{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XURWECXYOXNTSG5ZFS5O2WTGYY","short_pith_number":"pith:XURWECXY","canonical_record":{"source":{"id":"1808.09768","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T12:50:11Z","cross_cats_sorted":[],"title_canon_sha256":"4ab8b5eff084bffefa6268bcbe47673fcd9478dccbf7f94d423462ed49bff39c","abstract_canon_sha256":"0553f1335085866c930a47e4f2cad3425673134452535e8cd9f87a9bdb63f2e5"},"schema_version":"1.0"},"canonical_sha256":"bd23620af875db391bb92cbaed5a66c63c92bbaf2195516cc6901d39b4e4a517","source":{"kind":"arxiv","id":"1808.09768","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09768","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09768v4","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09768","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"pith_short_12","alias_value":"XURWECXYOXNT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XURWECXYOXNTSG5Z","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XURWECXY","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XURWECXYOXNTSG5ZFS5O2WTGYY","target":"record","payload":{"canonical_record":{"source":{"id":"1808.09768","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T12:50:11Z","cross_cats_sorted":[],"title_canon_sha256":"4ab8b5eff084bffefa6268bcbe47673fcd9478dccbf7f94d423462ed49bff39c","abstract_canon_sha256":"0553f1335085866c930a47e4f2cad3425673134452535e8cd9f87a9bdb63f2e5"},"schema_version":"1.0"},"canonical_sha256":"bd23620af875db391bb92cbaed5a66c63c92bbaf2195516cc6901d39b4e4a517","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:00.936529Z","signature_b64":"9KaR8Dp+n791TLA28PQe3L74vqgZB3EAONPyZnc1z4jalAJd2PoYm4bgfXNKslP5vGre/Q/USspMkAPYvpJiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd23620af875db391bb92cbaed5a66c63c92bbaf2195516cc6901d39b4e4a517","last_reissued_at":"2026-05-18T00:06:00.936112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:00.936112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.09768","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONuM8x6pwkoFnQ0GgxVlFlShREdXscS3MJ/bglqJQVitwEvFgZGVLfGfNNUCSMMx23Xrn5/76wmtpCPBLUpWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:43:57.372560Z"},"content_sha256":"0615ad9cafe978bfc16ab7dc57ebb9253578f5f572c69e4666d4a827e7f63681","schema_version":"1.0","event_id":"sha256:0615ad9cafe978bfc16ab7dc57ebb9253578f5f572c69e4666d4a827e7f63681"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XURWECXYOXNTSG5ZFS5O2WTGYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total positivity of a class of combinatorial matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ken Joffaniel M. Gonzales","submitted_at":"2018-08-29T12:50:11Z","abstract_excerpt":"In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices using the Lindstr\\\"om-Gessel-Viennot Lemma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09768","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fnfeEE31r30ikHt1LuSAPwk5wYic9wydEnMxZNQCaU8qsqCrS4kF+aeEvxzE97rHoJ0LZm4fTtOFpnKRBkW7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:43:57.372902Z"},"content_sha256":"09b8730c319932cce7961daff096d1bd68127665675ce3def117006fe5c49d4f","schema_version":"1.0","event_id":"sha256:09b8730c319932cce7961daff096d1bd68127665675ce3def117006fe5c49d4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/bundle.json","state_url":"https://pith.science/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/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":"2026-06-25T18:43:57Z","links":{"resolver":"https://pith.science/pith/XURWECXYOXNTSG5ZFS5O2WTGYY","bundle":"https://pith.science/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/bundle.json","state":"https://pith.science/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XURWECXYOXNTSG5ZFS5O2WTGYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XURWECXYOXNTSG5ZFS5O2WTGYY","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":"0553f1335085866c930a47e4f2cad3425673134452535e8cd9f87a9bdb63f2e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T12:50:11Z","title_canon_sha256":"4ab8b5eff084bffefa6268bcbe47673fcd9478dccbf7f94d423462ed49bff39c"},"schema_version":"1.0","source":{"id":"1808.09768","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09768","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09768v4","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09768","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"pith_short_12","alias_value":"XURWECXYOXNT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XURWECXYOXNTSG5Z","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XURWECXY","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:09b8730c319932cce7961daff096d1bd68127665675ce3def117006fe5c49d4f","target":"graph","created_at":"2026-05-18T00:06:00Z","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 paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices using the Lindstr\\\"om-Gessel-Viennot Lemma.","authors_text":"Ken Joffaniel M. Gonzales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T12:50:11Z","title":"Total positivity of a class of combinatorial matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09768","kind":"arxiv","version":4},"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":"sha256:0615ad9cafe978bfc16ab7dc57ebb9253578f5f572c69e4666d4a827e7f63681","target":"record","created_at":"2026-05-18T00:06:00Z","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":"0553f1335085866c930a47e4f2cad3425673134452535e8cd9f87a9bdb63f2e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T12:50:11Z","title_canon_sha256":"4ab8b5eff084bffefa6268bcbe47673fcd9478dccbf7f94d423462ed49bff39c"},"schema_version":"1.0","source":{"id":"1808.09768","kind":"arxiv","version":4}},"canonical_sha256":"bd23620af875db391bb92cbaed5a66c63c92bbaf2195516cc6901d39b4e4a517","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd23620af875db391bb92cbaed5a66c63c92bbaf2195516cc6901d39b4e4a517","first_computed_at":"2026-05-18T00:06:00.936112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:00.936112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9KaR8Dp+n791TLA28PQe3L74vqgZB3EAONPyZnc1z4jalAJd2PoYm4bgfXNKslP5vGre/Q/USspMkAPYvpJiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:00.936529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09768","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0615ad9cafe978bfc16ab7dc57ebb9253578f5f572c69e4666d4a827e7f63681","sha256:09b8730c319932cce7961daff096d1bd68127665675ce3def117006fe5c49d4f"],"state_sha256":"fa350c0660532e74aa3595c3ddebb23b2d0e6851aef4804190c984e01c180998"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jcX094ZoAiWTQR6gKMfd4xqxFMgHsBQOGTfPbioca5cv4531/VGwiA4GR7mSo4SiLb/lK0vuK/QhvJvgtJmqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:43:57.375179Z","bundle_sha256":"630243af1d6dbe6830a19e5c0439bf11e94fa79f10152ace5bb73881c0ad1283"}}