trace Deformation	Entanglement and connectivity, the growth of two-sided entanglement, and traversability by a boundary coupling, stated. The no-signaling identity is proved in the note.
24	Page, Information in Black Hole Radiation and Average Entropy of a Subsystem; Sen, Average Entropy of a Subsystem	The Page curve, the slow release of information, and the exact average entropy with a proof, stated. The note derives the Haar purity, the first correction to the average entropy and the two-qubit average $\frac{1}{3}$, and it distinguishes an ensemble from a history.
24	Hayden, Preskill, Black holes as mirrors: quantum information in random subsystems; Hayden, Horodecki, Winter, Yard, A decoupling approach to the quantum capacity	The mirror property and the decoupling method. The note derives the Haar-averaged purity of the reference and the remaining black hole and the decoupling bounds $2^{k-s}$ and $2^{k+b/2-s}$, checked by sampling; the decoding theorem is stated.
24	Harlow, Jerusalem Lectures on Black Holes and Quantum Information; Page, Time Dependence of Hawking Radiation Entropy; Sekino, Susskind, Fast Scramblers	A pedagogical account of the Page curve, the decoupling calculation and the firewall argument; the Page time of a four-dimensional black hole, whose fractions the note reproduces from the emission ratio; the scrambling time, stated.
24	Mathur, The information paradox: A pedagogical introduction; Almheiri, Marolf, Polchinski, Sully, Black Holes: Complementarity or Firewalls?	Small corrections and the firewall argument, stated as the motivation for the entropy calculations of Lectures 25–27.
25	Almheiri, Polchinski, Models of AdS_2 Backreaction and Holography; Maldacena, Stanford, Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space; Jensen, Chaos in AdS${}_2$ holography; Engelsöy, Mertens, Verlinde, An Investigation of AdS${}_2$ Backreaction and Holography	JT gravity as the theory of nearly AdS${}_2$ and its Schwarzian dynamics. The note derives the equations from the action, the Schwarzian from the extrinsic curvature of the boundary, and the thermodynamics of the thermal saddle.
25	Stanford, Witten, Fermionic Localization of the Schwarzian Theory; Mertens, Turiaci, Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity	The one-loop exactness of the Schwarzian, stated, and a review of JT gravity for self-study.
25	Penington, Entanglement Wedge Reconstruction and the Information Paradox; Almheiri, Engelhardt, Marolf, Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole; Almheiri, Mahajan, Maldacena, Zhao, The Page curve of Hawking radiation from semiclassical geometry	The quantum extremal surface of an evaporating black hole and the island rule, stated. The note specifies the equilibrium model, derives its Euclidean welding and its generalized-entropy functional, and poses the energy balance of evaporation as a research problem.
25–26	Almheiri, Mahajan, Maldacena, Islands outside the horizon	The black hole in equilibrium with a bath, the paradox of linear growth, and the island outside the horizon, whose consistency with causality is stated. The note derives the no-island growth and the late-time island with its endpoint and Page time.
25–27	Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini, Replica Wormholes and the Entropy of Hawking Radiation	The JT and bath setup, the replica mechanism, the zero-temperature endpoint and the two-sided thermal example. The note derives the finite-time functional from the free-fermion formula in Kruskal coordinates, checks it numerically, and sketches the replica derivation in Lecture 27.
26	Casini, Fosco, Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions; Casini, Huerta, Entanglement entropy in free quantum field theory	The entropy of several intervals for the free Dirac fermion, sketched in the note through the replica trick and bosonization, with its mutual information.
26	Almheiri, Mahajan, Santos, Entanglement islands in higher dimensions; Hashimoto, Iizuka, Matsuo, Islands in Schwarzschild black holes; Chen, Fisher, Hernandez, Myers, Ruan, Information Flow in Black Hole Evaporation	Islands in higher dimensions and for Schwarzschild black holes, and information flow in a doubly holographic model, for the research extensions.
26–27	The same authors, The entropy of Hawking radiation	The wider interpretation and its limitations. The thermal plateau of Lecture 26 is an equilibrium result, and the notes present it as such.
27	Dong, The Gravity Dual of Renyi Entropy; Dong, Lewkowycz, Entropy, Extremality, Euclidean Variations, and the Equations of Motion	Cosmic branes and Rényi entropies, and extremality from the equations of motion. The note derives the area formula, the extremality condition and the refined Rényi formula from one envelope argument, and checks the last exactly for the JT disk.
27	Penington, Shenker, Stanford, Yang, Replica wormholes and the black hole interior	Replica wormholes, the West Coast model and the Petz reconstruction of the interior, stated or sketched. The note derives the permutation sum for random states that the model reproduces at leading order.
27	Callan, Wilczek, On Geometric Entropy; Fursaev, Solodukhin, On the Description of the Riemannian Geometry in the Presence of Conical Defects	Entropy from a conical singularity and the curvature concentrated at a cone, for the history and the conical step of the replica derivation.
27	Saad, Shenker, Stanford, JT gravity as a matrix integral; Marolf, Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information; Maldacena, Maoz, Wormholes in AdS; Stanford, More quantum noise from wormholes	The matrix-integral dual of JT gravity, baby universes, the factorization puzzle and wormhole noise, stated.
28	Rehren, Algebraic Holography, A Proof of the AdS-CFT Correspondence, Local Quantum Observables in the Anti-deSitter - Conformal QFT Correspondence and QFT Lectures on AdS-CFT	The one-to-one correspondence of wedge and double-cone nets in general dimension and the identification of local observables, stated from the source records. The note proves the region map of AdS${}_3$ with its four properties, the transfer of isotony, locality, covariance and modular structure, the triviality of the three-arc intersection for a Haag-dual, strongly additive factor net, and the failure of strong additivity for the generalized free field of a free bulk field.
