Paper Citation Record · LEDGER

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier

As of 11 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2606.13057.

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

pith.paper-citation-record.v1
2606.13057 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T05:27:12.107754Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T22:58:45.929742Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

verified exact5
verified fuzzy0
unresolved43
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 51c3f645-22d4-4a5c-8c26-01a832646251 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c54342de-5f6c-4457-9894-6155dec34b40 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47d43aef-56b6-4f8e-baa5-3086215129eb · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e041ad7-59cc-4c4f-bfc4-920298a8da98 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4e6c98b-df2f-4a99-8edf-283aad373815 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07375f1c-6bf9-4a42-aad8-f550145ff2ec · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f075e396-8e44-45de-bac1-6843bbf9da3d · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18d231e1-e02b-4bbb-a2ba-a8bde0b64c8c · outbound

This paper cites Best-of-Both-Worlds Fair Allocation of Indivisible and Mixed Goods.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Best-of-Both-Worlds Fair Allocation of Indivisible and Mixed Goods

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:30:35.714453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d37f506a-501f-43c0-94e6-56d0a9a6e2cf · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab78d46d-5528-4f10-8fda-41feb424c134 · outbound

This paper cites Procaccia, Nisarg Shah, and Junxing Wang.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Procaccia, Nisarg Shah, and Junxing Wang

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 934c6f87-a305-42ad-9058-7c19b8811274 · outbound

This paper cites Improved maximin fair allocation of indivisible items to three agents.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Improved maximin fair allocation of indivisible items to three agents

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:30:35.717369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dfee3d7b-0d92-4364-8f40-68d411ec0df0 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3235cbb8-83ed-4aaf-b9a0-e83512ac236a · outbound

This paper cites 1958.Puzzle-Math.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier 1958.Puzzle-Math

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74cfa3f0-338f-4ad2-807e-27391a23349c · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5da3da4-dda5-4c77-b637-c79a47731f37 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6eb04092-223f-47d0-8295-f64d0c246d29 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ea9857d-0a16-40f2-8580-a32ba0875694 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af011f52-8f59-4149-8325-511a12c4c3cd · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:30:35.708277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1c6c9a93-95d6-4c32-90fb-28510a4df436 · outbound

This paper cites Huang and S.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Huang and S

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:30:35.714710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7c68be2c-bee8-4807-abe4-e3a0e2faa51a · outbound

This paper cites Procaccia, and Junxing Wang.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Procaccia, and Junxing Wang

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 775890d6-7fa4-4a57-bc2c-05e52d86dab2 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2f4ebc3-d5fe-43f9-a1df-d64d907f134d · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07bf9cb8-6a7e-43bc-8d2f-7d919f5be536 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4102d07-ffb7-4976-afb5-58cd5e76ffdd · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f63ae85b-64da-488e-8eda-116ca5546537 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bde602d1-7ee7-4f80-af6c-14caa46218fd · outbound

This paper cites 2003.Fair division and collective welfare.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier 2003.Fair division and collective welfare

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77524c61-f174-46c5-8d2c-8c8e4bc4a81b · outbound

This paper cites Envy-freeness and maximum Nash welfare for mixed divisible and indivisible goods.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Envy-freeness and maximum Nash welfare for mixed divisible and indivisible goods

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:30:35.717640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0e1aaac-7d2d-4a06-82dd-2ef17d6d9fef · outbound

This paper cites Procaccia.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Procaccia

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df0c393e-c947-44a7-a0cb-10281f8851eb · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 642b557e-622e-45d6-b184-9956fa98236f · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41fb581c-f60c-41a7-a3bb-1fa42cf166bd · outbound

This paper cites For agenta 2, since she selects the better one betweenBandB ′, her value is at least 1 2 ·v 2(M)≥ 1 2 · 4 3 = 2.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier For agenta 2, since she selects the better one betweenBandB ′, her value is at least 1 2 ·v 2(M)≥ 1 2 · 4 3 = 2

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6373c7d0-f4eb-473c-a542-bb34ba0f2fe4 · outbound

This paper cites By Lemma 5, if we are able to find a nice bundle when the original instance contains more than two agents, then we directly obtain a 2 3-MMS allocation.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier By Lemma 5, if we are able to find a nice bundle when the original instance contains more than two agents, then we directly obtain a 2 3-MMS allocation

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00f3db94-8876-4f28-8442-acd076ed7c11 · outbound

This paper cites Hence,v j(Aj)≥ 2 3 ≥ 2 3 MMSj.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Hence,v j(Aj)≥ 2 3 ≥ 2 3 MMSj

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1030f360-96e2-4468-9e57-e1d283c39c36 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b5c699c-e3f4-44a5-bbc7-0aada9afd2fa · outbound

