{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","short_pith_number":"pith:QF5IMZD5","canonical_record":{"source":{"id":"2607.16547","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-17T22:50:47Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"f5d62c9ca3f73aeb24ff682199edebb9a8b951f5a4a052c74d183ae5470a58f2","abstract_canon_sha256":"934b64eb46487c22a49e2476c1aa3d68269f9546aa9853e91b5648e32e1fc720"},"schema_version":"1.0"},"canonical_sha256":"817a86647d8c3f94d5980e74bc5d6af401bad742bce636d106109d4366347264","source":{"kind":"arxiv","id":"2607.16547","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16547","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16547v1","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16547","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"QF5IMZD5RQ7Z","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_16","alias_value":"QF5IMZD5RQ7ZJVMY","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_8","alias_value":"QF5IMZD5","created_at":"2026-07-21T00:20:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16547","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-17T22:50:47Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"f5d62c9ca3f73aeb24ff682199edebb9a8b951f5a4a052c74d183ae5470a58f2","abstract_canon_sha256":"934b64eb46487c22a49e2476c1aa3d68269f9546aa9853e91b5648e32e1fc720"},"schema_version":"1.0"},"canonical_sha256":"817a86647d8c3f94d5980e74bc5d6af401bad742bce636d106109d4366347264","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:24.735042Z","signature_b64":"197yg5wa1pAZvWkXw1OQxnT9mpBbmlfYu3ulVdLUpkPUw3oAf+W35jtsNConeDENpRds/XD4Le4q57ZYMb1qCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"817a86647d8c3f94d5980e74bc5d6af401bad742bce636d106109d4366347264","last_reissued_at":"2026-07-21T00:20:24.734141Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:24.734141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16547","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":"2026-07-21T00:20:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sI/kuzHaEEnvBJKXFkDxCyrcG0lc6P7gv60D2NXPasCnXhWTH7XlgLEgPJvKS7Ca/KmRnfawJn/xfj1vyQ8vAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:27:21.595336Z"},"content_sha256":"1556272716d2d19363568cc5f53ad613989c5f76acfc396a3f4c0bf4f89e7ca7","schema_version":"1.0","event_id":"sha256:1556272716d2d19363568cc5f53ad613989c5f76acfc396a3f4c0bf4f89e7ca7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective Maximum Entropy: Universality and Acceptance-Region Calibration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Hideitsu Hino","submitted_at":"2026-07-17T22:50:47Z","abstract_excerpt":"Maximum-entropy reference distributions are usually constructed on the normalized probability simplex. This formulation is less natural for unnormalized statistical models, in which positive multiples represent the same shape, and it does not directly explain how a prescribed admissible region should determine the deformation parameter of a bounded-support reference distribution. We formulate maximum entropy on the projective space of nonnegative measures and establish three results of statistical relevance. First, a universality theorem shows that every admissible monotone transform of the sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16547","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/2607.16547/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":"2026-07-21T00:20:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dJFdBJtiHR03Xu6DVWKIwESBIcpFWYziOAll9SWIJdbMOC3YVS/g7PMamQNOkLAvTM+iyvA7Pb18pw8xVCrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:27:21.596255Z"},"content_sha256":"5100551b1a949b8165cc8b9fe1dd746e073c6039f210673f7b1c9a1236534861","schema_version":"1.0","event_id":"sha256:5100551b1a949b8165cc8b9fe1dd746e073c6039f210673f7b1c9a1236534861"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1109/TIT.2004.840871) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Lutwak, E., Yang, D., Zhang, G.: Cram´ er–Rao and moment-entropy inequali- ties for R´ enyi entropy and generalized Fisher information. IEEE Transactions on Information Theory51(2), 473–478 (2005) https://doi.org/10.1109/TIT.2004. 