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Paper Citation Record · LEDGER

Transformers learn through gradual rank increase

As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2306.07042.

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

pith.paper-citation-record.v1
2306.07042 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 3 of 3 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:26:36.850936Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T06:19:38.266532Z

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 9285ac0d-c5c0-4f06-8fec-286356d5fa0e · inbound

Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points cites this paper.

Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points Transformers learn through gradual rank increase

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-15T17:26:36.850936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T17:26:36.850936Z digest=sha256:cbe76a9f7e68314261c974b93410201266d98131fca85a6486418623c88a8cc1

Observation c0a99193-4bce-448a-bf43-8401d6bc8fdd · inbound

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale cites this paper.

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale Transformers learn through gradual rank increase

Reference 6

Resolution
verified exact
arxiv_id, observed 2026-07-04T00:29:15.234678Z

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.

source=arxiv_source observed=2026-06-26T21:14:11.815522Z digest=sha256:78926629c654192558523ecab86168f188b98bc5531b73a59e41587f63c2d522

Observation 1ef6ea65-400b-47b9-bf6a-dcbbf69aa419 · inbound

Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity cites this paper.

Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity Transformers learn through gradual rank increase

Reference 4

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:19:38.268271Z

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.

source=arxiv_source observed=2026-06-26T14:36:17.793710Z digest=sha256:9418e54eee0e8bc932f33ca76213452d30dac9fd6b6c4180dd21b5611e2d4be2