Paper Citation Record · LEDGER

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy

As of 22 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2608.04871.

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

pith.paper-citation-record.v1
2608.04871 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:53:26.214156Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact20
verified fuzzy3
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a527457f-01ff-45e9-8ec4-6d6b0ae331ae · outbound

This paper cites Axt, Iteration of primitive recursion,Zeitschrift f¨ ur Mathematische Logik und Grundlagen der Mathematik11(1965), 253–255.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Axt, Iteration of primitive recursion,Zeitschrift f¨ ur Mathematische Logik und Grundlagen der Mathematik11(1965), 253–255

Reference 1

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.383339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9241ad6e-0cbb-46dc-a9d2-1c2da42495d4 · outbound

This paper cites Axt, Iteration of relative primitive recursion,Mathematische Annalen167(1966), 53–55.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Axt, Iteration of relative primitive recursion,Mathematische Annalen167(1966), 53–55

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.363010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0bf9b939-e5a1-422f-aedc-1473c16e632d · outbound

This paper cites Avanzini and U.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Avanzini and U

Reference 3

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.249455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 16447a35-3b77-4062-aa41-0fac4c44ab2b · outbound

This paper cites Avanzini and G.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Avanzini and G

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T14:53:26.015877Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4409b90-f020-4639-b7e5-06bd023c1da1 · outbound

This paper cites Bellantoni and S.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Bellantoni and S

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T14:53:26.020598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a5cf682-6484-46a0-bf2d-5cbc011eb323 · outbound

This paper cites Bellantoni and K.-H.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Bellantoni and K.-H

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.171399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 58c22f20-e1d7-48ef-9549-6c30e4fac002 · outbound

This paper cites Bournez and A.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Bournez and A

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.128241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 598643ec-6f06-4aaa-b7c9-cb7cd4d7ed0e · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.095289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e7829571-1c11-4aab-9450-97a16985fcf9 · outbound

This paper cites Clote, Computation models and function algebras, in E.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Clote, Computation models and function algebras, in E

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T14:53:27.050491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 24436cea-cc90-40aa-a145-b21e88688d55 · outbound

This paper cites Cobham, The intrinsic computational difficulty of functions, in Y.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Cobham, The intrinsic computational difficulty of functions, in Y

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:53:27.668948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cd0fed8d-87df-4024-8f54-44cbbbe99467 · outbound

This paper cites Curzi and A.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Curzi and A

Reference 11

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.979761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 65df31c3-d427-42db-880c-27b116a0c444 · outbound

This paper cites Dal Lago, S.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Dal Lago, S

Reference 12

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.914027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5ef138c9-810f-492b-a40a-08b3c1c2e3a7 · outbound

This paper cites Das and I.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Das and I

Reference 13

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.879803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5e0f47bb-b1cc-405f-98e2-60a448c2214b · outbound

This paper cites Georgieva, Another simplification of the recursion scheme,Archiv f¨ ur Mathematische Logik und Grundlagenforschung18(1977), 1–3.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Georgieva, Another simplification of the recursion scheme,Archiv f¨ ur Mathematische Logik und Grundlagenforschung18(1977), 1–3

Reference 14

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.808103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 63670f68-67ac-4559-b884-110e9063f223 · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 15

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.753121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 57f11199-6855-4d0a-85ff-cfd134245f7d · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.670172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8da93be6-7247-4482-8f7f-0b0701bdfe18 · outbound

This paper cites Goetze and W.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Goetze and W

Reference 17

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.594486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 80941358-78e2-4cf0-898e-cefdfcbcfdf5 · outbound

This paper cites Goetze and W.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Goetze and W

Reference 18

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.529976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0732fb7e-80d3-4f1b-92f3-2c5a67e007f3 · outbound

This paper cites Grozea, NP predicates computable in the weakest level of the Grzegorczyck hierarchy, Journal of Automata, Languages and Combinatorics9(2004), no.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Grozea, NP predicates computable in the weakest level of the Grzegorczyck hierarchy, Journal of Automata, Languages and Combinatorics9(2004), no

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:53:27.626887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b29f0684-111c-4da5-9907-d69cd3c03fe2 · outbound

This paper cites Grzegorczyk, Some classes of recursive functions,Rozprawy Matematyczne, no.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Grzegorczyk, Some classes of recursive functions,Rozprawy Matematyczne, no

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:53:27.560967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4fe157fb-ea49-42d7-b918-3e8e0186080f · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T14:53:26.177846Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51ea2053-1d7b-4015-92a8-9be9c13d2f3e · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 22

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T14:53:27.518829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f6be187f-fe0b-4caa-b489-fc5ea78cc7dd · outbound

This paper cites Parsons, Hierarchies of primitive recursive functions,Zeitschrift f¨ ur Mathematische Logik und Grundlagen der Mathematik14(1968), 357–376.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Parsons, Hierarchies of primitive recursive functions,Zeitschrift f¨ ur Mathematische Logik und Grundlagen der Mathematik14(1968), 357–376

Reference 23

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.451305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c709763d-6046-4c8a-9cd3-30504e8ecd81 · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 24

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.402716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 816f5dee-c556-4222-9d54-c62e2ad4ed70 · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 25

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.384418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0c1913f5-b106-4869-a5e6-9b47e4c2b833 · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:53:27.539908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a71dd271-a608-45ce-beac-863a1a516dbd · outbound

This paper cites Schwichtenberg, Rekursionszahlen und die Grzegorczyk-Hierarchie,Archiv f¨ ur Mathema- tische Logik und Grundlagenforschung12(1969), 85–97.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Schwichtenberg, Rekursionszahlen und die Grzegorczyk-Hierarchie,Archiv f¨ ur Mathema- tische Logik und Grundlagenforschung12(1969), 85–97

Reference 27

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.367566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 569773a4-893a-40d0-a316-9d34f1697982 · outbound

This paper cites an unresolved cited work.

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-15T14:53:26.280359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.