Paper Citation Record · LEDGER

On the Mathematical Impossibility of Safe Universal Approximators

As of 10 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2507.03031.

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

pith.paper-citation-record.v1
2507.03031 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:41:55.794436Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+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

17 of 17 outbound references displayed

verified exact5
verified fuzzy7
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 25ef7974-9a0f-476c-b91b-eaa4dc8435f0 · outbound

This paper cites Explaining and Harnessing Adversarial Examples.

On the Mathematical Impossibility of Safe Universal Approximators Explaining and Harnessing Adversarial Examples

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T20:41:54.199354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b6fcaf1-eb8d-416b-95ea-59207a9ad078 · outbound

This paper cites Multilayer feedforward networks are universal approximators.

On the Mathematical Impossibility of Safe Universal Approximators Multilayer feedforward networks are universal approximators

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:58.295823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5c480be6-d116-4e01-a70e-852e96ba3dd4 · outbound

This paper cites Universal statistics of fisher information in deep neural networks: Mean field approach.

On the Mathematical Impossibility of Safe Universal Approximators Universal statistics of fisher information in deep neural networks: Mean field approach

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:58.132222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0fab4f09-0c15-4e4b-892b-586f3a9bba19 · outbound

This paper cites Catastrophic forgetting in continual graph learning.

On the Mathematical Impossibility of Safe Universal Approximators Catastrophic forgetting in continual graph learning

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:57.903201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48bf4ec6-b7d0-459f-9b44-6a12b540c63d · outbound

This paper cites Stability of c ∞ mappings, ii.

On the Mathematical Impossibility of Safe Universal Approximators Stability of c ∞ mappings, ii

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:57.710878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b091529b-f704-4867-a2c0-bd5953d300c4 · outbound

This paper cites On the Nonlinearity of Layer Normalization.

On the Mathematical Impossibility of Safe Universal Approximators On the Nonlinearity of Layer Normalization

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:41:56.698573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5d92649f-ba75-4c80-aabf-33819e83cd30 · outbound

This paper cites Graph neural networks exponentially lose expressive power for node classification.

On the Mathematical Impossibility of Safe Universal Approximators Graph neural networks exponentially lose expressive power for node classification

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:57.428383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d17fc486-dda0-49dd-acb5-3bfba89e1e2e · outbound

This paper cites Classes of recursively enumerable sets and their decision problems.

On the Mathematical Impossibility of Safe Universal Approximators Classes of recursively enumerable sets and their decision problems

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:57.181817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8c4c67a7-aa15-4fef-a381-9a0916f24efb · outbound

This paper cites Bridgeout: stochastic bridge regularization for deep neural networks.

On the Mathematical Impossibility of Safe Universal Approximators Bridgeout: stochastic bridge regularization for deep neural networks

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:41:56.506714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f7469bc5-cdd0-4071-a657-e369be604cd3 · outbound

This paper cites Stabilize deep resnet with a sharp scaling factor τ.

On the Mathematical Impossibility of Safe Universal Approximators Stabilize deep resnet with a sharp scaling factor τ

Reference 12

Resolution: verified exact; doi, observed 2026-08-06T20:41:55.987157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f329d0f7-1584-4276-ae40-0689fc99ebd5 · outbound

This paper cites On the Training Instability of Shuffling SGD with Batch Normalization.

On the Mathematical Impossibility of Safe Universal Approximators On the Training Instability of Shuffling SGD with Batch Normalization

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:41:56.363546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e70b190b-5144-418e-a4ee-1a99270d50f4 · outbound

This paper cites On the equivalence between graph isomorphism testing and func- tion approximation with gnns.

On the Mathematical Impossibility of Safe Universal Approximators On the equivalence between graph isomorphism testing and func- tion approximation with gnns

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:41:56.902642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 36941140-0c54-4d2b-a716-20ac10fdcd4c · outbound

This paper cites Are Transformers universal approximators of sequence-to-sequence functions?.

On the Mathematical Impossibility of Safe Universal Approximators Are Transformers universal approximators of sequence-to-sequence functions?

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T20:41:55.587713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation baa9a4d6-6462-48ae-86d5-143f7089f0ff · outbound

This paper cites Stabilizing Transformer Training by Preventing Attention Entropy Collapse.

On the Mathematical Impossibility of Safe Universal Approximators Stabilizing Transformer Training by Preventing Attention Entropy Collapse

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T20:41:55.705061Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e7155f2-7a28-4183-8cd5-813ff7b2c950 · outbound

This paper cites Dropout in Training Neural Networks: Flatness of Solution and Noise Structure.

On the Mathematical Impossibility of Safe Universal Approximators Dropout in Training Neural Networks: Flatness of Solution and Noise Structure

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:41:56.185626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 97d43d9b-5efc-445c-b887-8668c52fb786 · outbound

This paper cites Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing.

On the Mathematical Impossibility of Safe Universal Approximators Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T20:41:54.104960Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6280ffc3-a12f-40fe-9030-78aab512c9ec · outbound

This paper cites Scalable-Softmax Is Superior for Attention.

On the Mathematical Impossibility of Safe Universal Approximators Scalable-Softmax Is Superior for Attention

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-06T20:41:54.830690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.