{"as_of":"2026-07-23T02:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c598f7790311d7867611d4d05cca574e1c5f5516c2ad5ff8df4eda070bf09185","coverage":[{"denominator":56,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":56,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T20:27:27.201641Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-07-22T06:31:00.163083+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2604.04659/citation-record","integrity":"/paper/2604.04659/integrity","json":"/paper/2604.04659/citation-record.json","paper":"/paper/2604.04659"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"93ff97f5-755b-496c-b519-8017f55132ef","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:531c6f52f9378029a3d4890661dfed6c697959ad5478463ea7e2c9f5c4dbabe1","observation_id":"c6462281-920a-4607-9eb9-de12e16d80a1","resolution":{"observed_at":"2026-05-16T01:30:30.049143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Again we follow the time evolution of the DF, and test if it reaches the expected statisti- cal equilibrium DF","venue":null,"work_id":"bf08694b-2551-44ee-8324-426c3ebefaa2","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:5bc1a0dd7795368d8c22aec69ad6752d8e2ff79fcdb24a65bdb5848e8a61ee9d","observation_id":"fb1ceb32-7ddd-4f95-bbd0-f032ec014091","resolution":{"observed_at":"2026-05-16T01:30:30.039897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c8aecd42-57ef-42e5-9103-e3d472edd8f1","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:50a592733aaaecf2b01f18fa8b721e7b4cb4e2bbaeb467e5565bcc5d44fd21bb","observation_id":"a26cacc8-5d7b-4d9f-8c81-6aa71a3f7917","resolution":{"observed_at":"2026-05-16T01:30:30.060552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"The sim- ulation algorithm is similar to the one described above FIG","venue":null,"work_id":"00b38d77-3787-45b6-b59f-d3fd951c14bc","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:865a52d81843d42f32bff96e57785fe520f68cf194cb3a907fe71736483aa0a1","observation_id":"f017c99b-39bf-4f49-b135-309a2a38b4c7","resolution":{"observed_at":"2026-05-16T01:30:30.033429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Here, we follow the evolution of the low-mass parti- cles DF from the non-relativistic to the ultra-relativistic regime","venue":null,"work_id":"aa3248bb-a837-45c1-8dd2-2da50a6712ad","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:bfe2371ee421ed731906f47577550be772edda3732579c5d9bf0575a3bc374bc","observation_id":"1c37dc59-22b8-48be-b30a-00e17802712b","resolution":{"observed_at":"2026-05-16T01:30:30.044045Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"The energy growth is exponential, rather than poly- nomial in time, leading to an exponential self-similarity in the time evolving DF","venue":null,"work_id":"cb28a637-2cd7-46c7-8bfc-9389702ece73","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:2dbd6172a2d84ca0ceecb625b376a95b31bdd1930b190ab7983ba89dd6d2e6ca","observation_id":"be4e5826-5542-40ec-9f4b-7f63aa7101d0","resolution":{"observed_at":"2026-05-16T01:30:30.024936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"The collision is re- alized based on the collision rate, i.e","venue":null,"work_id":"8c30f091-c004-48d0-80f6-06269e7abb99","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:615b515c57ffa9b1acb0755c444fb5c636ec0b2cf4a4932bcad2d226f0fe8d36","observation_id":"bac3c42c-f933-4270-a36b-fc47917c344c","resolution":{"observed_at":"2026-05-16T01:30:29.941183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Below we simulate the cascade process when the in- jected particle is in the ultra-relativistic regime, that is Ek ≫m","venue":null,"work_id":"bac8a508-d2a5-4969-9dbb-1e3f12e2b8cd","year":null},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:8052d3ac1221d7e10c2c0defb4e63e3bb8c6aa2351ee1047603e300418c2a872","observation_id":"4664acd7-0352-42d9-b51b-cb7038f08610","resolution":{"observed_at":"2026-05-16T01:30:30.006821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0412004","last_updated":"2006-05-29T20:26:24Z","snapshot_observed_at":"2026-07-07T02:13:33.048120Z","submitted_at":"2004-12-01T04:34:56Z","title":"Power laws, Pareto distributions and Zipf's law","version":3},"cited_work":{"arxiv_id":"cond-mat/0412004","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"cond-mat/0412004","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Newman, Power