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Paper Citation Record · LEDGER

Learning High-Degree Parities: The Crucial Role of the Initialization

As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2412.04910.

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

pith.paper-citation-record.v1
2412.04910 v3

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 2 of 2 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T12:23:57.799757Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-09T12:23:58.124801Z

Reference resolution

0 of 0 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved0
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 5ef45449-9471-4a80-b362-2a02d7e0eaa6 · inbound

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers cites this paper.

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers Learning High-Degree Parities: The Crucial Role of the Initialization

Reference 2024

Resolution
malformed identifier
local_arxiv, observed 2026-08-09T12:23:58.131874Z

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.

source=pdf_text observed=2026-08-09T12:23:57.799757Z digest=sha256:c79686c3f84c303e5490ce375fd5087134c170eddd6712dfbbe9ed6c7ab9935e

Observation 63e7fc53-68c9-4555-b752-2dc162014bbb · inbound

Unraveling Syntax: Language Modeling and the Substructure of Grammars cites this paper.

Unraveling Syntax: Language Modeling and the Substructure of Grammars Learning High-Degree Parities: The Crucial Role of the Initialization

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-04T12:47:18.978395Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-04T12:47:18.978395Z digest=sha256:d31a1aade14a30d160d974a2b1b24d45c59c5db20108324d617b31242b4e9d75