Paper Citation Record · LEDGER

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode

As of 21 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2507.13045.

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

pith.paper-citation-record.v1
2507.13045 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:41:39.682032Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:54:52.136373Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T14:54:52.219073Z

Reference resolution

14 of 14 outbound references displayed

verified exact1
verified fuzzy6
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e25aff4-e7e3-4589-ae86-f96a2fabeaf2 · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:42.305938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6e3089d1-fb13-41b1-9a01-aa42421f3800 · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:42.160134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 17c5e670-5529-45b6-9c2d-470270a14be5 · outbound

This paper cites Gessel,Lagrange Inversion, Journal of Combinatorial Theory, Series A144 (2016), 212-249.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Gessel,Lagrange Inversion, Journal of Combinatorial Theory, Series A144 (2016), 212-249

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:42.019671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 059824d6-01ce-4438-b19e-e831d9862e0f · outbound

This paper cites 4, 333-350.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode 4, 333-350

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:41.873519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b0c524e5-dc22-4141-b2fd-f26b6f964563 · outbound

This paper cites Earnshaw,On the Non-crossing Partitions of a Cycle,.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Earnshaw,On the Non-crossing Partitions of a Cycle,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:41.672006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d59b9f17-b7c3-4024-8876-0ee8135c8a4f · outbound

This paper cites Lambert, Observationes Variae in Mathesin Puram [Various Observations in Pure Math], Acta Helvetica Physico-Mathematico-Anatomico-Botanico-Medica3 (1758), 128-168.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Lambert, Observationes Variae in Mathesin Puram [Various Observations in Pure Math], Acta Helvetica Physico-Mathematico-Anatomico-Botanico-Medica3 (1758), 128-168

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:41.204624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation edaa6ace-aef3-4e15-9144-ce9b2057cf02 · outbound

This paper cites Multiparameter Fuss--Catalan numbers with application to algebraic equations.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Multiparameter Fuss--Catalan numbers with application to algebraic equations

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:41:39.893763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9353436b-e04c-4531-87f9-3e06e20d6050 · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:41.042771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation df2fc01e-c46b-42b7-bf83-69caf661c38b · outbound

This paper cites Raney, Functional composition patterns and power series reversion, Trans am math soc 94 (1960), 441-451.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Raney, Functional composition patterns and power series reversion, Trans am math soc 94 (1960), 441-451

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:40.819847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 81de511e-ed88-4d0e-bfea-17cc26d5d6ff · outbound

This paper cites Hyper-Catalan and Geode Recurrences and Three Conjectures of Wildberger.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Hyper-Catalan and Geode Recurrences and Three Conjectures of Wildberger

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T16:41:39.463365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae1b6a4b-fbce-47e6-aeb6-5f1ab6bd3e6b · outbound

This paper cites 2, 223 - 236.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode 2, 223 - 236

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:41:40.615722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dbe29867-842c-41f9-8277-1efac1ff3c31 · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:40.390211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3de86c26-422e-4f76-9889-452f1c188a0a · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:40.182368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 798853d5-c449-48fa-b41b-d0b007127eda · outbound

This paper cites an unresolved cited work.

Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode Unresolved cited work

Reference 2005

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:41:41.466140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation aa11e9c2-b2d6-41d1-b9e8-3d1ce867353d · inbound

Ordered trees and the Geode cites this paper.

Ordered trees and the Geode Exercises for A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:54:52.225468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.