laws, Pareto distributions and Zipf’s law, Contemporary Physics46, 323 (2005), cond-mat/0412004","venue":null,"work_id":"409a5974-d841-4536-ba39-7eca6129edaa","year":2005},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/cond-mat/0412004","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:a0f218b1f3a3ff9ffece0b8ade75a5b092ff413e049ad6a69801289186318107","observation_id":"ae5f2159-3c05-4b93-bbdf-610a14f8e93c","resolution":{"observed_at":"2026-05-10T21:55:51.792504Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Gabaix, P","venue":null,"work_id":"a78efd5b-4951-45ff-99cc-8e6f5f835f07","year":2003},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:c70174b24ee886f00fad81d2ca836b210be18601970a5b614ae094c84c26cbcd","observation_id":"214197ae-e88f-4b20-b360-fe74c3499c0a","resolution":{"observed_at":"2026-05-16T01:30:29.934658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"physics/0601192","last_updated":"2011-02-17T23:24:30Z","snapshot_observed_at":"2026-07-07T06:54:35.117821Z","submitted_at":"2006-01-25T01:08:58Z","title":"Re-inventing Willis","version":3},"cited_work":{"arxiv_id":"physics/0601192","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"physics/0601192","snapshot_observed_at":"2026-07-04T17:46:02.130130Z","title":null,"venue":null,"work_id":"21b0f9df-2323-4585-8c27-7ba72f089522","year":2006},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/physics/0601192","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:537cbccef23dd7279b079d046653e5afb6d27a3a32cc1d6e1e678eafae3592b3","observation_id":"d5a2ab09-9d43-4828-8a49-b7c671b58ce9","resolution":{"observed_at":"2026-07-04T17:46:02.130130Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1403.6528","last_updated":"2014-03-25T22:45:47Z","snapshot_observed_at":"2026-07-06T03:39:27.828306Z","submitted_at":"2014-03-25T22:45:47Z","title":"25 Years of Self-Organized Criticality: Solar and Astrophysics","version":1},"cited_work":{"arxiv_id":"1403.6528","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1403.6528","snapshot_observed_at":"2026-07-04T20:15:18.498596Z","title":null,"venue":null,"work_id":"5cbcd6d3-02b6-484a-a172-fb8bc02af5c1","year":2016},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/1403.6528","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:7fd537efbf149f8f284eba429430fb00a9e176a99927a0e4d9804bc390d23941","observation_id":"6b404dac-6a1b-496c-b9d0-e4607ac8d8c3","resolution":{"observed_at":"2026-07-04T20:15:18.498596Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Kleiber, Physiological Reviews27, 511–541 (1947), pMID 20267758","venue":null,"work_id":"987b8fbd-edb7-43a0-a164-fd310d875df8","year":1947},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:d0ffa211aba829418a661d0e5788a459765a97644d9d725ac3e2322da824432d","observation_id":"ad80f3f0-3965-406d-8df1-33c15fc3b2bd","resolution":{"observed_at":"2026-05-16T01:30:29.998998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c7d25894-1671-4074-94bc-787317718169","year":1996},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:ee1be4cb81f320d3d5c0449f59f564925bbd1d373d9ba135f97f56a1dd09a913","observation_id":"92f579ae-44dd-4692-9131-4892fcacf579","resolution":{"observed_at":"2026-05-16T01:30:29.948701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0607542","last_updated":"2006-07-21T15:30:00Z","snapshot_observed_at":"2026-07-07T05:58:57.964646Z","submitted_at":"2006-07-21T15:30:00Z","title":"Fast algorithms for computing the Boltzmann collision operator","version":1},"cited_work":{"arxiv_id":"math/0607542","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"math/0607542","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mouhot and L","venue":null,"work_id":"35ca36f9-ec93-4104-a759-f2b0235c0300","year":2006},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/math/0607542","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:07e840edaf68b757803635485ee41053a21da438d53f829206969203061f4571","observation_id":"6185c810-eadb-4fe4-9111-06347b2bde42","resolution":{"observed_at":"2026-06-03T22:06:20.128571Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"8746b74a-264a-4782-8052-32e09613e5fb","year":2013},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:488c13f3e469583e0c64db856d9d99c9807c1d714800dc955a3bfbed9ec0ed24","observation_id":"d026b7da-a70f-498a-967f-41d0e963d3bf","resolution":{"observed_at":"2026-05-16T01:30:29.994974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Cai