{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:L2THZPEACATXLMLHRAKBYTIVRA","short_pith_number":"pith:L2THZPEA","canonical_record":{"source":{"id":"hep-ph/0002152","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2000-02-14T19:58:32Z","cross_cats_sorted":[],"title_canon_sha256":"0a6cb109d9c2b43f5f9ca9e8ce5fd961ba185beb4d568d394418904c5bb96161","abstract_canon_sha256":"a3ec0808db6dd93a70406f1213b70bce59cb0aa360573a5b9fb2481502951e01"},"schema_version":"1.0"},"canonical_sha256":"5ea67cbc80102775b16788141c4d15880d237f277f826d8c1ad4f61b329133ad","source":{"kind":"arxiv","id":"hep-ph/0002152","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0002152","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0002152v2","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0002152","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"pith_short_12","alias_value":"L2THZPEACATX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"L2THZPEACATXLMLH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"L2THZPEA","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:L2THZPEACATXLMLHRAKBYTIVRA","target":"record","payload":{"canonical_record":{"source":{"id":"hep-ph/0002152","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2000-02-14T19:58:32Z","cross_cats_sorted":[],"title_canon_sha256":"0a6cb109d9c2b43f5f9ca9e8ce5fd961ba185beb4d568d394418904c5bb96161","abstract_canon_sha256":"a3ec0808db6dd93a70406f1213b70bce59cb0aa360573a5b9fb2481502951e01"},"schema_version":"1.0"},"canonical_sha256":"5ea67cbc80102775b16788141c4d15880d237f277f826d8c1ad4f61b329133ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:17.518662Z","signature_b64":"OrqtMZZXgEnmsz0mY7iOoa16ondSAXFHiosKvpW3Eu/TWt4Be9euEJoWFzF+yWobXZd94vmk93JJAA8ZGH25AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ea67cbc80102775b16788141c4d15880d237f277f826d8c1ad4f61b329133ad","last_reissued_at":"2026-05-18T04:34:17.518161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:17.518161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-ph/0002152","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":"2026-05-18T04:34:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3626L1Kx+jlykzYpD+IG1kHrU2pgrfXuAR/pJO5PY/CNu0YY2R1SfkmeXzy41kP8YKF3ai8rH6fLcR+LtB3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:49:50.994886Z"},"content_sha256":"3e42ef14678bb552a2e6aaf43cdc696a45c824f73cc16ae7a57338d867ac0b3a","schema_version":"1.0","event_id":"sha256:3e42ef14678bb552a2e6aaf43cdc696a45c824f73cc16ae7a57338d867ac0b3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:L2THZPEACATXLMLHRAKBYTIVRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The minimum width condition for neutrino conversion in matter","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Yu. Smirnov, C. Lunardini","submitted_at":"2000-02-14T19:58:32Z","abstract_excerpt":"We find that for small vacuum mixing angle $\\theta$ and low energies ($s\\ll M^2_Z$) the width of matter, $d_{1/2}$, needed to have conversion probability $P\\geq 1/2$ should be larger than $d_{min}= \\pi/(2\\sqrt{2} G_{F} \\tan 2 \\theta)$: $d_{1/2}\\geq d_{min}$. Here $G_F$ is the Fermi constant, $s$ is the total energy squared in the center of mass and $M_Z$ is the mass of the $Z$ boson. The absolute minimum $d_{1/2}=d_{min}$ is realized for oscillations in a uniform medium with resonance density. For all the other density distributions (monotonically varying density, castle wall profile, etc.) th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0002152","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":"2026-05-18T04:34:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHz7e8QK2AzohYL9PYeg47pvw5mne2JPEhuA1ndEeHR26Xbjwp2WTJ7r4+yGENEhG6q55IxUiBCQYiTVdWTeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:49:50.995253Z"},"content_sha256":"39c2e1325b03625371b5833ea9c47662477e8cd7766c5bc0bafb55cf70cc092f","schema_version":"1.0","event_id":"sha256:39c2e1325b03625371b5833ea9c47662477e8cd7766c5bc0bafb55cf70cc092f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2THZPEACATXLMLHRAKBYTIVRA/bundle.json","state_url":"https://pith.