{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SFJMBQV4CCXEP6MKQPJFVDDKEQ","short_pith_number":"pith:SFJMBQV4","canonical_record":{"source":{"id":"1704.06195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-20T15:49:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3e18b452c722a147c4a4ccee943eb0fb1a15d4eb6d5bed9ec447e39cc9e700e6","abstract_canon_sha256":"7e4bf1a0b1ebc2994a05dcb7943d6f166bb551b2f104d6c0137ddaaece6c5f40"},"schema_version":"1.0"},"canonical_sha256":"9152c0c2bc10ae47f98a83d25a8c6a242beb0e6e3031d1452495aa1d9052a1de","source":{"kind":"arxiv","id":"1704.06195","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06195","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06195v1","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06195","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"SFJMBQV4CCXE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SFJMBQV4CCXEP6MK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SFJMBQV4","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SFJMBQV4CCXEP6MKQPJFVDDKEQ","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-20T15:49:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3e18b452c722a147c4a4ccee943eb0fb1a15d4eb6d5bed9ec447e39cc9e700e6","abstract_canon_sha256":"7e4bf1a0b1ebc2994a05dcb7943d6f166bb551b2f104d6c0137ddaaece6c5f40"},"schema_version":"1.0"},"canonical_sha256":"9152c0c2bc10ae47f98a83d25a8c6a242beb0e6e3031d1452495aa1d9052a1de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:03.088149Z","signature_b64":"nU19dQhC1XtPpjlu9jnQ7z3tiUie7v+JEixgnd0OnV7G020KXBSzw252AKNvrkz7hw97V/gSUGQELi4RvnD/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9152c0c2bc10ae47f98a83d25a8c6a242beb0e6e3031d1452495aa1d9052a1de","last_reissued_at":"2026-05-18T00:46:03.087767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:03.087767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06195","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":"2026-05-18T00:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2yoK0rh7iGPKPt0zMmjy7k12eb1vzLTiiDMG289dXy67mYq4EVrvl10ONHczadG27Trp3/zkXWyL3OxYxjbqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T20:43:29.667557Z"},"content_sha256":"1f13b30f86bc2b60371530f65cf9784bdf4ca322394f289e779b0c4306c574f9","schema_version":"1.0","event_id":"sha256:1f13b30f86bc2b60371530f65cf9784bdf4ca322394f289e779b0c4306c574f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SFJMBQV4CCXEP6MKQPJFVDDKEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analytical Lieb-Sokal lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.FA","authors_text":"Mohan Ravichandran","submitted_at":"2017-04-20T15:49:59Z","abstract_excerpt":"A polynomial $p \\in \\mathbb{R}[z_1, \\cdots, z_n]$ is called real stable if it is non-vanishing whenever all the variables take values in the upper half plane. A well known result of Elliott Lieb and Alan Sokal states that if $p$ and $q$ are $n$ variate real stable polynomials, then the polynomial $q(\\partial)p := q(\\partial_1, \\cdots, \\partial_n)p$, is real stable as well. In this paper, we prove analytical estimates on the locations on the zeroes of the real stable polynomial $q(\\partial)p$ in the case when both $p$ and $q$ are multiaffine, an important special case, owing to connections to n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06195","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":"2026-05-18T00:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6l6/VYbRyuwjFAjHk24bjrs5a8F8vDsi3D0SR41yIv/xGh/fsP9G53VUryT4x78ZnFijutqwlUzpWw1fNtsmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T20:43:29.667895Z"},"content_sha256":"36d9eb5b73fba7bab7b8378fff9e24155de5eea9712c26fcfa44dd6e6e6db4aa","schema_version":"1.0","event_id":"sha256:36d9eb5b73fba7bab7b8378fff9e24155de5eea9712c26fcfa44dd6e6e6db4aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/bundle.json","state_url":"https://pith.science/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/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":"2026-07-02T20:43:29Z","links":{"resolver":"https://pith.science/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ","bundle":"https://pith.science/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/bundle.json","state":"https://pith.science/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFJMBQV4CCXEP6MKQPJFVDDKEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SFJMBQV4CCXEP6MKQPJFVDDKEQ","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":"7e4bf1a0b1ebc2994a05dcb7943d6f166bb551b2f104d6c0137ddaaece6c5f40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-20T15:49:59Z","title_canon_sha256":"3e18b452c722a147c4a4ccee943eb0fb1a15d4eb6d5bed9ec447e39cc9e700e6"},"schema_version":"1.0","source":{"id":"1704.06195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06195","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06195v1","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06195","created_at":"2026-05-18T00:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"SFJMBQV4CCXE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SFJMBQV4CCXEP6MK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SFJMBQV4","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:36d9eb5b73fba7bab7b8378fff9e24155de5eea9712c26fcfa44dd6e6e6db4aa","target":"graph","created_at":"2026-05-18T00:46:03Z","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":"A polynomial $p \\in \\mathbb{R}[z_1, \\cdots, z_n]$ is called real stable if it is non-vanishing whenever all the variables take values in the upper half plane. A well known result of Elliott Lieb and Alan Sokal states that if $p$ and $q$ are $n$ variate real stable polynomials, then the polynomial $q(\\partial)p := q(\\partial_1, \\cdots, \\partial_n)p$, is real stable as well. In this paper, we prove analytical estimates on the locations on the zeroes of the real stable polynomial $q(\\partial)p$ in the case when both $p$ and $q$ are multiaffine, an important special case, owing to connections to n","authors_text":"Mohan Ravichandran","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-20T15:49:59Z","title":"An analytical Lieb-Sokal lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06195","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":"sha256:1f13b30f86bc2b60371530f65cf9784bdf4ca322394f289e779b0c4306c574f9","target":"record","created_at":"2026-05-18T00:46:03Z","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":"7e4bf1a0b1ebc2994a05dcb7943d6f166bb551b2f104d6c0137ddaaece6c5f40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-20T15:49:59Z","title_canon_sha256":"3e18b452c722a147c4a4ccee943eb0fb1a15d4eb6d5bed9ec447e39cc9e700e6"},"schema_version":"1.0","source":{"id":"1704.06195","kind":"arxiv","version":1}},"canonical_sha256":"9152c0c2bc10ae47f98a83d25a8c6a242beb0e6e3031d1452495aa1d9052a1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9152c0c2bc10ae47f98a83d25a8c6a242beb0e6e3031d1452495aa1d9052a1de","first_computed_at":"2026-05-18T00:46:03.087767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:03.087767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nU19dQhC1XtPpjlu9jnQ7z3tiUie7v+JEixgnd0OnV7G020KXBSzw252AKNvrkz7hw97V/gSUGQELi4RvnD/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:03.088149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f13b30f86bc2b60371530f65cf9784bdf4ca322394f289e779b0c4306c574f9","sha256:36d9eb5b73fba7bab7b8378fff9e24155de5eea9712c26fcfa44dd6e6e6db4aa"],"state_sha256":"789deac595d06fcc4f187bc0cfb5dd35d02fe5b60a4f64af82f3e157862ded10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+uXqk6cKfjeuZv257ehLaDYTG9HCOIWi5vhL4vy9FyGm7QvwS0mqjiSLeZvymiy/Z7E28eCZqZwUSDsGY3ssCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T20:43:29.669745Z","bundle_sha256":"948627895a735277e8d0111a2e0bb565c4df1c8e79f943ce5736bb9759568bfa"}}