28	Brunetti, Guido, Longo, Modular Structure and Duality in Conformal Quantum Field Theory; Guido, Modular theory for the von Neumann algebras of Local Quantum Physics	The conformal Bisognano–Wichmann theorem and Haag duality on the universal cover, stated; the note uses them to identify the vacuum modular flow of a bulk wedge with the AdS–Rindler boost.
28	Bertola, Bros, Moschella, Schaeffer, AdS/CFT correspondence for n-point functions; Dütsch, Rehren, Generalized free fields and the AdS-CFT correspondence and A comment on the dual field in the AdS-CFT correspondence; Ribeiro, Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach	Boundary limits of interacting bulk fields, the holographic formula for the free field and its contrast with the algebraic notion, Witten graphs as limits of Feynman graphs, the singular stress tensor of the generalized free field, and asymptotically AdS spacetimes, stated. The note derives the AdS${}_3$ propagator and its boundary limit.
29	Leutheusser, Liu, Causal connectability between quantum systems and the black hole interior in holographic duality; Liu, Lectures on entanglement, von Neumann algebras, and emergence of spacetime	The large-$N$ algebras of the thermofield double, their phases and the emergence of sharp horizons only at infinite $N$, stated; type III${}_1$ in the black-hole phase is stated with these sources. The note proves the c-number commutator of a Gaussian family, the type I algebra of thermal AdS from the convergence of the single-particle partition function, and the exclusion of a type I factor by a decaying correlator, with the factor property from clustering.
29	Brigante, Festuccia, Liu, Inheritance principle and Non-renormalization theorems at finite temperature; Festuccia, Liu, The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories; Witten, Notes on Some Entanglement Properties of Quantum Field Theory	Thermal correlators of the low-temperature phase as image sums, mixing in the high-temperature phase, and background on algebraic types, stated or for self-study. The note computes the spectral densities of thermal AdS${}_3$ and of planar BTZ; the converse type I criterion of Araki and Woods (Publ. RIMS 4, 1968) is stated.
29, 31	Papadodimas, Raju, An Infalling Observer in AdS/CFT; Witten, Gravity and the Crossed Product; Chandrasekaran, Penington, Witten, Large N algebras and generalized entropy	Mirror operators defined relative to a state, the type II${}_{\infty }$ crossed product at order $1/N$, and the type II${}_{\infty }$ algebra of the microcanonical ensemble with its generalized entropy, stated.
30	Araki, Zsidó, Extension of the structure theorem of Borchers and its application to half-sided modular inclusions	Wiesbrock’s theorem with the gap in its proof filled and its extension to weights, stated in the course convention. The statements and conventions of Borchers’ theorem, Wiesbrock’s theorem and the type III${}_1$ property of algebras with half-sided translations were taken from Borchers’ review (J. Math. Phys. 41, 2000), read in full. The note sketches Borchers’ theorem through its analyticity argument, computes every relation in the chiral current, and proves the finite-dimensional obstruction.
30	Casini, Teste, Torroba, Modular Hamiltonians on the null plane and the Markov property of the vacuum state; Ceyhan, Faulkner, Recovering the QNEC from the ANEC	Local modular Hamiltonians of null cuts and the quantum null energy condition from half-sided inclusions, stated. The note derives the difference of the modular Hamiltonians of two half-lines in the chiral current.
30	Brunetti, Guido, Longo, Modular localization and Wigner particles; Guido, Longo, Wiesbrock, Extensions of Conformal Nets and Superselection Structures; Jefferson, Comments on black hole interiors and modular inclusions	Modular localization, the Möbius covariance of dual nets, and a modular inclusion in the traversable wormhole, stated for self-study and the research extensions.
30, 31	Leutheusser, Liu, Emergent times in holographic duality	The proposal of emergent times from half-sided modular inclusions of large-$N$ algebras, stated. The note constructs the proposal exactly in the outgoing sector of the JT model of Lecture 25: the band algebras, their half-sided inclusion, the product of modular unitaries and the Kruskal translation across the future horizon, with the ingoing sector and the translations of the Kruskal plane.
31	Penington, Witten, Algebras and States in JT Gravity; Chandrasekaran, Longo, Penington, Witten, An Algebra of Observables for de Sitter Space; Witten, Algebras, Regions, and Observers	The type II${}_{\infty }$ boundary algebra of JT gravity with matter, the type II${}_1$ algebra of an observer in de Sitter space, and observer algebras from the timelike tube theorem, stated for self-study.
32	Harlow, TASI Lectures on the Emergence of the Bulk in AdS/CFT; Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini, The entropy of Hawking radiation; Liu, Lectures on entanglement, von Neumann algebras, and emergence of spacetime	Reviews for the synthesis. The lecture collects the results of the course with the status each lecture assigned them and claims nothing new.

What students should not have to infer from a citation

A label such as “theorem” means that hypotheses and a source are given; it does not mean the course reproduces the full proof. A claimed worked calculation should be reproducible from the note itself. The free-field chain does not prove type-III classification. A graph cut does not derive a physical area. The Page formula does not specify evaporation dynamics. The affine representation does not alone construct a full local net.

For deeper research, use the older bibliography as a catalogue whose historical week labels and audit status must be respected. The active route is the 32-lecture sequence, not the earlier CFT-first ordering.