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Paper Citation Record · LEDGER

Coefficients of $q$-real numbers: their combinatorial meaning and growth

As of 16 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2608.06761.

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

pith.paper-citation-record.v1
2608.06761 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:21:12.201646Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

30 of 30 outbound references displayed

  • verified exact5
  • verified fuzzy13
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 80a60f50-5e51-4a5c-9dbd-b9db2cc177d9 · outbound

This paper cites Aval and S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Aval and S

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.062871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation af949a37-6a14-4068-841f-a6b792b8931f · outbound

This paper cites Bapat, L.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Bapat, L

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.067937Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.067937Z digest=sha256:925486b598530f0a9383427b4bfcee9f007dd129f84d590a1301c44cc625f567

Observation 09497fca-ba66-49b8-a6fe-b5f303697301 · outbound

This paper cites Cayley,On the theory of the analytical forms called trees, Phil.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Cayley,On the theory of the analytical forms called trees, Phil

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.925912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4eb9bcd6-6ba7-4faa-8b95-1507c67eed8f · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.911961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.076967Z digest=sha256:2ccbf66dbaa449a22535e5033748b767daefee7c272574a91fd0e412cd84abfd

Observation a825f172-03c6-4bdf-9f7b-cb1a731da7fa · outbound

This paper cites Deutsch and L.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Deutsch and L

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.898861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.081916Z digest=sha256:6e5a438cf6a34fc768139d450e3ac68a168d2bc4f26139d15e73dd4e96530fa4

Observation 9f8e9511-6a23-4e67-b088-40275b4d91f6 · outbound

This paper cites Bounding deformation spaces of Kleinian groups with two generators.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Bounding deformation spaces of Kleinian groups with two generators

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.086904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.086904Z digest=sha256:73987df94966f097002d7e0853856e539768c670acb794842147b9bee5a720cc

Observation e30f70d4-3e9f-4431-b3d1-d9a20c62a0dd · outbound

This paper cites On $q$-real and $q$-complex numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth On $q$-real and $q$-complex numbers

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.091519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.091519Z digest=sha256:dd6e25201c9ad1d2a7eb3f155f1eaa4d4f140e97c855e94c7d5d707be6e06764

Observation bccd78ad-9ab8-48c4-8cfb-b8da6dabb1b9 · outbound

This paper cites Evans, A.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Evans, A

Reference 8

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.276208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.096135Z digest=sha256:82bfe3cb55884c942ce0c1b4948295c299913aa7eaa17a29228b10a3cbca21d9

Observation 444ee2bb-d311-4aa1-b4bc-09e48123e9de · outbound

This paper cites Flajolet, R.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Flajolet, R

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.883975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.100680Z digest=sha256:bc013878612367d118fc8df3ad9bd0b48079c5c0405873261873cae89a19cf0b

Observation 2eb740a4-b249-4043-89ee-d2a0448bb7ec · outbound

This paper cites Euler,De evolutione potestatis polynomialis cuiuscunque(1 + x + x2 + x3 + x4 + etc.)n, Nova Acta Academiae Scientiarum Imperialis Petropolitanae,12(1801), 47–57.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Euler,De evolutione potestatis polynomialis cuiuscunque(1 + x + x2 + x3 + x4 + etc.)n, Nova Acta Academiae Scientiarum Imperialis Petropolitanae,12(1801), 47–57

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.871287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.105006Z digest=sha256:7218429231f27f549e6ec0c2ebad2b0af964b97b883c8cabda9c0be531547d55

Observation 1d563068-c1f7-45dd-a3c1-f4a7fc4f9560 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.858963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 92d76c31-152a-4489-9fb3-e35265f4b3c3 · outbound

This paper cites Han and E.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Han and E

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.113761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.113761Z digest=sha256:1dac2cf842a88656967be9d99a0af5d07cbbb1f6a1542916d55c1b9b15ab70f9

Observation 9224c04b-0176-4c92-96b1-b8987fc1dd8f · outbound

This paper cites Hirzebruch,Hilbert modular surfaces, Enseign.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Hirzebruch,Hilbert modular surfaces, Enseign

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.846984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.118237Z digest=sha256:bdc017130d4be67f7bd19eaa9bdf0c98d81a8195960dae9aa62610d89c4861ff

Observation b0d5c96b-e991-429c-9a48-5cc06fa11fe6 · outbound

This paper cites Leclere and S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Leclere and S

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.835394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.122933Z digest=sha256:d39ea3606a0ffd83cd9782e40f440d5aabdabb8cc97e92b0e22c6f5e43366488

Observation 6e069ddf-33d6-4d7f-ae76-950c981553f0 · outbound

This paper cites Leclere, S.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Leclere, S

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.823680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 23fb2bba-9843-4eac-af64-398505e89e42 · outbound

This paper cites McConville, J.

