{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CIGSUTBGWVR77R5P34N2Z42EGQ","short_pith_number":"pith:CIGSUTBG","canonical_record":{"source":{"id":"2505.22464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-28T15:18:04Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"87931d004469b9736301bb2ab5905ceca90c14d0803f02b8b6927162765e732e","abstract_canon_sha256":"5667b24255d5cb5e297d3685f053fbac424c6c1e4bcd6c0d5c91f76384b0b382"},"schema_version":"1.0"},"canonical_sha256":"120d2a4c26b563ffc7afdf1bacf3443401affa4ae0502b4a6077cb8a129a8fe5","source":{"kind":"arxiv","id":"2505.22464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22464","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22464v1","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22464","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"CIGSUTBGWVR7","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_16","alias_value":"CIGSUTBGWVR77R5P","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_8","alias_value":"CIGSUTBG","created_at":"2026-07-05T11:11:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CIGSUTBGWVR77R5P34N2Z42EGQ","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-28T15:18:04Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"87931d004469b9736301bb2ab5905ceca90c14d0803f02b8b6927162765e732e","abstract_canon_sha256":"5667b24255d5cb5e297d3685f053fbac424c6c1e4bcd6c0d5c91f76384b0b382"},"schema_version":"1.0"},"canonical_sha256":"120d2a4c26b563ffc7afdf1bacf3443401affa4ae0502b4a6077cb8a129a8fe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:24.619894Z","signature_b64":"ehLNXMa85yaNnrBbr5v+VrpolXXN6g5ORehBOSGhuynpKJbuRZDf77GbJ0vZZxmBx+SvA6VtO5vjdLHGB614Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"120d2a4c26b563ffc7afdf1bacf3443401affa4ae0502b4a6077cb8a129a8fe5","last_reissued_at":"2026-07-05T11:11:24.619378Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:24.619378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22464","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":"2026-07-05T11:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoKqj2u15A32nDCPL4jD8uoDEdpvy042BMRAJfmRN6hIQp08dgdEYF/lc3t/mqI3uMKfVxjcSEAZ9f927PP0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:33:38.081212Z"},"content_sha256":"9ea5c1aaeff23084e919c2e414321ff8f9ac15a3ff195fbbb9266e346352571a","schema_version":"1.0","event_id":"sha256:9ea5c1aaeff23084e919c2e414321ff8f9ac15a3ff195fbbb9266e346352571a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CIGSUTBGWVR77R5P34N2Z42EGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Jonas Knoerr","submitted_at":"2025-05-28T15:18:04Z","abstract_excerpt":"Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations of the smooth vectors of the natural representation of the group of translations on the space of these valuations. As an application, a complete classification of all closed and affine invariant subspaces is established, yielding density results for valuations defined in terms of mixed Monge-Amp\\`ere operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22464","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/2505.22464/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":"2026-07-05T11:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmv9LCY13Efjab5c3E4kba7k97hxCrq5OoXaJScjcW90RrIexioRWm0uRKtYxT8FEecha4Oy/ahGCwEb21F3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:33:38.081785Z"},"content_sha256":"51f6ff5c61e3b4612c9b0147a19872f053e863278065e0a45a5acf9788f764cf","schema_version":"1.0","event_id":"sha256:51f6ff5c61e3b4612c9b0147a19872f053e863278065e0a45a5acf9788f764cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/bundle.json","state_url":"https://pith.science/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/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":"2026-08-08T08:33:38Z","links":{"resolver":"https://pith.science/pith/CIGSUTBGWVR77R5P34N2Z42EGQ","bundle":"https://pith.science/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/bundle.json","state":"https://pith.science/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIGSUTBGWVR77R5P34N2Z42EGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CIGSUTBGWVR77R5P34N2Z42EGQ","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":"5667b24255d5cb5e297d3685f053fbac424c6c1e4bcd6c0d5c91f76384b0b382","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-28T15:18:04Z","title_canon_sha256":"87931d004469b9736301bb2ab5905ceca90c14d0803f02b8b6927162765e732e"},"schema_version":"1.0","source":{"id":"2505.22464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22464","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22464v1","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22464","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"CIGSUTBGWVR7","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_16","alias_value":"CIGSUTBGWVR77R5P","created_at":"2026-07-05T11:11:24Z"},{"alias_kind":"pith_short_8","alias_value":"CIGSUTBG","created_at":"2026-07-05T11:11:24Z"}],"graph_snapshots":[{"event_id":"sha256:51f6ff5c61e3b4612c9b0147a19872f053e863278065e0a45a5acf9788f764cf","target":"graph","created_at":"2026-07-05T11:11:24Z","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/2505.22464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations of the smooth vectors of the natural representation of the group of translations on the space of these valuations. As an application, a complete classification of all closed and affine invariant subspaces is established, yielding density results for valuations defined in terms of mixed Monge-Amp\\`ere operators.","authors_text":"Jonas Knoerr","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-28T15:18:04Z","title":"A Paley-Wiener-Schwartz Theorem for smooth valuations on convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22464","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":"sha256:9ea5c1aaeff23084e919c2e414321ff8f9ac15a3ff195fbbb9266e346352571a","target":"record","created_at":"2026-07-05T11:11:24Z","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":"5667b24255d5cb5e297d3685f053fbac424c6c1e4bcd6c0d5c91f76384b0b382","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-05-28T15:18:04Z","title_canon_sha256":"87931d004469b9736301bb2ab5905ceca90c14d0803f02b8b6927162765e732e"},"schema_version":"1.0","source":{"id":"2505.22464","kind":"arxiv","version":1}},"canonical_sha256":"120d2a4c26b563ffc7afdf1bacf3443401affa4ae0502b4a6077cb8a129a8fe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"120d2a4c26b563ffc7afdf1bacf3443401affa4ae0502b4a6077cb8a129a8fe5","first_computed_at":"2026-07-05T11:11:24.619378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:24.619378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ehLNXMa85yaNnrBbr5v+VrpolXXN6g5ORehBOSGhuynpKJbuRZDf77GbJ0vZZxmBx+SvA6VtO5vjdLHGB614Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:24.619894Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ea5c1aaeff23084e919c2e414321ff8f9ac15a3ff195fbbb9266e346352571a","sha256:51f6ff5c61e3b4612c9b0147a19872f053e863278065e0a45a5acf9788f764cf"],"state_sha256":"c6bb47ff95739694234d003f1d3dca82a50545941e8b19f44ad1696089a47ade"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2eVot4OBIrS966FI5QckZHXhydh1Phpga0iX/TXttNp0OzOLwe6GtCXdD5mzN9Jv7vzT/l1OjCF7hCb//ftBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:33:38.086898Z","bundle_sha256":"99e8af6ce79f956e6d723ed47bb2400fd2bb9b451caba78f3878f7dd72a7fe3c"}}