{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4HAW7XLXSBQMP3SHDFRIXU4PTI","short_pith_number":"pith:4HAW7XLX","canonical_record":{"source":{"id":"1202.2142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-09T22:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"331ee5b2b6448a77d4185c781c45aad2db99f5aaa4d551281900a113e6a3f625","abstract_canon_sha256":"f6cb0f6378686e2e56babbaa3610709b59f6bdeb37470076514a3dab93e32075"},"schema_version":"1.0"},"canonical_sha256":"e1c16fdd779060c7ee4719628bd38f9a2dc76513f856234348e1e992159bf58c","source":{"kind":"arxiv","id":"1202.2142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2142","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2142v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2142","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"4HAW7XLXSBQM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4HAW7XLXSBQMP3SH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4HAW7XLX","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4HAW7XLXSBQMP3SHDFRIXU4PTI","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-09T22:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"331ee5b2b6448a77d4185c781c45aad2db99f5aaa4d551281900a113e6a3f625","abstract_canon_sha256":"f6cb0f6378686e2e56babbaa3610709b59f6bdeb37470076514a3dab93e32075"},"schema_version":"1.0"},"canonical_sha256":"e1c16fdd779060c7ee4719628bd38f9a2dc76513f856234348e1e992159bf58c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.057910Z","signature_b64":"ucsmtlK5GjbfxqIlNaFCsXxS/46nzpB5mN0bzPS19lHcs/Cina4WlFbtFQ6AOLGU9XcVQBEV9Rm3YQFGRFDKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1c16fdd779060c7ee4719628bd38f9a2dc76513f856234348e1e992159bf58c","last_reissued_at":"2026-05-18T03:12:58.057181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.057181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2142","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/woBoXibd6JpYh7X9tSubnS4XOrE760TQdJTOE1/3VAke3/oxDCYuKGs+lQN9JOizmuKoskoVOqI7K7WggDODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:10:39.441040Z"},"content_sha256":"9d1ddff728b8d50a1f4777e534a90ef106da0a0f62df37c2b7de4b58f450da23","schema_version":"1.0","event_id":"sha256:9d1ddff728b8d50a1f4777e534a90ef106da0a0f62df37c2b7de4b58f450da23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4HAW7XLXSBQMP3SHDFRIXU4PTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The unconditional case of the complex S-inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Nayar, Tomasz Tkocz","submitted_at":"2012-02-09T22:05:22Z","abstract_excerpt":"In this note we prove the complex counterpart of the S-inequality for complete Reinhardt sets. In particular, this result implies that the complex S-inequality holds for unconditional convex sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2142","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQX5fZwV1ktDWkbrVZZVUqkZOJbF+cM5Xg1tqAFlSxtBCbs1GFvCyXuMjfISmRMyICussoZfAtubUgl2fIKrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:10:39.441395Z"},"content_sha256":"34ffcbb84276ce34d7a4a8f41e29d0430460805d72550f88ab1b20a20d2e541b","schema_version":"1.0","event_id":"sha256:34ffcbb84276ce34d7a4a8f41e29d0430460805d72550f88ab1b20a20d2e541b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/bundle.json","state_url":"https://pith.science/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/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":"2026-06-25T08:10:39Z","links":{"resolver":"https://pith.science/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI","bundle":"https://pith.science/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/bundle.json","state":"https://pith.science/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HAW7XLXSBQMP3SHDFRIXU4PTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4HAW7XLXSBQMP3SHDFRIXU4PTI","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":"f6cb0f6378686e2e56babbaa3610709b59f6bdeb37470076514a3dab93e32075","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-09T22:05:22Z","title_canon_sha256":"331ee5b2b6448a77d4185c781c45aad2db99f5aaa4d551281900a113e6a3f625"},"schema_version":"1.0","source":{"id":"1202.2142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2142","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2142v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2142","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"4HAW7XLXSBQM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4HAW7XLXSBQMP3SH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4HAW7XLX","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:34ffcbb84276ce34d7a4a8f41e29d0430460805d72550f88ab1b20a20d2e541b","target":"graph","created_at":"2026-05-18T03:12:58Z","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 this note we prove the complex counterpart of the S-inequality for complete Reinhardt sets. In particular, this result implies that the complex S-inequality holds for unconditional convex sets.","authors_text":"Piotr Nayar, Tomasz Tkocz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-09T22:05:22Z","title":"The unconditional case of the complex S-inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2142","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":"sha256:9d1ddff728b8d50a1f4777e534a90ef106da0a0f62df37c2b7de4b58f450da23","target":"record","created_at":"2026-05-18T03:12:58Z","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":"f6cb0f6378686e2e56babbaa3610709b59f6bdeb37470076514a3dab93e32075","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-09T22:05:22Z","title_canon_sha256":"331ee5b2b6448a77d4185c781c45aad2db99f5aaa4d551281900a113e6a3f625"},"schema_version":"1.0","source":{"id":"1202.2142","kind":"arxiv","version":1}},"canonical_sha256":"e1c16fdd779060c7ee4719628bd38f9a2dc76513f856234348e1e992159bf58c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1c16fdd779060c7ee4719628bd38f9a2dc76513f856234348e1e992159bf58c","first_computed_at":"2026-05-18T03:12:58.057181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.057181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucsmtlK5GjbfxqIlNaFCsXxS/46nzpB5mN0bzPS19lHcs/Cina4WlFbtFQ6AOLGU9XcVQBEV9Rm3YQFGRFDKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.057910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d1ddff728b8d50a1f4777e534a90ef106da0a0f62df37c2b7de4b58f450da23","sha256:34ffcbb84276ce34d7a4a8f41e29d0430460805d72550f88ab1b20a20d2e541b"],"state_sha256":"67a5a8e8b1f51d3cce089aa5ad486ed96740afaf97ef45cf1b2278dd6eccccf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+dh3Ph3h7S8gBQs2g04KU/e6BLyJ+xkJVmjaOurSPTIhnEuKM/k3kBhtmjDZ7FiMCFrj6TA+y10KE1Kcp5WCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:10:39.443323Z","bundle_sha256":"a6c1bc2c4bc8479d440f48e3bdacf5679bf6e6a0321c2d723d2eb4b7c2db8354"}}