Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Characterizing Propositional Proofs as Non-Commutative Formulas
As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:1412.8746.
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 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:23:26.535531Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-10T23:46:58.224453Z
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 0d7f41c9-b975-4524-8323-f710e1f8913f · inbound
Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers cites this paper.
Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Characterizing Propositional Proofs as Non-Commutative Formulas
Reference 30
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T23:46:58.239169Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 62cdf3b2-d991-4a27-928f-1c20881cf584 · inbound
Lower Bounds against the Ideal Proof System in Finite Fields cites this paper.
Lower Bounds against the Ideal Proof System in Finite Fields Characterizing Propositional Proofs as Non-Commutative Formulas
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:23:26.535531Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.