and M","venue":null,"work_id":"b26908f1-ec23-4713-be2c-8329bf0bce4c","year":2015},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:5945a8a1cb14279228833c9c67431738dcc4b52189d9b7ec985136c10338c26b","observation_id":"8bb6e8f0-6572-400b-b1f4-8e4e9cb5222f","resolution":{"observed_at":"2026-05-16T01:30:29.952664Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"400057e7-82e3-4eee-8bb6-ae989b9b5d33","year":1979},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:8d73534851f5ffdc363a27b22cd5426ae85cdea324912bbd8e65c104ca27e8d9","observation_id":"f97eb05c-82da-4960-bf65-328ef4202eb7","resolution":{"observed_at":"2026-05-16T01:30:29.944712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"2ee426f7-2c2d-43d1-bc01-51635ad5ac7f","year":1976},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:1f9665c67ec04d6e207031073b86de6e9db0e78e1411aec22ad0a20d46350883","observation_id":"464d0c87-fa50-44ce-89fd-982949bb4d33","resolution":{"observed_at":"2026-05-16T01:30:29.956292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"453a5999-1db6-4709-8ad9-38cb0bcf9865","year":1993},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:b51b1fd08e265f9ecda58bda3c669be41f0f996bfc358336eb027d66081b9e2d","observation_id":"096f61eb-2e5d-4b60-bfb5-a57692a8ea69","resolution":{"observed_at":"2026-05-16T01:30:29.987378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"mat/0509773","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hanel and S","venue":null,"work_id":"8f422464-5152-4379-93b9-33a0d1dfb2fb","year":2006},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:24694a83156af102e754daa1cfec8e08ed6d4c1d3cc9c335af0f401ecd1d649d","observation_id":"3bac1eea-3084-4c7a-b281-5642d33478c7","resolution":{"observed_at":"2026-05-10T21:55:51.781337Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Hankey and H","venue":null,"work_id":"9c634d57-748f-4b8e-a554-0f92c720265d","year":1972},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:8b0b5b929033aacd41278f8bda1bb9d78219b7761172a9ee558a0298aa57b119","observation_id":"b0e4b690-425a-44f0-bf85-7bcbf7677c48","resolution":{"observed_at":"2026-05-16T01:30:30.002374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"79fca222-bfd4-4bca-97b6-94b59a48eb62","year":1967},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:9366cba403850e2d720464480229ecd76b88d9b286a571854b499d131fa455e3","observation_id":"186cd5e8-e720-41b6-ab3a-4729895b2517","resolution":{"observed_at":"2026-05-16T01:30:29.991272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c009ca0e-39d4-4bbd-807e-d3648b606aa3","year":2014},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:6fcb4987f2546dcf045e970029cebf32760431df7fbf23ce1646b7f130ac7a73","observation_id":"a2220e10-a86d-4e58-bece-c032fe3d8c8e","resolution":{"observed_at":"2026-05-16T01:30:30.013883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"2c45c408-2391-4f80-8434-6a3ff75d1000","year":2010},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:baef1c5aaff4ff96d6489f49d3eb2d2a92feb3fe414ec80236cf0dc2c3341f50","observation_id":"fe50acbc-a728-4596-b626-b81878e90fa8","resolution":{"observed_at":"2026-05-16T01:30:29.960459Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"dfaed751-b1c3-481f-9a61-153c3374eee7","year":1983},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:80e613401c8d9ccd8a422b160e96e80f0b6ca1333c81b8b1fb9da825435c831d","observation_id":"e130953b-68d1-40a8-9ce5-c6117e9774eb","resolution":{"observed_at":"2026-05-16T01:30:29.983539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"75b66fdb-bba1-4b19-adee-f740c369a86f","year":1994},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:99d328eca28dd373b4c33c79099e341f0339c5ae52c5fe54e9c1e38a65307136","observation_id":"f966bacb-ebe1-4a1c-a6d2-d655b3cc192b","resolution":{"observed_at":"2026-05-16T01:30:29.979700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ph/0107530","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Achterberg, Y","venue":null,"work_id":"f7acbcf5-a540-4eec-844f-49ba4065380d","year":2001},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:113557d23fdc35170208186a54eca1b0d6ca991206f5ca7285fa1b8e6c0807a1","observation_id":"aa512641-4b37-4676-84da-f1c26e57c07f","resolution":{"observed_at":"2026-05-10T21:55:51.683770Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/0510522","last_updated":"2005-10-18T15:17:24Z","snapshot_observed_at":"2026-07-07T00:55:10.990537Z","submitted_at":"2005-10-18T15:17:24Z","title":"Relativistic