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Paper Citation Record · LEDGER

When it pays to teach: a population threshold for dedicated teaching

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.

pith.paper-citation-record.v1
2507.02327 v1

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:40:33.347470Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

57 of 57 outbound references displayed

  • verified exact0
  • verified fuzzy32
  • unresolved24
  • parse uncertain1
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8f41a920-f4c1-47ff-beb9-313e036998e9 · outbound

This paper cites Substituting this equilibrium into Eq.

When it pays to teach: a population threshold for dedicated teaching Substituting this equilibrium into Eq

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:43.689901Z

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.

source=pdf_text observed=2026-08-06T20:40:26.816973Z digest=sha256:90d76327201518a321a6f35689be3197aa694c5a9458b59900f6ea26ab4221f1

Observation 02f41b9a-c78b-41a7-ae0c-a7b66b37fd0b · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:43.466613Z

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.

source=pdf_text observed=2026-08-06T20:40:26.988419Z digest=sha256:fe3f22e1acfee0b1b7dffcf961cd7e1d20a13b5d707187a343005a73b3fc1288

Observation 5f1c32c7-6906-439a-9c0e-f5dca056095e · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:42.338785Z

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.

source=pdf_text observed=2026-08-06T20:40:27.673896Z digest=sha256:fef9db24ab85a6a0482d7c17ac119e3c4a8f41f89379c1d2a760c6875b312760

Observation 4f64d3e7-1c54-4275-b0ca-ca50114217c5 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:43.362691Z

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.

source=pdf_text observed=2026-08-06T20:40:27.082396Z digest=sha256:2e7de4da0a0364081e47590ad64061fa08cd28fe1d764f6eba1759de79be9675

Observation 72973ece-d94d-4cf5-9a2d-a1957607c550 · outbound

This paper cites 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).

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:43.569073Z

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.

source=pdf_text observed=2026-08-06T20:40:26.896846Z digest=sha256:e4337dae8ab40343176d363d82ef8cbde75453574395cc1bc9d8ff6217a8e6fd

Observation 7c166fbf-4f3a-4da9-ae3f-12244fa8e729 · outbound

This paper cites go up” first and then “go down.

When it pays to teach: a population threshold for dedicated teaching go up” first and then “go down

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:43.258660Z

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.

source=pdf_text observed=2026-08-06T20:40:27.171372Z digest=sha256:e454790491be2c872c1eec6d4263b01dd49914a476d4992e03bb67821a44e73b

Observation b24cb358-383b-45a3-bb28-a5b7b3df963c · outbound

This paper cites 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.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:43.134329Z

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.

source=pdf_text observed=2026-08-06T20:40:27.261592Z digest=sha256:c6807ebd4d83ac0d2a6f085e75d6ef8456ee0aa79e7d23020f01ceb490ef43ed

Observation 3fb683c0-2eeb-4ba9-b1c8-86c1cfc6ccea · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:43.037911Z

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.

source=pdf_text observed=2026-08-06T20:40:27.352542Z digest=sha256:d3b0b58e252d45bade62a86c668e149a3f3b1d2aea609bdcfeb7a4ca7e25d1ad

Observation 6440290c-ee93-495b-80ac-58380d51ac6d · outbound

This paper cites M -stage model.

When it pays to teach: a population threshold for dedicated teaching M -stage model

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:42.915668Z

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.

source=pdf_text observed=2026-08-06T20:40:27.411299Z digest=sha256:6c9b5ae1c0e531297cabac2dc7d77ac08ebf201d67e1b9cc2604abe8d2939600

Observation f5e2d05a-e9b0-468e-ac04-c1fab138623b · outbound

This paper cites lower risk of losing essential worker functions if workers are lost,.

When it pays to teach: a population threshold for dedicated teaching lower risk of losing essential worker functions if workers are lost,

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:42.767687Z

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.

source=pdf_text observed=2026-08-06T20:40:27.459451Z digest=sha256:6c0008b8deb19e966ccbce389f9113f05ebee716bdd875ee80416ab5bdbe43eb

Observation 5414a0d5-c1ba-486d-bc0b-677e3b0159e8 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:42.662535Z

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.

source=pdf_text observed=2026-08-06T20:40:27.518384Z digest=sha256:71d9a5832f5236f467da5d5747c17b6ade8d9a755541bc900d7b5056cd883e02

Observation c2e17b37-4a4c-43a9-8c93-d68249df1599 · outbound

This paper cites Allchin, C.

