{"as_of":"2026-08-09T11:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f9c7088539c6cdbb0af799e3318eefded79a5c8fee3bf2dd9ef4c02f37d5a7c2","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:16:32.100151Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:04:16.890081Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-15T06:39:48.600341Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16050","snapshot_observed_at":"2026-08-07T13:04:16.890081Z","title":"Bridi, F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.22941","last_updated":"2025-06-02T22:43:50Z","snapshot_observed_at":"2026-08-08T15:12:18.993766Z","submitted_at":"2025-05-28T23:45:27Z","title":"The only Class 0 Flower snark is the smallest","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:04:16.890081Z"},"links":{"cited_paper":"/paper/2505.16050","citing_paper":"/paper/2505.22941"},"observation_digest":"sha256:75027583b0ecd2ea47e1b84b2593f2dd52a1ebf2faf9e5ddd0fa2b10a0a0d147","observation_id":"433ce7bc-2de6-4888-8e2c-3dc1c551cd81","resolution":{"observed_at":"2026-08-07T13:04:16.890081Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"cited_work":{"arxiv_id":"2505.16050","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.16050","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"95383d29-9253-4f2f-a20b-a287e557308c","year":2025},"citing_paper":{"arxiv_id":"2605.07014","last_updated":"2026-05-14T17:47:39Z","snapshot_observed_at":"2026-08-07T16:32:16.165708Z","submitted_at":"2026-05-07T22:52:07Z","title":"Improved Upper Bounds on the Pebbling Numbers of the Blanu\\v{s}a Snarks","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-15T06:38:08.974959Z"},"links":{"cited_paper":"/paper/2505.16050","citing_paper":"/paper/2605.07014"},"observation_digest":"sha256:10d7eaf2591ed4131eedd35447e5c819bae4cddfffe060aa89aef588948fa7a9","observation_id":"a734d0d7-f48b-4b63-bbb6-dae7636f1328","resolution":{"observed_at":"2026-05-15T06:39:48.604594Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.16050/citation-record","integrity":"/paper/2505.16050/integrity","json":"/paper/2505.16050/citation-record.json","paper":"/paper/2505.16050"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.418698Z","title":"Hurlbert, F","venue":null,"work_id":"cc7500a1-fe31-447b-9eb6-37c8c63a0d03","year":1900},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.230085Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:27cd3e6d76636d0777b4ac70970c96d794e2039809dca039317214ad74442832","observation_id":"ca98b87a-03a6-438d-abd6-881ae0af90ef","resolution":{"observed_at":"2026-08-07T15:16:34.421720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.408932Z","title":"Milans, B","venue":null,"work_id":"1c2dcbe4-6525-4ef3-8cdb-64d585b090fb","year":2006},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.349438Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:23414212300ac5644b8c2a378d82be83cdc3be45b6ea3cf8f01fa36ac31d8515","observation_id":"3799fe23-e8f5-467c-b452-d8f4c82c76db","resolution":{"observed_at":"2026-08-07T15:16:34.412371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.398468Z","title":"Hurlbert, The weight function lemma for graph pebbling, Journal of Combinatorial Opti- mization 34 (2) (2017) 343–361","venue":null,"work_id":"27ad0f8b-82cb-4936-bd34-29fba86e1d53","year":2017},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.504740Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:5531d2c10fa749318accbdddcd26f7df9cc4c3e11805ad4cc48e17da993bbcf2","observation_id":"e6312015-93a3-491d-873e-aaff56d1f7ae","resolution":{"observed_at":"2026-08-07T15:16:34.402181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.388534Z","title":null,"venue":null,"work_id":"f233c5c3-2086-4807-a244-1ad5f7bce878","year":1998},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.601857Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:17900571c612e3167edcfe8d54d40ba08dd4541402aa20388591b5fa096db659","observation_id":"07deac92-8d87-4be8-af71-8caf9c2cac6f","resolution":{"observed_at":"2026-08-07T15:16:34.392006Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.376835Z","title":"Adauto, C","venue":null,"work_id":"64aa207c-a9ae-40a2-aeb2-b7e089e7a0a0","year":2025},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.745555Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:5ddd63a3945e9d09981f63a130263bc4ec215f66efc35c3531b02682983f63a8","observation_id":"479e7e88-08b5-4c35-bb77-58fa66e72d76","resolution":{"observed_at":"2026-08-07T15:16:34.380752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.367831Z","title":"Adauto, V","venue":null,"work_id":"c2c80963-2363-4e69-aa37-e2ba65132d27","year":2024},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.874037Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:f083313987234c2794cf899f3addba9f6e555e65eba2392f0126abc9d83c7d46","observation_id":"880395d6-9aa6-428f-ba3e-5c54000df989","resolution":{"observed_at":"2026-08-07T15:16:34.370592Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.358725Z","title":"Alc´ on, M","venue":null,"work_id":"1d04f925-e5bf-4fd8-9da7-215fb922992b","year":2014},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:28.983556Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:573964c98b2bf55fbb2930121bf90a880bd6cab1e75b12f97736cf0ad9e64122","observation_id":"9ffd965f-1dc2-4975-9afc-2a7f9dbcc9c9","resolution":{"observed_at":"2026-08-07T15:16:34.361771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:29.158520Z","title":"Cavicchioli, M","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.158520Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:ee749bb328d5785e02a51d669cf393026c092011933bee25128c725cfc09b844","observation_id":"2a06e10f-b2a2-42d0-b800-60f55402aa36","resolution":{"observed_at":"2026-08-07T15:16:29.158520Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:29.274352Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.274352Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:66b963e369a5fb977421d9dc1aad5be1714ee7de9da90d7342a0146f379df673","observation_id":"3c057dbb-2b2a-4067-a53a-f669f99ac13b","resolution":{"observed_at":"2026-08-07T15:16:29.274352Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.333240Z","title":"Petersen, Sur le th´ eor` eme de Tait, L’Interm´ ediaire des Math´ ematiciens 15 (1898) 225–227","venue":null,"work_id":"f968795a-1346-4d95-ba61-a0215d1a5dc5","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.418711Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:910b2073688b7712e049fef3a33280d13f66563eca7326afbb49c4cc915c1a8f","observation_id":"c6c02a1e-9963-4a0c-bca6-2c77414be10e","resolution":{"observed_at":"2026-08-07T15:16:34.336738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.311922Z","title":"Campos, S","venue":null,"work_id":"83427fbf-71dc-4035-90ee-d18884e36a68","year":2011},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.590404Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:c25b392d0e2ac017be686b9f635677c3f0ccb3c4d1ac3f35f9e0de19d2c18539","observation_id":"74f43fd5-96b3-4320-8902-730894f36239","resolution":{"observed_at":"2026-08-07T15:16:34.316318Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0503511","last_updated":"2005-04-21T08:32:46Z","snapshot_observed_at":"2026-07-07T05:47:26.679830Z","submitted_at":"2005-03-24T10:25:24Z","title":"The Complexity of Pebbling and Cover Pebbling","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0503511","snapshot_observed_at":"2026-08-07T15:16:29.768056Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.768056Z"},"links":{"cited_paper":"/paper/math/0503511","citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:1ad9b7c447579163edad25a0f4dc2086a323407b8d6d296b14f7b9cb16c4e7fc","observation_id":"57675117-300b-4e72-9405-655eb36ed6a7","resolution":{"observed_at":"2026-08-07T15:16:29.768056Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:29.895952Z","title":"Hurlbert, A survey of graph pebbling, Congressus Numerantium 139 (1999) 41–64","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.895952Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:3805afe2b72d4ad9e674a996e97ac8f5f7d226e38204849daa0afc33b82e31eb","observation_id":"74ca01e7-6001-467a-a59e-2e4eaa0e2ed4","resolution":{"observed_at":"2026-08-07T15:16:29.895952Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.291911Z","title":null,"venue":null,"work_id":"10f1b128-4515-41bb-8722-a2403f4def24","year":2008},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:29.996022Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:949179db9323a3cf92c6a835681736da83d29db54ccf55cd4409fa09e002804d","observation_id":"3ef04b7f-083f-4301-be50-898e80eb5b98","resolution":{"observed_at":"2026-08-07T15:16:34.298067Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.281379Z","title":null,"venue":null,"work_id":"f1df7c60-f1d8-42f4-8b3e-49089297aca8","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.155053Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:c03f59b79b0ce1fe5a46633e89e62651404a70a984a0ff0aa0ab20544463072e","observation_id":"b9dcb315-6ea9-4247-9338-55a78482a0f6","resolution":{"observed_at":"2026-08-07T15:16:34.286517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.271872Z","title":null,"venue":null,"work_id":"531a23c3-488b-439f-b6ac-acd04f5ba591","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.258612Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:a744efb207c85a7ba142db30cb2e4f626325e1d9d5f62a97775fec9d5f524669","observation_id":"8ca116fc-82c8-4607-bc82-fba913649e73","resolution":{"observed_at":"2026-08-07T15:16:34.275110Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.261255Z","title":null,"venue":null,"work_id":"27ae0453-34de-4292-b25c-11f8bd559e11","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.399800Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:9a2aaf9407798aa52647ee827438f98c8f44409bb6554ea2b4867ee30f82d939","observation_id":"9fea5170-7aa3-4163-bdba-1a013d6dc627","resolution":{"observed_at":"2026-08-07T15:16:34.265060Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.252