{"as_of":"2026-08-19T13:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ed410f6c6b809e380c84445b8f0dc9c8650f8a519960d347415e170e2fcaa141","coverage":[{"denominator":49,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":49,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:06:07.649933Z","state":"measured"},{"denominator":51,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":51,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-08-02T19:19:34.469748Z","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":"2026-05-11T11:56:30.349797Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.21189","snapshot_observed_at":"2026-08-02T19:19:34.469748Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.03393","last_updated":"2026-07-16T12:33:27Z","snapshot_observed_at":"2026-08-12T21:06:01.269193Z","submitted_at":"2026-03-03T10:36:27Z","title":"Curve integral formula for the M\\\"obius strip","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T19:19:34.469748Z"},"links":{"cited_paper":"/paper/2412.21189","citing_paper":"/paper/2603.03393"},"observation_digest":"sha256:c1f8afde032057b16636a955a33bf985a14a6cfe1daa0ca598cc22e0905905ca","observation_id":"b8a3eb01-e6dd-448f-aa27-4c93eaaabccc","resolution":{"observed_at":"2026-08-02T19:19:34.469748Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"cited_work":{"arxiv_id":"2412.21189","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.21189","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Many Colours of Amplitudes","venue":null,"work_id":"eac87c82-dd06-4c1c-b00e-09bd8f15de6e","year":null},"citing_paper":{"arxiv_id":"2604.18672","last_updated":"2026-04-20T18:00:00Z","snapshot_observed_at":"2026-07-06T23:05:30.879164Z","submitted_at":"2026-04-20T18:00:00Z","title":"Tree Amplitudes with Charged Matter in Pure Gauge Theory","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-10T04:26:15.531487Z"},"links":{"cited_paper":"/paper/2412.21189","citing_paper":"/paper/2604.18672"},"observation_digest":"sha256:675bd956e494d381ece8d8f99e2aca7485652bc9f961e28cbff111a64cfe01b4","observation_id":"31c98244-77b7-49ca-af11-2f13f92f22af","resolution":{"observed_at":"2026-05-11T11:56:30.354980Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.21189/citation-record","integrity":"/paper/2412.21189/integrity","json":"/paper/2412.21189/citation-record.json","paper":"/paper/2412.21189"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"0705.4305","last_updated":"2008-01-17T20:40:23Z","snapshot_observed_at":"2026-08-15T10:39:51.169013Z","submitted_at":"2007-05-29T22:01:28Z","title":"Consistency Conditions on the S-Matrix of Massless Particles","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0705.4305","snapshot_observed_at":"2026-08-10T23:06:07.119975Z","title":"Consistency Conditions on the S-Matrix of Massless Particles,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.119975Z"},"links":{"cited_paper":"/paper/0705.4305","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:9acd50a2a6bf215bb54c19cb40e333828a0982f58857850587f4aeb2801e8be0","observation_id":"c8c45833-b44b-4b11-a707-3c934141638c","resolution":{"observed_at":"2026-08-10T23:06:07.119975Z","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":"2026-08-10T23:06:09.428015Z","title":"The Color Structure of Gluon Emission,","venue":null,"work_id":"b91c2ff9-76a2-472f-8948-f068a3ad8bd9","year":1988},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.127674Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:830f1b2c86617b6dba1fcb049b5ccd313fca6f3383737be6e921475bbd29c568","observation_id":"9148bdbe-9483-44bc-9f98-d8b14b6377cb","resolution":{"observed_at":"2026-08-10T23:06:09.441758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0509223","last_updated":"2005-09-29T18:43:37Z","snapshot_observed_at":"2026-08-17T15:00:31.482915Z","submitted_at":"2005-09-29T18:43:37Z","title":"Multi-Parton Amplitudes in Gauge Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0509223","snapshot_observed_at":"2026-08-10T23:06:07.135964Z","title":"Multiparton Amplitudes in Gauge Theories,","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.135964Z"},"links":{"cited_paper":"/paper/hep-th/0509223","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:af2df47b93f1809e4c0aad3cc100929e46d1e5c6d131f9ff3486050cd4bb25c7","observation_id":"a24510f5-2663-4c95-85a7-e060690d531d","resolution":{"observed_at":"2026-08-10T23:06:07.135964Z","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":"2026-08-10T23:06:07.144905Z","title":"Cvitanovi´ c,Group Theory","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.144905Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:273cd96e9414bb30370286414404242d8f529b5d119a1bf2568e9fdc0a87cdbf","observation_id":"89aa5361-bdc0-430c-a23b-18b16bbe473c","resolution":{"observed_at":"2026-08-10T23:06:07.144905Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/9910563","last_updated":"1999-11-01T18:14:08Z","snapshot_observed_at":"2026-08-16T21:59:32.468215Z","submitted_at":"1999-11-01T18:14:08Z","title":"New Color Decompositions for Gauge Amplitudes at Tree and Loop Level","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-ph/9910563","snapshot_observed_at":"2026-08-10T23:06:07.154949Z","title":"New Color Decompositions for Gauge Amplitudes at Tree and Loop Level,","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.154949Z"},"links":{"cited_paper":"/paper/hep-ph/9910563","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:f909e9769ef2386058e45d1b6316e5ea7d92a301bedf87393c31731e0f685ed9","observation_id":"c994e2fd-9b6a-4642-81c2-44ac28b1c878","resolution":{"observed_at":"2026-08-10T23:06:07.154949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1310.5353","last_updated":"2013-10-20T17:49:17Z","snapshot_observed_at":"2026-08-14T23:58:20.063867Z","submitted_at":"2013-10-20T17:49:17Z","title":"A brief introduction to modern amplitude methods","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1310.5353","snapshot_observed_at":"2026-08-10T23:06:07.167367Z","title":"A Brief Introduction to Modern Amplitude Methods,","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.167367Z"},"links":{"cited_paper":"/paper/1310.5353","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:0dc2fd76dddae282aa23a2891fabe3f7cb2990136f976528cf44a073b72e5135","observation_id":"8e663613-3ba8-4a02-a0e3-a66e972e2fae","resolution":{"observed_at":"2026-08-10T23:06:07.167367Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1509.03297","last_updated":"2015-11-15T08:23:30Z","snapshot_observed_at":"2026-08-14T22:32:54.521649Z","submitted_at":"2015-09-10T19:52:42Z","title":"Proof of a new colour decomposition for QCD amplitudes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1509.03297","snapshot_observed_at":"2026-08-10T23:06:07.176843Z","title":"Proof of a New Colour Decomposition for QCD Amplitudes,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.176843Z"},"links":{"cited_paper":"/paper/1509.03297","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:69229a903257496aa5e27980a5d06e5acbc362f66ba7044dbbc14460751d8ca6","observation_id":"65a90d7e-5aba-4f1b-aaec-f207f13abeaf","resolution":{"observed_at":"2026-08-10T23:06:07.176843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1507.00332","last_updated":"2015-12-07T11:52:15Z","snapshot_observed_at":"2026-08-15T07:59:18.906482Z","submitted_at":"2015-07-01T19:58:06Z","title":"Color-Kinematics Duality for QCD Amplitudes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.00332","snapshot_observed_at":"2026-08-10T23:06:07.198978Z","title":"Color-Kinematics Duality for QCD Amplitudes,","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.198978Z"},"links":{"cited_paper":"/paper/1507.00332","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:bdfad35cc8ecccce7273d462450f78111777a3abfab87cdf2fdb9ead443c7aeb","observation_id":"1a7308af-468f-428e-ae0b-ad76a6145b20","resolution":{"observed_at":"2026-08-10T23:06:07.198978Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02695","last_updated":"2019-09-27T14:46:17Z","snapshot_observed_at":"2026-08-18T01:13:35.506000Z","submitted_at":"2019-08-07T16:01:51Z","title":"Multi-Quark Colour Decompositions from Unitarity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02695","snapshot_observed_at":"2026-08-10T23:06:07.211554Z","title":"Multi-Quark Colour Decompositions from Unitarity,","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.211554Z"},"links":{"cited_paper":"/paper/1908.02695","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:fd3c74aada13d8b706b402565d4ac584af3c438fa3db26ef66f3fab401ca4805","observation_id":"68ec9ac6-5492-4fc3-857e-aa1fcb7d463a","resolution":{"observed_at":"2026-08-10T23:06:07.211554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0805.3993","last_updated":"2008-10-10T23:08:40Z","snapshot_observed_at":"2026-08-15T10:14:38.118426Z","submitted_at":"2008-05-26T18:56:06Z","title":"New