science/pith/L2THZPEACATXLMLHRAKBYTIVRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2THZPEACATXLMLHRAKBYTIVRA/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":"2026-05-30T18:49:50Z","links":{"resolver":"https://pith.science/pith/L2THZPEACATXLMLHRAKBYTIVRA","bundle":"https://pith.science/pith/L2THZPEACATXLMLHRAKBYTIVRA/bundle.json","state":"https://pith.science/pith/L2THZPEACATXLMLHRAKBYTIVRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2THZPEACATXLMLHRAKBYTIVRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:L2THZPEACATXLMLHRAKBYTIVRA","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":"a3ec0808db6dd93a70406f1213b70bce59cb0aa360573a5b9fb2481502951e01","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2000-02-14T19:58:32Z","title_canon_sha256":"0a6cb109d9c2b43f5f9ca9e8ce5fd961ba185beb4d568d394418904c5bb96161"},"schema_version":"1.0","source":{"id":"hep-ph/0002152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0002152","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0002152v2","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0002152","created_at":"2026-05-18T04:34:17Z"},{"alias_kind":"pith_short_12","alias_value":"L2THZPEACATX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"L2THZPEACATXLMLH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"L2THZPEA","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:39c2e1325b03625371b5833ea9c47662477e8cd7766c5bc0bafb55cf70cc092f","target":"graph","created_at":"2026-05-18T04:34:17Z","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 find that for small vacuum mixing angle $\\theta$ and low energies ($s\\ll M^2_Z$) the width of matter, $d_{1/2}$, needed to have conversion probability $P\\geq 1/2$ should be larger than $d_{min}= \\pi/(2\\sqrt{2} G_{F} \\tan 2 \\theta)$: $d_{1/2}\\geq d_{min}$. Here $G_F$ is the Fermi constant, $s$ is the total energy squared in the center of mass and $M_Z$ is the mass of the $Z$ boson. The absolute minimum $d_{1/2}=d_{min}$ is realized for oscillations in a uniform medium with resonance density. For all the other density distributions (monotonically varying density, castle wall profile, etc.) th","authors_text":"A. Yu. Smirnov, C. Lunardini","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2000-02-14T19:58:32Z","title":"The minimum width condition for neutrino conversion in matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0002152","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":"sha256:3e42ef14678bb552a2e6aaf43cdc696a45c824f73cc16ae7a57338d867ac0b3a","target":"record","created_at":"2026-05-18T04:34:17Z","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":"a3ec0808db6dd93a70406f1213b70bce59cb0aa360573a5b9fb2481502951e01","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2000-02-14T19:58:32Z","title_canon_sha256":"0a6cb109d9c2b43f5f9ca9e8ce5fd961ba185beb4d568d394418904c5bb96161"},"schema_version":"1.0","source":{"id":"hep-ph/0002152","kind":"arxiv","version":2}},"canonical_sha256":"5ea67cbc80102775b16788141c4d15880d237f277f826d8c1ad4f61b329133ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ea67cbc80102775b16788141c4d15880d237f277f826d8c1ad4f61b329133ad","first_computed_at":"2026-05-18T04:34:17.518161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:17.518161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OrqtMZZXgEnmsz0mY7iOoa16ondSAXFHiosKvpW3Eu/TWt4Be9euEJoWFzF+yWobXZd94vmk93JJAA8ZGH25AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:17.518662Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0002152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e42ef14678bb552a2e6aaf43cdc696a45c824f73cc16ae7a57338d867ac0b3a","sha256:39c2e1325b03625371b5833ea9c47662477e8cd7766c5bc0bafb55cf70cc092f"],"state_sha256":"319105b92c90b5ace45a63a642c26cba4ff7b0ad9f2e47c3dee1486ed7bb0d30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBRX95yNT7s1Uo0Fbtc0/YI2jmI8lC60SiXHDP2TjuuSPcnmxIjnUgmsvFcCO/lQYr0MCJ2ic/5cr+NGPEfXAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:49:50.997551Z","bundle_sha256":"146bb6323086cef1c765173ae1bf7dcbadde1417c10325ae711c5cbd04ad8422"}}