{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XMGV4O7ZM46JIGLJII7S2WPQUT","short_pith_number":"pith:XMGV4O7Z","canonical_record":{"source":{"id":"1808.00772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-02T12:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"e993a43b9eeb0e502802cd0fa1250ff71ccf4eeb3b9834ec4decfcfba499c6b2","abstract_canon_sha256":"ef8b0577bafef850f87e810282f3d51531dead436da1a241c29a30087aa7c4a2"},"schema_version":"1.0"},"canonical_sha256":"bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3","source":{"kind":"arxiv","id":"1808.00772","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00772","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00772v1","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00772","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"XMGV4O7ZM46J","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XMGV4O7ZM46JIGLJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XMGV4O7Z","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XMGV4O7ZM46JIGLJII7S2WPQUT","target":"record","payload":{"canonical_record":{"source":{"id":"1808.00772","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-02T12:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"e993a43b9eeb0e502802cd0fa1250ff71ccf4eeb3b9834ec4decfcfba499c6b2","abstract_canon_sha256":"ef8b0577bafef850f87e810282f3d51531dead436da1a241c29a30087aa7c4a2"},"schema_version":"1.0"},"canonical_sha256":"bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:55.812945Z","signature_b64":"GgffWrd4C3uvlr6cdka+PFySyLAwwsIDB8xQ0M2BJT0OeCMCdacIrhG7T2NGTxdVB0S0T6fERnZU0ONyG/CsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3","last_reissued_at":"2026-05-17T23:55:55.812253Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:55.812253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.00772","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":"2026-05-17T23:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FF10F3qPEFGoHDUmFiSQ/8HDwYOxW5L7flvcla9hpeLvFL5pJqP4wpG3kIIa8rvD9058TGWkuamS0IbJV3zLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:28:54.228005Z"},"content_sha256":"38b419f3b565cf3ef7c7bad4ee50b42a700e4eff190631e80f1d1ccbd21bfb71","schema_version":"1.0","event_id":"sha256:38b419f3b565cf3ef7c7bad4ee50b42a700e4eff190631e80f1d1ccbd21bfb71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XMGV4O7ZM46JIGLJII7S2WPQUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper and lower bounds for the Bregman divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Benjamin Sprung","submitted_at":"2018-08-02T12:03:04Z","abstract_excerpt":"In this paper we study upper and lower bounds on the Bregman divergence $\\Delta_{\\mathcal{F}}^{\\xi}(y,x):=\\mathcal{F}(y)-\\mathcal{F}(x)-\\langle \\xi, y-x\\rangle $ for some convex functional $\\mathcal{F}$ on a normed space $\\mathcal{X}$, with subgradient $\\xi\\in\\partial\\mathcal{F}(x)$. We give a considerably simpler new proof of the inequalities by Xu and Roach for the special case $\\mathcal{F}(x)=\\left\\| x\\right\\|^p, p>1$. The results can be transfered to more general functions as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00772","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":"2026-05-17T23:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8xySHbKbKmjV2TyL3r1XRvVTbg29pGC7LqAn/vRRt31UjXsR+P+higTKqRjtwM42H1ad4kHMHWo/G0OcWSkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:28:54.228668Z"},"content_sha256":"618da9d07a3a585fc0cda1e1e505d54d196b50cf2e09b0f7a580998655224ac3","schema_version":"1.0","event_id":"sha256:618da9d07a3a585fc0cda1e1e505d54d196b50cf2e09b0f7a580998655224ac3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/bundle.json","state_url":"https://pith.science/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/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":"2026-05-26T20:28:54Z","links":{"resolver":"https://pith.science/pith/XMGV4O7ZM46JIGLJII7S2WPQUT","bundle":"https://pith.science/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/bundle.json","state":"https://pith.science/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XMGV4O7ZM46JIGLJII7S2WPQUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XMGV4O7ZM46JIGLJII7S2WPQUT","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":"ef8b0577bafef850f87e810282f3d51531dead436da1a241c29a30087aa7c4a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-02T12:03:04Z","title_canon_sha256":"e993a43b9eeb0e502802cd0fa1250ff71ccf4eeb3b9834ec4decfcfba499c6b2"},"schema_version":"1.0","source":{"id":"1808.00772","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00772","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00772v1","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00772","created_at":"2026-05-17T23:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"XMGV4O7ZM46J","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XMGV4O7ZM46JIGLJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XMGV4O7Z","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:618da9d07a3a585fc0cda1e1e505d54d196b50cf2e09b0f7a580998655224ac3","target":"graph","created_at":"2026-05-17T23:55:55Z","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":"In this paper we study upper and lower bounds on the Bregman divergence $\\Delta_{\\mathcal{F}}^{\\xi}(y,x):=\\mathcal{F}(y)-\\mathcal{F}(x)-\\langle \\xi, y-x\\rangle $ for some convex functional $\\mathcal{F}$ on a normed space $\\mathcal{X}$, with subgradient $\\xi\\in\\partial\\mathcal{F}(x)$. We give a considerably simpler new proof of the inequalities by Xu and Roach for the special case $\\mathcal{F}(x)=\\left\\| x\\right\\|^p, p>1$. The results can be transfered to more general functions as well.","authors_text":"Benjamin Sprung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-02T12:03:04Z","title":"Upper and lower bounds for the Bregman divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00772","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":"sha256:38b419f3b565cf3ef7c7bad4ee50b42a700e4eff190631e80f1d1ccbd21bfb71","target":"record","created_at":"2026-05-17T23:55:55Z","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":"ef8b0577bafef850f87e810282f3d51531dead436da1a241c29a30087aa7c4a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-02T12:03:04Z","title_canon_sha256":"e993a43b9eeb0e502802cd0fa1250ff71ccf4eeb3b9834ec4decfcfba499c6b2"},"schema_version":"1.0","source":{"id":"1808.00772","kind":"arxiv","version":1}},"canonical_sha256":"bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb0d5e3bf9673c941969423f2d59f0a4c65204c24b2866ece881b68986651ee3","first_computed_at":"2026-05-17T23:55:55.812253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:55.812253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GgffWrd4C3uvlr6cdka+PFySyLAwwsIDB8xQ0M2BJT0OeCMCdacIrhG7T2NGTxdVB0S0T6fERnZU0ONyG/CsAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:55.812945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00772","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38b419f3b565cf3ef7c7bad4ee50b42a700e4eff190631e80f1d1ccbd21bfb71","sha256:618da9d07a3a585fc0cda1e1e505d54d196b50cf2e09b0f7a580998655224ac3"],"state_sha256":"16bd18c5b8abeb1d90f4f6e4a967adac74a97ecf3d637c56d9edfb2915223fbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXNu6vSUGJKNR0AlnAQZ4MOKM2Zbl9pBoARFwdFuL+MzGNoA0F+v/zdgCWGC/oS25YKgcJJQETLne1pTQNpdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:28:54.232086Z","bundle_sha256":"9e1f5f8ece2ade2942957a0e8a83fe4d30c6d5bd01fe19500c15b36809b8a6c2"}}