Paper Citation Record · LEDGER

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment

As of 15 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.00373.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.00373 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T05:34:47.129160Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

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

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact1
verified fuzzy19
unresolved7
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ded27548-0100-4ef9-8f7c-947b1dfd223b · outbound

This paper cites Flamingo: a Visual Language Model for Few-Shot Learning.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Flamingo: a Visual Language Model for Few-Shot Learning

Reference 1

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Source-reported events for the cited work

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Observation 88e0904a-bdbd-4467-bd4d-330de6158961 · outbound

This paper cites Bruno buchberger's phd thesis 1965: An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Bruno buchberger's phd thesis 1965: An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.464198Z

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.

Observation 52f2c636-2bec-4961-a695-c597c90f2756 · outbound

This paper cites Topology and data.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Topology and data

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.034694Z

Source-reported events for the cited work

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Observation 0d2363b8-29c3-4e49-8ad5-570f7f323a1a · outbound

This paper cites UNITER: UNiversal Image-TExt Representation Learning.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment UNITER: UNiversal Image-TExt Representation Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.038879Z

Source-reported events for the cited work

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Observation e1aa5c5e-487e-4cda-8763-29b38999baf3 · outbound

This paper cites BpForms and BcForms: Tools for concretely describing non-canonical polymers and complexes to facilitate comprehensive biochemical networks.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment BpForms and BcForms: Tools for concretely describing non-canonical polymers and complexes to facilitate comprehensive biochemical networks

Reference 5

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Source-reported events for the cited work

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Observation 1bfb8b16-972b-4ef7-af29-e0210866231c · outbound

This paper cites Canonical correlation analysis: An overview with application to learning methods.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Canonical correlation analysis: An overview with application to learning methods

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.444996Z

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.

Observation 33bbe072-f66a-43c0-84f0-01881f0db4d9 · outbound

This paper cites Moduli of Curves.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Moduli of Curves

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.433318Z

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.

Observation 457086c5-4747-4293-be17-9be1a31e6bb3 · outbound

This paper cites Algebraic Geometry.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Algebraic Geometry

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.422191Z

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.

Observation b3d18db1-d6a6-41bd-864b-1060c79e8f55 · outbound

This paper cites Disentangling factors of variation in deep representations using adversarial training.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Disentangling factors of variation in deep representations using adversarial training

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.410643Z

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.

Observation ad555ab5-4583-4d38-94b3-ff0c322cd9d8 · outbound

This paper cites Scaling up visual and vision-language representation learning with noisy text supervision.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Scaling up visual and vision-language representation learning with noisy text supervision

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.398761Z

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.

Observation c748854c-eb43-461b-aba2-60ca860c32d0 · outbound

This paper cites Principal Component Analysis.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Principal Component Analysis

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.387087Z

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.

Observation 6fe500ab-a484-4dd5-b390-ff3486035b2d · outbound

This paper cites Supervised Multimodal Bitransformers for Classifying Images and Text.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Supervised Multimodal Bitransformers for Classifying Images and Text

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.070068Z

Source-reported events for the cited work

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Observation 7edb4ce8-1d4a-4f7c-8542-e76d49a7bad8 · outbound

This paper cites Tensors: Geometry and Applications.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Tensors: Geometry and Applications

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.375601Z

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.

Observation ce2fc6c3-3ec0-4da8-81d6-87a3bd5b2f11 · outbound

This paper cites Learning the parts of objects by non-negative matrix factorization.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Learning the parts of objects by non-negative matrix factorization

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.077744Z

Source-reported events for the cited work

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Observation dbdd4931-48a4-4fe3-848f-75f8e5632aea · outbound

This paper cites VisualBERT: A Simple and Performant Baseline for Vision and Language.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment VisualBERT: A Simple and Performant Baseline for Vision and Language

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.081316Z

Source-reported events for the cited work

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Observation a2a4fefa-fb81-4788-a5d6-880b504677ab · outbound

This paper cites Oscar: Object-semantics aligned pre-training for vision-language tasks.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Oscar: Object-semantics aligned pre-training for vision-language tasks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.357340Z

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.

Observation 1be2970d-36d7-4ea1-880d-3c7ca63f9ab8 · outbound

This paper cites Vilbert: Pretraining task-agnostic visiolinguistic representations for vision-and-language tasks.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Vilbert: Pretraining task-agnostic visiolinguistic representations for vision-and-language tasks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.346361Z

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.

Observation e46ce8bd-c577-487e-9a54-74d1174d1921 · outbound

This paper cites Modeling modality-specific and shared information for multimodal data representation learning.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Modeling modality-specific and shared information for multimodal data representation learning

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.335930Z

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.

Observation dc9bc803-1a12-4238-a41d-af4138ab9184 · outbound

This paper cites Topology and generalization in neural networks.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Topology and generalization in neural networks

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.324145Z

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.

Observation 675fc86e-dab6-4313-ba9f-da6572c38832 · outbound

This paper cites Polynomial Optimization and Applications.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Polynomial Optimization and Applications

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.311689Z

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.

Observation c6570bd9-2db4-4ff4-8256-23cacad53590 · outbound

This paper cites Learning transferable visual models from natural language supervision.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Learning transferable visual models from natural language supervision

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.298890Z

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.

Observation a6ee92e0-b43f-4b36-95d3-8c1f74364481 · outbound

This paper cites Doomsdays in a modified theory of gravity: A classical and a quantum approach.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Doomsdays in a modified theory of gravity: A classical and a quantum approach

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:34:47.175431Z

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.

Observation 942b7788-9539-4412-a52a-0fbec5204ce6 · outbound

This paper cites Variational bi-lstm for multimodal conditional text generation.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Variational bi-lstm for multimodal conditional text generation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.287201Z

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.

Observation a15005a5-bc12-459f-8d43-dfc1e9432acd · outbound

This paper cites Lxmert: Learning cross-modality encoder representations from transformers.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Lxmert: Learning cross-modality encoder representations from transformers

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.276107Z

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.

Observation cad459e7-1e8d-484d-824b-228c42643e96 · outbound

This paper cites Learning and Generalization: With Applications to Neural Networks.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Learning and Generalization: With Applications to Neural Networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.265056Z

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.

Observation 040705a9-8312-4ed4-a44a-ac133edb7b69 · outbound

This paper cites On deep multimodal representation learning.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment On deep multimodal representation learning

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.253732Z

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.

Observation cfb59902-4345-426a-a4df-0ace90b9d2fb · outbound

This paper cites Cross-Modal Contrastive Learning for Text-to-Image Generation.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Cross-Modal Contrastive Learning for Text-to-Image Generation

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T05:34:47.124307Z

Source-reported events for the cited work

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Observation 9c505c68-aa1c-4e65-a345-09510b118ad4 · outbound

This paper cites Split neural networks for multimodal fusion.

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment Split neural networks for multimodal fusion

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:34:47.242702Z

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.

Pith citing papers

No inbound Pith citation observations are available.