{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HBP4PCXKPWV54FNNIYKCQCMCB2","short_pith_number":"pith:HBP4PCXK","canonical_record":{"source":{"id":"1111.3757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2011-11-16T10:42:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"54caad89d2d0406ca98e2f768387a044a48f6d21be9e164d961b8fcc5b47d72b","abstract_canon_sha256":"001a205abfc89031a8e7ca9ce75e06fed715052833bbf840e95a3b9d4df7079d"},"schema_version":"1.0"},"canonical_sha256":"385fc78aea7dabde15ad46142809820e824eb3404b7d48ba85c6e56c33b7f8bc","source":{"kind":"arxiv","id":"1111.3757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3757","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3757v1","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3757","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"HBP4PCXKPWV5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HBP4PCXKPWV54FNN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HBP4PCXK","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HBP4PCXKPWV54FNNIYKCQCMCB2","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2011-11-16T10:42:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"54caad89d2d0406ca98e2f768387a044a48f6d21be9e164d961b8fcc5b47d72b","abstract_canon_sha256":"001a205abfc89031a8e7ca9ce75e06fed715052833bbf840e95a3b9d4df7079d"},"schema_version":"1.0"},"canonical_sha256":"385fc78aea7dabde15ad46142809820e824eb3404b7d48ba85c6e56c33b7f8bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:32.482664Z","signature_b64":"+u3D2+/SqtpxvvHbWByBbiRF4naRTgq9hDPuaA83h+UpHUbCgSsitIvvRi8t8uJsQaKksonWo8VmksaeddD4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"385fc78aea7dabde15ad46142809820e824eb3404b7d48ba85c6e56c33b7f8bc","last_reissued_at":"2026-05-18T01:59:32.481822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:32.481822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3757","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":"2026-05-18T01:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6/vD0/Msxddu4FUHCA7B6Qj81XbbemY6f8Sk+XkOLZ+2jB6svO82Wh+T4o06UOK+Xx8hzUysc65DO6Pzj/rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:39.241464Z"},"content_sha256":"82f325494c5d7288c528cba6df8f31ec0d81efae1b3802f58400a98b1dc0d105","schema_version":"1.0","event_id":"sha256:82f325494c5d7288c528cba6df8f31ec0d81efae1b3802f58400a98b1dc0d105"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HBP4PCXKPWV54FNNIYKCQCMCB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interest Rates and Information Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.GN","authors_text":"Dorje C. Brody, Lane P. Hughston","submitted_at":"2011-11-16T10:42:58Z","abstract_excerpt":"The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discoun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3757","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":""},"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":"2026-05-18T01:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UY+JC6ie/aD12dH2XDsPFmA0s4YMu+0vPc7aujcy0njPPNIO8hIbiH3fvSx7XYBKx2R/3GY3G83cURZQwu5RBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:39.242118Z"},"content_sha256":"c07542ada312ccbd9ab5c0de05ac62bef83052406ef06fda4f98e0c454146a5b","schema_version":"1.0","event_id":"sha256:c07542ada312ccbd9ab5c0de05ac62bef83052406ef06fda4f98e0c454146a5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/bundle.json","state_url":"https://pith.science/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/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":"2026-05-27T15:52:39Z","links":{"resolver":"https://pith.science/pith/HBP4PCXKPWV54FNNIYKCQCMCB2","bundle":"https://pith.science/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/bundle.json","state":"https://pith.science/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBP4PCXKPWV54FNNIYKCQCMCB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HBP4PCXKPWV54FNNIYKCQCMCB2","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":"001a205abfc89031a8e7ca9ce75e06fed715052833bbf840e95a3b9d4df7079d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2011-11-16T10:42:58Z","title_canon_sha256":"54caad89d2d0406ca98e2f768387a044a48f6d21be9e164d961b8fcc5b47d72b"},"schema_version":"1.0","source":{"id":"1111.3757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3757","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3757v1","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3757","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"HBP4PCXKPWV5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HBP4PCXKPWV54FNN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HBP4PCXK","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:c07542ada312ccbd9ab5c0de05ac62bef83052406ef06fda4f98e0c454146a5b","target":"graph","created_at":"2026-05-18T01:59:32Z","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":"The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discoun","authors_text":"Dorje C. Brody, Lane P. Hughston","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2011-11-16T10:42:58Z","title":"Interest Rates and Information Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3757","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":"sha256:82f325494c5d7288c528cba6df8f31ec0d81efae1b3802f58400a98b1dc0d105","target":"record","created_at":"2026-05-18T01:59:32Z","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":"001a205abfc89031a8e7ca9ce75e06fed715052833bbf840e95a3b9d4df7079d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2011-11-16T10:42:58Z","title_canon_sha256":"54caad89d2d0406ca98e2f768387a044a48f6d21be9e164d961b8fcc5b47d72b"},"schema_version":"1.0","source":{"id":"1111.3757","kind":"arxiv","version":1}},"canonical_sha256":"385fc78aea7dabde15ad46142809820e824eb3404b7d48ba85c6e56c33b7f8bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"385fc78aea7dabde15ad46142809820e824eb3404b7d48ba85c6e56c33b7f8bc","first_computed_at":"2026-05-18T01:59:32.481822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:32.481822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+u3D2+/SqtpxvvHbWByBbiRF4naRTgq9hDPuaA83h+UpHUbCgSsitIvvRi8t8uJsQaKksonWo8VmksaeddD4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:32.482664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f325494c5d7288c528cba6df8f31ec0d81efae1b3802f58400a98b1dc0d105","sha256:c07542ada312ccbd9ab5c0de05ac62bef83052406ef06fda4f98e0c454146a5b"],"state_sha256":"29bf1822a294bb846bed82748beb3985a2795766f92a6926d637f4a86308ac1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJh08bYPriaEwzK9ALj/SucPR7bGhc6jluZCYdl5OABnfjbedZF4A9LHgAGM/YydRKyR5xoP77Q3rxBDg0RyAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:52:39.245347Z","bundle_sha256":"a5958a89528af81470e067271e5d1900fa2cac81d69c1ed76c8a935165379a47"}}