{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BDQUMYUC3EYK3SS26HUOYAVGVQ","short_pith_number":"pith:BDQUMYUC","schema_version":"1.0","canonical_sha256":"08e1466282d930adca5af1e8ec02a6ac0504efac0f1edc3e47b7a0b64dfc78c5","source":{"kind":"arxiv","id":"1908.10724","version":1},"attestation_state":"computed","paper":{"title":"A homogeneous decomposition theorem for valuations on convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"A. Colesanti, F. Mussnig, M. Ludwig","submitted_at":"2019-08-28T13:52:53Z","abstract_excerpt":"The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.10724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-08-28T13:52:53Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b0cdedd90cfdd6379bee99617517bfb66641f00aa92ef4e959359beb1bf9c398","abstract_canon_sha256":"6abcaba2ee28afdf8cfce67b80f5a615c00a185d50e8895af6127af1ecb4d8ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:02:43.792937Z","signature_b64":"0EWy0YP0jw9xePgoA7lBnVCf1C1EjAj7ST+P5Y+chkPExwASQqhjJ396OLfEHIp3Q7OsWs7meO9ZjvdocdlsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08e1466282d930adca5af1e8ec02a6ac0504efac0f1edc3e47b7a0b64dfc78c5","last_reissued_at":"2026-07-05T01:02:43.792406Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:02:43.792406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A homogeneous decomposition theorem for valuations on convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"A. Colesanti, F. Mussnig, M. Ludwig","submitted_at":"2019-08-28T13:52:53Z","abstract_excerpt":"The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10724","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/1908.10724/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.10724","created_at":"2026-07-05T01:02:43.792480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.10724v1","created_at":"2026-07-05T01:02:43.792480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10724","created_at":"2026-07-05T01:02:43.792480+00:00"},{"alias_kind":"pith_short_12","alias_value":"BDQUMYUC3EYK","created_at":"2026-07-05T01:02:43.792480+00:00"},{"alias_kind":"pith_short_16","alias_value":"BDQUMYUC3EYK3SS2","created_at":"2026-07-05T01:02:43.792480+00:00"},{"alias_kind":"pith_short_8","alias_value":"BDQUMYUC","created_at":"2026-07-05T01:02:43.792480+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ","json":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ.json","graph_json":"https://pith.science/api/pith-number/BDQUMYUC3EYK3SS26HUOYAVGVQ/graph.json","events_json":"https://pith.science/api/pith-number/BDQUMYUC3EYK3SS26HUOYAVGVQ/events.json","paper":"https://pith.science/paper/BDQUMYUC"},"agent_actions":{"view_html":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ","download_json":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ.json","view_paper":"https://pith.science/paper/BDQUMYUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.10724&json=true","fetch_graph":"https://pith.science/api/pith-number/BDQUMYUC3EYK3SS26HUOYAVGVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BDQUMYUC3EYK3SS26HUOYAVGVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ/action/storage_attestation","attest_author":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ/action/author_attestation","sign_citation":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ/action/citation_signature","submit_replication":"https://pith.science/pith/BDQUMYUC3EYK3SS26HUOYAVGVQ/action/replication_record"}},"created_at":"2026-07-05T01:02:43.792480+00:00","updated_at":"2026-07-05T01:02:43.792480+00:00"}