052Z","title":null,"venue":null,"work_id":"9d5dca5a-2a4c-4ef8-aaa0-4ae8fa556cf1","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.518463Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:67acc3079eb0eaaff83af8fc8682dd2f7d79af6b1cbd544ac5ad350b28d984e6","observation_id":"7a7bd06d-f18e-4079-bd90-31fcb6798ef4","resolution":{"observed_at":"2026-08-07T15:16:34.255241Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.243003Z","title":null,"venue":null,"work_id":"0866501e-bf71-4f57-8b9c-6c372805d869","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.654634Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:4b7b0c13b7c29cea3616e4140b85c262fee0c1488585a85794e6d6bf445186ba","observation_id":"da41f0c3-221a-401a-b628-31648f0e7d19","resolution":{"observed_at":"2026-08-07T15:16:34.245861Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.233360Z","title":null,"venue":null,"work_id":"34294c05-0139-48bd-9c5c-0c4be3543f38","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.818282Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:e2176ee5295634b99aed402ef4bcc25328366a9c499851504f91a8b1b3481461","observation_id":"885a015e-85ad-403c-a20e-86207f500a35","resolution":{"observed_at":"2026-08-07T15:16:34.236331Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.223420Z","title":null,"venue":null,"work_id":"b4f9ec76-3299-4142-8287-4ea683c6eb5e","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:30.948681Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:8634bb369069930c2752cc16ee168dd553ffdd7d0fecc6c06945a82da568eab6","observation_id":"32869f2c-7eed-4796-b85c-ea7710a73f92","resolution":{"observed_at":"2026-08-07T15:16:34.226921Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.214187Z","title":null,"venue":null,"work_id":"2648ae35-8192-4632-b929-72550939c9dc","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.082098Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:1f39f7e197381234f28e83545cae6f0905784bccd0c4bca1a91552027dbdeffd","observation_id":"7d020fc9-9a58-45ea-adab-c75bdee7bb10","resolution":{"observed_at":"2026-08-07T15:16:34.217302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.203306Z","title":null,"venue":null,"work_id":"b6daed37-bff7-445a-9b7e-12d8cc29b9f4","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.159235Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:f3c699ff712b7a9f0d6252be383d1697773b442825a789c31cd027f640471e0a","observation_id":"2648a7c1-edf3-42cc-acc0-b9d1d39f883b","resolution":{"observed_at":"2026-08-07T15:16:34.207379Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.192666Z","title":null,"venue":null,"work_id":"96f2e714-0634-494a-a91e-bc3281e8db66","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.257420Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:0e857809b04fe9f6d68be12fbd31f1173f800e81ad29c066c172d145d1324c24","observation_id":"83a3e166-c93d-4125-b1b2-932bbbfc404c","resolution":{"observed_at":"2026-08-07T15:16:34.195914Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.182778Z","title":null,"venue":null,"work_id":"b09b781c-7968-4298-b7ab-f7405a6a2406","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.272643Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:b5e77b58a85658151d5acf173bc31c62d5b0c0748e0956757484234b6b7ad332","observation_id":"f95fd4aa-07a8-4e55-86ab-e4e55d49d0d8","resolution":{"observed_at":"2026-08-07T15:16:34.186131Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.173830Z","title":null,"venue":null,"work_id":"82279f26-9a98-4e88-aae2-01ad1b285447","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.310648Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:57b16a0680a3387c807034064fc91713d424763fd8f39045e65a815b8fd08843","observation_id":"3b2be968-8037-4bff-9514-9bf5617be239","resolution":{"observed_at":"2026-08-07T15:16:34.176860Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:34.106080Z","title":null,"venue":null,"work_id":"f5dc6a56-a298-420e-a9cf-cfeef007dfbc","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.388111Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:345b551d20e4c373db2128bce2f4d5a90dfbfc91a72371a6ec3f9b02a9d3d34e","observation_id":"536bee65-e205-4a32-8952-fb9cb9efde98","resolution":{"observed_at":"2026-08-07T15:16:34.168128Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:33.893658Z","title":null,"venue":null,"work_id":"6aeca8f6-332e-49a1-b41c-7ef969f8eb64","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.552103Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:a9a0e1f60e37128082f304703e91bfc605a25b028ee4c6c173a4e9fd79bc2a1c","observation_id":"18e1c276-43a0-4fba-b7c5-a6c076db48fa","resolution":{"observed_at":"2026-08-07T15:16:34.020588Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:33.747412Z","title":null,"venue":null,"work_id":"7300a106-a2c3-42bc-9a58-3dd5ddfeed8b","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.648908Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:dce8eb6ff504dcd62eb7214c1c3afc58de1e7a2b6b434bfb04006eeabc66ee41","observation_id":"