Relations for Gauge-Theory Amplitudes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0805.3993","snapshot_observed_at":"2026-08-10T23:06:07.219493Z","title":"New Relations for Gauge-Theory Amplitudes,","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.219493Z"},"links":{"cited_paper":"/paper/0805.3993","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:3e28a68f2d402d69fa947fc8bb74ce037627734099f000afb1cc1a55550b6146","observation_id":"35a9b40c-8df2-4b87-a1c3-1b551f5f4c6e","resolution":{"observed_at":"2026-08-10T23:06:07.219493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1004.0476","last_updated":"2010-07-30T01:07:58Z","snapshot_observed_at":"2026-08-15T05:22:34.769245Z","submitted_at":"2010-04-04T00:40:44Z","title":"Perturbative Quantum Gravity as a Double Copy of Gauge Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1004.0476","snapshot_observed_at":"2026-08-10T23:06:07.226642Z","title":"Perturbative Quantum Gravity as a Double Copy of Gauge Theory,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.226642Z"},"links":{"cited_paper":"/paper/1004.0476","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:7d7c579907cab638e36b6c2e52832442f0ebc92d129332611cfe62210211f741","observation_id":"9f2c35c2-f779-418c-8d9b-be19c03dc048","resolution":{"observed_at":"2026-08-10T23:06:07.226642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.01358","last_updated":"2019-09-03T18:00:02Z","snapshot_observed_at":"2026-08-18T02:39:58.214319Z","submitted_at":"2019-09-03T18:00:02Z","title":"The Duality Between Color and Kinematics and its Applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.01358","snapshot_observed_at":"2026-08-10T23:06:07.234748Z","title":"The Duality Between Color and Kinematics and its Applications,","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.234748Z"},"links":{"cited_paper":"/paper/1909.01358","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:419bb41780a23408d34f17fd2717db37876d1fa3d24d8700bcde32ee53501794","observation_id":"5017b2a0-ced6-4f1b-8fb7-8c52e8d602da","resolution":{"observed_at":"2026-08-10T23:06:07.234748Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.06547","last_updated":"2022-04-13T17:50:06Z","snapshot_observed_at":"2026-08-16T17:07:07.629150Z","submitted_at":"2022-04-13T17:50:06Z","title":"Snowmass White Paper: the Double Copy and its Applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.06547","snapshot_observed_at":"2026-08-10T23:06:07.246396Z","title":"Snowmass White Paper: the Double Copy and its Applications,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.246396Z"},"links":{"cited_paper":"/paper/2204.06547","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:0d77aa81b9e9bad0d5254b14a48438664b18a6c17453b898230e8126fcc36e4c","observation_id":"9afbe6e8-d882-440f-8775-21c64cc94740","resolution":{"observed_at":"2026-08-10T23:06:07.246396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.07392","last_updated":"2023-04-14T21:10:47Z","snapshot_observed_at":"2026-08-16T15:40:18.780936Z","submitted_at":"2023-04-14T21:10:47Z","title":"Supergravity amplitudes, the double copy and ultraviolet behavior","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.07392","snapshot_observed_at":"2026-08-10T23:06:07.259670Z","title":"Supergravity Amplitudes, the Double Copy and Ultraviolet Behavior,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.259670Z"},"links":{"cited_paper":"/paper/2304.07392","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:6c517dc31ecf8ec3fc2eb826d11a15f62fa930a82009e49712f35a1541b15733","observation_id":"09446531-0faa-44b2-b888-3de361729fef","resolution":{"observed_at":"2026-08-10T23:06:07.259670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.02542","last_updated":"2023-07-05T18:00:03Z","snapshot_observed_at":"2026-08-17T02:53:12.479679Z","submitted_at":"2023-07-05T18:00:03Z","title":"Gauge-Invariant Double-Copies via Recursion","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.02542","snapshot_observed_at":"2026-08-10T23:06:07.291134Z","title":"Gauge-Invariant Double Copies via Recursion,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.291134Z"},"links":{"cited_paper":"/paper/2307.02542","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:fdd4acbd4dd3ebdbe2650852cb9780fc99fadbe3e370ca9536844415fce9361d","observation_id":"11707911-bcb1-4f5a-9814-616537e88d98","resolution":{"observed_at":"2026-08-10T23:06:07.291134Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.17745","last_updated":"2023-12-29T18:58:40Z","snapshot_observed_at":"2026-08-16T14:30:51.733978Z","submitted_at":"2023-12-29T18:58:40Z","title":"Computational