{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7K5RJLHVG4R5XWYFLLCH7SUSG2","short_pith_number":"pith:7K5RJLHV","canonical_record":{"source":{"id":"2512.19751","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-12-18T16:26:36Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"a0cc082f3c764b1839ae0d762de39fcb29041ab5668ae5d0bbcdc98b12d8b333","abstract_canon_sha256":"7c6804f3f7a09cf481f844b659e7769600c04ebd9543d61bd1aa2d9de5d7fb04"},"schema_version":"1.0"},"canonical_sha256":"fabb14acf53723dbdb055ac47fca923692743f127ab4215716cb8eb5977fb806","source":{"kind":"arxiv","id":"2512.19751","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.19751","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.19751v2","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.19751","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"7K5RJLHVG4R5","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_16","alias_value":"7K5RJLHVG4R5XWYF","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_8","alias_value":"7K5RJLHV","created_at":"2026-06-04T01:09:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7K5RJLHVG4R5XWYFLLCH7SUSG2","target":"record","payload":{"canonical_record":{"source":{"id":"2512.19751","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-12-18T16:26:36Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"a0cc082f3c764b1839ae0d762de39fcb29041ab5668ae5d0bbcdc98b12d8b333","abstract_canon_sha256":"7c6804f3f7a09cf481f844b659e7769600c04ebd9543d61bd1aa2d9de5d7fb04"},"schema_version":"1.0"},"canonical_sha256":"fabb14acf53723dbdb055ac47fca923692743f127ab4215716cb8eb5977fb806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:40.515144Z","signature_b64":"CrP1oMiS24G8LkU2S0QWwV33PIbY2WOrHvoP5ZD27sAXZ2lIeGjkH8bTdPv1t5nu9Lu/q95UyUZpoBkJyo8EAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fabb14acf53723dbdb055ac47fca923692743f127ab4215716cb8eb5977fb806","last_reissued_at":"2026-06-04T01:09:40.514664Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:40.514664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.19751","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"se/XawEgSNwYaZHQEWxGrPrFuuwGxBlnLrEhMXVuXG4cO2OW19VMQCpiWPHju9kLlTPTh9Ky01lLks83/2NMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:51:33.574284Z"},"content_sha256":"02054ae9ed568038170741a8544573a0cd7b0b8f0be0cf17813c91903dae9b36","schema_version":"1.0","event_id":"sha256:02054ae9ed568038170741a8544573a0cd7b0b8f0be0cf17813c91903dae9b36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7K5RJLHVG4R5XWYFLLCH7SUSG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Radial Distribution and Quasi-exact Solvability of Brioschi-Halphen Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.CA","authors_text":"O.S. Obabiyi, U.N. Bassey, U.S. Idiong","submitted_at":"2025-12-18T16:26:36Z","abstract_excerpt":"The Brioschi-Halphen equation (BHE) is a second order complex differential equation obtained by a two step transformation of the Lam\\'e equation. The Lam\\'e equation is an equation in Astronomical physics used in the study of motion of planetary bodies. In this paper, the radial part of the BHE for sufficiently large $r$ and the argument limit $2\\pi$ is obtained. The asymptotic radial wave function associated with BHE is obtained in terms of canonical polynomials $\\mathscr{P}_{n+1},$ and spherical function in $L^{2}(G,{\\rm d}\\mu), G=SL(2,\\mathbb{R})$ using point canonical transformation and di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.19751","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.19751/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cASSIdu1uhbwm8z1U+7a4Q4dLR/59qO6Vt7XKc16JZzMDMH9vyl8SvTub1FfovLYegiJABWB0jkhTnkM9+t2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:51:33.574617Z"},"content_sha256":"0d91681a88efaf723b4ce604ea6a93b33a7208b27d79990ec54e563b66cbfe3a","schema_version":"1.0","event_id":"sha256:0d91681a88efaf723b4ce604ea6a93b33a7208b27d79990ec54e563b66cbfe3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/bundle.json","state_url":"https://pith.science/