Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:44:06.087078Z
Paper Citation Record · LEDGER
A Proof of First Digit Law from Laplace Transform
As of 16 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:1908.04670.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
42 of 42 outbound references displayed
- verified exact0
- verified fuzzy8
- unresolved34
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b839ce60-0e78-4f99-ac33-b4830c2c5343 · outbound
This paper cites 2: Images of g1(x) (upper) and g2(x) (lower), from which we notice that the gap between the colored areas in g2(x) is wider than than that is g1(x).
A Proof of First Digit Law from Laplace Transform 2: Images of g1(x) (upper) and g2(x) (lower), from which we notice that the gap between the colored areas in g2(x) is wider than than that is g1(x)
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:07.140347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6666d7f8-e3db-45f8-a055-4bc46a1c52ac · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:07.116258Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6c198009-7c58-4fb6-9107-06b5bdee74bf · outbound
This paper cites well-behaved.
A Proof of First Digit Law from Laplace Transform well-behaved
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:07.093070Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ace709f9-5742-4ff1-815f-f5a72aba724c · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:07.063127Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5891ed7a-bc25-4486-8af2-866a779b260d · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:07.032533Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation eea4abbd-6ff7-4465-9920-1d5d57df51ab · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:07.005192Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 18b4ffed-e4be-4aa5-9ad3-e625f17ee92d · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.980275Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b9fdb0d5-3a37-4ddb-a945-b815b7c4ab7d · outbound
This paper cites In fact, numerical results are 0.0005 and 0.009.
A Proof of First Digit Law from Laplace Transform In fact, numerical results are 0.0005 and 0.009
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.956628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c80e6cd6-e1a8-476a-b644-407bd0ca9e9e · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.937177Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 78824cf1-6369-45bc-a69d-a5b15f6d36fa · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.916999Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c9649732-7def-4640-b40f-e8a78bfeb524 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.895242Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 613b7237-6450-41f6-9546-dfc04a2de080 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.872432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ee897dd2-b56a-4aaf-8134-a9fa9fca41bb · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.851437Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e29b4668-d29b-4ba0-a01a-ac78d09fd90e · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.822634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a3133f4f-4e44-4159-a498-40dcfcf3efb8 · outbound
This paper cites 130 1280.
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.799086Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1fbb9d25-f6a0-4348-9f66-bd929531b1d9 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.776121Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2d6129e5-d23c-4779-a69b-867822212aea · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.756139Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c106f42a-c78d-4922-9836-c76ffc2f409d · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.732729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation daebd648-1c71-4f44-8ba0-f4113d1eb083 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.699076Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 21ca3ff1-0bbd-4965-9572-d770db84a185 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.667490Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 88f9c0da-f303-498a-8808-1dea4b2fc548 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.642154Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5fec748c-0548-4efe-95e9-721ea40db1e3 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.617354Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b06190e5-903a-4cb0-af7e-cd5eba9a9866 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.591998Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 34bf9f81-8f95-4648-97ee-a2015fe2887c · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.571235Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e042a195-dce9-4aba-bd35-5321e47b8a0c · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.549981Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation be0df8c5-1087-4f02-a931-c3002361c995 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.529477Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 47eb8e61-065f-4753-8b73-ac30064ed572 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.507919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation bb45fb7b-8bea-46bc-a40d-c960355ac2cc · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.486440Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 745e46aa-1909-4b2b-97b6-e42c3c189c35 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.466389Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 16eee05f-5730-47e6-bee7-e1c4b8bb02f8 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.444928Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6ccd3b22-1025-407f-aa04-4fe9f1f7e18e · outbound
This paper cites Auditor 56 21.
A Proof of First Digit Law from Laplace Transform Auditor 56 21
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.421648Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 53f257f2-0a90-4bb6-95f0-8ce42e24e702 · outbound
This paper cites Accountancy 196 58.
A Proof of First Digit Law from Laplace Transform Accountancy 196 58
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.397666Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation eca8203d-1aa3-4216-a48f-d6c19c5562ce · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.373403Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation adc4b93b-097b-4e3a-a10f-53eab34af633 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.346959Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 78efccea-296c-41d8-8cdf-d60a1af507ca · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.324758Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8b2e5b7b-d7e1-4a1b-9344-41267065881c · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.298408Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ea94f2c8-31c2-4706-82bd-f4fa3c4eb2f4 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.269439Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6d15b6e9-0a4e-4a17-90f8-e07fe6b7114f · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.237549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1c9d8534-efd6-4564-819d-f9b4a80938f8 · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.213667Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 32e50252-368a-41cf-bfc5-95ca55a58eba · outbound
This paper cites an unresolved cited work.
A Proof of First Digit Law from Laplace Transform Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:44:06.188995Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4788f12a-40be-44bb-b4e1-f64386f4fc1a · outbound
This paper cites (New York: W.
A Proof of First Digit Law from Laplace Transform (New York: W
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.165613Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 24b52800-802b-4a60-9072-3a20be5f8250 · outbound
This paper cites Probabil.
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:44:06.141640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Pith citing papers
No inbound Pith citation observations are available.