Tools for Trees in Gauge Theory and Gravity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.17745","snapshot_observed_at":"2026-08-10T23:06:07.304301Z","title":"Computational Tools for Trees in Gauge Theory and Gravity,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.304301Z"},"links":{"cited_paper":"/paper/2312.17745","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:93f7c33dc84ac4875666fe4a40932751d94a430b06a0c8e973c31d3d7978bbf4","observation_id":"6199a266-2771-4b7e-8c5e-c3c8f8fb669a","resolution":{"observed_at":"2026-08-10T23:06:07.304301Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.01287","last_updated":"2023-06-27T19:48:01Z","snapshot_observed_at":"2026-08-16T15:43:05.711770Z","submitted_at":"2023-04-03T18:21:29Z","title":"Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.01287","snapshot_observed_at":"2026-08-10T23:06:07.323960Z","title":"Color-Factor Symmetry of the Amplitudes of Yang-Mills and Biadjoint Scalar Theory using Perturbiner Methods,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.323960Z"},"links":{"cited_paper":"/paper/2304.01287","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:296a2e9747e52c053e9c62d26fb693569756e44f78395dccd8a68e749fc22728","observation_id":"6e69e197-ce1b-44c2-97b4-d321300767b6","resolution":{"observed_at":"2026-08-10T23:06:07.323960Z","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":"2026-08-10T23:06:07.332375Z","title":"Group Theory for Unified Model Building,","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.332375Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:913eb2e8cf2b349a65b7197403f2549192989e29162df42a9b10da29b74f73fd","observation_id":"84fa7f2d-ca48-4a45-a3a5-662431cc328d","resolution":{"observed_at":"2026-08-10T23:06:07.332375Z","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":"2026-08-10T23:06:09.380929Z","title":"Fulton and J","venue":null,"work_id":"c8a2b121-7c6b-4b19-8536-1b8787420a39","year":1991},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.342438Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:4a9d1eae0480bb5defb9c5fc20af4917795ac4d920d08baecc6bcabeb419d07e","observation_id":"18f16d8b-17d9-48df-b094-d85db591167e","resolution":{"observed_at":"2026-08-10T23:06:09.389215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:07.352503Z","title":"Di Francesco, P","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.352503Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:5e89f40b7eea9c30cbfd6c0c9b78873a492954490f47a8653cd124ecfcbfb285","observation_id":"14e040be-fb99-4968-9e69-10e1ff973274","resolution":{"observed_at":"2026-08-10T23:06:07.352503Z","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":"2026-08-10T23:06:07.360452Z","title":"Die Zusammensetzung der Stetigen Endlichen Transformationsgruppen,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.360452Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:d61b1bd86bb488ab7f80dcea2399d75de63e3a8b19abcf563be950f894c231df","observation_id":"c21c5db8-5399-42a7-b9b5-485b79ac9e71","resolution":{"observed_at":"2026-08-10T23:06:07.360452Z","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":"2026-08-10T23:06:09.347067Z","title":"Sur la Structure des Groupes Infinis de Transformation,","venue":null,"work_id":"a6f61089-dfa5-4f1a-ac10-f45dda127aa9","year":1904},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.370188Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:9db2ab9a7d4898fe310724a4bb00100c4245bff78f8f67b8db5c68d0e3749c87","observation_id":"52c090b5-ffea-4595-ac2c-049f52bf3688","resolution":{"observed_at":"2026-08-10T23:06:09.356745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.309062Z","title":"Sur la Structure des Groupes Infinis de Transformation (suite),","venue":null,"work_id":"d59d80c6-3608-47ce-a136-960a366b5af2","year":1905},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.382812Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:85387d0f1dd36c9c284ff13bced0fe4e4d00e2c601180f73652b1baf3b27f70f","observation_id":"2dda3a4f-3a12-4444-905f-5cf5e393902a","resolution":{"observed_at":"2026-08-10T23:06:09.319375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.271443Z","title":"Zur