When it pays to teach: a population threshold for dedicated teaching Allchin, C

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:42.535301Z

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.

source=pdf_text observed=2026-08-06T20:40:27.589802Z digest=sha256:c82660177aa5c432d303e34949d7b1c4f649e3d12ab227286cfc6bff6f21da96

Observation 716c5dfc-d393-4f6d-ab82-064e1c0db113 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:42.109588Z

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.

source=pdf_text observed=2026-08-06T20:40:27.757965Z digest=sha256:4bc1a5102d70c2fbe42dc00ec78c0c687ea27f5677ddc79ba0239dd10748f10d

Observation a2830845-4acd-4392-9a2b-3189175d5b96 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:41.956878Z

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.

source=pdf_text observed=2026-08-06T20:40:27.830007Z digest=sha256:229d08857e0453ce45273be5edf3bfeb87837be979c46d124306f024283ecbef

Observation 83a4c7b3-50d9-45f5-beff-4e8201040d4d · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:41.796786Z

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.

source=pdf_text observed=2026-08-06T20:40:27.881675Z digest=sha256:59968282014a4ac966bc290beb235a85cf3f8bc7eee44796cab8c58cf4065c45

Observation 21e655f7-9c5d-444d-ab82-3e5f084da5a5 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:41.646149Z

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.

source=pdf_text observed=2026-08-06T20:40:27.941147Z digest=sha256:1e8b031ef4ce4e8db879442b4bb2857ba76ad15c000e71c57faa5260ccd1a733

Observation 04319316-39cd-4e03-836a-04a953cfc1ec · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:41.438831Z

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.

source=pdf_text observed=2026-08-06T20:40:27.993456Z digest=sha256:6ac46dd1203bf071fe4383fcd77bc47c7e7ffc1da934e3500dcddb2df3e5cc85

Observation 15b89b7d-0da0-4f55-ae22-d2eac5f1fd9d · outbound

This paper cites Hawkes, Nature 428, 128 (2004).

When it pays to teach: a population threshold for dedicated teaching Hawkes, Nature 428, 128 (2004)

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:41.283335Z

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.

source=pdf_text observed=2026-08-06T20:40:28.051249Z digest=sha256:614f75fc519d7522c4cedb279ca23d7850e898687581fac2059eb0c87a5738bd

Observation f2555b0f-5ddd-42e0-a2fb-d2e16e6ac2e6 · outbound

This paper cites Blell, in The International Encyclopedia of Anthro- pology (Wiley, 2018) pp.

When it pays to teach: a population threshold for dedicated teaching Blell, in The International Encyclopedia of Anthro- pology (Wiley, 2018) pp

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:41.133777Z

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.

source=pdf_text observed=2026-08-06T20:40:28.103678Z digest=sha256:71da88dde28e9dcd576a06fc73c76e825a434099bc25f1307d59c9f59153b51a

Observation 10eb29dc-3cc6-4241-afe5-50c4deaa9940 · outbound

This paper cites Hawkes, J.

When it pays to teach: a population threshold for dedicated teaching Hawkes, J

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:40.943792Z

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.

source=pdf_text observed=2026-08-06T20:40:28.202490Z digest=sha256:2f37f9cb0fa9a85d74273a54d0f5b5c85e191b5c75e95c75fe1810a53df09f8d

Observation dd7cfd54-a27e-4282-8b90-3076eb32381b · outbound

This paper cites Lahdenper¨ a, A.

When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, A

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:40.783807Z

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.

source=pdf_text observed=2026-08-06T20:40:28.312678Z digest=sha256:892bbd31f8c45b4105d4cff03ab570cf050da57243d9c187eddb713669007964

Observation 50422a0e-665f-4dbb-be47-e648916e5e15 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:40.557110Z

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.

source=pdf_text observed=2026-08-06T20:40:28.562042Z digest=sha256:e066b317f8bacb1f482b04a2079b55dc85a325eef8f3fabc0078c1564197adf9

Observation 3f5a53e3-8db0-4999-8ca8-05c7e6cce704 · outbound

This paper cites Nattrass, D.