Fermi acceleration with shock compressed turbulence","version":1},"cited_work":{"arxiv_id":"astro-ph/0510522","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"astro-ph/0510522","snapshot_observed_at":"2026-07-04T17:15:19.180773Z","title":"Lemoine and B","venue":null,"work_id":"181544a4-bb46-4ba0-a447-417ef0f2843f","year":2006},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/astro-ph/0510522","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:f4e27a789efcd0719dbe0e60e759e909e6fb0dce70b0ca45a2fc7b66c37f1436","observation_id":"032afe81-00ec-4920-9fe9-d96e60d793a5","resolution":{"observed_at":"2026-07-04T17:15:19.180773Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.19136","last_updated":"2025-07-04T08:31:54Z","snapshot_observed_at":"2026-07-06T20:29:02.246836Z","submitted_at":"2025-01-31T13:46:07Z","title":"Effective theory for stochastic particle acceleration, with application to magnetized turbulence","version":2},"cited_work":{"arxiv_id":"2501.19136","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.19136","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lemoine, Phys","venue":null,"work_id":"6646faaa-3620-4a55-8ff1-efceb970b246","year":2025},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/2501.19136","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:40f35c790cb3b693c969457e28ce293856a5aacb31566797ac2cde753feead9d","observation_id":"1fd016ea-92fd-4c84-acc4-9e3f8a372510","resolution":{"observed_at":"2026-05-10T21:55:51.693982Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"34ecb6f1-68d3-4b42-9708-933a3a468bc3","year":1971},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:f44f60d849372404e258e671ea37dd97a35fe14c071db4ef62c1097236fc73d5","observation_id":"9b319ac6-fc74-4e5a-8f02-9be37633c282","resolution":{"observed_at":"2026-05-16T01:30:30.010618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"22a07062-3b9b-4215-b8ac-e3f475dd5963","year":1998},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:14b38382561756dc21cdc54d9663d1c63c8dbce15e186d25345bbf1ed891d1ac","observation_id":"457bce0e-2e43-41f7-853f-d17bb11e26f8","resolution":{"observed_at":"2026-05-16T01:30:30.056238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ph/9901061","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f981487b-4e96-4fa8-a9e5-fcd78c8eccf2","year":1999},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:cf04440cf728351b77a732e86061735f7fa6f6c8ef1364daf16760fa6f988f57","observation_id":"355bf113-c872-4d56-8a20-dbe464903774","resolution":{"observed_at":"2026-05-10T21:55:51.758367Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0704.0044","last_updated":"2009-05-09T19:26:10Z","snapshot_observed_at":"2026-07-06T01:24:58.192438Z","submitted_at":"2007-03-31T17:47:54Z","title":"Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas","version":4},"cited_work":{"arxiv_id":"0704.0044","doi":null,"metadata_source":"pith","pith_arxiv_id":"0704.0044","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas","venue":"astro-ph","work_id":"d57022ca-eb2b-461e-bb6b-9ab8d3a55e21","year":2007},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/0704.0044","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:0335b43cd70068c607a58d983b41e465fc84865a8b39002c2e1e0d00806b24b0","observation_id":"8641825a-a9ac-4ea3-a3b1-4d9b69abfc25","resolution":{"observed_at":"2026-05-10T21:55:51.754008Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6251c314-c4c7-4a50-9d1a-d6e44513d8e2","year":1995},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:0e34bde99145899a107e584aea152fdfef00d48eeac8a9b35b2c75231b5e8081","observation_id":"921def5b-c3c1-4440-92bc-086ff7e478dc","resolution":{"observed_at":"2026-05-16T01:30:30.052861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0110607","last_updated":"2002-05-09T16:11:41Z","snapshot_observed_at":"2026-07-07T01:46:26.278865Z","submitted_at":"2001-10-29T23:04:02Z","title":"Velocity