Paper Citation Record · LEDGER

Catalytic Computing and Register Programs Beyond Log-Depth

As of 21 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2504.17412.

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

pith.paper-citation-record.v1
2504.17412 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T10:55:23.570399Z

measured 47 of 47 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 2026-08-15T16:29:06.997448Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T16:29:07.889095Z

Reference resolution

46 of 46 outbound references displayed

verified exact2
verified fuzzy39
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5ba3ad21-72b9-4f3f-b7d2-068e9d1f541e · outbound

This paper cites Bipartite matching is in catalytic logspace.

Catalytic Computing and Register Programs Beyond Log-Depth Bipartite matching is in catalytic logspace

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.245930Z

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 7f4f64b1-b19d-4f91-80e8-70db2aa8cd20 · outbound

This paper cites Representations of multivariate polynomials by sums of univariate polynomials in linear forms.

Catalytic Computing and Register Programs Beyond Log-Depth Representations of multivariate polynomials by sums of univariate polynomials in linear forms

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.232328Z

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 989fa5c6-b571-4628-8100-0f8fb930a592 · outbound

This paper cites Computing algebraic formulas using a constant number of registers.

Catalytic Computing and Register Programs Beyond Log-Depth Computing algebraic formulas using a constant number of registers

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.218294Z

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 db3b1c67-1f5d-4cae-8277-66567a42935e · outbound

This paper cites Cook, Patrick W.

Catalytic Computing and Register Programs Beyond Log-Depth Cook, Patrick W

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.202336Z

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 da16082a-a6d1-4d12-b985-e4804ce88ae9 · outbound

This paper cites Computing with a full memory: catalytic space.

Catalytic Computing and Register Programs Beyond Log-Depth Computing with a full memory: catalytic space

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.189748Z

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 226a4c59-eed9-4548-8d27-a57c4bf4bcb5 · outbound

This paper cites Parallel computation for well-endowed rings and space-bounded probabilistic machines.

Catalytic Computing and Register Programs Beyond Log-Depth Parallel computation for well-endowed rings and space-bounded probabilistic machines

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.176906Z

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 7d234987-999a-4d27-a8bd-10d9f18db3c6 · outbound

This paper cites Almost-catalytic Computation.

Catalytic Computing and Register Programs Beyond Log-Depth Almost-catalytic Computation

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T10:55:23.430214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 588734cd-7fd5-4134-8a84-48dbbc5215e3 · outbound

This paper cites On pure space vs catalytic space.

Catalytic Computing and Register Programs Beyond Log-Depth On pure space vs catalytic space

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.164848Z

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 8786d6d6-5afc-4465-9889-4e728fcf78e5 · outbound

This paper cites The polynomial method in circuit complexity.

Catalytic Computing and Register Programs Beyond Log-Depth The polynomial method in circuit complexity

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.152461Z

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 1b4455e1-4922-4a2c-a8d0-f7fa34929b46 · outbound

This paper cites Catalytic space: Non-determinism and hierarchy.

Catalytic Computing and Register Programs Beyond Log-Depth Catalytic space: Non-determinism and hierarchy

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.139132Z

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 0691c130-021d-49c6-a132-b9ef01a80087 · outbound

This paper cites On relating time and space to size and depth.

Catalytic Computing and Register Programs Beyond Log-Depth On relating time and space to size and depth

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:24.126031Z

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 a878ceec-b272-4bc7-a3ac-ebc217d725f4 · outbound

This paper cites Generators for certain alternating groups with applications to cryptography.

Catalytic Computing and Register Programs Beyond Log-Depth Generators for certain alternating groups with applications to cryptography

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.983558Z

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 def4e2f6-29ad-43ce-88c9-8fc2e1cf923f · outbound

This paper cites Computing algebraic formulas with a constant number of registers.

Catalytic Computing and Register Programs Beyond Log-Depth Computing algebraic formulas with a constant number of registers

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.972980Z

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 0e415136-6d52-499b-adde-1b3c758e92e5 · outbound

This paper cites Methodologies for designing block ciphers and cryptographic protocols.

Catalytic Computing and Register Programs Beyond Log-Depth Methodologies for designing block ciphers and cryptographic protocols

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.961988Z

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 6c150e39-dd49-402c-a52e-73a5750a189e · outbound

This paper cites The structure of catalytic space: Capturing randomness and time via compression.