When it pays to teach: a population threshold for dedicated teaching Nattrass, D

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:40.334804Z

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.

source=pdf_text observed=2026-08-06T20:40:28.996729Z digest=sha256:1cb495907211357b829ba0166b4cd9fdd359f4721d5a39086c3147f151cd7fa2

Observation ca4e6cca-41fa-4f97-b6ba-f300d5c9109e · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:40.039230Z

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.

source=pdf_text observed=2026-08-06T20:40:29.429441Z digest=sha256:5bb3d7772330cbc7d9804411352221811e217da01261994ff928b34790548078

Observation 8feb7dc3-be32-4225-9c80-8b7fda3c2a35 · outbound

This paper cites Lahdenper¨ a, K.

When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, K

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:39.867838Z

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.

source=pdf_text observed=2026-08-06T20:40:29.588055Z digest=sha256:9efd68422fa290f7a81cdb8e9894ec4d773c30fa696a4204762c44a49579ae9b

Observation 6accddff-4444-49bb-b25f-fc47f0091a30 · outbound

This paper cites Muller and S.

When it pays to teach: a population threshold for dedicated teaching Muller and S

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:39.661225Z

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.

source=pdf_text observed=2026-08-06T20:40:29.836530Z digest=sha256:e7a784b766ca9afb620fa5e7aa7b6a87cad6b9f05445066894a88c195cc77cc7

Observation afa86235-3985-49fd-8daa-1239e4c59338 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:39.499168Z

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.

source=pdf_text observed=2026-08-06T20:40:30.040070Z digest=sha256:e3487058bc217aa1f5b8ad607553bbb3701f21e501ab02d166e0105e0abe6bce

Observation 70de610a-5394-412e-9e14-42615d892fab · outbound

This paper cites Pichugin, J.

When it pays to teach: a population threshold for dedicated teaching Pichugin, J

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:39.348316Z

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.

source=pdf_text observed=2026-08-06T20:40:30.203946Z digest=sha256:502af4fa26f3d1ccb2d18857f4a57366b3ebb60951f8c27cfa19e3c36420ac4f

Observation 305a6669-1020-42ac-92bc-4e8c1dd834ed · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:39.181172Z

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.

source=pdf_text observed=2026-08-06T20:40:30.376586Z digest=sha256:79a60bafe442da893e14cb2c07afcbc6dc4ce048eb5092dd49fb5c9f4837b8c3

Observation eecc2493-0ff3-4403-99df-70938a61edec · outbound

This paper cites Tannenbaum, J.

When it pays to teach: a population threshold for dedicated teaching Tannenbaum, J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:38.952188Z

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.

source=pdf_text observed=2026-08-06T20:40:30.458599Z digest=sha256:a58801283a4eab113e847b8f3a26b595c273dca2f399c5a687ee015c1cd1a7a1

Observation dac8d48c-8bc9-4bc4-989e-2fcebeb59de5 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:38.775244Z

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.

source=pdf_text observed=2026-08-06T20:40:30.522605Z digest=sha256:484f9459634d45cd169ea258d8283e83eef3138cbf5a2346a3a2e7db9154107d

Observation 95fbd014-a29c-4850-8e9a-4c53a5608a99 · outbound

This paper cites Fogarty, P.

When it pays to teach: a population threshold for dedicated teaching Fogarty, P

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:38.569719Z

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.

source=pdf_text observed=2026-08-06T20:40:30.624405Z digest=sha256:561f07fb024d77732b79304319a19a941ec6022ac2db1f3530f67726f4b983ce

Observation 79ba25e4-2770-490a-a5d2-ae90cae29bed · outbound

This paper cites Maisonneuve, L.

When it pays to teach: a population threshold for dedicated teaching Maisonneuve, L

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:38.334048Z

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.

source=pdf_text observed=2026-08-06T20:40:30.733259Z digest=sha256:53ca20b68cd00de930a7a702e1e709999af922bb51ac10a813c0b422400d2483

Observation 0a5c184d-c69d-4c38-a133-84ff4edaf00f · outbound

This paper cites Powell and C.