Fluctuations in Electrostatically Driven Granular Media","version":2},"cited_work":{"arxiv_id":"cond-mat/0110607","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"cond-mat/0110607","snapshot_observed_at":"2026-07-04T21:20:09.588759Z","title":null,"venue":null,"work_id":"24bcd2eb-64c8-45cf-8ac5-c18230932896","year":2002},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/cond-mat/0110607","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:d1c1750862c07a59406f488f570af9094ebdec099863f10aa7cd1f3c3bde363b","observation_id":"6699e756-d80d-4235-9524-3b5665714a4e","resolution":{"observed_at":"2026-07-04T21:20:09.588759Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0504187","last_updated":"2005-04-07T21:45:54Z","snapshot_observed_at":"2026-07-07T02:16:46.894496Z","submitted_at":"2005-04-07T21:45:54Z","title":"Power-law velocity distributions in granular gases","version":1},"cited_work":{"arxiv_id":"cond-mat/0504187","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"cond-mat/0504187","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ben-Naim, B","venue":null,"work_id":"1568eb51-b41e-44f9-a165-e8afc48e5c8c","year":2005},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/cond-mat/0504187","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:550de8635fd2e8f0eb6a359a074c25a662086f251c97047fa5fc348f67581fb8","observation_id":"c0d514cd-a949-4c66-96ac-5ba997cb672b","resolution":{"observed_at":"2026-05-13T18:05:05.375326Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.06938","last_updated":"2022-10-13T12:14:09Z","snapshot_observed_at":"2026-07-06T14:04:44.193264Z","submitted_at":"2022-10-13T12:14:09Z","title":"A Collisional-Energy-Cascade Model for Nonthermal Velocity Distributions of Neutral Atoms in Plasmas","version":1},"cited_work":{"arxiv_id":"2210.06938","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2210.06938","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fujii, Phys","venue":null,"work_id":"b06fce04-034e-4171-8c57-083d73be748c","year":2023},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/2210.06938","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:36280d0344f64f206a3fe3941fa2ebb7a077c0fb807cbbdf1c4dea44dd38c215","observation_id":"94e6768b-ce50-401b-9b8c-a3e6db3a0219","resolution":{"observed_at":"2026-05-10T21:55:51.813281Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b422d915-34d0-4834-b06a-6bdc72df2a29","year":1980},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:b8c270ca9e39545a2fb8af8bd08c9e4c3c1ee54c675b3fa30bc5221efd450fb1","observation_id":"8369c668-07b9-4092-8296-7e41bf5cee73","resolution":{"observed_at":"2026-05-16T01:30:30.030392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0f156cbe-6a59-4bfc-8cc6-c3da461c6fc0","year":2012},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:f11dc2ef6f28c987db8ce6cda67b05277f98231da566ed7f7da6a1c3c771c37d","observation_id":"33b0bb24-1747-49a5-a3aa-4dc5b7c92fc3","resolution":{"observed_at":"2026-05-16T01:30:30.028228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e8b9fd63-c346-4ba5-9d0e-71b3ebaa78b3","year":1997},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:d4b7a20de84636a3554c7bb2738b9bd6c0bb45d6fadb9eadada579a690d52d13","observation_id":"5ec7ce02-0286-4eaa-95b6-907673cbf7ce","resolution":{"observed_at":"2026-05-16T01:30:30.036377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Patriarca and C","venue":null,"work_id":"98116850-76f5-4778-a036-320cd4a3d238","year":2013},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:71f3ef464698b476e8b51e3d9fe0afc90ac199f5e00b685478bf99010c93ddcd","observation_id":"3272b96b-37c8-4945-b271-2c6b95daf39f","resolution":{"observed_at":"2026-05-16T01:30:30.020678Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2004.00940","last_updated":"2020-04-30T06:33:29Z","snapshot_observed_at":"2026-07-06T09:09:21.344833Z","submitted_at":"2020-04-02T11:22:33Z","title":"Power-law distribution in the number of confirmed COVID-19 cases","version":2},"cited_work":{"arxiv_id":"2004.00940","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2004.00940","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Blasius, Chaos30, 093123 (2020), arXiv:2004.00940 [q-bio.PE]","venue":null,"work_id":"99ffaeb8-4657-47d7-a200-dc48adf68a98","year":2020},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/2004.00940","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:af4dad552b8b788c9e12d25a30ac7a697b6d4a6e5aa2a5402741ae7642be66c6","observation_id":"aa7243a3-f4a3-4e34-b69d-b09c03b022cc","resolution":{"observed_at":"2026-05-10T21:55:51.703199Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Barab´ asi and R","venue":null,"work_id":"5af933ce-2956-4f9c-a889-b50ed790a028","year":1999},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:7424d257285436139922c1f2ab5ea2ca0e5c7bef9822114754decc3875050d05","observation_id":"1ad6e6e2-68be-4212-96bb-46faa1a25428","resolution":{"observed_at":"2026-05-16T01:30:29.976072Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.18642015","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Gitelman and A","venue":null,"work_id":"ec5460c7-be30-4be7-b1c7-96d317b97f3f","year":2026},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:bacf3860573ae75aeb403252b3978cb291b5705a927609d105b8ce614305acd3","observation_id":"776f793f-b5ae-4eda-84ff-22ac23f321a0","resolution":{"observed_at":"2026-05-10T20:30:47.365254Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Cubero, J","venue":null,"work_id":"f62d2f9a-2e5a-4669-99af-f257fdb762dd","year":2007},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:56a8fd45832e28dc9fc44dc6b7adc3a1bcb9567641704a90e480144183a88cd9","observation_id":"88fcec4f-c543-48b8-b918-83ecf24916bd","resolution":{"observed_at":"2026-05-16T01:30:29.972267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0812.0466","last_updated":"2008-12-02T10:56:12Z","snapshot_observed_at":"2026-07-06T01:51:40.412367Z","submitted_at":"2008-12-02T10:56:12Z","title":"Time parameters and Lorentz transformations of relativistic stochastic processes","version":1},"cited_work":{"arxiv_id":"0812.0466","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"0812.0466","snapshot_observed_at":"2026-07-04T15:38:59.218892Z","title":"Dunkel, P","venue":null,"work_id":"f0a41c12-31dd-4c90-80bf-761db2c70002","year":2009},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/0812.0466","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:d32f3c6e4afd572d7a8669691201207da062a4ae93b0a00a4922eaddab54b61d","observation_id":"a0ebcbb2-9865-46a7-b26b-3ee6b967fb34","resolution":{"observed_at":"2026-07-04T15:38:59.218892Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.04633","last_updated":"2020-09-10T01:58:52Z","snapshot_observed_at":"2026-07-06T09:54:22.812172Z","submitted_at":"2020-09-10T01:58:52Z","title":"Empirical test for relativistic kinetic theories based on the Sunyaev-Zel'dovich effect","version":1},"cited_work":{"arxiv_id":"2009.04633","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2009.04633","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"7898c25e-4748-4cd5-92f7-81e47484b58b","year":2020},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/2009.04633","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:4c8430e1524363d4da736448575d627b5f37ade49c50e03b978aca961f5fcc17","observation_id":"57d65ec6-bf45-4c90-a35f-5044d67c85b4","resolution":{"observed_at":"2026-05-10T21:55:51.787480Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e6958963-dd6a-470a-b135-14625c1ca583","year":1980},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:47c07faf231152210a8c75deea2b98b306e3f10fdcc17cf9260e3b92cb331970","observation_id":"be4c4829-4716-4640-adce-89367607904e","resolution":{"observed_at":"2026-05-16T01:30:30.017479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Peano, M","venue":null,"work_id":"80f73f80-61af-4e82-ba44-ce515eead912","year":2009},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:5762581d853336fa32e979e62d9e3f8cefef67aa40292cf6216277594863b90e","observation_id":"6c171826-9a0d-43f1-980e-37e982dc7f1d","resolution":{"observed_at":"2026-05-16T01:30:29.931378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1003.3532","last_updated":"2010-03-18T09:24:43Z","snapshot_observed_at":"2026-07-06T02:04:39.697629Z","submitted_at":"2010-03-18T09:24:43Z","title":"Kappa distributions: theory and applications in space plasmas","version":1},"cited_work":{"arxiv_id":"1003.3532","doi":null,"metadata_source":"pith","pith_arxiv_id":"1003.3532","snapshot_observed_at":"2026-06-30T00:54:07.100616Z","title":"Kappa