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Paper Citation Record · LEDGER

Ninth degree analogue of Ramanujan's septic theta function identity

As of 8 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2506.01181.

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

pith.paper-citation-record.v1
2506.01181 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:58:20.654449Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

25 of 25 outbound references displayed

  • verified exact0
  • verified fuzzy5
  • unresolved20
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 924b980b-e734-41a7-9bee-7dcbbb9e9145 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:24.411199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:18.935380Z digest=sha256:a749e67798862d90aa75a5813601200cf2eb8983871e9f9b5344d7995dd38a4d

Observation 658d4f89-fac0-4e45-9ea1-d77d320054b1 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:24.232884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.005304Z digest=sha256:af3b4ac17a53863ad099145fc93c1c1944618ccb740e31216943a8dc55c04bdb

Observation 30125a44-1b53-475c-a762-471f8ce06154 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:24.126255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.077051Z digest=sha256:2cada7cb4a1fa0ba69c260778db448e1b68d0870c66cea107da136a877dbbbb8

Observation 1198750d-7984-4827-b1f5-d828b09cb0da · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.997952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.166918Z digest=sha256:024ae0b97ef18e8e8f4451f723cbd66af77e57b76f112aa6edfe359159084611

Observation 0993664e-fa07-4cd1-9dd3-7a3352c7d291 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.848837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.229293Z digest=sha256:7b80cc28f886be53405b86f87225c4b0b89b7d1fbbd75d870ed8a0dba24b1a5d

Observation 984d4222-a81b-4c2b-b002-627bb6f65c0d · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.681662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.298882Z digest=sha256:9c4338de66883f7908b16efbf7ce934fa5c2b19e14bd1e196d23fca5517190fa

Observation bf127f39-15c0-4b30-ab0c-972b6069568c · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.545409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.370579Z digest=sha256:4169a36ed36e6cf8df25facf6857189db53d292b4c4dc933bf24a409c218f6b7

Observation 51dcab62-1666-44e3-9283-5aa1b618588a · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.435674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.436078Z digest=sha256:592297cff1dab4379fa94904df5ce5a2cacdc8ad1916ae2ea42682654e8c9452

Observation 947f22c1-2e79-4943-8879-fe0243227ffb · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.305497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.521913Z digest=sha256:f16f6fb8ea080dac4ab39ea62314948847a57bc961e74f6ef28ffc5b98f157f6

Observation 6ea6c524-fe44-42f6-bc10-e139f0063c50 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:23.184379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.565721Z digest=sha256:b036fee67e657e794d9aaaf038f0483a5dc312768a8d84e79170e291b714a475

Observation 69a63cb0-28c3-47e1-adc1-c478f6924bb8 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:22.982472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.627969Z digest=sha256:f84368773e7fbe83d71da6bc4b25c990fc5e0306fc367077ed34993573517274

Observation 1383a5f7-a86f-463a-bbf7-01ee542fffec · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:22.813792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.690295Z digest=sha256:30b1ac3ac4189d94317bd80c3825439f6ab28c0cbbc568df7ac283e3ef716395

Observation f22b8ee9-57c2-482d-9a77-d720fe5f0686 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:22.672356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.732547Z digest=sha256:42755cca9121a0138f923c44200ad3cb7a20efafe0dbc30542297a0fb6efbc29

Observation 3eb8047a-7c46-4534-bc0e-235a08cd0332 · outbound

This paper cites Ramanujan.

Ninth degree analogue of Ramanujan's septic theta function identity Ramanujan

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:22.531104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.812203Z digest=sha256:c55ee306d8199b82dc23b436b007454d718fa5dbe17fc296c3f572eb0b6221d6

Observation 885a5d43-a879-4bdb-8269-a18cadfde33b · outbound

This paper cites Ramanujan.Collected Papers of Srinivasa Ramanujan.

Ninth degree analogue of Ramanujan's septic theta function identity Ramanujan.Collected Papers of Srinivasa Ramanujan

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:22.368502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.871739Z digest=sha256:0496f2c5af8c6171da13b7e6a596805cafcb92cfe563b7e8c391a75bfda71caa

Observation c4e1e91a-e08a-4d29-b024-6fa3a503cb97 · outbound

This paper cites Ramanujan.Notebooks of Srinivasa Ramanujan, Volume II.Tata Institute of Fundamental Research, Bombay, 1957.

Ninth degree analogue of Ramanujan's septic theta function identity Ramanujan.Notebooks of Srinivasa Ramanujan, Volume II.Tata Institute of Fundamental Research, Bombay, 1957

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:22.204309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:19.944554Z digest=sha256:f6933d6f8683c063b7cbfec7b2e09dc14bf9a0729317224657e6d4174843c569

Observation 14c2f454-0e53-4228-bd9d-03cd9180f6a8 · outbound

This paper cites Ramanujan.The Lost Notebook and Other Unpublished Papers.

Ninth degree analogue of Ramanujan's septic theta function identity Ramanujan.The Lost Notebook and Other Unpublished Papers

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:22.104298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.014751Z digest=sha256:0fb1b0936b7ebfeff10b2b89c34032c769b26096e137dd1acc38d2bdbc7699e0

Observation 88e71680-9915-48db-9dca-9625ab40fa33 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.981666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.057161Z digest=sha256:dc51fb3e6603c62d1ddf53b901d8dbbe872a86d25f45a7615c37b39ddac5bed4

Observation 1e44304f-03a7-4f7a-995e-855ef22a91ed · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.847760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.130421Z digest=sha256:38b24053017ec10e8a5a327f075c9a310691f7b5885b87446892ceccbffd9e99

Observation c01c859c-a873-41ed-a406-dee9ab467e67 · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.690375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.182108Z digest=sha256:ea9a2fd085ed49c010d956cd039818dba79e394d5edef06a066a2edcd8946282

Observation 3a209731-4a74-4324-a362-5f9e1a0e4fca · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.554241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.311791Z digest=sha256:dd77bfe85d0f9242bb01ec5a6b73c409bbbf5f8d31cba2f15adcb1000c933100

Observation f3b4327a-5d17-4f07-9cd8-3806af18255f · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.454937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.378353Z digest=sha256:56538ca1760e5af5ce83bde9e9c2ceaa6b339d8b1c57141aeace9859a48cbd47

Observation 1901d2cc-930a-4efe-9509-12a9360cd45d · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:21.202089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.468036Z digest=sha256:d8b47f87f2e70303051f30bcaa490d7de5ffcf7c473a05f09d2b49aaf027ef20

Observation 5bbc95dc-0a7e-469e-8c81-9229003b2d26 · outbound

This paper cites Yi.The Construction and Applications of Modular Equations.

Ninth degree analogue of Ramanujan's septic theta function identity Yi.The Construction and Applications of Modular Equations

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:20.956799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.561392Z digest=sha256:943b64d248d1fd5ccbbcd96f80d7537de473733d3932ac222e9868fd0f26a906

Observation f353c3e2-96fd-49c2-96e4-2b93be15b32e · outbound

This paper cites an unresolved cited work.

Ninth degree analogue of Ramanujan's septic theta function identity Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:20.807899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:58:20.654449Z digest=sha256:d2559afa58964deed8fa9675799412ba7fa2555a2f99eadb0f50f3e5c3c15a25

Pith citing papers

No inbound Pith citation observations are available.