{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XA5B5KIFRXUELMRAEIQB26Q3EW","short_pith_number":"pith:XA5B5KIF","canonical_record":{"source":{"id":"1712.02499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-07T05:40:30Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"50e175bd7c898d2533cfc5397ad901e8e1a8845ecdf33d391ca7efd77415a4f8","abstract_canon_sha256":"5dd7c3d3afe22090372d7179482f8bb48ea5125d059f0b6a585e168b4b72fd50"},"schema_version":"1.0"},"canonical_sha256":"b83a1ea9058de845b22022201d7a1b259158148dbcc374f96299d1cbc5e94938","source":{"kind":"arxiv","id":"1712.02499","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02499","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02499v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02499","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"XA5B5KIFRXUE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XA5B5KIFRXUELMRA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XA5B5KIF","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XA5B5KIFRXUELMRAEIQB26Q3EW","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-07T05:40:30Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"50e175bd7c898d2533cfc5397ad901e8e1a8845ecdf33d391ca7efd77415a4f8","abstract_canon_sha256":"5dd7c3d3afe22090372d7179482f8bb48ea5125d059f0b6a585e168b4b72fd50"},"schema_version":"1.0"},"canonical_sha256":"b83a1ea9058de845b22022201d7a1b259158148dbcc374f96299d1cbc5e94938","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:33.857888Z","signature_b64":"VnNFD3OXEdpO6Qdn+yKZH6Y2YWklwNGB3+1FebBSbuXNqpp4wBQV64VuLbvnhcGNBrueGKHE0VOqCG7voobBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b83a1ea9058de845b22022201d7a1b259158148dbcc374f96299d1cbc5e94938","last_reissued_at":"2026-05-18T00:28:33.857125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:33.857125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02499","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kJfwmU49XBhI4QN6JSgeE+io12T7bDE5dBwOyULVAK1d5fZzSJX5xrNzGahS8Mk0iPLdXdLef5Va/n9OJJOoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:56:35.897548Z"},"content_sha256":"e473400b7a1dbd550ae0f87edeab1829cd5f3164ab03c5716789aaa55b5a3f45","schema_version":"1.0","event_id":"sha256:e473400b7a1dbd550ae0f87edeab1829cd5f3164ab03c5716789aaa55b5a3f45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XA5B5KIFRXUELMRAEIQB26Q3EW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connecting the q-Multiplicative Convolution and the Finite Difference Convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Jonathan Leake, Nick Ryder","submitted_at":"2017-12-07T05:40:30Z","abstract_excerpt":"In a recent paper, Br\\\"and\\'en, Krasikov, and Shapiro consider root location preservation properties of finite difference operators. To this end, the authors describe a natural polynomial convolution operator and conjecture that it preserves root mesh properties. We prove this conjecture using two methods. The first develops a novel connection between the additive (Walsh) and multiplicative (Grace-Szeg\\\"o) convolutions, which can be generically used to transfer results from multiplicative to additive. We then use this to transfer an analogous result, due to Lamprecht, which demonstrates logari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02499","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tKXdokhmY8dXmXQv8AivY+FY5R02EY+2n3SW80qhgISiXbpiatfdvBKEEnAqEPCpt2L5COFr9ouMt9LLlCrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:56:35.898227Z"},"content_sha256":"f4a1421bce4c83bdc93416583a34153159cd1c10f024b8246bdcab3946a36a40","schema_version":"1.0","event_id":"sha256:f4a1421bce4c83bdc93416583a34153159cd1c10f024b8246bdcab3946a36a40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/bundle.json","state_url":"https://pith.science/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/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":"2026-05-27T03:56:35Z","links":{"resolver":"https://pith.science/pith/XA5B5KIFRXUELMRAEIQB26Q3EW","bundle":"https://pith.science/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/bundle.json","state":"https://pith.science/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XA5B5KIFRXUELMRAEIQB26Q3EW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XA5B5KIFRXUELMRAEIQB26Q3EW","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":"5dd7c3d3afe22090372d7179482f8bb48ea5125d059f0b6a585e168b4b72fd50","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-07T05:40:30Z","title_canon_sha256":"50e175bd7c898d2533cfc5397ad901e8e1a8845ecdf33d391ca7efd77415a4f8"},"schema_version":"1.0","source":{"id":"1712.02499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02499","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02499v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02499","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"XA5B5KIFRXUE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XA5B5KIFRXUELMRA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XA5B5KIF","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f4a1421bce4c83bdc93416583a34153159cd1c10f024b8246bdcab3946a36a40","target":"graph","created_at":"2026-05-18T00:28:33Z","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 a recent paper, Br\\\"and\\'en, Krasikov, and Shapiro consider root location preservation properties of finite difference operators. To this end, the authors describe a natural polynomial convolution operator and conjecture that it preserves root mesh properties. We prove this conjecture using two methods. The first develops a novel connection between the additive (Walsh) and multiplicative (Grace-Szeg\\\"o) convolutions, which can be generically used to transfer results from multiplicative to additive. We then use this to transfer an analogous result, due to Lamprecht, which demonstrates logari","authors_text":"Jonathan Leake, Nick Ryder","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-07T05:40:30Z","title":"Connecting the q-Multiplicative Convolution and the Finite Difference Convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02499","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:e473400b7a1dbd550ae0f87edeab1829cd5f3164ab03c5716789aaa55b5a3f45","target":"record","created_at":"2026-05-18T00:28:33Z","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":"5dd7c3d3afe22090372d7179482f8bb48ea5125d059f0b6a585e168b4b72fd50","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-07T05:40:30Z","title_canon_sha256":"50e175bd7c898d2533cfc5397ad901e8e1a8845ecdf33d391ca7efd77415a4f8"},"schema_version":"1.0","source":{"id":"1712.02499","kind":"arxiv","version":1}},"canonical_sha256":"b83a1ea9058de845b22022201d7a1b259158148dbcc374f96299d1cbc5e94938","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b83a1ea9058de845b22022201d7a1b259158148dbcc374f96299d1cbc5e94938","first_computed_at":"2026-05-18T00:28:33.857125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:33.857125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VnNFD3OXEdpO6Qdn+yKZH6Y2YWklwNGB3+1FebBSbuXNqpp4wBQV64VuLbvnhcGNBrueGKHE0VOqCG7voobBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:33.857888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e473400b7a1dbd550ae0f87edeab1829cd5f3164ab03c5716789aaa55b5a3f45","sha256:f4a1421bce4c83bdc93416583a34153159cd1c10f024b8246bdcab3946a36a40"],"state_sha256":"6464f0f5c97b48a98ee6c5326521255da98ab157a1b278ab1bfd2b28b4e14199"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNX96wieP1rHZYSfSaXDWrwumsNAfl58tPeugkvUmH7bxAeWLlC48VKQwcrcGxPOidamtUjrOJ1Jp5hEMVMOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:56:35.905063Z","bundle_sha256":"2760ce67f2e8fdcb1746c6e57f37bc622ccefe7a09c63176092d12c9e8852f0e"}}