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Paper Citation Record · LEDGER

Chip-Firing and Riemann-Roch Theory for Directed Graphs

As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:1012.0287.

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

pith.paper-citation-record.v1
1012.0287 v2

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 2026-08-16T06:30:59.297886+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:29:17.179553Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T13:55:39.239467Z

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 e48c2663-2e19-4ef5-a6e4-c7858d2ff1b6 · inbound

Chip-Firing Games and Critical Groups cites this paper.

Chip-Firing Games and Critical Groups Chip-Firing and Riemann-Roch Theory for Directed Graphs

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:55:39.244084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:55:38.737773Z digest=sha256:3ccf775d100bceda6743bfb9bf94c24872ffaca19738ff0f0bd72f29ee427a1e

Observation d8fd1c9f-2c5e-4243-b467-ce26768db5d3 · inbound

Generalized chip firing and critical groups of arithmetical structures on trees cites this paper.

Generalized chip firing and critical groups of arithmetical structures on trees Chip-Firing and Riemann-Roch Theory for Directed Graphs

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-15T23:29:17.179553Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T23:29:17.179553Z digest=sha256:d458c53316447d91ebff7a40efc58f71a508c99b6cebe8bfbe4ca8f32678ba1c