Coefficients of $q$-real numbers: their combinatorial meaning and growth McConville, J

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.810365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.133904Z digest=sha256:42e3e4dd3ce4a0ed29a89d34078c48743239dcaf5fe5a0d9dfc2240166910d97

Observation eaf622d3-7f2b-4638-975f-540ae07696fb · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.796077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.138394Z digest=sha256:7e49c1ed1c9fe5bed51f49be5fa659aeefee06ae9ba3cad8993fc75897249499

Observation a75d7b90-f34e-4a77-bf1d-77f86cd1b249 · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.771668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.143047Z digest=sha256:17742fe3cc6a71b3e19f7a63165f1e92a71c4bd669f0b99ba148fd29ab344265

Observation 0697f705-30a8-4517-bd35-16ea72682c71 · outbound

This paper cites Morier-Genoud and V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud and V

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.147574Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.147574Z digest=sha256:745f15b7e635a559a014854260f77020ea36d1d43a182d90e8eca5ba22c390b6

Observation 9af810ad-8a48-4a15-ae0b-0b1ed1e82b07 · outbound

This paper cites $q$-deformed rationals and irrationals.

Coefficients of $q$-real numbers: their combinatorial meaning and growth $q$-deformed rationals and irrationals

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-10T21:21:12.152584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:21:12.152584Z digest=sha256:56bfd2af8cc8a2ec83cab70d69b7d7f2501282b2b2505e7d3d4fc5a06f5ec4e1

Observation a56c4c9d-5078-4a27-bb2a-a5bf3068bebe · outbound

This paper cites Morier-Genoud, V.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Morier-Genoud, V

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.758209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation c857fcbb-a0b9-4aa6-9eda-959525feffb6 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.745534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 22065148-967e-4657-bf80-046fa64f81de · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.734693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.171130Z digest=sha256:25ee07df6743bf3b56a2b694cde1dda8d9228054aea5c56091626b0e2840858e

Observation 064cacbe-ebd7-4fbc-83d8-22341a4d60f3 · outbound

This paper cites Ovenhouse,q-rationals and Finite Schubert Varieties, C.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ovenhouse,q-rationals and Finite Schubert Varieties, C

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.722852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.175812Z digest=sha256:9fb313006cae9898faff58888adaecc757fc4e640ddb3142412f592f255ebc25

Observation ba124cd9-dd66-46d3-806d-a8b59b253916 · outbound

This paper cites Ovsienko and E.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ovsienko and E

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:21:12.709319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.180352Z digest=sha256:5d5583daea977192afea59daedfa290437c6bd61a0856a32c72c6fab4555e079

Observation 41dc409e-b4d3-43ff-b2a5-98e1dd491d12 · outbound

This paper cites Analytical properties of $q$-metallic numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Analytical properties of $q$-metallic numbers

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:21:12.328454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.184267Z digest=sha256:5ce28bbf5334515d42aa03dffe4be355d02aac83c699eed0e29c62c86bb62b3a

Observation 51297070-7da8-4262-9fa0-8ed58a63d837 · outbound

This paper cites Dimers, filters, and $q$-deformed real numbers.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Dimers, filters, and $q$-deformed real numbers

Reference 27

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:21:12.310137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.188443Z digest=sha256:21a9933030ab6a8bf0508fb49923564e7b1b0bd4996202273d3962f4377bbbc2

Observation a5a125e9-f9bb-4ebc-825e-9c60928387f0 · outbound

This paper cites Ren,On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ren,On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res

Reference 28

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.261192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.193125Z digest=sha256:3e7ea263e9489e07bc98d5c8565e6cbaaf13fe7c710f9084c9ac5f7c86d10317

Observation 6bc4f5d0-6254-472f-944b-e91d28720fcd · outbound

This paper cites Ren,Corrigendum to: On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Ren,Corrigendum to: On radiuses of convergence of q-metallic numbers and related q-rational numbers, Res

Reference 29

Resolution
verified exact
doi, observed 2026-08-10T21:21:12.243196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.197364Z digest=sha256:8f9c86c9287efabd689abfc2f9e04aad53d99582cdfc0cb2c9fb7ef7abfbaaba

Observation aabb6e74-79f5-4fb6-8631-1ed5a8926698 · outbound

This paper cites an unresolved cited work.

Coefficients of $q$-real numbers: their combinatorial meaning and growth Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:21:12.698008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T21:21:12.201646Z digest=sha256:f559ff33a6612c86924dd2484e62260bb811a6fa4bdadadf02e40b3a3ad0ea01

Pith citing papers

No inbound Pith citation observations are available.