9b9939bd-ff24-4f51-97a9-09c541357558","resolution":{"observed_at":"2026-08-07T15:16:33.784346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:33.570853Z","title":null,"venue":null,"work_id":"78aeacc2-525d-428b-ade5-cb9b36905195","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.707501Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:c521c8b0676b18ed955e072ab6790b8f13e38ce54a472c89cd4df6c81434c1c3","observation_id":"6c59ee1c-f497-4923-8ec4-203f112fa2e9","resolution":{"observed_at":"2026-08-07T15:16:33.704740Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:33.367181Z","title":null,"venue":null,"work_id":"ea6584b2-731b-4507-9e9c-749612e3f71e","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.750753Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:218300532f6463c456d78be832e79fe60fb0cb0571711473e3676ef5a42af7eb","observation_id":"031b1c97-7d98-453f-8e9e-2b5a58a3ca44","resolution":{"observed_at":"2026-08-07T15:16:33.461245Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:33.111285Z","title":null,"venue":null,"work_id":"2f5509f0-1712-4d20-9916-e62768975954","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.801517Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:6c8ba43a63a9df9e1a82d961ccaa5be2bf77afd33a0bda558201972c28014a23","observation_id":"96caf3ac-6b7c-4954-bd32-eba939cc78fa","resolution":{"observed_at":"2026-08-07T15:16:33.278003Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.950651Z","title":null,"venue":null,"work_id":"13a30081-9228-4a8e-9e78-52a2dce191e8","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.861536Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:2145c1fb499f5311263e4755861fe308be4911f69d05cebf6e404ea8a1d3128e","observation_id":"cf21db63-1552-46e0-9ede-c2297e99831b","resolution":{"observed_at":"2026-08-07T15:16:33.016500Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.722602Z","title":null,"venue":null,"work_id":"32a65792-863d-4a0a-a759-64803a5c35b9","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.920942Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:53b1368defc9315be9f11b73c4eeb6b0235d9f4befddb70be1ec19d2ab55bded","observation_id":"86d195db-ddfd-49b9-8888-3f4b19a8519b","resolution":{"observed_at":"2026-08-07T15:16:32.861151Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.566428Z","title":null,"venue":null,"work_id":"f7bf4797-6e2f-4154-9d06-9798c50938dc","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.950276Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:b7441f6e95f78d0a651689b39602009bf2bd857903e3ad0bc2bbc68d9f6eabdb","observation_id":"c0be5067-7a63-47db-8864-b5bf14dd5b83","resolution":{"observed_at":"2026-08-07T15:16:32.597779Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.484419Z","title":null,"venue":null,"work_id":"db4c5947-56a0-4ae5-b685-456245e7ff3d","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:31.981692Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:b003a6b0f5269e366a8abae0d846864b8df4ac28f57840542b82940a4527cc0e","observation_id":"26c7461f-ba60-4cba-99bb-3fd7726461b2","resolution":{"observed_at":"2026-08-07T15:16:32.524364Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.364237Z","title":null,"venue":null,"work_id":"23617235-ea4e-420e-97ad-59ba09013246","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:32.045068Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:d05f04e0e815ef565f64825bc4b84f0fc5a5a7a56affa7f221f8b118ac775dc2","observation_id":"7ba0a10d-929b-4f07-aa40-0ff6ec477a74","resolution":{"observed_at":"2026-08-07T15:16:32.427714Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.257222Z","title":null,"venue":null,"work_id":"ac300142-d197-4dc4-a49b-9b5b980eeae6","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:32.067628Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:1ee5693324b329407ba7075ec7e855285c86f7362333d9d007480f966324def6","observation_id":"d5a0fbe9-3ea8-4094-914b-1905a9c6ba3e","resolution":{"observed_at":"2026-08-07T15:16:32.297817Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:16:32.169504Z","title":"For each strategy, we omit the root and highlight the vertices of the trunk in bold","venue":null,"work_id":"aaf6ab7f-0135-481d-8c88-e1f9f123c2fa","year":null},"citing_paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T15:16:32.100151Z"},"links":{"citing_paper":"/paper/2505.16050"},"observation_digest":"sha256:56adfbf5dfa441faba131318a1ddd3870ec026a44945b605c1baf7968f4ea0b7","observation_id":"03ed91ff-fca1-4467-8ed7-2bd235ac676d","resolution":{"observed_at":"2026-08-07T15:16:32.212956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.16050","last_updated":"2025-05-21T22:01:49Z","latest_version":1,"primary_category":"cs.DM","snapshot_observed_at":"2026-08-09T08:01:33.107181Z","submitted_at":"2025-05-21T22:01:49Z","title":"A Weight Function Lemma Heuristic for Graph Pebbling"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":39},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 2 inbound Pith citation observations for arXiv:2505.16050."}