{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:WC3E3KOIXVZPILQK4LVKCHYX6V","short_pith_number":"pith:WC3E3KOI","canonical_record":{"source":{"id":"math/9609213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1996-09-25T00:00:00Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"c8eeca56d5317548f0fbee32ed2c91ab01c7cc2f3f69d4ff491b5a143a5f11cb","abstract_canon_sha256":"600d16671c83385327f01e49649239a1a46f6641efa90b635c134be1e51ce6c2"},"schema_version":"1.0"},"canonical_sha256":"b0b64da9c8bd72f42e0ae2eaa11f17f54ba97484dff1c565f843ddc36cbe03a4","source":{"kind":"arxiv","id":"math/9609213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9609213","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/9609213v1","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9609213","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"WC3E3KOIXVZP","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_16","alias_value":"WC3E3KOIXVZPILQK","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_8","alias_value":"WC3E3KOI","created_at":"2026-07-04T15:50:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:WC3E3KOIXVZPILQK4LVKCHYX6V","target":"record","payload":{"canonical_record":{"source":{"id":"math/9609213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1996-09-25T00:00:00Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"c8eeca56d5317548f0fbee32ed2c91ab01c7cc2f3f69d4ff491b5a143a5f11cb","abstract_canon_sha256":"600d16671c83385327f01e49649239a1a46f6641efa90b635c134be1e51ce6c2"},"schema_version":"1.0"},"canonical_sha256":"b0b64da9c8bd72f42e0ae2eaa11f17f54ba97484dff1c565f843ddc36cbe03a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:50:57.985476Z","signature_b64":"c0B36j7Y/CY0H3Ff8z8xBZT0B7fZBnt+vCWa8k2uGvCYBWyCZSmbZIDeskxyoMKEtPLV4fIT/Y6Ks7cpce2zAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0b64da9c8bd72f42e0ae2eaa11f17f54ba97484dff1c565f843ddc36cbe03a4","last_reissued_at":"2026-07-04T15:50:57.985099Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:50:57.985099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9609213","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHByKD59JZZfHtTbMgWVS6HQmbjxpD3BLQTMjchKkcRxPrVV4QIaTPhlkJgYjj1mzvq9GlVahRFm5P/6v8z4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T03:13:57.177085Z"},"content_sha256":"d7cd2f0d7c505144297084ac7e990d3d53f9108706705ba0fb21c1838d37b5aa","schema_version":"1.0","event_id":"sha256:d7cd2f0d7c505144297084ac7e990d3d53f9108706705ba0fb21c1838d37b5aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:WC3E3KOIXVZPILQK4LVKCHYX6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On thermonuclear reaction rates","license":"","headline":"","cross_cats":["astro-ph"],"primary_cat":"math.CA","authors_text":"Arak Mathai Mathai, Hans J. Haubold","submitted_at":"1996-09-25T00:00:00Z","abstract_excerpt":"Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction probability integrals for nuclear reactions in the cases of nonresonant, modified nonresonant, screened nonresonant and resonant cases are given. These are expressed in terms of H-functions, G-functions and in computable series forms. Computational aspects are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9609213","kind":"arxiv","version":1},"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/math/9609213/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":"2026-07-04T15:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k9r/Kp/YpBIJg/5H9oLMk/5dJNfngEhIwUP3AtufHE5bIr/+NSdZoSUXaxzcmUPRthtXn3Gxmr5RmSMak765Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T03:13:57.177477Z"},"content_sha256":"e6f8a681bb73a57d79e735e43b48ba4c0ec3972a0f37fd44aa9117d66656715b","schema_version":"1.0","event_id":"sha256:e6f8a681bb73a57d79e735e43b48ba4c0ec3972a0f37fd44aa9117d66656715b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/bundle.json","state_url":"https://pith.science/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/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":"2026-07-27T03:13:57Z","links":{"resolver":"https://pith.science/pith/WC3E3KOIXVZPILQK4LVKCHYX6V","bundle":"https://pith.science/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/bundle.json","state":"https://pith.science/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WC3E3KOIXVZPILQK4LVKCHYX6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:WC3E3KOIXVZPILQK4LVKCHYX6V","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":"600d16671c83385327f01e49649239a1a46f6641efa90b635c134be1e51ce6c2","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"math.CA","submitted_at":"1996-09-25T00:00:00Z","title_canon_sha256":"c8eeca56d5317548f0fbee32ed2c91ab01c7cc2f3f69d4ff491b5a143a5f11cb"},"schema_version":"1.0","source":{"id":"math/9609213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9609213","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/9609213v1","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9609213","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"WC3E3KOIXVZP","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_16","alias_value":"WC3E3KOIXVZPILQK","created_at":"2026-07-04T15:50:57Z"},{"alias_kind":"pith_short_8","alias_value":"WC3E3KOI","created_at":"2026-07-04T15:50:57Z"}],"graph_snapshots":[{"event_id":"sha256:e6f8a681bb73a57d79e735e43b48ba4c0ec3972a0f37fd44aa9117d66656715b","target":"graph","created_at":"2026-07-04T15:50:57Z","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/math/9609213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction probability integrals for nuclear reactions in the cases of nonresonant, modified nonresonant, screened nonresonant and resonant cases are given. These are expressed in terms of H-functions, G-functions and in computable series forms. Computational aspects are also discussed.","authors_text":"Arak Mathai Mathai, Hans J. Haubold","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1996-09-25T00:00:00Z","title":"On thermonuclear reaction rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9609213","kind":"arxiv","version":1},"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:d7cd2f0d7c505144297084ac7e990d3d53f9108706705ba0fb21c1838d37b5aa","target":"record","created_at":"2026-07-04T15:50:57Z","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":"600d16671c83385327f01e49649239a1a46f6641efa90b635c134be1e51ce6c2","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"math.CA","submitted_at":"1996-09-25T00:00:00Z","title_canon_sha256":"c8eeca56d5317548f0fbee32ed2c91ab01c7cc2f3f69d4ff491b5a143a5f11cb"},"schema_version":"1.0","source":{"id":"math/9609213","kind":"arxiv","version":1}},"canonical_sha256":"b0b64da9c8bd72f42e0ae2eaa11f17f54ba97484dff1c565f843ddc36cbe03a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0b64da9c8bd72f42e0ae2eaa11f17f54ba97484dff1c565f843ddc36cbe03a4","first_computed_at":"2026-07-04T15:50:57.985099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:50:57.985099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0B36j7Y/CY0H3Ff8z8xBZT0B7fZBnt+vCWa8k2uGvCYBWyCZSmbZIDeskxyoMKEtPLV4fIT/Y6Ks7cpce2zAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:50:57.985476Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9609213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7cd2f0d7c505144297084ac7e990d3d53f9108706705ba0fb21c1838d37b5aa","sha256:e6f8a681bb73a57d79e735e43b48ba4c0ec3972a0f37fd44aa9117d66656715b"],"state_sha256":"e8cb9deb37b3fb64da1dfa6c3dc317b9537480c2beb0ddee9f2265270ac5f465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfLfLTMcZsfvsJhZPvymXU7/eBqp8v/LmQOuV1GhTDsH2Tr6hgl1CxzRSaw9+dhq2X5v+67I6LcVJysq91BlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-27T03:13:57.179680Z","bundle_sha256":"24228d8c27bd34b83f8ff29041335364292fb618364fd59877a5ef42ac3aa5e7"}}