Paper Citation Record · LEDGER

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems

As of 7 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2509.02054.

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

pith.paper-citation-record.v1
2509.02054 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:02:40.299059Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:02:38.880350Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T00:14:46.949984Z

Reference resolution

23 of 23 outbound references displayed

verified exact1
verified fuzzy17
unresolved3
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0b9592ce-a713-400a-9fe8-70561bad5e09 · outbound

This paper cites In machine learning field, applications increas- ingly rely on discretized models for training and inference.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems In machine learning field, applications increas- ingly rely on discretized models for training and inference

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:44.287130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation da699f64-0dbd-449b-8ae5-fff0bdbd4475 · outbound

This paper cites Definition ofα-Approximation In the process of discretization of analog systems, the well- known mapping from the s-domain to the z-domain can be used by substitution.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Definition ofα-Approximation In the process of discretization of analog systems, the well- known mapping from the s-domain to the z-domain can be used by substitution

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:44.064299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 852f86be-56cc-41fb-b92b-8bc946f3336d · outbound

This paper cites Figure 2(a) illustrates the Euler transformation (also known as the backward-difference approximation) geometrically.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Figure 2(a) illustrates the Euler transformation (also known as the backward-difference approximation) geometrically

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:43.856586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 03a80a83-ae29-48c3-86c9-264a465ed21d · outbound

This paper cites an unresolved cited work.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-05T12:02:43.724354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 80e61f9d-d57d-4088-9cf5-9806c9a74ada · outbound

This paper cites Figure 3 shows the amplitude and phase distortion of a low-pass filter (LPF) with differentα.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Figure 3 shows the amplitude and phase distortion of a low-pass filter (LPF) with differentα

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:43.583810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e5fddcb7-11d4-4fa1-8adf-ef1ae2bdbe69 · outbound

This paper cites For this reason, we proposed the following hypothesis: Exclusion Hypothesis:Suppose the analog system is in- ternally stable.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems For this reason, we proposed the following hypothesis: Exclusion Hypothesis:Suppose the analog system is in- ternally stable

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:43.407845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 02ddeb85-6584-492a-8bea-aea86a9716f8 · outbound

This paper cites an unresolved cited work.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-05T12:02:43.184502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e30fc190-6ec0-41ff-96ac-d4405e6053ae · outbound

This paper cites A new accurate discretization method for high-frequency component mechatronics systems,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems A new accurate discretization method for high-frequency component mechatronics systems,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:41.960899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b9ac0967-1a38-4ec2-87a7-e453c0799607 · outbound

This paper cites Mamba: Linear-time sequence modeling with selective state spaces,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Mamba: Linear-time sequence modeling with selective state spaces,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:42.937568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4cacaf93-c2ef-4c92-98a4-585ba793f00a · outbound

This paper cites Digital Twins in Industrial Applications: Concepts, Mathematical Modeling, and Use Cases.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Digital Twins in Industrial Applications: Concepts, Mathematical Modeling, and Use Cases

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:02:40.628089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a2796bf8-c51a-4445-9eca-9a0894f6d9fa · outbound

This paper cites Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-05T12:02:38.880350Z

Source-reported events for the cited work

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Observation 56dd959f-ad4e-4c95-b046-6b153ce095b4 · outbound

This paper cites Accu- racy analysis of the zero-order hold model for digital pulse width modulation,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Accu- racy analysis of the zero-order hold model for digital pulse width modulation,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:42.708879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 861fb9fa-475d-447b-a0d0-0c8d803e04a9 · outbound

This paper cites Method using bilinear transformation for measurement of impedance parameters of a multielement two- terminal network,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Method using bilinear transformation for measurement of impedance parameters of a multielement two- terminal network,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:42.546196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 934d47a9-05fb-48f3-8e5a-0dcc1d90bb40 · outbound

This paper cites Digital iir filter design using bilinear transformation in matlab,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Digital iir filter design using bilinear transformation in matlab,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:42.386406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9eb2565d-1f7f-481c-a5db-bb859b390db0 · outbound

This paper cites Novel approach to analog-to-digital trans- forms,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Novel approach to analog-to-digital trans- forms,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:42.268544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9be299ff-1d91-4ab0-9bcc-87d6bedd87ab · outbound

This paper cites Discretization of nonlinear non-affine time delay systems based on second-order hold,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Discretization of nonlinear non-affine time delay systems based on second-order hold,

Reference 16

Resolution: malformed identifier; raw_fallback, observed 2026-08-05T12:02:42.122944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 92acde0f-4df6-445e-b665-1f97ef283442 · outbound

This paper cites Al-alaoui operator and the new transformation polynomials for discretization of analogue systems,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Al-alaoui operator and the new transformation polynomials for discretization of analogue systems,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:41.817762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2821b527-d288-4ec1-8ff6-a7949530a61e · outbound

This paper cites Application of theα- approximation for discretization of analog systems,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Application of theα- approximation for discretization of analog systems,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:41.601767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 063f3437-ccdc-458a-bc7e-d1874970aa60 · outbound

This paper cites Al-alaoui operator and theα-approximation for discretization of analog systems,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Al-alaoui operator and theα-approximation for discretization of analog systems,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:41.398229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d4e77222-d32a-4326-a50f-74029abbe908 · outbound

This paper cites Digital redesign via the gener- alised bilinear transformation,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Digital redesign via the gener- alised bilinear transformation,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:41.208367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7bcfb64a-5323-4652-989a-dd093d7cf3d2 · outbound

This paper cites Generating conjectures on fundamen- tal constants with the ramanujan machine,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Generating conjectures on fundamen- tal constants with the ramanujan machine,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:40.999712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f77f2f13-fd36-4914-8bdc-0150a9a50e52 · outbound

This paper cites Associated Quarkonium Hadroproduction at High-Energy Colliders.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Associated Quarkonium Hadroproduction at High-Energy Colliders

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T12:02:40.466497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ed92fd3-bd9b-463b-9503-2edbf79fb312 · outbound

This paper cites Hypertree proof search for neural theorem proving,.

Comprehensive Analysis and Exclusion Hypothesis of $\alpha$-Approximation Method for Discretizing Analog Systems Hypertree proof search for neural theorem proving,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:02:40.841275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation a2796bf8-c51a-4445-9eca-9a0894f6d9fa · inbound