{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2V2YJBD4JGCLTA57L7TBKNJHIU","short_pith_number":"pith:2V2YJBD4","canonical_record":{"source":{"id":"1809.04448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-12T13:53:53Z","cross_cats_sorted":[],"title_canon_sha256":"1f8b047847fca4d66f684c409a9a81212b90ee93ac7ebc634bd76b1838e8cb0c","abstract_canon_sha256":"255e135e1556c33dc0f2c740b50eb7bee6b650f92394fdd6387d4e00999ab938"},"schema_version":"1.0"},"canonical_sha256":"d57584847c4984b983bf5fe6153527451a181526f74b46c81511634a9601bd23","source":{"kind":"arxiv","id":"1809.04448","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04448","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04448v1","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04448","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"2V2YJBD4JGCL","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2V2YJBD4JGCLTA57","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2V2YJBD4","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2V2YJBD4JGCLTA57L7TBKNJHIU","target":"record","payload":{"canonical_record":{"source":{"id":"1809.04448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-12T13:53:53Z","cross_cats_sorted":[],"title_canon_sha256":"1f8b047847fca4d66f684c409a9a81212b90ee93ac7ebc634bd76b1838e8cb0c","abstract_canon_sha256":"255e135e1556c33dc0f2c740b50eb7bee6b650f92394fdd6387d4e00999ab938"},"schema_version":"1.0"},"canonical_sha256":"d57584847c4984b983bf5fe6153527451a181526f74b46c81511634a9601bd23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:52.360033Z","signature_b64":"edc1W0nBDk4+sky++natfK2AKzHskj3OWO1zluBq8z4UNbjEBvw1HkISU/kFMl5BTR90lxUG5bz+fdlsPadrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d57584847c4984b983bf5fe6153527451a181526f74b46c81511634a9601bd23","last_reissued_at":"2026-05-18T00:05:52.359232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:52.359232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.04448","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":"2026-05-18T00:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqHjdZ1BTWG2mIF3eOZU+ld8808C66a4T5+Z5inld+Xm3Xt8cvzgvGQcDavoWQx2rmfS2kzwde3wzA3rkCBhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:47:57.375502Z"},"content_sha256":"e0254e8472c5ee3663a1d8a5d50edf1d8991a7de5cdbd046690250de4b31f107","schema_version":"1.0","event_id":"sha256:e0254e8472c5ee3663a1d8a5d50edf1d8991a7de5cdbd046690250de4b31f107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2V2YJBD4JGCLTA57L7TBKNJHIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"What is Schur positivity and how common is it?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rebecca Patrias","submitted_at":"2018-09-12T13:53:53Z","abstract_excerpt":"This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new result of the author with F. Bergeron and V. Reiner that gives the probability that a homogeneous symmetric polynomial with positive coefficients is Schur positive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04448","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":"2026-05-18T00:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l11puYP5kya0eGHG4L2deSCyZWdJkBewCv8jdtoWtZbBnOUKpcoyG7wMMl8YQfdA0LheVpRRodKAMyzN8gQvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:47:57.375836Z"},"content_sha256":"fd54dfb835bd5eecea8c38768814b606b712e7c0197fb83e39071c010042bdf4","schema_version":"1.0","event_id":"sha256:fd54dfb835bd5eecea8c38768814b606b712e7c0197fb83e39071c010042bdf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/bundle.json","state_url":"https://pith.science/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/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":"2026-06-08T14:47:57Z","links":{"resolver":"https://pith.science/pith/2V2YJBD4JGCLTA57L7TBKNJHIU","bundle":"https://pith.science/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/bundle.json","state":"https://pith.science/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2V2YJBD4JGCLTA57L7TBKNJHIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2V2YJBD4JGCLTA57L7TBKNJHIU","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":"255e135e1556c33dc0f2c740b50eb7bee6b650f92394fdd6387d4e00999ab938","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-12T13:53:53Z","title_canon_sha256":"1f8b047847fca4d66f684c409a9a81212b90ee93ac7ebc634bd76b1838e8cb0c"},"schema_version":"1.0","source":{"id":"1809.04448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04448","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04448v1","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04448","created_at":"2026-05-18T00:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"2V2YJBD4JGCL","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2V2YJBD4JGCLTA57","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2V2YJBD4","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:fd54dfb835bd5eecea8c38768814b606b712e7c0197fb83e39071c010042bdf4","target":"graph","created_at":"2026-05-18T00:05:52Z","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":"This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new result of the author with F. Bergeron and V. Reiner that gives the probability that a homogeneous symmetric polynomial with positive coefficients is Schur positive.","authors_text":"Rebecca Patrias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-12T13:53:53Z","title":"What is Schur positivity and how common is it?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04448","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:e0254e8472c5ee3663a1d8a5d50edf1d8991a7de5cdbd046690250de4b31f107","target":"record","created_at":"2026-05-18T00:05:52Z","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":"255e135e1556c33dc0f2c740b50eb7bee6b650f92394fdd6387d4e00999ab938","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-12T13:53:53Z","title_canon_sha256":"1f8b047847fca4d66f684c409a9a81212b90ee93ac7ebc634bd76b1838e8cb0c"},"schema_version":"1.0","source":{"id":"1809.04448","kind":"arxiv","version":1}},"canonical_sha256":"d57584847c4984b983bf5fe6153527451a181526f74b46c81511634a9601bd23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d57584847c4984b983bf5fe6153527451a181526f74b46c81511634a9601bd23","first_computed_at":"2026-05-18T00:05:52.359232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:52.359232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"edc1W0nBDk4+sky++natfK2AKzHskj3OWO1zluBq8z4UNbjEBvw1HkISU/kFMl5BTR90lxUG5bz+fdlsPadrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:52.360033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0254e8472c5ee3663a1d8a5d50edf1d8991a7de5cdbd046690250de4b31f107","sha256:fd54dfb835bd5eecea8c38768814b606b712e7c0197fb83e39071c010042bdf4"],"state_sha256":"6a3ee39670e4eef03df14dedd36a2dcd0546ac3f8cb3ec6b7fa1a4390299157d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h6kz42LaDftpkZ7nuW4Bs/udMtrIFCwpTm13faLtmPeF3JAayx65sVDrQPg1JX+ch/+QzBrffOfs4UFFqsHVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:47:57.377676Z","bundle_sha256":"a5661bb1368c9a4857b1301b076904b0f3e2462145b4b9569daff13a2f8cfa25"}}