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Paper Citation Record · LEDGER

Stochastic optimization over expectation-formulated generalized Stiefel manifold

As of 15 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2412.20008.

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pith.paper-citation-record.v1
2412.20008 v1

Coverage vector

measured 50 of 50 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:47:19.458404Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

50 of 50 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8eda736d-25b6-4222-ae4e-ffa96e30fb8b · outbound

This paper cites Steepest descent algorithms for optimization under unitary matrix constraint.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Steepest descent algorithms for optimization under unitary matrix constraint

Reference 1

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Observation aa85100a-ea21-406c-a5db-c203613d588e · outbound

This paper cites Trust-region methods on riemannian manifolds.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Trust-region methods on riemannian manifolds

Reference 2

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Observation f8df705f-790d-4a66-9d98-ea2e5acfc42b · outbound

This paper cites Absil, R.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Absil, R

Reference 3

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Observation d25fb050-ad25-4d5d-ab3c-6fb444d300c0 · outbound

This paper cites Newton’s method on riemannian manifolds and a geometric model for the human spine.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Newton’s method on riemannian manifolds and a geometric model for the human spine

Reference 4

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Observation 32a62b12-30d8-444f-94d5-6affbec578d3 · outbound

This paper cites Stochastic approx- imation for canonical correlation analysis.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Stochastic approx- imation for canonical correlation analysis

Reference 5

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Observation 7264dcdb-5633-4077-a7b0-671ef0e1eccc · outbound

This paper cites Riemannian manifold trust-region methods with applications to eigenprob- lems.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Riemannian manifold trust-region methods with applications to eigenprob- lems

Reference 6

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Observation fdaf1881-a1e3-4035-8512-8c56a26db458 · outbound

This paper cites Learning sparse feature representa- tions using probabilistic quadtrees and deep belief nets.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Learning sparse feature representa- tions using probabilistic quadtrees and deep belief nets

Reference 7

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Source-reported events for the cited work

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Observation 5eff538e-a96c-4364-b37e-06ea06a33f4c · outbound

This paper cites Stochastic approximations and differential inclusions.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Stochastic approximations and differential inclusions

Reference 8

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Source-reported events for the cited work

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Observation 517f3966-86c4-4c5f-b1f4-a76bde86aaf9 · outbound

This paper cites Non-convex phase retrieval from stft measurements.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Non-convex phase retrieval from stft measurements

Reference 9

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Observation 111dfc7c-e84f-474c-b35f-f305b6c027da · outbound

This paper cites Subgradient sampling for nonsmooth nonconvex minimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Subgradient sampling for nonsmooth nonconvex minimization

Reference 10

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Observation 4ad95a0d-9366-4f5e-8a06-3c5ea3ec8965 · outbound

This paper cites Stochastic first-order methods for convex and nonconvex functional constrained optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Stochastic first-order methods for convex and nonconvex functional constrained optimization

Reference 11

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Source-reported events for the cited work

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Observation 01368d39-ac58-4fe0-b584-c963f95920b9 · outbound

This paper cites An introduction to optimization on smooth manifolds.

Stochastic optimization over expectation-formulated generalized Stiefel manifold An introduction to optimization on smooth manifolds

Reference 12

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Source-reported events for the cited work

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Observation 450eedad-6d47-4287-9bdd-374806d319c9 · outbound

This paper cites Manopt, a matlab toolbox for optimization on manifolds.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Manopt, a matlab toolbox for optimization on manifolds

Reference 13

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Source-reported events for the cited work

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Observation 6f802841-8ddb-4c21-bf43-a2e22e7b23c3 · outbound

This paper cites Sparse CCA via Precision Adjusted Iterative Thresholding.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Sparse CCA via Precision Adjusted Iterative Thresholding

Reference 14

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Observation bf3f9dc7-5628-411a-9525-ef72ab886277 · outbound

This paper cites Solving stochastic compositional optimization is nearly as easy as solving stochastic optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Solving stochastic compositional optimization is nearly as easy as solving stochastic optimization

Reference 15

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Source-reported events for the cited work

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Observation cb1cd21b-0e0c-41c2-8ab9-e1c8419f1a28 · outbound

This paper cites On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization

Reference 16

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Source-reported events for the cited work

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Observation 857eec86-947e-499b-aa78-f97ab49c6236 · outbound

This paper cites An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory.