Quantenmechanik des Magnetischen Elektrons,","venue":null,"work_id":"6c7e95d8-612a-4c77-93b5-53d57de5121a","year":1927},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.392859Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:d8192f8b94c8f4fcb1534ef293d149ccc0442cc8b89d2473429e717f9f6e92f9","observation_id":"b2424b49-a97b-4078-8c15-8c6dc3939dcd","resolution":{"observed_at":"2026-08-10T23:06:09.280204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.244388Z","title":"Entry A005043 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"1d5d51c1-951c-424a-8699-4ae7555abd4c","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.402003Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:a80e989d9e3bc3e10ca0ff12c0fdf5193221a2cc11ca0cf758bff728a514c573","observation_id":"9bbcc130-7c9c-403b-b800-c26080604362","resolution":{"observed_at":"2026-08-10T23:06:09.255360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.217055Z","title":"New Color Decompositions for Gauge Amplitudes at Tree and Loop Level,","venue":null,"work_id":"6744240b-3c35-4133-8338-cb86514ca402","year":1999},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.413814Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:ce73d3182b40c4ba823ea05efb6e2051d8d8fdaa3970fd6aab2636789c3a7fca","observation_id":"7a6d1a34-223f-40ae-8fea-31635c0ab8a8","resolution":{"observed_at":"2026-08-10T23:06:09.225924Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.190389Z","title":"Entry A000166 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"d2f0edc6-e1c5-4bb1-8023-46d11cbede75","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.425076Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:a055b2586deb3a21445d5a46f429af0dfb4c15fc60224fd948fde4a4767307cc","observation_id":"2a8c14b1-c6f9-45ef-ad6b-f8f3e68a8bb0","resolution":{"observed_at":"2026-08-10T23:06:09.198672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:07.430842Z","title":"A Planar Diagram Theory for Strong Interactions,","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.430842Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:5c50afa3db4f701f5f6ac2c0e6cd4b4d31b4b8f3b985afe29e3f2df0244daf69","observation_id":"227f11c4-e48d-4e31-90f9-72229da58357","resolution":{"observed_at":"2026-08-10T23:06:07.430842Z","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":"2026-08-10T23:06:09.118025Z","title":"Entry A002137 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"5d5a6559-27aa-4981-9696-82434d69d1ce","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.440298Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:580825e8fb9d830ce848d76ba57dbd1d65700e9574c8f0062104411e341cb7e7","observation_id":"a5d70de9-36b6-478f-b9b9-9f28959c96a3","resolution":{"observed_at":"2026-08-10T23:06:09.133523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.082072Z","title":"Stein et al","venue":null,"work_id":"bfeeabf4-4f0c-406a-a744-19b9154ed1e7","year":2022},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.452239Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:f8547871260bb604cc003cbc95a524fa66ad48a1a3e578982d94c94d4203f49c","observation_id":"e5dac418-54cb-4d1e-8353-adabbff14784","resolution":{"observed_at":"2026-08-10T23:06:09.093857Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:07.463685Z","title":"The Magma Algebra System. I. The User Language,","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.463685Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:ef7ebbf890ccb2fe84efd8cbf712efc65ee6fe37aa550a54ae5d5b129c089693","observation_id":"a7425c0e-0656-4aad-aaca-bdd04f46cd14","resolution":{"observed_at":"2026-08-10T23:06:07.463685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.10969","last_updated":"2020-08-27T19:47:00Z","snapshot_observed_at":"2026-08-09T13:37:22.600672Z","submitted_at":"2019-12-20T17:03:44Z","title":"LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.10969","snapshot_observed_at":"2026-08-10T23:06:07.474504Z","title":"LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.474504Z"},"links":{"cited_paper":"/paper/1912.10969","citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:39b9bd6d7cfd8842694194fca1579b33b5e5f07b58fbb268f03d0028cd15a0fe","observation_id":"57c2a277-5c7a-43db-887c-a986b53af51b","resolution":{"observed_at":"2026-08-10T23:06:07.474504Z","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":"2026-08-10T23:06:09.051751Z","title":"The On-Line