Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-13T20:48:51.783586Z
Paper Citation Record · LEDGER
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason
As of 1 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 1 inbound Pith citation observation for arXiv:2604.15350.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-01T06:32:01.292127+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-13T05:02:55.608400Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
8 of 8 outbound references displayed
- verified exact0
- verified fuzzy5
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 2a33b218-8d16-4b9e-aee6-3c8ef38b7a68 · outbound
This paper cites an unresolved cited work.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-05-14T01:03:31.705211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation a6a2ca4e-1d06-40a3-a6af-7cd7c118656a · outbound
This paper cites an unresolved cited work.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-05-14T01:03:31.713165Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation 998a3b28-84c0-4bb8-ad88-a1d19059b300 · outbound
This paper cites an unresolved cited work.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-14T01:03:31.707797Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation c975f2a4-9fd7-4ee3-9987-d9caa7ffe614 · outbound
This paper cites For token-level dynamics (Finding 5–6), we use a sliding window of w= 10 tokens, computing SVD on H(ℓ) window ∈ Rw×d at each generation step.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason For token-level dynamics (Finding 5–6), we use a sliding window of w= 10 tokens, computing SVD on H(ℓ) window ∈ Rw×d at each generation step
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T01:03:31.715664Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation 022d5260-e205-4261-a321-23009d896462 · outbound
This paper cites The spectral trajectory shows clear α gradient spikes at calculation boundaries (e.g., after “=”), with Layer 9 showing the most pronounced punctuation effect.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason The spectral trajectory shows clear α gradient spikes at calculation boundaries (e.g., after “=”), with Layer 9 showing the most pronounced punctuation effect
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T01:03:31.710809Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation 12ce60fa-2fb1-4796-a431-4f7ad663af2a · outbound
This paper cites Similar punctuation pattern to Task 0, with additional spikes at variable introduction (“Letx=”).
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason Similar punctuation pattern to Task 0, with additional spikes at variable introduction (“Letx=”)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T01:03:31.702574Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation 25f08585-038b-400c-be9b-17b4181a0ede · outbound
This paper cites therefore.
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T01:03:31.717859Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Observation db7519c9-2ad5-4536-bf9c-c1deb8718727 · outbound
This paper cites Step 1:”, “therefore.
The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason Step 1:”, “therefore
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T01:03:31.720027Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-01T06:32:01.292127+00:00.
Pith citing papers
Observation cae8744d-8b3d-488b-ad1f-b8cd9e7e5eca · inbound
KV-PRM: Efficient Process Reward Modeling via KV-Cache Transfer for Multi-Agent Test-Time Scaling cites this paper.
KV-PRM: Efficient Process Reward Modeling via KV-Cache Transfer for Multi-Agent Test-Time Scaling The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-07-13T05:02:55.608400Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.