Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:40:33.347470Z
Paper Citation Record · LEDGER
As of 11 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2507.02327.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:40:33.347470Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 8f41a920-f4c1-47ff-beb9-313e036998e9 · outbound
When it pays to teach: a population threshold for dedicated teaching Substituting this equilibrium into Eq
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 02f41b9a-c78b-41a7-ae0c-a7b66b37fd0b · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5f1c32c7-6906-439a-9c0e-f5dca056095e · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4f64d3e7-1c54-4275-b0ca-ca50114217c5 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 72973ece-d94d-4cf5-9a2d-a1957607c550 · outbound
When it pays to teach: a population threshold for dedicated teaching As this expression shows, there is a critical population size nc required before it is beneficial to dedicate anyone to teaching, given by nc = (1 + rη)(1 + η) ν(r 2 1)
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7c166fbf-4f3a-4da9-ae3f-12244fa8e729 · outbound
When it pays to teach: a population threshold for dedicated teaching go up” first and then “go down
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation b24cb358-383b-45a3-bb28-a5b7b3df963c · outbound
When it pays to teach: a population threshold for dedicated teaching tion G(x) := x 2 1:x (1 + :x) , x > 1, which can be approximated as G(x) j G 2(1)(x 2 1) = 1 2 (x 2 1) around x = 1, up to first order
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 3fb683c0-2eeb-4ba9-b1c8-86c1cfc6ccea · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 6440290c-ee93-495b-80ac-58380d51ac6d · outbound
When it pays to teach: a population threshold for dedicated teaching M -stage model
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f5e2d05a-e9b0-468e-ac04-c1fab138623b · outbound
When it pays to teach: a population threshold for dedicated teaching lower risk of losing essential worker functions if workers are lost,
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5414a0d5-c1ba-486d-bc0b-677e3b0159e8 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c2e17b37-4a4c-43a9-8c93-d68249df1599 · outbound
When it pays to teach: a population threshold for dedicated teaching Allchin, C
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 716c5dfc-d393-4f6d-ab82-064e1c0db113 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation a2830845-4acd-4392-9a2b-3189175d5b96 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 83a4c7b3-50d9-45f5-beff-4e8201040d4d · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 21e655f7-9c5d-444d-ab82-3e5f084da5a5 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 04319316-39cd-4e03-836a-04a953cfc1ec · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 15b89b7d-0da0-4f55-ae22-d2eac5f1fd9d · outbound
When it pays to teach: a population threshold for dedicated teaching Hawkes, Nature 428, 128 (2004)
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f2555b0f-5ddd-42e0-a2fb-d2e16e6ac2e6 · outbound
When it pays to teach: a population threshold for dedicated teaching Blell, in The International Encyclopedia of Anthro- pology (Wiley, 2018) pp
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 10eb29dc-3cc6-4241-afe5-50c4deaa9940 · outbound
When it pays to teach: a population threshold for dedicated teaching Hawkes, J
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation dd7cfd54-a27e-4282-8b90-3076eb32381b · outbound
When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, A
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 50422a0e-665f-4dbb-be47-e648916e5e15 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 3f5a53e3-8db0-4999-8ca8-05c7e6cce704 · outbound
When it pays to teach: a population threshold for dedicated teaching Nattrass, D
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation ca4e6cca-41fa-4f97-b6ba-f300d5c9109e · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 8feb7dc3-be32-4225-9c80-8b7fda3c2a35 · outbound
When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, K
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 6accddff-4444-49bb-b25f-fc47f0091a30 · outbound
When it pays to teach: a population threshold for dedicated teaching Muller and S
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation afa86235-3985-49fd-8daa-1239e4c59338 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 70de610a-5394-412e-9e14-42615d892fab · outbound
When it pays to teach: a population threshold for dedicated teaching Pichugin, J
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 305a6669-1020-42ac-92bc-4e8c1dd834ed · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation eecc2493-0ff3-4403-99df-70938a61edec · outbound
When it pays to teach: a population threshold for dedicated teaching Tannenbaum, J
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation dac8d48c-8bc9-4bc4-989e-2fcebeb59de5 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 95fbd014-a29c-4850-8e9a-4c53a5608a99 · outbound
When it pays to teach: a population threshold for dedicated teaching Fogarty, P
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 79ba25e4-2770-490a-a5d2-ae90cae29bed · outbound
When it pays to teach: a population threshold for dedicated teaching Maisonneuve, L
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 0a5c184d-c69d-4c38-a133-84ff4edaf00f · outbound
When it pays to teach: a population threshold for dedicated teaching Powell and C
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f6138ed8-2d56-4b1b-9b63-07103bfc0c65 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4636158b-ae59-47d7-a417-7d96fbec5248 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 98d8eb2d-923a-471c-8c18-883e7a3e8aa7 · outbound
When it pays to teach: a population threshold for dedicated teaching Shemesh, J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c6f440ab-9317-4290-8d3a-0b35d1b489ca · outbound
When it pays to teach: a population threshold for dedicated teaching Irwin, T
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d14f2772-116f-47c3-a2a4-c9f87f1add7b · outbound
When it pays to teach: a population threshold for dedicated teaching Feinman and J
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 77dd0466-d60e-4a02-b81a-e34f25c23416 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 9f3149e0-197d-4d39-8007-9d024cdda085 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e23ebebd-d44c-47d1-b1e4-446562cea63e · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 1d30c99e-ab68-4d1b-a221-d2d61aecdc51 · outbound
When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, K
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5847830d-1803-4003-b26d-2b6dc1cb238c · outbound
When it pays to teach: a population threshold for dedicated teaching Caplan, U.S
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4b8ecf8e-6461-42a8-a11f-f405cb82cbaa · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2ad03826-27e2-4827-a63e-55e5fc66867a · outbound
When it pays to teach: a population threshold for dedicated teaching Ellis, D
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e50a8797-a73e-4341-a4e4-d6dbfc06e7ca · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 80ef4dcf-d3c3-4ab4-8816-23f3a7aa319e · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 36a1fd44-f1f0-4c92-9095-a79d447fb8ef · outbound
When it pays to teach: a population threshold for dedicated teaching Bell and A
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f96e7366-0fec-4076-b256-5fbea5c59b13 · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation b784b8cc-7a2a-4b57-a8fb-0ab96b25a6f2 · outbound
When it pays to teach: a population threshold for dedicated teaching Bell-Roberts, J
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 64a25c04-7340-4fa8-a83f-26ec8f6c77fe · outbound
When it pays to teach: a population threshold for dedicated teaching Ferguson-Gow, S
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 9b2e984a-7606-4c64-b635-bb1480fbe2e9 · outbound
When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, V
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f9a6ae4b-545a-49cf-9ee3-ad54b9713ba9 · outbound
When it pays to teach: a population threshold for dedicated teaching Sear and R
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5a892129-1f1b-4f64-a5e8-f3f1e6090192 · outbound
When it pays to teach: a population threshold for dedicated teaching When it pays to teach: a populat ion threshold for dedicated teaching
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 244242a5-e721-4f6c-b3a7-9e68c1eab967 · outbound
When it pays to teach: a population threshold for dedicated teaching Therefore, the ratio of those numbers at equilibrium is computed by n∗ 1 n∗ 0 = η + ντ χ(n)n
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 1915f565-42a0-44c8-96ed-bdcb5501d45a · outbound
When it pays to teach: a population threshold for dedicated teaching Unresolved cited work
Reference 2024
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
No inbound Pith citation observations are available.