Stochastic optimization over expectation-formulated generalized Stiefel manifold An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory

Reference 17

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Observation 2c86febf-dfa9-49ec-823e-7ab0e173f8b2 · outbound

This paper cites Sparse GCA and Thresholded Gradient Descent.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Sparse GCA and Thresholded Gradient Descent

Reference 18

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Source-reported events for the cited work

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Observation 3af1b293-c5d8-4d81-b50a-0ab0f58753f4 · outbound

This paper cites Efficient algorithms for large- scale generalized eigenvector computation and canonical correlation analysis.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Efficient algorithms for large- scale generalized eigenvector computation and canonical correlation analysis

Reference 19

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Source-reported events for the cited work

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Observation c9cb4984-2f22-42f2-a96e-63b79d45a724 · outbound

This paper cites A single timescale stochastic approxi- mation method for nested stochastic optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold A single timescale stochastic approxi- mation method for nested stochastic optimization

Reference 20

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Observation 5adbec97-bb51-4c36-91fa-cae003b89868 · outbound

This paper cites Hardoon, Sandor Szedmak, and John Shawe-Taylor.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Hardoon, Sandor Szedmak, and John Shawe-Taylor

Reference 21

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Source-reported events for the cited work

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Observation 8d9d1866-ff2f-42aa-8057-03747c6e3e8d · outbound

This paper cites Relations between two sets of variables.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Relations between two sets of variables

Reference 22

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Observation aa8e283f-49e6-46c9-9351-80c7043f64af · outbound

This paper cites Generalized canonical correlations and their application to experimental data.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Generalized canonical correlations and their application to experimental data

Reference 23

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Source-reported events for the cited work

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Observation 95ca01b8-d45e-4326-aa6e-cd6e2a581312 · outbound

This paper cites A brief introduction to manifold opti- mization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold A brief introduction to manifold opti- mization

Reference 24

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Observation ab19b73c-2d99-4be6-be81-c9d8281c8ba7 · outbound

This paper cites A broyden class of quasi-newton methods for riemannian optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold A broyden class of quasi-newton methods for riemannian optimization

Reference 25

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Observation 714755b0-8ed4-48dc-8075-c36d79a43557 · outbound

This paper cites Robust estimation of a location parameter.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Robust estimation of a location parameter

Reference 26

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Source-reported events for the cited work

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Observation 4a3d968f-3adb-4060-ab94-cb71c4b7ef8f · outbound

This paper cites The riemannian barzilai–borwein method with non- monotone line search and the matrix geometric mean computation.

Stochastic optimization over expectation-formulated generalized Stiefel manifold The riemannian barzilai–borwein method with non- monotone line search and the matrix geometric mean computation

Reference 27

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Source-reported events for the cited work

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Stochastic optimization over expectation-formulated generalized Stiefel manifold Riemannian stochastic recursive gradient algorithm

Reference 28

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Source-reported events for the cited work

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Stochastic optimization over expectation-formulated generalized Stiefel manifold Unresolved cited work

Reference 29

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Observation fec66ed7-eb0c-4464-bcf9-2508112de02a · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Adam: A Method for Stochastic Optimization

Reference 30

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Source-reported events for the cited work

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Stochastic optimization over expectation-formulated generalized Stiefel manifold Nonsmooth nonconvex stochastic heavy ball

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 3d045f2f-0bbb-411a-b212-268cf4cb008d · outbound

This paper cites The mnist database of handwritten digits.

Stochastic optimization over expectation-formulated generalized Stiefel manifold The mnist database of handwritten digits

Reference 32

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unresolved
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 12f153bc-c83a-4d66-ba06-92255014624c · outbound

This paper cites Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization

Reference 33

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local_arxiv, observed 2026-08-10T23:47:19.804539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 4aaad49c-5a17-4802-a13a-5054714492f4 · outbound

This paper cites Linear discriminant analysis: New formulations and overfit analysis.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Linear discriminant analysis: New formulations and overfit analysis

Reference 34

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation b138697c-7c3d-476f-b6f9-d9b8d71d9cb9 · outbound

This paper cites Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints

Reference 35

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:47:19.775657Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 754e4acd-81ee-4f38-9e2f-e20b20e84627 · outbound

This paper cites Finding linear structure in large datasets with scalable canonical correlation analysis.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Finding linear structure in large datasets with scalable canonical correlation analysis

Reference 36

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Observation 94f4bfbc-d2b4-4417-85be-7b56585df594 · outbound

This paper cites An online riemannian pca for stochastic canonical correlation analysis.

