{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:SKRE3B5JSNKELLXMHNVIBKG6Y7","short_pith_number":"pith:SKRE3B5J","schema_version":"1.0","canonical_sha256":"92a24d87a9935445aeec3b6a80a8dec7fc2675d8c5a499288a604044871b4c59","source":{"kind":"arxiv","id":"0904.1347","version":4},"attestation_state":"computed","paper":{"title":"The product on smooth and generalized valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andreas Bernig, Semyon Alesker","submitted_at":"2009-04-08T14:09:59Z","abstract_excerpt":"The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula on compact rank one symmetric spaces."},"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":"0904.1347","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-04-08T14:09:59Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"50a82efb50ffc7b8db16596b99f1d04267a23010fc1479568d389135f8feec1d","abstract_canon_sha256":"9db0b0fe9e7cf7f2aec3e2257aa6bb58992b84892536ea97ffbd0728cd14f0c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:02.543223Z","signature_b64":"u4fcVVJUTi3jFEI16peF0dG6Hs5v/AsyPRrGmTd13hdKyvgQac9sIEjUyWdriiS5fIlflQSpoPOb+Fmdh9HQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a24d87a9935445aeec3b6a80a8dec7fc2675d8c5a499288a604044871b4c59","last_reissued_at":"2026-05-18T03:07:02.542587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:02.542587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The product on smooth and generalized valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Andreas Bernig, Semyon Alesker","submitted_at":"2009-04-08T14:09:59Z","abstract_excerpt":"The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula on compact rank one symmetric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1347","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0904.1347","created_at":"2026-05-18T03:07:02.542660+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.1347v4","created_at":"2026-05-18T03:07:02.542660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1347","created_at":"2026-05-18T03:07:02.542660+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKRE3B5JSNKE","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKRE3B5JSNKELLXM","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKRE3B5J","created_at":"2026-05-18T12:26:01.383474+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/SKRE3B5JSNKELLXMHNVIBKG6Y7","json":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7.json","graph_json":"https://pith.science/api/pith-number/SKRE3B5JSNKELLXMHNVIBKG6Y7/graph.json","events_json":"https://pith.science/api/pith-number/SKRE3B5JSNKELLXMHNVIBKG6Y7/events.json","paper":"https://pith.science/paper/SKRE3B5J"},"agent_actions":{"view_html":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7","download_json":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7.json","view_paper":"https://pith.science/paper/SKRE3B5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.1347&json=true","fetch_graph":"https://pith.science/api/pith-number/SKRE3B5JSNKELLXMHNVIBKG6Y7/graph.json","fetch_events":"https://pith.science/api/pith-number/SKRE3B5JSNKELLXMHNVIBKG6Y7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7/action/storage_attestation","attest_author":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7/action/author_attestation","sign_citation":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7/action/citation_signature","submit_replication":"https://pith.science/pith/SKRE3B5JSNKELLXMHNVIBKG6Y7/action/replication_record"}},"created_at":"2026-05-18T03:07:02.542660+00:00","updated_at":"2026-05-18T03:07:02.542660+00:00"}