Encyclopedia of Integer Sequences,","venue":null,"work_id":"60dfe209-bdc7-4fdb-ba2c-efbe73d77d6d","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.503176Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:b902d72d0a7bc239a2f5f2440e16106e207aeb67208aabdf6e31492a8c0dbcf1","observation_id":"97cbf1e2-2e49-44a7-81f5-3ccc2e8473d5","resolution":{"observed_at":"2026-08-10T23:06:09.059799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:09.023037Z","title":"Entry A179684 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"a317f82f-9582-4676-8ada-b27244c9606f","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.519378Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:4a710ef1d9f943d2036ffdf4b81aee5b6394452b3778760981cd386d7b6b0a0f","observation_id":"3f2a118d-bc23-4e00-bf9c-76303c056ed6","resolution":{"observed_at":"2026-08-10T23:06:09.032293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.990940Z","title":"Entry A179683 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"48796fef-e442-4015-b2eb-7ed376f8d900","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.526056Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:775120cc5041db1d7778eb3122c2f869ab0b5255525dd3d70eb462fa6ec72ecf","observation_id":"3e2d9371-d6e9-4239-9e03-a475a4b4fa28","resolution":{"observed_at":"2026-08-10T23:06:09.000446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.960903Z","title":"Entry A179663 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"41d491ec-914a-4b02-bd89-50d454c4eee1","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.541743Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:e111e08797917d9264ce38681d95d68d94b78f89434f7342fc513193edae24d0","observation_id":"3930ae25-f12b-445c-8751-91058bcff468","resolution":{"observed_at":"2026-08-10T23:06:08.970015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.921561Z","title":"Entry A179685 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"9849ad79-b8e4-480a-97a5-67845a6861a0","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.554552Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:b23b6f12319b9eac34d3ae7f09ca160222107ca2c1a415bc62ec1586ce3c5191","observation_id":"22f7776d-4ddd-4dba-a019-277ede03a862","resolution":{"observed_at":"2026-08-10T23:06:08.928469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.882773Z","title":"Entry A227292 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"2d9d50f1-3330-458b-8ff6-e39cd9c2cf65","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.560715Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:a69182ae03f635356c73651446b64106e9cf4a62d6cf0109172dbfa1c8f5ccbf","observation_id":"e4eb00d8-2390-484c-84c1-b61d2e9bd630","resolution":{"observed_at":"2026-08-10T23:06:08.893021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.848393Z","title":"Entry A000108 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"f5a1a877-1cf2-4dd8-ae4d-eb9416011506","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.565901Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:d70bb61fd810e9e82d971173ed5edc16acb7ee348c8d92a67832b20877edbd50","observation_id":"e1392551-e8c6-4e52-8739-cbc1709008d9","resolution":{"observed_at":"2026-08-10T23:06:08.859810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.812689Z","title":"Entry A001006 in The On-Line Encyclopedia of Integer Sequences","venue":null,"work_id":"5254481c-3686-4d2e-9abd-268abfc5fdf6","year":2024},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.578003Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:9d911a84c4e7c01de641a8aa559044b5ca57b34543d19e8acaaf8065b87bbab1","observation_id":"2acf2392-7232-40da-9d2e-3f8caca6da50","resolution":{"observed_at":"2026-08-10T23:06:08.822809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.783663Z","title":"Polchinski, Spinors and SUSY in Various Dimensions , pp","venue":null,"work_id":"b16957cc-a9b5-4701-aee6-ddaec20a776d","year":1998},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.586238Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:14b3573804b82d419bc1aed112d29e48cc2088d7d9f3e174eae1bb5fc9b3460d","observation_id":"27a38492-8c5a-430d-bbab-3b8d8661f4b8","resolution":{"observed_at":"2026-08-10T23:06:08.790720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.750432Z","title":"Bases for Color