Paper Citation Record · LEDGER

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning

As of 7 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.11116.

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

pith.paper-citation-record.v1
2607.11116 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T06:57:31.514910Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

30 of 30 outbound references displayed

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verified fuzzy0
unresolved30
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malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 00f91019-3fde-420c-8e90-18d79f10cfd2 · outbound

This paper cites Zico Kolter, and Vladlen Koltun.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Zico Kolter, and Vladlen Koltun

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation 1fcd05c0-a29c-46cf-9d89-3182ed94a82d · outbound

This paper cites Uni- versal transformers.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Uni- versal transformers

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation 9de43db6-8111-4b94-92ee-fc4a05504d2a · outbound

This paper cites Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation e136c14d-ccb3-49c0-a6cd-1d8aab3e884d · outbound

This paper cites Adaptive Computation Time for Recurrent Neural Networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Adaptive Computation Time for Recurrent Neural Networks

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 8710e4c9-399b-42c4-a135-8d7e8d79b8a6 · outbound

This paper cites Hamiltonian neural networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Hamiltonian neural networks

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 15f7d86b-346c-440a-8657-93b614160ca3 · outbound

This paper cites SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems.Neural Networks, 132:166–179, 2020.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems.Neural Networks, 132:166–179, 2020

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 08417bce-2d34-44cf-a764-dd53d121cc60 · outbound

This paper cites Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas, and Stephen J.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas, and Stephen J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1839b3c-8b56-439c-a460-b102d9edfcfb · outbound

This paper cites Zico Kolter.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Zico Kolter

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0a750c5-918b-4e2e-b29e-4cfbea9f26ce · outbound

This paper cites Implicit deep learning.SIAM Journal on Mathematics of Data Science, 3(3):930–958, 2021.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Implicit deep learning.SIAM Journal on Mathematics of Data Science, 3(3):930–958, 2021

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 348ddbf7-94a7-4b59-a437-68d9262818a7 · outbound

This paper cites Zico Kolter.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Zico Kolter

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

Source-reported events for the cited work

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Observation 75c41a4d-7e48-4979-bd4f-5e3a136a6459 · outbound

This paper cites Anderson.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Anderson

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 707c4ab6-add1-4c9f-8bfa-bceb9f533964 · outbound

This paper cites Zico Kolter.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Zico Kolter

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation c04824cf-8bbb-4896-9656-0fda280b6ae1 · outbound

This paper cites JFB: Jacobian-Free Backpropagation for Implicit Networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning JFB: Jacobian-Free Backpropagation for Implicit Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation dd738453-b16d-405c-bedd-46145e7d5670 · outbound

This paper cites Zico Kolter, and Roger B.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Zico Kolter, and Roger B

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation bb3c5dfd-5fd9-4cc1-a13f-ec17984e2105 · outbound

This paper cites Lagrangian Neural Networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Lagrangian Neural Networks

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation b5e372b2-2d18-4d05-9d92-b8ddd71542f1 · outbound

This paper cites Neural Ordinary Differential Equations.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Neural Ordinary Differential Equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation b6f7a5b9-75b6-4985-8d5c-754b090c43a7 · outbound

This paper cites PonderNet: Learning to Ponder.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning PonderNet: Learning to Ponder

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 5d2266d9-5771-4583-b4b3-fe2f90dba5e7 · outbound

This paper cites Can you learn an algorithm? Generalizing from easy to hard problems with recurrent networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Can you learn an algorithm? Generalizing from easy to hard problems with recurrent networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation ee59ea79-b184-4f2b-b39d-53b9d8437e59 · outbound

This paper cites End-to-end algorithm synthesis with recurrent networks: Extrapolation without overthinking.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning End-to-end algorithm synthesis with recurrent networks: Extrapolation without overthinking

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 89b7a40e-9868-483b-8447-9b303b98d6a2 · outbound

This paper cites Nowak, and Dimitris Papailiopoulos.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Nowak, and Dimitris Papailiopoulos

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation a133d40c-c127-42da-973b-c08bf391a49b · outbound

This paper cites Hierarchical Reasoning Model.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Hierarchical Reasoning Model

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation c101359a-fc11-4a1e-9025-ba73f4314cbc · outbound

This paper cites Less is More: Recursive Reasoning with Tiny Networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Less is More: Recursive Reasoning with Tiny Networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation abc6c49d-e214-40f7-b5d0-0319baedfc72 · outbound

This paper cites The CLRS algorithmic reasoning benchmark.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning The CLRS algorithmic reasoning benchmark

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 676e7afb-a257-4998-b62e-682040756b6a · outbound

This paper cites Understanding intermediate layers using linear classifier probes.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Understanding intermediate layers using linear classifier probes

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation c7fd43e2-1b6f-46ce-b49d-5bb6736a0182 · outbound

This paper cites Designing and interpreting probes with control tasks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Designing and interpreting probes with control tasks

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation 1b1fb8d4-6aa2-445c-8604-37bc93a9368a · outbound

This paper cites Gradient starvation: A learning proclivity in neural networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Gradient starvation: A learning proclivity in neural networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation 20bd1a1f-ebd7-4e6e-897f-506204470a16 · outbound

This paper cites Shortcut Learning in Deep Neural Networks.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Shortcut Learning in Deep Neural Networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation 0603fc2b-213a-435c-ae18-97bd74c426f4 · outbound

This paper cites ProofWriter: Generating implications, proofs, and abductive statements over natural language.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning ProofWriter: Generating implications, proofs, and abductive statements over natural language

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Observation a5a46cfa-bbdb-4bdc-93d5-18dba150a4b9 · outbound

This paper cites DeBERTaV3: Improving DeBERTa using ELECTRA-style pre-training with gradient-disentangled embedding sharing.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning DeBERTaV3: Improving DeBERTa using ELECTRA-style pre-training with gradient-disentangled embedding sharing

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Unavailable: canonical work link unavailable.

Observation d522053a-9dd7-4ea5-bbf8-a79889df019e · outbound

This paper cites an unresolved cited work.

The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-14T06:57:31.514910Z

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Pith citing papers

No inbound Pith citation observations are available.