{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ARA7QIE6P7G3SDWON6H7KHYMGI","short_pith_number":"pith:ARA7QIE6","canonical_record":{"source":{"id":"2607.02943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-03T04:32:25Z","cross_cats_sorted":[],"title_canon_sha256":"efc8c5c264063a6d04840e379a172ed8fe62c61f9acb2109881feba39c7d9b20","abstract_canon_sha256":"ab94645507c22ab31da64f08335c7c26ace3f8f2b3f643e60013c89cbc124100"},"schema_version":"1.0"},"canonical_sha256":"0441f8209e7fcdb90ece6f8ff51f0c3228b3f63fc17a1cdde37be0e2fe8c95bc","source":{"kind":"arxiv","id":"2607.02943","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02943","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02943v1","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02943","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_12","alias_value":"ARA7QIE6P7G3","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_16","alias_value":"ARA7QIE6P7G3SDWO","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_8","alias_value":"ARA7QIE6","created_at":"2026-07-07T01:16:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ARA7QIE6P7G3SDWON6H7KHYMGI","target":"record","payload":{"canonical_record":{"source":{"id":"2607.02943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-03T04:32:25Z","cross_cats_sorted":[],"title_canon_sha256":"efc8c5c264063a6d04840e379a172ed8fe62c61f9acb2109881feba39c7d9b20","abstract_canon_sha256":"ab94645507c22ab31da64f08335c7c26ace3f8f2b3f643e60013c89cbc124100"},"schema_version":"1.0"},"canonical_sha256":"0441f8209e7fcdb90ece6f8ff51f0c3228b3f63fc17a1cdde37be0e2fe8c95bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T01:16:37.435969Z","signature_b64":"ptet/qcEXqhL71U/ni9ljKMQLU+Fsv5NSthWLUOCKsuMiiub0uczu4fLo2n8BNH2uaMXKQmVvk/hYU47zfY5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0441f8209e7fcdb90ece6f8ff51f0c3228b3f63fc17a1cdde37be0e2fe8c95bc","last_reissued_at":"2026-07-07T01:16:37.435528Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T01:16:37.435528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.02943","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":"2026-07-07T01:16:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ytL7ExPAOb3AFeZ22sLiS4SpeOm7DBTblBBGijq0a5PcvjRYzSUrsZclN9gHHZQMJDLksE/a9xX8xw0IqUsCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:49:59.000665Z"},"content_sha256":"7667a8670f6d93d09dc9e0c88d4036ec4275bd57b5b05abeef86cb4fa4a4a863","schema_version":"1.0","event_id":"sha256:7667a8670f6d93d09dc9e0c88d4036ec4275bd57b5b05abeef86cb4fa4a4a863"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ARA7QIE6P7G3SDWON6H7KHYMGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Information Decomposition for Weighted Empirical Measures on the Sphere","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Kisung You","submitted_at":"2026-07-03T04:32:25Z","abstract_excerpt":"We study directional uncertainty when the data already represent a weighted probability measure on the unit sphere, as in importance samples, quadrature rules, or attention-weighted embeddings. A standard approach fits a von Mises-Fisher distribution and reports its concentration or entropy. This is principled but incomplete because vMF uses only mean-direction information and can miss antipodal, axial, girdle-like, or multimodal structure. We introduce the geometric information decomposition (GID), which fits a nested sequence of maximum-entropy projections using spherical features and report"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02943","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/2607.02943/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":"2026-07-07T01:16:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNGNAX/SIrWzFf7K/9ZLuGT3ezpl5MDen7z9IyncxXcMCHBhbhOdZiiL13HWvFmcry2Mwwc0WD4tzN9eQIMlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:49:59.001159Z"},"content_sha256":"3cdf640aca5a76fe2ae066005223308a92816bb9d1affd3cd5a1ed24c1472c17","schema_version":"1.0","event_id":"sha256:3cdf640aca5a76fe2ae066005223308a92816bb9d1affd3cd5a1ed24c1472c17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/bundle.json","state_url":"https://pith.science/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/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":"2026-08-03T17:49:59Z","links":{"resolver":"https://pith.science/pith/ARA7QIE6P7G3SDWON6H7KHYMGI","bundle":"https://pith.science/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/bundle.json","state":"https://pith.science/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARA7QIE6P7G3SDWON6H7KHYMGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARA7QIE6P7G3SDWON6H7KHYMGI","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":"ab94645507c22ab31da64f08335c7c26ace3f8f2b3f643e60013c89cbc124100","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-03T04:32:25Z","title_canon_sha256":"efc8c5c264063a6d04840e379a172ed8fe62c61f9acb2109881feba39c7d9b20"},"schema_version":"1.0","source":{"id":"2607.02943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02943","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02943v1","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02943","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_12","alias_value":"ARA7QIE6P7G3","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_16","alias_value":"ARA7QIE6P7G3SDWO","created_at":"2026-07-07T01:16:37Z"},{"alias_kind":"pith_short_8","alias_value":"ARA7QIE6","created_at":"2026-07-07T01:16:37Z"}],"graph_snapshots":[{"event_id":"sha256:3cdf640aca5a76fe2ae066005223308a92816bb9d1affd3cd5a1ed24c1472c17","target":"graph","created_at":"2026-07-07T01:16:37Z","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/2607.02943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study directional uncertainty when the data already represent a weighted probability measure on the unit sphere, as in importance samples, quadrature rules, or attention-weighted embeddings. A standard approach fits a von Mises-Fisher distribution and reports its concentration or entropy. This is principled but incomplete because vMF uses only mean-direction information and can miss antipodal, axial, girdle-like, or multimodal structure. We introduce the geometric information decomposition (GID), which fits a nested sequence of maximum-entropy projections using spherical features and report","authors_text":"Kisung You","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-03T04:32:25Z","title":"Geometric Information Decomposition for Weighted Empirical Measures on the Sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02943","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":"sha256:7667a8670f6d93d09dc9e0c88d4036ec4275bd57b5b05abeef86cb4fa4a4a863","target":"record","created_at":"2026-07-07T01:16:37Z","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":"ab94645507c22ab31da64f08335c7c26ace3f8f2b3f643e60013c89cbc124100","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-03T04:32:25Z","title_canon_sha256":"efc8c5c264063a6d04840e379a172ed8fe62c61f9acb2109881feba39c7d9b20"},"schema_version":"1.0","source":{"id":"2607.02943","kind":"arxiv","version":1}},"canonical_sha256":"0441f8209e7fcdb90ece6f8ff51f0c3228b3f63fc17a1cdde37be0e2fe8c95bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0441f8209e7fcdb90ece6f8ff51f0c3228b3f63fc17a1cdde37be0e2fe8c95bc","first_computed_at":"2026-07-07T01:16:37.435528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T01:16:37.435528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptet/qcEXqhL71U/ni9ljKMQLU+Fsv5NSthWLUOCKsuMiiub0uczu4fLo2n8BNH2uaMXKQmVvk/hYU47zfY5Bg==","signature_status":"signed_v1","signed_at":"2026-07-07T01:16:37.435969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7667a8670f6d93d09dc9e0c88d4036ec4275bd57b5b05abeef86cb4fa4a4a863","sha256:3cdf640aca5a76fe2ae066005223308a92816bb9d1affd3cd5a1ed24c1472c17"],"state_sha256":"809e6b6e20438ea54c44976a754cde1ff4329131a0a5e557fd31db285d9c0720"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9c1RFNNBEAhmd7DacCAA5ask7+YcJvp59XQJt75yeRPoOcvGiqe2FYZDmd2B+5QwQsIH1deEYsOI79F0SuvXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:49:59.005979Z","bundle_sha256":"05264a529c0077c8f81621bd146efd309867a957d1e5c1141723a9615e1af6f1"}}