{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AX4C6WSUBZHWGDP23QFWDQFQYR","short_pith_number":"pith:AX4C6WSU","canonical_record":{"source":{"id":"2606.27090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-25T14:26:42Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"3783fd267eddeb2cbb33c99f7897009fdbb4622fda0f76f12fcb02635907a811","abstract_canon_sha256":"35864a888719894ec1e4e927e607121eb1d193c1d06c02e49023cc60c8d86504"},"schema_version":"1.0"},"canonical_sha256":"05f82f5a540e4f630dfadc0b61c0b0c4674f3f3ce3067a20ff6bfdc6e0b0823c","source":{"kind":"arxiv","id":"2606.27090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27090","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27090v1","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27090","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"AX4C6WSUBZHW","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_16","alias_value":"AX4C6WSUBZHWGDP2","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_8","alias_value":"AX4C6WSU","created_at":"2026-06-26T01:16:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AX4C6WSUBZHWGDP23QFWDQFQYR","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-25T14:26:42Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"3783fd267eddeb2cbb33c99f7897009fdbb4622fda0f76f12fcb02635907a811","abstract_canon_sha256":"35864a888719894ec1e4e927e607121eb1d193c1d06c02e49023cc60c8d86504"},"schema_version":"1.0"},"canonical_sha256":"05f82f5a540e4f630dfadc0b61c0b0c4674f3f3ce3067a20ff6bfdc6e0b0823c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:09.178027Z","signature_b64":"NvpHqbxFkd3EzpXk6ClDdZHYbxgjysLZe3wMY6OotNHqf1qpm/7YTuu001KhGAb8aEBtjFPH5aDj7hEMiiW3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05f82f5a540e4f630dfadc0b61c0b0c4674f3f3ce3067a20ff6bfdc6e0b0823c","last_reissued_at":"2026-06-26T01:16:09.177640Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:09.177640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27090","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":"2026-06-26T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CX+bPX5Njq/cjcgqS6MrLIO8nWtrKeopyjSKWG5qQSZCQDIg0w7fOQbPX9IknfSpMNZFKEJ93JBdmZb1hnU9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:04:17.686775Z"},"content_sha256":"1f9c05d7ad84a373666660561f826bd4d4be98263c1e4fe99cfc826aa1e54fa2","schema_version":"1.0","event_id":"sha256:1f9c05d7ad84a373666660561f826bd4d4be98263c1e4fe99cfc826aa1e54fa2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AX4C6WSUBZHWGDP23QFWDQFQYR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Fengxiang He, Hanli Xu, Sarat Moka","submitted_at":"2026-06-25T14:26:42Z","abstract_excerpt":"Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies their local-mass behaviour that is not directly captured by such objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characterise how Bayesian updating changes local mass: (1) power-log likelihood factors shi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27090","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/2606.27090/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":"2026-06-26T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phcNRC2F3qSAPhYYgGzqRFAlFG2n2Br41/pOwAT0aAIespRJx+MnZdDBI+fPzGb10GHhxSGkjfzIRDkQdPeODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:04:17.687148Z"},"content_sha256":"8b35417d66d860e26b497b9280e28d53c4f94f64cf9679f9992f3de8d2435afd","schema_version":"1.0","event_id":"sha256:8b35417d66d860e26b497b9280e28d53c4f94f64cf9679f9992f3de8d2435afd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/bundle.json","state_url":"https://pith.science/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/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":"2026-06-27T02:04:17Z","links":{"resolver":"https://pith.science/pith/AX4C6WSUBZHWGDP23QFWDQFQYR","bundle":"https://pith.science/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/bundle.json","state":"https://pith.science/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AX4C6WSUBZHWGDP23QFWDQFQYR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AX4C6WSUBZHWGDP23QFWDQFQYR","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":"35864a888719894ec1e4e927e607121eb1d193c1d06c02e49023cc60c8d86504","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-25T14:26:42Z","title_canon_sha256":"3783fd267eddeb2cbb33c99f7897009fdbb4622fda0f76f12fcb02635907a811"},"schema_version":"1.0","source":{"id":"2606.27090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27090","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27090v1","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27090","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"AX4C6WSUBZHW","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_16","alias_value":"AX4C6WSUBZHWGDP2","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_8","alias_value":"AX4C6WSU","created_at":"2026-06-26T01:16:09Z"}],"graph_snapshots":[{"event_id":"sha256:8b35417d66d860e26b497b9280e28d53c4f94f64cf9679f9992f3de8d2435afd","target":"graph","created_at":"2026-06-26T01:16:09Z","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/2606.27090/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies their local-mass behaviour that is not directly captured by such objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characterise how Bayesian updating changes local mass: (1) power-log likelihood factors shi","authors_text":"Fengxiang He, Hanli Xu, Sarat Moka","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-25T14:26:42Z","title":"Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27090","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":"sha256:1f9c05d7ad84a373666660561f826bd4d4be98263c1e4fe99cfc826aa1e54fa2","target":"record","created_at":"2026-06-26T01:16:09Z","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":"35864a888719894ec1e4e927e607121eb1d193c1d06c02e49023cc60c8d86504","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-25T14:26:42Z","title_canon_sha256":"3783fd267eddeb2cbb33c99f7897009fdbb4622fda0f76f12fcb02635907a811"},"schema_version":"1.0","source":{"id":"2606.27090","kind":"arxiv","version":1}},"canonical_sha256":"05f82f5a540e4f630dfadc0b61c0b0c4674f3f3ce3067a20ff6bfdc6e0b0823c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05f82f5a540e4f630dfadc0b61c0b0c4674f3f3ce3067a20ff6bfdc6e0b0823c","first_computed_at":"2026-06-26T01:16:09.177640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:09.177640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvpHqbxFkd3EzpXk6ClDdZHYbxgjysLZe3wMY6OotNHqf1qpm/7YTuu001KhGAb8aEBtjFPH5aDj7hEMiiW3Aw==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:09.178027Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f9c05d7ad84a373666660561f826bd4d4be98263c1e4fe99cfc826aa1e54fa2","sha256:8b35417d66d860e26b497b9280e28d53c4f94f64cf9679f9992f3de8d2435afd"],"state_sha256":"30a110d09c3d227da300d4997ea7c4658fd265ae3472c26e3c1151e4b3ed3dcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fe3EYYiOX7AKCoqll0V4jktqEwt9eWsHstU+HQkgNtGYkhfLhNpLvUTScAGHIh09tiO0nHtUzs6R9HghWwEEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:04:17.689120Z","bundle_sha256":"41753396e27b1b0324c6e98ff1029bc5a25f20f5a46607f1991861e2ec88a053"}}