When it pays to teach: a population threshold for dedicated teaching Powell and C

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:38.131278Z

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.

source=pdf_text observed=2026-08-06T20:40:30.804860Z digest=sha256:bbb9592f986abe309e39112696165f89527a29e2bcc0f56342bdfd412019e9e5

Observation f6138ed8-2d56-4b1b-9b63-07103bfc0c65 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:37.858252Z

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.

source=pdf_text observed=2026-08-06T20:40:30.870500Z digest=sha256:33d589ec2e2276d514512f78db6ff6baa60fff23578c5f4b1927782350f401d8

Observation 4636158b-ae59-47d7-a417-7d96fbec5248 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:37.669433Z

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.

source=pdf_text observed=2026-08-06T20:40:31.001416Z digest=sha256:7e753a7abf7d305c8cb9a77a641490254cb8f9993da4a8d851ba4aaaba32c81b

Observation 98d8eb2d-923a-471c-8c18-883e7a3e8aa7 · outbound

This paper cites Shemesh, J.

When it pays to teach: a population threshold for dedicated teaching Shemesh, J

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:37.480328Z

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.

source=pdf_text observed=2026-08-06T20:40:31.132074Z digest=sha256:244c557e82171f5608d227dfdac1faa43389f5c145db65af3d7235ff1958465f

Observation c6f440ab-9317-4290-8d3a-0b35d1b489ca · outbound

This paper cites Irwin, T.

When it pays to teach: a population threshold for dedicated teaching Irwin, T

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:37.191882Z

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.

source=pdf_text observed=2026-08-06T20:40:31.259864Z digest=sha256:4c11213d2cafdaead31e643dfd609ad187af6eb5dfa2ad994e6935a38ba528e7

Observation d14f2772-116f-47c3-a2a4-c9f87f1add7b · outbound

This paper cites Feinman and J.

When it pays to teach: a population threshold for dedicated teaching Feinman and J

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:35.150357Z

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.

source=pdf_text observed=2026-08-06T20:40:32.590474Z digest=sha256:09fff4651087b2ae999036b51d46d7605615b5bf258e1b805fbf982cf1d436f5

Observation 77dd0466-d60e-4a02-b81a-e34f25c23416 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:36.813163Z

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.

source=pdf_text observed=2026-08-06T20:40:31.458882Z digest=sha256:c332e278c90df8bc16584bfad16b1cf8ac0693a53715b97421fea5bd0f417625

Observation 9f3149e0-197d-4d39-8007-9d024cdda085 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:36.623804Z

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.

source=pdf_text observed=2026-08-06T20:40:31.569599Z digest=sha256:e88d5760738cbe60f446045114827ddb95502bdc9a3566a780bc5177bf67c972

Observation e23ebebd-d44c-47d1-b1e4-446562cea63e · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:36.407842Z

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.

source=pdf_text observed=2026-08-06T20:40:31.682720Z digest=sha256:7c9daa1f6f54d12c686bb50408806ddec277f5a9ecf34321b86f402f2336b632

Observation 1d30c99e-ab68-4d1b-a221-d2d61aecdc51 · outbound

This paper cites Lahdenper¨ a, K.

When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, K

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:36.222203Z

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.

source=pdf_text observed=2026-08-06T20:40:31.823475Z digest=sha256:8d3de93ce53d3c3ac9bcd4dd72b0a11c104f74a46c630b9a3bb3c08ed37691bd

Observation 5847830d-1803-4003-b26d-2b6dc1cb238c · outbound

This paper cites Caplan, U.S.

When it pays to teach: a population threshold for dedicated teaching Caplan, U.S

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:36.002509Z

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.

source=pdf_text observed=2026-08-06T20:40:31.921013Z digest=sha256:4b9d80aedaf91eaa7bb3f4f2346f222d7d6987c2381cd68035932191c1a3103e

Observation 4b8ecf8e-6461-42a8-a11f-f405cb82cbaa · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:35.831435Z

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.

source=pdf_text observed=2026-08-06T20:40:32.049494Z digest=sha256:166f98a4ea40ce00945ff301defaed374054f337674cbcac92d7a28d9d6c6dcf

Observation 2ad03826-27e2-4827-a63e-55e5fc66867a · outbound

This paper cites Ellis, D.

