{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BMQVOPYILSE7MBGACDBQTDLUDD","short_pith_number":"pith:BMQVOPYI","canonical_record":{"source":{"id":"1008.2905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-08-17T14:32:59Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"5bd1abaf8dba99b53043d995e95fc40cb5e0ff59569391c72fe1f06f442734f9","abstract_canon_sha256":"c259b9bc7931457a0683dc0eca08630958a7df316c4fd6fbe79ef24a69e00e6d"},"schema_version":"1.0"},"canonical_sha256":"0b21573f085c89f604c010c3098d7418fd3aaa9fb1289de36ae5cb792bad0a2c","source":{"kind":"arxiv","id":"1008.2905","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2905","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2905v2","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2905","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"BMQVOPYILSE7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BMQVOPYILSE7MBGA","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BMQVOPYI","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BMQVOPYILSE7MBGACDBQTDLUDD","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-08-17T14:32:59Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"5bd1abaf8dba99b53043d995e95fc40cb5e0ff59569391c72fe1f06f442734f9","abstract_canon_sha256":"c259b9bc7931457a0683dc0eca08630958a7df316c4fd6fbe79ef24a69e00e6d"},"schema_version":"1.0"},"canonical_sha256":"0b21573f085c89f604c010c3098d7418fd3aaa9fb1289de36ae5cb792bad0a2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:47.459258Z","signature_b64":"q31ttcqQFHTsXRqlEq5v10QiB21KjSAp7NB0RQDfZW4SdsjCiLbpaSatoPNPg4DV22YDiM1YhF4faWwaXyEKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b21573f085c89f604c010c3098d7418fd3aaa9fb1289de36ae5cb792bad0a2c","last_reissued_at":"2026-05-18T02:05:47.458437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:47.458437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2905","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":"2026-05-18T02:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5UtJm0FjvjZXFfrCfwkuMkhkmF2amS8J1xWQdf9xkAI1+R6Vs3TysTLdNMMciIwzi/9UEit5o6FVBXPEKnLaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:17:06.064744Z"},"content_sha256":"46b9f9a26d2a66ac36f93792e8ae570dc5862ad429e8852d65cdb45976babd77","schema_version":"1.0","event_id":"sha256:46b9f9a26d2a66ac36f93792e8ae570dc5862ad429e8852d65cdb45976babd77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BMQVOPYILSE7MBGACDBQTDLUDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermal abundance of non-relativistic relics with Sommerfeld enhancement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph.CO","authors_text":"Hoernisa Iminniyaz, Mitsuru Kakizaki","submitted_at":"2010-08-17T14:32:59Z","abstract_excerpt":"We propose an analytic treatment for computing the relic abundances of non-relativistic particles whose annihilation rate at chemical decoupling is increased by Sommerfeld enhancement. We find approximate rational functions that closely fit the thermal average of Sommerfeld-enhanced cross sections in the massless limit of force carriers for s- and p-wave annihilations. We demonstrate that, with the approximate thermally-averaged cross sections implemented, the standard analytic method for the final relic abundances provides accuracy to within 1% even for the case of Sommerfeld enhancement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2905","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":""},"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":"2026-05-18T02:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zpaTkyYJbaKl4HkByk/PVg4gxkvfGeyGO2qBE/aO1fmNku7SPqQORx4cB21vdqiuKEFj0hAXtQVNYjfyxh1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:17:06.065444Z"},"content_sha256":"84f7e532acd802e50deed2bcef3ce6157b8449e76daa734a6741f9f0fde7ec34","schema_version":"1.0","event_id":"sha256:84f7e532acd802e50deed2bcef3ce6157b8449e76daa734a6741f9f0fde7ec34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMQVOPYILSE7MBGACDBQTDLUDD/bundle.json","state_url":"https://pith.science/pith/BMQVOPYILSE7MBGACDBQTDLUDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMQVOPYILSE7MBGACDBQTDLUDD/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":"2026-05-30T02:17:06Z","links":{"resolver":"https://pith.science/pith/BMQVOPYILSE7MBGACDBQTDLUDD","bundle":"https://pith.science/pith/BMQVOPYILSE7MBGACDBQTDLUDD/bundle.json","state":"https://pith.science/pith/BMQVOPYILSE7MBGACDBQTDLUDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMQVOPYILSE7MBGACDBQTDLUDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BMQVOPYILSE7MBGACDBQTDLUDD","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":"c259b9bc7931457a0683dc0eca08630958a7df316c4fd6fbe79ef24a69e00e6d","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-08-17T14:32:59Z","title_canon_sha256":"5bd1abaf8dba99b53043d995e95fc40cb5e0ff59569391c72fe1f06f442734f9"},"schema_version":"1.0","source":{"id":"1008.2905","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2905","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2905v2","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2905","created_at":"2026-05-18T02:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"BMQVOPYILSE7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BMQVOPYILSE7MBGA","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BMQVOPYI","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:84f7e532acd802e50deed2bcef3ce6157b8449e76daa734a6741f9f0fde7ec34","target":"graph","created_at":"2026-05-18T02:05:47Z","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"},"paper":{"abstract_excerpt":"We propose an analytic treatment for computing the relic abundances of non-relativistic particles whose annihilation rate at chemical decoupling is increased by Sommerfeld enhancement. We find approximate rational functions that closely fit the thermal average of Sommerfeld-enhanced cross sections in the massless limit of force carriers for s- and p-wave annihilations. We demonstrate that, with the approximate thermally-averaged cross sections implemented, the standard analytic method for the final relic abundances provides accuracy to within 1% even for the case of Sommerfeld enhancement.","authors_text":"Hoernisa Iminniyaz, Mitsuru Kakizaki","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-08-17T14:32:59Z","title":"Thermal abundance of non-relativistic relics with Sommerfeld enhancement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2905","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":"sha256:46b9f9a26d2a66ac36f93792e8ae570dc5862ad429e8852d65cdb45976babd77","target":"record","created_at":"2026-05-18T02:05:47Z","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":"c259b9bc7931457a0683dc0eca08630958a7df316c4fd6fbe79ef24a69e00e6d","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-08-17T14:32:59Z","title_canon_sha256":"5bd1abaf8dba99b53043d995e95fc40cb5e0ff59569391c72fe1f06f442734f9"},"schema_version":"1.0","source":{"id":"1008.2905","kind":"arxiv","version":2}},"canonical_sha256":"0b21573f085c89f604c010c3098d7418fd3aaa9fb1289de36ae5cb792bad0a2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b21573f085c89f604c010c3098d7418fd3aaa9fb1289de36ae5cb792bad0a2c","first_computed_at":"2026-05-18T02:05:47.458437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:47.458437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q31ttcqQFHTsXRqlEq5v10QiB21KjSAp7NB0RQDfZW4SdsjCiLbpaSatoPNPg4DV22YDiM1YhF4faWwaXyEKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:47.459258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2905","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b9f9a26d2a66ac36f93792e8ae570dc5862ad429e8852d65cdb45976babd77","sha256:84f7e532acd802e50deed2bcef3ce6157b8449e76daa734a6741f9f0fde7ec34"],"state_sha256":"1705f5832928704477ef2cce3950c6b3628c922ab747573c7df8f7b47d5b3144"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyXP7MB15/iVs8JWcSA55kzV+0hC7yjxAk900Li67lefh0r25qAhN+Jq9ro1K2KO02iK+FPKr6kAFKTcoeF+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:17:06.069744Z","bundle_sha256":"51c4f44a54d0c228de3e248507bf20711c96fbd4c2a81dfdea5d117e9374844a"}}