{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GQYMKKUFEZSCR4NWH4MUZHOTIH","short_pith_number":"pith:GQYMKKUF","canonical_record":{"source":{"id":"1502.06074","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-02-21T07:01:01Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"738017e657ee602b4def7a10c600a2eeabe5b3076d219cad493fb78bbb88e03b","abstract_canon_sha256":"5f299aca247788f32a1950b37637743680e4d03a23aa966075c3b2308e135444"},"schema_version":"1.0"},"canonical_sha256":"3430c52a85266428f1b63f194c9dd341fbf35cdc61cf7c83184a1a3a152d5e4b","source":{"kind":"arxiv","id":"1502.06074","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06074","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06074v3","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06074","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"GQYMKKUFEZSC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQYMKKUFEZSCR4NW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQYMKKUF","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GQYMKKUFEZSCR4NWH4MUZHOTIH","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06074","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-02-21T07:01:01Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"738017e657ee602b4def7a10c600a2eeabe5b3076d219cad493fb78bbb88e03b","abstract_canon_sha256":"5f299aca247788f32a1950b37637743680e4d03a23aa966075c3b2308e135444"},"schema_version":"1.0"},"canonical_sha256":"3430c52a85266428f1b63f194c9dd341fbf35cdc61cf7c83184a1a3a152d5e4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:08.199011Z","signature_b64":"RFk7nIUIBBW7WSPY18uFHz3b1ex4TIQzJnWpnPgqxlTaN7tgLBQ4ohGzvdtwUdVD9aKhKBWMhqLHpI9giF9BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3430c52a85266428f1b63f194c9dd341fbf35cdc61cf7c83184a1a3a152d5e4b","last_reissued_at":"2026-05-18T01:22:08.198514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:08.198514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06074","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":"2026-05-18T01:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xFAKOsl52gvhA3jVLC3kSZY8JZ6GiSgSCll/PYuMBECmLrL6iwppVHbtzVRZoyDFeTwjDqkW0JsgVSY02B77CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T06:07:19.333091Z"},"content_sha256":"13bdb733dc183a74bd5c8721840c710795f21b175ba57016ae2c8efac81d09c0","schema_version":"1.0","event_id":"sha256:13bdb733dc183a74bd5c8721840c710795f21b175ba57016ae2c8efac81d09c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GQYMKKUFEZSCR4NWH4MUZHOTIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coping with Negative Short-Rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"q-fin.MF","authors_text":"Zura Kakushadze","submitted_at":"2015-02-21T07:01:01Z","abstract_excerpt":"We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the short-rate process. Our extension amounts to introducing one or two reflecting barriers for the underlying Brownian motion (as opposed to the short-rate), which allows to have more realistic time-dependent drift (as opposed to constant drift). In our model the spectrum -- or, roughl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06074","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":"2026-05-18T01:22:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/b7nbPjQ+1/NDXrRhj6dBjnWhU9G9D8baArM92LkfWDHxJb6ZMj89Jk5N195LSGhsHN/ilrU1z1xfWMzynVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T06:07:19.333537Z"},"content_sha256":"2ac58cdb85e5825b45cae7899e3f11c3acbf17200fd99de7ebb486e33d2a401a","schema_version":"1.0","event_id":"sha256:2ac58cdb85e5825b45cae7899e3f11c3acbf17200fd99de7ebb486e33d2a401a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/bundle.json","state_url":"https://pith.science/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/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":"2026-05-23T06:07:19Z","links":{"resolver":"https://pith.science/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH","bundle":"https://pith.science/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/bundle.json","state":"https://pith.science/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQYMKKUFEZSCR4NWH4MUZHOTIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GQYMKKUFEZSCR4NWH4MUZHOTIH","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":"5f299aca247788f32a1950b37637743680e4d03a23aa966075c3b2308e135444","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-02-21T07:01:01Z","title_canon_sha256":"738017e657ee602b4def7a10c600a2eeabe5b3076d219cad493fb78bbb88e03b"},"schema_version":"1.0","source":{"id":"1502.06074","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06074","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06074v3","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06074","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"GQYMKKUFEZSC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQYMKKUFEZSCR4NW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQYMKKUF","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:2ac58cdb85e5825b45cae7899e3f11c3acbf17200fd99de7ebb486e33d2a401a","target":"graph","created_at":"2026-05-18T01:22:08Z","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 discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the short-rate process. Our extension amounts to introducing one or two reflecting barriers for the underlying Brownian motion (as opposed to the short-rate), which allows to have more realistic time-dependent drift (as opposed to constant drift). In our model the spectrum -- or, roughl","authors_text":"Zura Kakushadze","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-02-21T07:01:01Z","title":"Coping with Negative Short-Rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06074","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":"sha256:13bdb733dc183a74bd5c8721840c710795f21b175ba57016ae2c8efac81d09c0","target":"record","created_at":"2026-05-18T01:22:08Z","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":"5f299aca247788f32a1950b37637743680e4d03a23aa966075c3b2308e135444","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-02-21T07:01:01Z","title_canon_sha256":"738017e657ee602b4def7a10c600a2eeabe5b3076d219cad493fb78bbb88e03b"},"schema_version":"1.0","source":{"id":"1502.06074","kind":"arxiv","version":3}},"canonical_sha256":"3430c52a85266428f1b63f194c9dd341fbf35cdc61cf7c83184a1a3a152d5e4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3430c52a85266428f1b63f194c9dd341fbf35cdc61cf7c83184a1a3a152d5e4b","first_computed_at":"2026-05-18T01:22:08.198514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:08.198514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RFk7nIUIBBW7WSPY18uFHz3b1ex4TIQzJnWpnPgqxlTaN7tgLBQ4ohGzvdtwUdVD9aKhKBWMhqLHpI9giF9BDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:08.199011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06074","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13bdb733dc183a74bd5c8721840c710795f21b175ba57016ae2c8efac81d09c0","sha256:2ac58cdb85e5825b45cae7899e3f11c3acbf17200fd99de7ebb486e33d2a401a"],"state_sha256":"f4124cdf9df8e3493f1a62a56dd13384ae8048130a8b1b8f36928fa13882d5aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KSAPOfHL/opOSUQ0Fly8lGjrJwr+aaLPQMJdYz258TYXc63r1I47pL8DVEe+8cSn8FMk8NvRJpzWDdw3pu6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T06:07:19.336374Z","bundle_sha256":"33fdf4bba022901d0f975e6a8931e26673d74bb4d7de43611ddba4ed9c781752"}}