{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2HEH4VBIULGOXPSHV7J5G4M6AW","short_pith_number":"pith:2HEH4VBI","canonical_record":{"source":{"id":"2608.04315","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-08-05T00:47:01Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7386e4317624ec4a590760a2d8368588136d5d547effea0f3b3d02becaba17aa","abstract_canon_sha256":"b2cf995d7fc52c86e6127fddaaedc9af28b1c68942c89f9729ab092f3c92bb33"},"schema_version":"1.0"},"canonical_sha256":"d1c87e5428a2ccebbe47afd3d3719e059b5eed139369a3c5b5b26c87a810cd6a","source":{"kind":"arxiv","id":"2608.04315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04315","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04315v1","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04315","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"2HEH4VBIULGO","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"2HEH4VBIULGOXPSH","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"2HEH4VBI","created_at":"2026-08-06T01:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2HEH4VBIULGOXPSHV7J5G4M6AW","target":"record","payload":{"canonical_record":{"source":{"id":"2608.04315","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-08-05T00:47:01Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7386e4317624ec4a590760a2d8368588136d5d547effea0f3b3d02becaba17aa","abstract_canon_sha256":"b2cf995d7fc52c86e6127fddaaedc9af28b1c68942c89f9729ab092f3c92bb33"},"schema_version":"1.0"},"canonical_sha256":"d1c87e5428a2ccebbe47afd3d3719e059b5eed139369a3c5b5b26c87a810cd6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:32:16.632693Z","signature_b64":"1iYLgHAmBJLh1pxSSU5gv4CUR7lALtnHLfFi0bEZ76eFmAMhTkLQtBy0uB+i9QFxr5YqAhCAIefdwq/98BvBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1c87e5428a2ccebbe47afd3d3719e059b5eed139369a3c5b5b26c87a810cd6a","last_reissued_at":"2026-08-06T01:32:16.631173Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:32:16.631173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.04315","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":"2026-08-06T01:32:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2d/jYYl5EIJK7ci8nfEmjVoQHjWlzABqMpjQfmF5PcT9he+FY13HcUg4QN4kPdmQmY/RyfEL1jxYUlge8CnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:42:40.111149Z"},"content_sha256":"378f1a770da329ca767116ac6a9e149f616c936c4e9fec675a5b5304abef2747","schema_version":"1.0","event_id":"sha256:378f1a770da329ca767116ac6a9e149f616c936c4e9fec675a5b5304abef2747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2HEH4VBIULGOXPSHV7J5G4M6AW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed-Point Characterisations of Extremal Distributions under Partial Distributional Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kizito Salako, Rabiu Tsoho Muhammad","submitted_at":"2026-08-05T00:47:01Z","abstract_excerpt":"We present a methodological framework for solving robust inference problems with partially specified distributions over measurable subsets of a parameter space. Partial specifications define a set of admissible distributions. The goal is to determine extremal values (over these admissible distributions) for statistical quantities, where these quantities---these objective functions---are ratios of expectations of analytic functions, continuous functions, piecewise continuous functions, and uniform limits of piecewise continuous functions. We show that extremal values are approached by sequences"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04315","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04315/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-06T01:32:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kthFz5NmewPrdWfVPq/k4DQ7bAis+tXEpM1ChGjrE7CxvgiNYGkGMpXQyC8WUIUhpVX0Z54YVzTgHyZx5eG6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:42:40.111990Z"},"content_sha256":"8a57979fe49e235a1a1167ca6141502071480d41131ef15205bae8b5bf344474","schema_version":"1.0","event_id":"sha256:8a57979fe49e235a1a1167ca6141502071480d41131ef15205bae8b5bf344474"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/bundle.json","state_url":"https://pith.science/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/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":"2026-08-16T19:42:40Z","links":{"resolver":"https://pith.science/pith/2HEH4VBIULGOXPSHV7J5G4M6AW","bundle":"https://pith.science/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/bundle.json","state":"https://pith.science/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HEH4VBIULGOXPSHV7J5G4M6AW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2HEH4VBIULGOXPSHV7J5G4M6AW","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":"b2cf995d7fc52c86e6127fddaaedc9af28b1c68942c89f9729ab092f3c92bb33","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-08-05T00:47:01Z","title_canon_sha256":"7386e4317624ec4a590760a2d8368588136d5d547effea0f3b3d02becaba17aa"},"schema_version":"1.0","source":{"id":"2608.04315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04315","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04315v1","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04315","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"2HEH4VBIULGO","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"2HEH4VBIULGOXPSH","created_at":"2026-08-06T01:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"2HEH4VBI","created_at":"2026-08-06T01:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:8a57979fe49e235a1a1167ca6141502071480d41131ef15205bae8b5bf344474","target":"graph","created_at":"2026-08-06T01:32:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.04315/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a methodological framework for solving robust inference problems with partially specified distributions over measurable subsets of a parameter space. Partial specifications define a set of admissible distributions. The goal is to determine extremal values (over these admissible distributions) for statistical quantities, where these quantities---these objective functions---are ratios of expectations of analytic functions, continuous functions, piecewise continuous functions, and uniform limits of piecewise continuous functions. We show that extremal values are approached by sequences","authors_text":"Kizito Salako, Rabiu Tsoho Muhammad","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-08-05T00:47:01Z","title":"Fixed-Point Characterisations of Extremal Distributions under Partial Distributional Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04315","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":"sha256:378f1a770da329ca767116ac6a9e149f616c936c4e9fec675a5b5304abef2747","target":"record","created_at":"2026-08-06T01:32:16Z","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":"b2cf995d7fc52c86e6127fddaaedc9af28b1c68942c89f9729ab092f3c92bb33","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-08-05T00:47:01Z","title_canon_sha256":"7386e4317624ec4a590760a2d8368588136d5d547effea0f3b3d02becaba17aa"},"schema_version":"1.0","source":{"id":"2608.04315","kind":"arxiv","version":1}},"canonical_sha256":"d1c87e5428a2ccebbe47afd3d3719e059b5eed139369a3c5b5b26c87a810cd6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1c87e5428a2ccebbe47afd3d3719e059b5eed139369a3c5b5b26c87a810cd6a","first_computed_at":"2026-08-06T01:32:16.631173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:32:16.631173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1iYLgHAmBJLh1pxSSU5gv4CUR7lALtnHLfFi0bEZ76eFmAMhTkLQtBy0uB+i9QFxr5YqAhCAIefdwq/98BvBDQ==","signature_status":"signed_v1","signed_at":"2026-08-06T01:32:16.632693Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378f1a770da329ca767116ac6a9e149f616c936c4e9fec675a5b5304abef2747","sha256:8a57979fe49e235a1a1167ca6141502071480d41131ef15205bae8b5bf344474"],"state_sha256":"2813c12570301f53772ef09b6bff73561513b8b05fcd8e6210cd2885fc4f07fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bwl/o0NH+u5BcOuYUP1Y8tCbRp0jkQBFUnobRGlBksvQYPLmay5SddHdRhVVV7N9UBqg0pML8IQ6kk6J5x2pDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:42:40.117575Z","bundle_sha256":"1f0ef33babdada6a8d64cbb2ca9fa086d74985dc86549beb3ab6030e9c2deab6"}}