Structures","venue":null,"work_id":"d6a04d45-e807-480b-bb0d-e375a7969de3","year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.594686Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:53f6105681fcf7ed1bbf88bc69a4d9464482b85a59215278a7b94dba2603e12f","observation_id":"5d8ab467-8531-4df7-b60a-783b86ca9d59","resolution":{"observed_at":"2026-08-10T23:06:08.755955Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0002-9904-1961-10644-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:06:07.717813Z","title":"A General Clebsch-Gordan Theorem,","venue":null,"work_id":"98f98fb5-5c7d-4a0a-baed-4abafedae99a","year":1961},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.608335Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:5faedc1501b9e3bbf329e7236b1f987d49644bd5833a549fe3d1550103fa23a4","observation_id":"68903d8b-dc4b-4e51-8c7d-cd386c7b2c93","resolution":{"observed_at":"2026-08-10T23:06:07.728110Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.721214Z","title":"Lectures on Lie Groups,","venue":null,"work_id":"e74c6ba0-cb65-4909-857f-a9bc32e858d1","year":1964},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.615002Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:3eada5e10871f023a1891dcdcc23bd8806dd8a270627a110dc05e644f0d7ee81","observation_id":"0527134c-9423-425b-92c6-ee4f52302d97","resolution":{"observed_at":"2026-08-10T23:06:08.728508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.693602Z","title":"Theory of Compact Lie Groups and Some Applications to Elementary Particle Physics,","venue":null,"work_id":"d0203b5f-1ed4-4cf9-b847-e08187be58ae","year":1962},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.623421Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:dcc609445c8e3e177d0c9a85789ba233a76d100b191d53c6cc11f0849e27a697","observation_id":"8b927ba1-f648-4b54-b8f1-cd6694a6c340","resolution":{"observed_at":"2026-08-10T23:06:08.700363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.665019Z","title":"Estimation Asymptotique des Multiplicit´ es dans les Puissances Tensorielles d’un g-Module,","venue":null,"work_id":"017c997a-4f3f-4c6e-ad6e-2b7e28db48a0","year":1993},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.629241Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:99b492f913cdfdcb52cd61726a72cb9174013a6ec999050b1fa754f6e6b79f24","observation_id":"4d8785ae-a183-4ded-90f6-e6616b32edb6","resolution":{"observed_at":"2026-08-10T23:06:08.673233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.634463Z","title":"Lattice Path Combinatorics and Asymptotics of Multiplicities of Weights in Tensor Powers,","venue":null,"work_id":"5a749676-7e9b-43b9-8326-6f4f9e2cd8af","year":2004},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.634882Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:7bd79423d10fbec1f41de4708138cb3b175ab8482bde8906844684485392e8d8","observation_id":"2559930f-7597-4c85-9abe-318f0746060f","resolution":{"observed_at":"2026-08-10T23:06:08.645897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-10T23:06:08.614909Z","title":"Freudenthal and H","venue":null,"work_id":"cbe7a15f-d65b-4809-9566-9ac58f252845","year":1969},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.640100Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:4ef3435f4e9321732e58be70684f0d2ece8928aad9d0c73fe956987d7a6d27f3","observation_id":"7aa542ba-7a34-49ae-8cbe-e662ed2fb487","resolution":{"observed_at":"2026-08-10T23:06:08.620599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"q/4977010","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:06:07.920830Z","title":"Proof that P n 2 −1 i=0 n i+1 n−i−1 i < P n 2 −1 i=0 n i n−i i","venue":null,"work_id":"0a157eee-e8fd-4670-b17d-b2ee8e889f7c","year":null},"citing_paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T23:06:07.649933Z"},"links":{"citing_paper":"/paper/2412.21189"},"observation_digest":"sha256:7ba233074d2a6ae2b3b0c994cae7ce57b1f86aea681aab3ef823307524b9a816","observation_id":"cb2d62ac-56a9-4968-ac83-ef3425a4b472","resolution":{"observed_at":"2026-08-10T23:06:07.933818Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.21189","last_updated":"2024-12-30T18:55:53Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-18T11:59:34.806531Z","submitted_at":"2024-12-30T18:55:53Z","title":"The Many Colours of Amplitudes"},"reference_resolution":{"displayed":49,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":2,"verified_fuzzy":25},"total_outbound_references":49},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 2 inbound Pith citation observations for arXiv:2412.21189."}