Catalytic Computing and Register Programs Beyond Log-Depth The structure of catalytic space: Capturing randomness and time via compression

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.951474Z

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 7dc0fb34-0d4b-4991-8934-a839d4774b87 · outbound

This paper cites Catalytic approaches to the tree evaluation problem.

Catalytic Computing and Register Programs Beyond Log-Depth Catalytic approaches to the tree evaluation problem

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.941209Z

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 d091e883-53c4-4d6a-9476-d15004d0370f · outbound

This paper cites Encodings and the tree evaluation problem.

Catalytic Computing and Register Programs Beyond Log-Depth Encodings and the tree evaluation problem

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.931063Z

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 8668673e-befb-49bb-9503-4b0aabb9228c · outbound

This paper cites Trading time and space in catalytic branching programs.

Catalytic Computing and Register Programs Beyond Log-Depth Trading time and space in catalytic branching programs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.921284Z

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 bfb92b5f-3851-4074-98b9-994f3923b28b · outbound

This paper cites Tree evaluation is in space o (log n log log n).

Catalytic Computing and Register Programs Beyond Log-Depth Tree evaluation is in space o (log n log log n)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.911554Z

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 9687155f-fe84-40b3-b3b9-f9b13d3b6689 · outbound

This paper cites Pebbles and branching programs for tree evaluation.

Catalytic Computing and Register Programs Beyond Log-Depth Pebbles and branching programs for tree evaluation

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.901523Z

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 11a6449c-5aa3-43ae-b3aa-03a269678928 · outbound

This paper cites The classification of problems which have fast parallel algorithms.

Catalytic Computing and Register Programs Beyond Log-Depth The classification of problems which have fast parallel algorithms

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.891530Z

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 6d8a294b-e707-480b-8575-dd7487d97fbe · outbound

This paper cites Randomized and symmetric catalytic computation.

Catalytic Computing and Register Programs Beyond Log-Depth Randomized and symmetric catalytic computation

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.880638Z

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 c6004204-b025-4611-9265-b041b9c91abd · outbound

This paper cites Opening up the distinguisher: A hardness to randomness approach for bpl= l that uses properties of bpl.

Catalytic Computing and Register Programs Beyond Log-Depth Opening up the distinguisher: A hardness to randomness approach for bpl= l that uses properties of bpl

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.870559Z

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 78b354eb-8146-4a1e-b756-f933364b73e4 · outbound

This paper cites Hardness of function composition for semantic read once branching programs.

Catalytic Computing and Register Programs Beyond Log-Depth Hardness of function composition for semantic read once branching programs

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.860590Z

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 e7f6ca2c-13c9-4717-a8a3-6447440c3a4a · outbound

This paper cites Fully Characterizing Lossy Catalytic Computation.

Catalytic Computing and Register Programs Beyond Log-Depth Fully Characterizing Lossy Catalytic Computation

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-16T10:55:23.645131Z

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 2de37dcf-c890-4432-9590-8904cacbdb4e · outbound

This paper cites Unambiguous catalytic computation.

Catalytic Computing and Register Programs Beyond Log-Depth Unambiguous catalytic computation

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.849745Z

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 af919f27-41ca-4d91-9d57-27fa78ea8265 · outbound

This paper cites Lossy Catalytic Computation.

Catalytic Computing and Register Programs Beyond Log-Depth Lossy Catalytic Computation

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T10:55:23.499996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e837abf3-21ca-4b16-9690-9efec85633d4 · outbound

This paper cites Solving tree evaluation in o (log n log log n) space.

Catalytic Computing and Register Programs Beyond Log-Depth Solving tree evaluation in o (log n log log n) space

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.838428Z

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 410d7b21-da13-473e-aa15-b366ca569d7e · outbound

This paper cites Read-once branching programs for tree evaluation problems.

Catalytic Computing and Register Programs Beyond Log-Depth Read-once branching programs for tree evaluation problems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.826065Z

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 4f627717-25f2-422e-a660-38bd9aa04666 · outbound

This paper cites Catalytic computation.

Catalytic Computing and Register Programs Beyond Log-Depth Catalytic computation

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.814652Z

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 30144dd0-5f98-44d5-8ec7-c42e3b66f090 · outbound

This paper cites Collapsing catalytic classes.

Catalytic Computing and Register Programs Beyond Log-Depth Collapsing catalytic classes

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.803624Z

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 dd174826-4268-4761-9b18-5909ae264bce · outbound

This paper cites Pebbling Arguments for Tree Evaluation.