When it pays to teach: a population threshold for dedicated teaching Ellis, D

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:35.640696Z

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.

source=pdf_text observed=2026-08-06T20:40:32.156018Z digest=sha256:6c8938f8b7fd4c49ec07822d61c9fa6cfa210fc891fd2e8cd2c88cd4dce925c5

Observation e50a8797-a73e-4341-a4e4-d6dbfc06e7ca · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:35.483364Z

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.

source=pdf_text observed=2026-08-06T20:40:32.319077Z digest=sha256:e4e574c0439180f2a864de4b301760608fd2439e24c1b42901383323d2b5f8cf

Observation 80ef4dcf-d3c3-4ab4-8816-23f3a7aa319e · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:35.304819Z

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.

source=pdf_text observed=2026-08-06T20:40:32.497154Z digest=sha256:1e3b8bc73da4a476283ea69255c21ed3707fcd3562fefb0f80bd0fcb442d7f79

Observation 36a1fd44-f1f0-4c92-9095-a79d447fb8ef · outbound

This paper cites Bell and A.

When it pays to teach: a population threshold for dedicated teaching Bell and A

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:34.980999Z

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.

source=pdf_text observed=2026-08-06T20:40:32.690343Z digest=sha256:485aa5a03aabcd317fc2a2fdffeb6cf5f1794c13f180c151266b07001e6d0e79

Observation f96e7366-0fec-4076-b256-5fbea5c59b13 · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-06T20:40:34.831161Z

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.

source=pdf_text observed=2026-08-06T20:40:32.816956Z digest=sha256:2008be5997767b5275482d51a6125ae1bc77e5b544867aa192ac288d366f251d

Observation b784b8cc-7a2a-4b57-a8fb-0ab96b25a6f2 · outbound

This paper cites Bell-Roberts, J.

When it pays to teach: a population threshold for dedicated teaching Bell-Roberts, J

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:34.695683Z

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.

source=pdf_text observed=2026-08-06T20:40:32.912409Z digest=sha256:629dabc664d39ad5e1672d09d06d818e826b683c8c8cd4ddb41ecb76448d383a

Observation 64a25c04-7340-4fa8-a83f-26ec8f6c77fe · outbound

This paper cites Ferguson-Gow, S.

When it pays to teach: a population threshold for dedicated teaching Ferguson-Gow, S

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:34.543202Z

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.

source=pdf_text observed=2026-08-06T20:40:32.997673Z digest=sha256:6a9ae7ca3b52bbc4d120518515f5b8d9d127666b894b4cad574d4ddbec54a6b4

Observation 9b2e984a-7606-4c64-b635-bb1480fbe2e9 · outbound

This paper cites Lahdenper¨ a, V.

When it pays to teach: a population threshold for dedicated teaching Lahdenper¨ a, V

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:34.352028Z

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.

source=pdf_text observed=2026-08-06T20:40:33.080870Z digest=sha256:686536708f40c66aa04ec0c641cc51eac21c0fe097febc64c912d0cbc475b24f

Observation f9a6ae4b-545a-49cf-9ee3-ad54b9713ba9 · outbound

This paper cites Sear and R.

When it pays to teach: a population threshold for dedicated teaching Sear and R

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:34.157225Z

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.

source=pdf_text observed=2026-08-06T20:40:33.178997Z digest=sha256:eed13d7268f158c3d14b025e3d073e56e44450fb4d4105f280fc397ba7d47748

Observation 5a892129-1f1b-4f64-a5e8-f3f1e6090192 · outbound

This paper cites When it pays to teach: a populat ion threshold for dedicated teaching.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:33.976655Z

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.

source=pdf_text observed=2026-08-06T20:40:33.253044Z digest=sha256:6c16f161e1db38f240c640e1d661393d150b2fa9903d594fa80f7c1814f7279a

Observation 244242a5-e721-4f6c-b3a7-9e68c1eab967 · outbound

This paper cites Therefore, the ratio of those numbers at equilibrium is computed by n∗ 1 n∗ 0 = η + ντ χ(n)n.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T20:40:33.686767Z

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.

source=pdf_text observed=2026-08-06T20:40:33.347470Z digest=sha256:da751a8262026ac2e1a4e7ff0db9ad21f017f0c9f7b171953d10b46e4f7db387

Observation 1915f565-42a0-44c8-96ed-bdcb5501d45a · outbound

This paper cites an unresolved cited work.

When it pays to teach: a population threshold for dedicated teaching Unresolved cited work

Reference 2024

Resolution
parse uncertain
raw_fallback, observed 2026-08-06T20:40:37.010355Z

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.

source=pdf_text observed=2026-08-06T20:40:31.355566Z digest=sha256:7e9ce01459631119ab695a7a9e8d97beb95331f2ff40dc273e0b49fed793bb6d

Pith citing papers

No inbound Pith citation observations are available.