{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:IA3NO7UJCTWE7EQ6ZQ2UO5JJS2","short_pith_number":"pith:IA3NO7UJ","canonical_record":{"source":{"id":"0807.3533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2008-07-22T18:17:00Z","cross_cats_sorted":[],"title_canon_sha256":"9ea8d34dc510ee0e53f6e2bcac518b945618d9d74171f77dd0b5c5357e0650fd","abstract_canon_sha256":"af5223bc81de56920f5dccae6730da4e39e84b76ae3b14d9a22d6c57b32cd2e4"},"schema_version":"1.0"},"canonical_sha256":"4036d77e8914ec4f921ecc35477529969126d59e559cee3c2869e6ebab87000f","source":{"kind":"arxiv","id":"0807.3533","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3533","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3533v3","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3533","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"IA3NO7UJCTWE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IA3NO7UJCTWE7EQ6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IA3NO7UJ","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:IA3NO7UJCTWE7EQ6ZQ2UO5JJS2","target":"record","payload":{"canonical_record":{"source":{"id":"0807.3533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2008-07-22T18:17:00Z","cross_cats_sorted":[],"title_canon_sha256":"9ea8d34dc510ee0e53f6e2bcac518b945618d9d74171f77dd0b5c5357e0650fd","abstract_canon_sha256":"af5223bc81de56920f5dccae6730da4e39e84b76ae3b14d9a22d6c57b32cd2e4"},"schema_version":"1.0"},"canonical_sha256":"4036d77e8914ec4f921ecc35477529969126d59e559cee3c2869e6ebab87000f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:43.324842Z","signature_b64":"xGYObChPX/T+xTtbI4r6siie3ie15YXMQiT0+/JNXv6TMBK8xVCaKO2iPn2AzNpOVZ+768hiBlhMpypc6n9VCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4036d77e8914ec4f921ecc35477529969126d59e559cee3c2869e6ebab87000f","last_reissued_at":"2026-05-18T03:28:43.324145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:43.324145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.3533","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpnqckyusQ6DfRV6YgjMMumYmcvXfWIdM+x3ywL2vQW7IppZqV5g6b3ibU5izCzeL3oJsouGZy1eeEG9TZ7eDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:08:45.800617Z"},"content_sha256":"7d912accc6ea1773fa261139d1108e8be9d7f394a620edc667f430ed9ae096d1","schema_version":"1.0","event_id":"sha256:7d912accc6ea1773fa261139d1108e8be9d7f394a620edc667f430ed9ae096d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:IA3NO7UJCTWE7EQ6ZQ2UO5JJS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametric down-conversion from a wave-equations approach: geometry and absolute brightness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Morgan W. Mitchell","submitted_at":"2008-07-22T18:17:00Z","abstract_excerpt":"Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode overlap integrals for the absolute pair production rate into single spatial modes, and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and non-degener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3533","kind":"arxiv","version":3},"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":"2026-05-18T03:28:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1iAEyMSozKtDkSDdgzlPL3Xk0cWP1vhmBNnn8IIlCIAJiG4jgQ5RoUPCoLrN9Se/wIt9AcUnfVASvBBVvwtIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:08:45.801335Z"},"content_sha256":"f6d167017689080d321d6de43142af5c8144d40a6a13d71bf9a0455d542b11b0","schema_version":"1.0","event_id":"sha256:f6d167017689080d321d6de43142af5c8144d40a6a13d71bf9a0455d542b11b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/bundle.json","state_url":"https://pith.science/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/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":"2026-05-30T16:08:45Z","links":{"resolver":"https://pith.science/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2","bundle":"https://pith.science/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/bundle.json","state":"https://pith.science/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IA3NO7UJCTWE7EQ6ZQ2UO5JJS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IA3NO7UJCTWE7EQ6ZQ2UO5JJS2","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":"af5223bc81de56920f5dccae6730da4e39e84b76ae3b14d9a22d6c57b32cd2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2008-07-22T18:17:00Z","title_canon_sha256":"9ea8d34dc510ee0e53f6e2bcac518b945618d9d74171f77dd0b5c5357e0650fd"},"schema_version":"1.0","source":{"id":"0807.3533","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3533","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3533v3","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3533","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"IA3NO7UJCTWE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IA3NO7UJCTWE7EQ6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IA3NO7UJ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:f6d167017689080d321d6de43142af5c8144d40a6a13d71bf9a0455d542b11b0","target":"graph","created_at":"2026-05-18T03:28:43Z","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":"Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode overlap integrals for the absolute pair production rate into single spatial modes, and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and non-degener","authors_text":"Morgan W. Mitchell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2008-07-22T18:17:00Z","title":"Parametric down-conversion from a wave-equations approach: geometry and absolute brightness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3533","kind":"arxiv","version":3},"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":"sha256:7d912accc6ea1773fa261139d1108e8be9d7f394a620edc667f430ed9ae096d1","target":"record","created_at":"2026-05-18T03:28:43Z","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":"af5223bc81de56920f5dccae6730da4e39e84b76ae3b14d9a22d6c57b32cd2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2008-07-22T18:17:00Z","title_canon_sha256":"9ea8d34dc510ee0e53f6e2bcac518b945618d9d74171f77dd0b5c5357e0650fd"},"schema_version":"1.0","source":{"id":"0807.3533","kind":"arxiv","version":3}},"canonical_sha256":"4036d77e8914ec4f921ecc35477529969126d59e559cee3c2869e6ebab87000f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4036d77e8914ec4f921ecc35477529969126d59e559cee3c2869e6ebab87000f","first_computed_at":"2026-05-18T03:28:43.324145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.324145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGYObChPX/T+xTtbI4r6siie3ie15YXMQiT0+/JNXv6TMBK8xVCaKO2iPn2AzNpOVZ+768hiBlhMpypc6n9VCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.324842Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.3533","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d912accc6ea1773fa261139d1108e8be9d7f394a620edc667f430ed9ae096d1","sha256:f6d167017689080d321d6de43142af5c8144d40a6a13d71bf9a0455d542b11b0"],"state_sha256":"59dc151ede7f204dcbe0ca97a8e9d55c420d81ab8a4b08c2f686215946eec895"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hy7ez7ezmbUsRkZAjBlLW74R+os6JlpIbDZsi384FqDdMI3iI9juIYJC8NVzosU4S2hIJbVKZlfTgKUeJ9WSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:08:45.805475Z","bundle_sha256":"8a08652778d8f86eabe19d5e5f65dd4cf13eb6ae71319fac1cab5af6b8b8c841"}}