This paper cites For the remaining agents inN ′ and items inG 1, we can allocate each agenta i ∈N ′ two itemsg 1, g2 inG 1 such thatv i(g1)> 1 3 andv i(g2)> 1.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier For the remaining agents inN ′ and items inG 1, we can allocate each agenta i ∈N ′ two itemsg 1, g2 inG 1 such thatv i(g1)> 1 3 andv i(g2)> 1

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c785c29-44df-4901-b93f-bdfc0f2d756f · outbound

This paper cites Hence, the lemma is proved.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Hence, the lemma is proved

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d64a7748-ea6a-4936-a35e-33c267a5bf8f · outbound

This paper cites Based on Observation 3, every item inG 1 is medium to each agent in Cases 3 and 4.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Based on Observation 3, every item inG 1 is medium to each agent in Cases 3 and 4

Reference 37

Resolution: malformed identifier; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d7bdf2d-5af6-49f4-a971-0fe1540af24b · outbound

This paper cites Therefore, v3(M\ {g 1, gd, g2})≥3−2 = 1 and we get a 2 3-MMS allocation.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Therefore, v3(M\ {g 1, gd, g2})≥3−2 = 1 and we get a 2 3-MMS allocation

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9230f1f-eed5-4970-8372-a26d3441acc1 · outbound

This paper cites an unresolved cited work.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 704c48fb-974b-4af8-bafb-a07d3629ce56 · outbound

This paper cites Based on that, we add the sixth condition for further analysis: •(6) Each agent considers at least one item in ˆG1 divisible.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Based on that, we add the sixth condition for further analysis: •(6) Each agent considers at least one item in ˆG1 divisible

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 271b654e-52ec-4ac6-83a5-58ee36bd7bd5 · outbound

This paper cites We now consider the situation when we reduce the instance with 4 agents by giving one single itemgto one agent who values it by no less than 2.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier We now consider the situation when we reduce the instance with 4 agents by giving one single itemgto one agent who values it by no less than 2

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f6c68e7-de79-40e5-9eb4-993730cb368e · outbound

This paper cites Ifgis divisible for agenta i,gis allocated partially and the value of the allocated fraction ofgfor her is no larger than 2.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Ifgis divisible for agenta i,gis allocated partially and the value of the allocated fraction ofgfor her is no larger than 2

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47dcffff-6a5b-40c2-b7ae-9288363c7edb · outbound

This paper cites Hence we have an additional condition: •(7) At least two items are removed.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Hence we have an additional condition: •(7) At least two items are removed

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b108a53c-32f8-4f34-bb8a-8f982462955a · outbound

This paper cites After this reduction, agenta 1 inN ′ r thinks the items inG 1 are all indivisible, which breaks Condition (6).

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier After this reduction, agenta 1 inN ′ r thinks the items inG 1 are all indivisible, which breaks Condition (6)

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 948d3d69-0023-4782-bb65-3273f093afd2 · outbound

This paper cites Based on Claim 6, the new instance does not satisfy Conditions (2) and (3) at the same time.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Based on Claim 6, the new instance does not satisfy Conditions (2) and (3) at the same time

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b235cc8-5110-4e21-8cb2-7f06d8f61a99 · outbound

This paper cites After this reduction, the reduced instance violates Condition (6).

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier After this reduction, the reduced instance violates Condition (6)

Reference 46

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e544dd3b-6e72-48a7-a98d-61004d5cdfce · outbound

This paper cites Subcase 2:|G 1| ≥7.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Subcase 2:|G 1| ≥7

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2238f791-4ac1-4b1e-9fdf-ea5da616476b · outbound

This paper cites Since Condition (4) shows any item in ˆG1 is medium for any agent inN r, there are 6 items{g 1,.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Since Condition (4) shows any item in ˆG1 is medium for any agent inN r, there are 6 items{g 1,

Reference 48

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e17cad51-666b-4413-bdf9-9526e68b63ca · outbound

This paper cites Case 2:v i(G2)< 2 3 −v i(g0) for eacha i ∈N, g 0 ∈G 1;|G 1| ≥8.

Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier Case 2:v i(G2)< 2 3 −v i(g0) for eacha i ∈N, g 0 ∈G 1;|G 1| ≥8

Reference 49

Resolution: unresolved; no resolver link, observed 2026-06-27T05:27:12.107754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5fab86e4-c2bd-4ce1-826c-c237863ca70f · inbound

Fair Allocation of Divisible Goods under Non-Linear Valuations cites this paper.

Fair Allocation of Divisible Goods under Non-Linear Valuations Approximate Maximin Share with Subjective Divisibility: Beating the 1/2 Barrier

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T22:58:45.929742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.