840871","arxiv_id":"2607.16547","detector":"doi_compliance","evidence":{"ref_index":2,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1109/tit.2004","reconstructed_doi":"10.1109/TIT.2004.840871"},"severity":"advisory","ref_index":2,"audited_at":"2026-08-01T20:49:03.319167Z","event_type":"pith.integrity.v1","detected_doi":"10.1109/TIT.2004.840871","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"e0b3d260a307261eb497687ae5327d4a008869f32721251c6929c9a8fb93c354","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":16589,"payload_sha256":"95f23c29559852c4813a9d87e0f8e8b62e1a743aa76cf4fa3b4da148c9c0f13b","signature_b64":"wI5Q80r6nGaoK2RtGSaSzmZGydu1oPG28BvNZhWtXIY7rNpxUGwX4UsJJXvXbOCk6TOWv0O6GPSEMsN5TkgmBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T20:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOccJ+mOO84Y5TMEzyvYrRGAEivy4N+H2ne9bRwPRl995+LB1rzA3WB6p7ZMNmHuJ91fcVx76R7q823rAuzfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T18:27:21.600203Z"},"content_sha256":"0051597097f0d01813e6feff6b80807f37042345ee571bd9f9e4271fda8b20f0","schema_version":"1.0","event_id":"sha256:0051597097f0d01813e6feff6b80807f37042345ee571bd9f9e4271fda8b20f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/bundle.json","state_url":"https://pith.science/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/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":"2026-08-10T18:27:21Z","links":{"resolver":"https://pith.science/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","bundle":"https://pith.science/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/bundle.json","state":"https://pith.science/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QF5IMZD5RQ7ZJVMYBZ2LYXLK6Q","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"934b64eb46487c22a49e2476c1aa3d68269f9546aa9853e91b5648e32e1fc720","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-17T22:50:47Z","title_canon_sha256":"f5d62c9ca3f73aeb24ff682199edebb9a8b951f5a4a052c74d183ae5470a58f2"},"schema_version":"1.0","source":{"id":"2607.16547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16547","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16547v1","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16547","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"QF5IMZD5RQ7Z","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_16","alias_value":"QF5IMZD5RQ7ZJVMY","created_at":"2026-07-21T00:20:24Z"},{"alias_kind":"pith_short_8","alias_value":"QF5IMZD5","created_at":"2026-07-21T00:20:24Z"}],"graph_snapshots":[{"event_id":"sha256:5100551b1a949b8165cc8b9fe1dd746e073c6039f210673f7b1c9a1236534861","target":"graph","created_at":"2026-07-21T00:20:24Z","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/2607.16547/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Maximum-entropy reference distributions are usually constructed on the normalized probability simplex. This formulation is less natural for unnormalized statistical models, in which positive multiples represent the same shape, and it does not directly explain how a prescribed admissible region should determine the deformation parameter of a bounded-support reference distribution. We formulate maximum entropy on the projective space of nonnegative measures and establish three results of statistical relevance. First, a universality theorem shows that every admissible monotone transform of the sa","authors_text":"Hideitsu Hino","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-17T22:50:47Z","title":"Projective Maximum Entropy: Universality and Acceptance-Region Calibration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16547","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":"sha256:1556272716d2d19363568cc5f53ad613989c5f76acfc396a3f4c0bf4f89e7ca7","target":"record","created_at":"2026-07-21T00:20:24Z","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":"934b64eb46487c22a49e2476c1aa3d68269f9546aa9853e91b5648e32e1fc720","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-17T22:50:47Z","title_canon_sha256":"f5d62c9ca3f73aeb24ff682199edebb9a8b951f5a4a052c74d183ae5470a58f2"},"schema_version":"1.0","source":{"id":"2607.16547","kind":"arxiv","version":1}},"canonical_sha256":"817a86647d8c3f94d5980e74bc5d6af401bad742bce636d106109d4366347264","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"817a86647d8c3f94d5980e74bc5d6af401bad742bce636d106109d4366347264","first_computed_at":"2026-07-21T00:20:24.734141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:24.734141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"197yg5wa1pAZvWkXw1OQxnT9mpBbmlfYu3ulVdLUpkPUw3oAf+W35jtsNConeDENpRds/XD4Le4q57ZYMb1qCQ==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:24.735042Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1556272716d2d19363568cc5f53ad613989c5f76acfc396a3f4c0bf4f89e7ca7","sha256:5100551b1a949b8165cc8b9fe1dd746e073c6039f210673f7b1c9a1236534861","sha256:0051597097f0d01813e6feff6b80807f37042345ee571bd9f9e4271fda8b20f0"],"state_sha256":"12652634150eecc136f1b3e3d3f73f9a87e849eefa3c7be5b38ea576df7fe4a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qt6qn4IGcVBYqLFIBUI+Iq4sbJbv90CMbwwSSj5/e8uerwwd0YcfGo1pnjF4/7ltOLAaREtG/Y90asgGHqTiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T18:27:21.604314Z","bundle_sha256":"8bddfab96e32f40f898b47c7a00038c855e64bfa3ec985f4b1b8e8b1341225f3"}}