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T16:51:33Z","links":{"resolver":"https://pith.science/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2","bundle":"https://pith.science/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/bundle.json","state":"https://pith.science/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K5RJLHVG4R5XWYFLLCH7SUSG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7K5RJLHVG4R5XWYFLLCH7SUSG2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7c6804f3f7a09cf481f844b659e7769600c04ebd9543d61bd1aa2d9de5d7fb04","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-12-18T16:26:36Z","title_canon_sha256":"a0cc082f3c764b1839ae0d762de39fcb29041ab5668ae5d0bbcdc98b12d8b333"},"schema_version":"1.0","source":{"id":"2512.19751","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.19751","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.19751v2","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.19751","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"7K5RJLHVG4R5","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_16","alias_value":"7K5RJLHVG4R5XWYF","created_at":"2026-06-04T01:09:40Z"},{"alias_kind":"pith_short_8","alias_value":"7K5RJLHV","created_at":"2026-06-04T01:09:40Z"}],"graph_snapshots":[{"event_id":"sha256:0d91681a88efaf723b4ce604ea6a93b33a7208b27d79990ec54e563b66cbfe3a","target":"graph","created_at":"2026-06-04T01:09:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.19751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Brioschi-Halphen equation (BHE) is a second order complex differential equation obtained by a two step transformation of the Lam\\'e equation. The Lam\\'e equation is an equation in Astronomical physics used in the study of motion of planetary bodies. In this paper, the radial part of the BHE for sufficiently large $r$ and the argument limit $2\\pi$ is obtained. The asymptotic radial wave function associated with BHE is obtained in terms of canonical polynomials $\\mathscr{P}_{n+1},$ and spherical function in $L^{2}(G,{\\rm d}\\mu), G=SL(2,\\mathbb{R})$ using point canonical transformation and di","authors_text":"O.S. Obabiyi, U.N. Bassey, U.S. Idiong","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-12-18T16:26:36Z","title":"On Radial Distribution and Quasi-exact Solvability of Brioschi-Halphen Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.19751","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:02054ae9ed568038170741a8544573a0cd7b0b8f0be0cf17813c91903dae9b36","target":"record","created_at":"2026-06-04T01:09:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7c6804f3f7a09cf481f844b659e7769600c04ebd9543d61bd1aa2d9de5d7fb04","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-12-18T16:26:36Z","title_canon_sha256":"a0cc082f3c764b1839ae0d762de39fcb29041ab5668ae5d0bbcdc98b12d8b333"},"schema_version":"1.0","source":{"id":"2512.19751","kind":"arxiv","version":2}},"canonical_sha256":"fabb14acf53723dbdb055ac47fca923692743f127ab4215716cb8eb5977fb806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fabb14acf53723dbdb055ac47fca923692743f127ab4215716cb8eb5977fb806","first_computed_at":"2026-06-04T01:09:40.514664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:40.514664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CrP1oMiS24G8LkU2S0QWwV33PIbY2WOrHvoP5ZD27sAXZ2lIeGjkH8bTdPv1t5nu9Lu/q95UyUZpoBkJyo8EAA==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:40.515144Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.19751","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02054ae9ed568038170741a8544573a0cd7b0b8f0be0cf17813c91903dae9b36","sha256:0d91681a88efaf723b4ce604ea6a93b33a7208b27d79990ec54e563b66cbfe3a"],"state_sha256":"c20a14a5a28139bad142b9d793ac9f92f20cdfc0f0bdc393c37f741b99ab33a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NROyALrT+b4akrI04Uv/5mtA0GCVIRWHN+6gJJ84gs3M37ptbab1TcU0wXd0uoe5yJhI7JI5BhHb0n7FcxP/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:51:33.577807Z","bundle_sha256":"edace09e36a993774d86c53d22a8949a2217143aedd32e523a56823a43d3ebcf"}}