distributions: theory and applications in space plasmas","venue":"physics.space-ph","work_id":"d158f6fb-2179-4d67-996b-f8053d6d7bf8","year":2010},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/1003.3532","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:f44878aecffa7a194ba0e6120f9017613723c7cf5d336dee26eb2abd8d8cb05b","observation_id":"2f963f28-cff2-49c9-a3cb-e5f27e86a6a3","resolution":{"observed_at":"2026-05-10T21:55:51.818863Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Livadiotis and D","venue":null,"work_id":"fd8ceccf-abea-4e8a-bc7a-ba166b9ca194","year":2011},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:770abdc28f897fe833ae21198eb0a230358c0f64b3b3ee78209d6b3427c97a6e","observation_id":"87f0b6f3-9f4c-4e45-8472-132b7c03fa73","resolution":{"observed_at":"2026-05-16T01:30:29.937897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Livadiotis and D","venue":null,"work_id":"5f6cd09d-86de-40b4-bf7a-7daf47126d01","year":2013},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:ff521979dc81fa7633ad33375aab97d64553aa9730ef6b2593c86a6ccad6e462","observation_id":"066fd32f-ac96-4e90-bc02-8731c66556b9","resolution":{"observed_at":"2026-05-16T01:30:29.964603Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+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":"2026-06-05T21:23:00.469572Z","title":"Arbutina and V","venue":null,"work_id":"ddb18fa8-87c3-420c-a945-d3ffc7106e38","year":2021},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:7fe12a8e9f05d79797912914d2e74c1ee3a3846164bfe4b51abf329c63c60ca4","observation_id":"922c7cd1-908b-418c-a513-9bfcc1e2a699","resolution":{"observed_at":"2026-05-16T01:30:29.968491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1204.3880","last_updated":"2012-06-19T11:06:40Z","snapshot_observed_at":"2026-07-06T02:46:35.291420Z","submitted_at":"2012-04-17T19:02:21Z","title":"Resolving the electron temperature discrepancies in HII Regions and Planetary Nebulae: kappa-distributed electrons","version":2},"cited_work":{"arxiv_id":"1204.3880","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1204.3880","snapshot_observed_at":"2026-07-04T18:07:57.905072Z","title":null,"venue":null,"work_id":"1d5574da-5d44-4a92-ae53-eee10e6fe9d0","year":2012},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/1204.3880","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:f1b39c343d337b27efe7f857c781739c05a38c1862a434b07cce9c9111815ba5","observation_id":"2ea8b860-94cb-4e43-b845-a44e2fef7967","resolution":{"observed_at":"2026-07-04T18:07:57.905072Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1803.10003","last_updated":"2018-07-20T16:58:02Z","snapshot_observed_at":"2026-07-06T06:30:24.004718Z","submitted_at":"2018-03-27T10:33:11Z","title":"Electron Energy Distributions in HII Regions and Planetary Nebulae: kappa-Distributions Do Not Apply","version":2},"cited_work":{"arxiv_id":"1803.10003","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1803.10003","snapshot_observed_at":"2026-07-04T22:55:23.806534Z","title":null,"venue":null,"work_id":"ed1ca3ed-9b52-4d8a-9bf7-7cf3b02d717f","year":2018},"citing_paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-10T20:27:27.201641Z"},"links":{"cited_paper":"/paper/1803.10003","citing_paper":"/paper/2604.04659"},"observation_digest":"sha256:ab573ca724ff931a1b235a78744682156eb72f5f923e4d9b34b52463625dbf14","observation_id":"3e1441c7-8121-43b4-a150-74667686f878","resolution":{"observed_at":"2026-07-04T22:55:23.806534Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-22T06:31:00.163083+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.04659","last_updated":"2026-04-06T13:14:06Z","latest_version":1,"primary_category":"astro-ph.HE","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-06T13:14:06Z","title":"On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law"},"reference_resolution":{"displayed":56,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":20,"verified_fuzzy":36},"total_outbound_references":56},"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":"2026-07-22T06:31:00.163083+00:00","source":"crossref"},{"observed_at":"2026-07-22T06:30:55.410749+00:00","source":"retraction_watch"}],"thesis":"As of 23 July 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2604.04659."}