Stochastic optimization over expectation-formulated generalized Stiefel manifold An online riemannian pca for stochastic canonical correlation analysis

Reference 37

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Observation afc17ca9-791b-4527-a485-9c437a416af1 · outbound

This paper cites Numerical optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Numerical optimization

Reference 38

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Observation 2642a459-a2a4-48aa-83da-530b3ddec712 · outbound

This paper cites Riemannian conjugate gradient methods: General framework and specific algo- rithms with convergence analyses.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Riemannian conjugate gradient methods: General framework and specific algo- rithms with convergence analyses

Reference 39

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Observation 4941a08e-a4b3-4cb2-a010-689f1ce133f8 · outbound

This paper cites Cholesky QR-based retraction on the generalized Stiefel manifold.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Cholesky QR-based retraction on the generalized Stiefel manifold

Reference 40

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Observation 857b9d8d-9100-4ff4-80b6-6ab9a3b0d536 · outbound

This paper cites A new, globally convergent riemannian conjugate gradient method.

Stochastic optimization over expectation-formulated generalized Stiefel manifold A new, globally convergent riemannian conjugate gradient method

Reference 41

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Observation 2198431e-d197-4a93-b668-bb8e771dc916 · outbound

This paper cites Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold

Reference 42

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Observation 027b71c7-f755-4570-8ae2-3b330a658d26 · outbound

This paper cites The challenge problem for automated detection of 101 semantic concepts in multi- media.

Stochastic optimization over expectation-formulated generalized Stiefel manifold The challenge problem for automated detection of 101 semantic concepts in multi- media

Reference 43

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source=pdf_text observed=2026-08-10T23:47:19.416181Z digest=sha256:6f7aa89d8ffb80578d3e04a5f222352131b37430c5d2a4c063aced1fb2f15bdc

Observation 51c06b11-f319-4f4b-a7d5-e9a8fc82408f · outbound

This paper cites Minimum generalized variance for a set of linear functions.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Minimum generalized variance for a set of linear functions

Reference 44

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Observation 2847e2ce-42ac-4d4e-8e02-1de0415c7676 · outbound

This paper cites Generalized Canonical Correlation Analysis: A Subspace Intersection Approach.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Generalized Canonical Correlation Analysis: A Subspace Intersection Approach

Reference 45

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source=pdf_text observed=2026-08-10T23:47:19.427534Z digest=sha256:f2008a35a957fbb2c223a7685d5b79aae2e0df53d2d004dbbe842f8613343f6d

Observation fbaa098c-77a3-4359-9e2d-cf858cf9778e · outbound

This paper cites Optimization without retraction on the random generalized stiefel manifold.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Optimization without retraction on the random generalized stiefel manifold

Reference 46

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source=pdf_text observed=2026-08-10T23:47:19.433099Z digest=sha256:1f2fa36298c39d6a88d8776de6e8d3fd8daa172420d16c7fabd6af84355dcd0c

Observation daf513eb-93ce-4350-a22d-7e829873e25e · outbound

This paper cites Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions

Reference 47

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source=pdf_text observed=2026-08-10T23:47:19.438931Z digest=sha256:af20ca5dd0bf827b76dbb072da55d78164ef1c19846b2bdb21bd9931612f89a5

Observation 425f49d0-32e0-4bf0-b519-9f700f69ff91 · outbound

This paper cites Accelerating stochastic composition optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Accelerating stochastic composition optimization

Reference 48

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source=pdf_text observed=2026-08-10T23:47:19.446393Z digest=sha256:308c9dccad6c60bf966f90c1f87dca7295f222ed1b0a1f4537db583df758b94f

Observation 69515468-3184-4c5e-a4dd-55bc3a9581d1 · outbound

This paper cites Dissolving Constraints for Riemannian Optimization.

Stochastic optimization over expectation-formulated generalized Stiefel manifold Dissolving Constraints for Riemannian Optimization

Reference 49

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source=pdf_text observed=2026-08-10T23:47:19.451667Z digest=sha256:bfd9b12398246727f740fed9f26e2bfa1342b5a868a8c223b11bb22df8a132fe

Observation e1f02ee6-d075-4fb4-b9fa-e2bcf7f26dd2 · outbound

This paper cites A stochastic composite gradient method with incremental variance reduction.

Stochastic optimization over expectation-formulated generalized Stiefel manifold A stochastic composite gradient method with incremental variance reduction

Reference 50

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source=pdf_text observed=2026-08-10T23:47:19.458404Z digest=sha256:783c2470470ad808c4be5f52f628be8dc689c00797fdded9f48a730b24bb7543

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