{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:42LOVEQS4UBH24PNBHDSQCOY5Y","short_pith_number":"pith:42LOVEQS","canonical_record":{"source":{"id":"1507.04851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T07:19:59Z","cross_cats_sorted":[],"title_canon_sha256":"23d5795f5d887e4c58102ac0c879975f30f1bb35255e8ab5f9bb7b82429ee9c5","abstract_canon_sha256":"504a1030d49047743c61b53865c0d6eea077a5fdd6cb38e2ad7ea5b26f76425e"},"schema_version":"1.0"},"canonical_sha256":"e696ea9212e5027d71ed09c72809d8ee0900cb3811a19f6b54ae58c87b2b4181","source":{"kind":"arxiv","id":"1507.04851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04851","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04851v1","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04851","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"42LOVEQS4UBH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42LOVEQS4UBH24PN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42LOVEQS","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:42LOVEQS4UBH24PNBHDSQCOY5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T07:19:59Z","cross_cats_sorted":[],"title_canon_sha256":"23d5795f5d887e4c58102ac0c879975f30f1bb35255e8ab5f9bb7b82429ee9c5","abstract_canon_sha256":"504a1030d49047743c61b53865c0d6eea077a5fdd6cb38e2ad7ea5b26f76425e"},"schema_version":"1.0"},"canonical_sha256":"e696ea9212e5027d71ed09c72809d8ee0900cb3811a19f6b54ae58c87b2b4181","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:02.428987Z","signature_b64":"YqK0ycLxsDAgiWLUsOhUdGT5uaUBFDKXCCf+IOo3cmCOixZaWdfE54t35bqfgo1JPSYZ3spt1/C+Vr3TxsX1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e696ea9212e5027d71ed09c72809d8ee0900cb3811a19f6b54ae58c87b2b4181","last_reissued_at":"2026-05-18T00:25:02.428622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:02.428622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04851","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":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HuahqseaZDoU4IoGxr+FapVKNMkg2J+pa9op0mxhvySfzziPKf28ZP4wckO9A1yXsBLGGV/LpBErswg6G3gCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:20:48.640438Z"},"content_sha256":"38bc46be70bad7ed94936d5c082917ac9c66cd4cae915da622827b45c93cb2c4","schema_version":"1.0","event_id":"sha256:38bc46be70bad7ed94936d5c082917ac9c66cd4cae915da622827b45c93cb2c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:42LOVEQS4UBH24PNBHDSQCOY5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolution of valuations on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Bernig, Semyon Alesker","submitted_at":"2015-07-17T07:19:59Z","abstract_excerpt":"We introduce the new notion of convolution of a (smooth or generalized) valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the group. In the case of a transitive group action, we prove that the spaces of smooth and generalized valuations on $M$ are modules over the algebra of compactly supported generalized valuations on $G$ satisfying some technical condition of tameness.\n  The case of a vector space acting on itself is studied in detail. We prove explicit formulas in this case and show that the new convolution is an extension of the convolution on smooth translation inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04851","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":"2026-05-18T00:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgG8L91SG72x2Sk4eNef/RCJ9u0T5LI8s2wlgTLrBEZ60ECMyv1dRJM6FjVaMwucMKarjQqJHqEMEug/osWrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:20:48.640786Z"},"content_sha256":"06025232466afbcdfa53823f9c707ee83572a663a91c1d73e56a64ba03328f97","schema_version":"1.0","event_id":"sha256:06025232466afbcdfa53823f9c707ee83572a663a91c1d73e56a64ba03328f97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/bundle.json","state_url":"https://pith.science/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/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":"2026-06-21T01:20:48Z","links":{"resolver":"https://pith.science/pith/42LOVEQS4UBH24PNBHDSQCOY5Y","bundle":"https://pith.science/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/bundle.json","state":"https://pith.science/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42LOVEQS4UBH24PNBHDSQCOY5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:42LOVEQS4UBH24PNBHDSQCOY5Y","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":"504a1030d49047743c61b53865c0d6eea077a5fdd6cb38e2ad7ea5b26f76425e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T07:19:59Z","title_canon_sha256":"23d5795f5d887e4c58102ac0c879975f30f1bb35255e8ab5f9bb7b82429ee9c5"},"schema_version":"1.0","source":{"id":"1507.04851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04851","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04851v1","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04851","created_at":"2026-05-18T00:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"42LOVEQS4UBH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42LOVEQS4UBH24PN","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42LOVEQS","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:06025232466afbcdfa53823f9c707ee83572a663a91c1d73e56a64ba03328f97","target":"graph","created_at":"2026-05-18T00:25:02Z","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":"We introduce the new notion of convolution of a (smooth or generalized) valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the group. In the case of a transitive group action, we prove that the spaces of smooth and generalized valuations on $M$ are modules over the algebra of compactly supported generalized valuations on $G$ satisfying some technical condition of tameness.\n  The case of a vector space acting on itself is studied in detail. We prove explicit formulas in this case and show that the new convolution is an extension of the convolution on smooth translation inv","authors_text":"Andreas Bernig, Semyon Alesker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T07:19:59Z","title":"Convolution of valuations on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04851","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":"sha256:38bc46be70bad7ed94936d5c082917ac9c66cd4cae915da622827b45c93cb2c4","target":"record","created_at":"2026-05-18T00:25:02Z","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":"504a1030d49047743c61b53865c0d6eea077a5fdd6cb38e2ad7ea5b26f76425e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-17T07:19:59Z","title_canon_sha256":"23d5795f5d887e4c58102ac0c879975f30f1bb35255e8ab5f9bb7b82429ee9c5"},"schema_version":"1.0","source":{"id":"1507.04851","kind":"arxiv","version":1}},"canonical_sha256":"e696ea9212e5027d71ed09c72809d8ee0900cb3811a19f6b54ae58c87b2b4181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e696ea9212e5027d71ed09c72809d8ee0900cb3811a19f6b54ae58c87b2b4181","first_computed_at":"2026-05-18T00:25:02.428622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:02.428622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YqK0ycLxsDAgiWLUsOhUdGT5uaUBFDKXCCf+IOo3cmCOixZaWdfE54t35bqfgo1JPSYZ3spt1/C+Vr3TxsX1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:02.428987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38bc46be70bad7ed94936d5c082917ac9c66cd4cae915da622827b45c93cb2c4","sha256:06025232466afbcdfa53823f9c707ee83572a663a91c1d73e56a64ba03328f97"],"state_sha256":"023ffbb8fb849ccdf2ec049347c2b2a6e41e9b043d7ccfbdb22a76c8e46aa0cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGKJIb7hxEOR7m62Ijk7Zq2CVRvpsrOGYjuftSbq734rwdHtni7XNpYuJvgtO80xvGP0yww/rJhO4fQ6xIByAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T01:20:48.642958Z","bundle_sha256":"55cb47435b84c5a0e747b0fc10c2666d44a29ddb75d650bdc69af286d3df7ff2"}}