Catalytic Computing and Register Programs Beyond Log-Depth Pebbling Arguments for Tree Evaluation

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-16T10:55:23.518334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9305958c-b839-4589-85ad-7bb655f5d2c8 · outbound

This paper cites Distinguishing, predicting, and certifying: On the long reach of partial notions of pseudorandomness.

Catalytic Computing and Register Programs Beyond Log-Depth Distinguishing, predicting, and certifying: On the long reach of partial notions of pseudorandomness

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.791774Z

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 c901a2c5-8042-4e57-9370-08fac359206a · outbound

This paper cites Catalytic computing, tree evaluation, & clean computation, 2020.

Catalytic Computing and Register Programs Beyond Log-Depth Catalytic computing, tree evaluation, & clean computation, 2020

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.780392Z

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 03edc7e8-57a7-47de-95b2-dc89b1a1bc45 · outbound

This paper cites Reusing space: Techniques and open problems.

Catalytic Computing and Register Programs Beyond Log-Depth Reusing space: Techniques and open problems

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-16T10:55:23.529711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94ec5714-b2bb-4e1f-9b1f-1e64cc8f48d8 · outbound

This paper cites On simultaneous resource bounds.

Catalytic Computing and Register Programs Beyond Log-Depth On simultaneous resource bounds

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.762824Z

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 e2bd8014-ebe3-49c7-ab29-e1d5be008b39 · outbound

This paper cites A Note on Amortized Branching Program Complexity.

Catalytic Computing and Register Programs Beyond Log-Depth A Note on Amortized Branching Program Complexity

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-16T10:55:23.605587Z

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 444fcbd1-6522-43bb-b75a-10f9e90992ad · outbound

This paper cites Sheffield, and William Wang.

Catalytic Computing and Register Programs Beyond Log-Depth Sheffield, and William Wang

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.752050Z

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 0e650bb2-fcbe-4741-be97-5212670be9ba · outbound

This paper cites Derandomizing logspace with a small shared hard drive.

Catalytic Computing and Register Programs Beyond Log-Depth Derandomizing logspace with a small shared hard drive

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.741106Z

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 100806c5-f695-41ea-999b-7f55cabc49fc · outbound

This paper cites On uniform circuit complexity.

Catalytic Computing and Register Programs Beyond Log-Depth On uniform circuit complexity

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.729239Z

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 d3078b90-5bcb-43d3-a1bc-958367d2a11f · outbound

This paper cites Amortized circuit complexity, formal complexity measures, and catalytic algorithms.

Catalytic Computing and Register Programs Beyond Log-Depth Amortized circuit complexity, formal complexity measures, and catalytic algorithms

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.718283Z

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 a52d6b7a-0251-49d0-90de-f0d40619066b · outbound

This paper cites On a decomposition of polynomials in several variables.

Catalytic Computing and Register Programs Beyond Log-Depth On a decomposition of polynomials in several variables

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.706626Z

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 b8cfd27c-164f-4e71-a7c3-fb18268a0f3f · outbound

This paper cites The synthesis of two-terminal switching circuits.

Catalytic Computing and Register Programs Beyond Log-Depth The synthesis of two-terminal switching circuits

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.695468Z

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 e0f3b789-a448-43a9-82dd-b9d9f0e8445a · outbound

This paper cites Circuit definitions of nondeterministic complexity classes.

Catalytic Computing and Register Programs Beyond Log-Depth Circuit definitions of nondeterministic complexity classes

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.684449Z

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 75a68fd8-1f83-4c1e-9e8a-d62cd9a45e41 · outbound

This paper cites Introduction to circuit complexity: a uniform approach.

Catalytic Computing and Register Programs Beyond Log-Depth Introduction to circuit complexity: a uniform approach

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-16T10:55:23.566878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9037d88-df7e-41ec-b485-2b65908f11ba · outbound

This paper cites Simulating time with square-root space.

Catalytic Computing and Register Programs Beyond Log-Depth Simulating time with square-root space

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:55:23.668248Z

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 0112003b-6e92-4f74-aab4-77f4f650f855 · inbound

Linear Matroid Intersection is in Catalytic Logspace cites this paper.

Linear Matroid Intersection is in Catalytic Logspace Catalytic Computing and Register Programs Beyond Log-Depth

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:29:07.894427Z

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.