Paper Citation Record · LEDGER

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete

As of 20 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.12469.

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

pith.paper-citation-record.v1
2507.12469 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:50:30.007638Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

25 of 25 outbound references displayed

verified exact0
verified fuzzy9
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0c2139ec-560c-4449-b9e3-a3be481a826d · outbound

This paper cites merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.895390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 292fb422-788a-4ef8-b4b6-00c256d7bc8c · outbound

This paper cites merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.901501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9147488-844a-4c67-86ee-5b806f927494 · outbound

This paper cites merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.906689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9d42ec9-fc8c-4f7f-8872-4ad273862e05 · outbound

This paper cites merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.911599Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3305ee14-b51f-4672-92c4-f7ee52cb4b9f · outbound

This paper cites merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.917086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5f6b987-a3fb-4593-a31a-266df3dc10a1 · outbound

This paper cites Structured denoising diffusion models in discrete state-spaces.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Structured denoising diffusion models in discrete state-spaces

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.922055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 008136a2-0c92-47ac-ae9e-5578b3f2d193 · outbound

This paper cites Reverse-time diffusion equation models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Reverse-time diffusion equation models

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.293882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dc72cba3-07da-4876-a139-ac2aaac5b577 · outbound

This paper cites Block diffusion: Interpolating between autoregressive and diffusion language models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Block diffusion: Interpolating between autoregressive and diffusion language models

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.278491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 34d7a256-0b12-41c0-9e4d-4aeedbfdec95 · outbound

This paper cites Diffusion models beat gans on image synthesis.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Diffusion models beat gans on image synthesis

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.936002Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a58be5b-e3ff-46d6-8c82-838feb9646cf · outbound

This paper cites Counter machines and counter languages.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Counter machines and counter languages

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.255580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1bac6d04-130a-4662-8a68-7588ea7023f1 · outbound

This paper cites Towards revealing the mystery behind chain of thought: a theoretical perspective.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Towards revealing the mystery behind chain of thought: a theoretical perspective

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.241339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f945fd4d-23ac-45a0-800d-2b952fb1317f · outbound

This paper cites DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.948935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70008f87-b7f9-4638-bba5-6d0a28c410d0 · outbound

This paper cites Threshold circuits of bounded depth.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Threshold circuits of bounded depth

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.226846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9ee15fe6-af62-47d5-9b64-06352d1524c0 · outbound

This paper cites Variational diffusion models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Variational diffusion models

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.211631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 278c5135-f367-4484-b2b4-3e9fadf21ad2 · outbound

This paper cites Ash, Surbhi Goel, Akshay Krishnamurthy, and Cyril Zhang.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Ash, Surbhi Goel, Akshay Krishnamurthy, and Cyril Zhang

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.962215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f06463c-7236-4ac6-8d99-6fe319957e02 · outbound

This paper cites Chain of Thought Empowers Transformers to Solve Inherently Serial Problems.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Chain of Thought Empowers Transformers to Solve Inherently Serial Problems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.966263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53a21e2d-bc5a-40d0-b06d-38d2fcc2cf88 · outbound

This paper cites Understanding Diffusion Models: A Unified Perspective.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Understanding Diffusion Models: A Unified Perspective

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.970884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c3adfb5-dc4c-4e3b-8af1-53ddb9effac7 · outbound

This paper cites O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.975412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa8f7a10-8e98-4487-b310-4d64cee57896 · outbound

This paper cites Computation: Finite and Infinite Machines.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Computation: Finite and Infinite Machines

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.186990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c696a32b-386d-4a79-9a6a-706e9a8e9d17 · outbound

This paper cites The Illusion of State in State-Space Models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete The Illusion of State in State-Space Models

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.983949Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7e22955-cfaf-4a66-9448-b20e211a7199 · outbound

This paper cites The parallelism tradeoff: Limitations of log-precision transformers.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete The parallelism tradeoff: Limitations of log-precision transformers

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.988738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7cd7497-0bea-4ff0-b19c-410b12fe1550 · outbound

This paper cites Parallel computation with threshold functions.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Parallel computation with threshold functions

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.162472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4f0d569b-3af3-4b5d-ad76-926b708c4bce · outbound

This paper cites Scaling Properties of Diffusion Models for Perceptual Tasks.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Scaling Properties of Diffusion Models for Perceptual Tasks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:29.998263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21f51047-2b03-4749-9eda-50a582d12fa6 · outbound

This paper cites Deep unsupervised learning using nonequilibrium thermodynamics.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Deep unsupervised learning using nonequilibrium thermodynamics

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:50:30.146594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 927c89ae-566d-4a54-bb4b-c9c7333c6ca9 · outbound

This paper cites Spatial Reasoning with Denoising Models.

Perfect diffusion is $\mathsf{TC}^0$ -- Bad diffusion is Turing-complete Spatial Reasoning with Denoising Models

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-16T11:50:30.007638Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.