{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:X54O7MVLZCLJFIGAY6N4OHLJUG","short_pith_number":"pith:X54O7MVL","canonical_record":{"source":{"id":"1805.04341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-11T11:49:19Z","cross_cats_sorted":[],"title_canon_sha256":"7e99cacaa85a150c64104e520a1841ad545f7a31a0f38f9d46ca85cda07ae9ec","abstract_canon_sha256":"b8b96a260780152a54af45561f1a72697074ac833310aa3f1ea6e262601a590e"},"schema_version":"1.0"},"canonical_sha256":"bf78efb2abc89692a0c0c79bc71d69a1933524c92a343d7f10c1654fb54a210c","source":{"kind":"arxiv","id":"1805.04341","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04341","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04341v1","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04341","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"X54O7MVLZCLJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X54O7MVLZCLJFIGA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X54O7MVL","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:X54O7MVLZCLJFIGAY6N4OHLJUG","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-11T11:49:19Z","cross_cats_sorted":[],"title_canon_sha256":"7e99cacaa85a150c64104e520a1841ad545f7a31a0f38f9d46ca85cda07ae9ec","abstract_canon_sha256":"b8b96a260780152a54af45561f1a72697074ac833310aa3f1ea6e262601a590e"},"schema_version":"1.0"},"canonical_sha256":"bf78efb2abc89692a0c0c79bc71d69a1933524c92a343d7f10c1654fb54a210c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:12.771532Z","signature_b64":"I1QL24I3EwJv64O2SYZ07lUM8HKfSY/h2iqrruQnlB9aOZIwrhCFJ7MCjzH+HgEC+F09IkQPABA+tekdl5kpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf78efb2abc89692a0c0c79bc71d69a1933524c92a343d7f10c1654fb54a210c","last_reissued_at":"2026-05-18T00:16:12.770627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:12.770627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04341","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":"2026-05-18T00:16:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YSMXFn1qwwJQhzN0SiWhJqhbBlP61vKPG3exuAzu+53acYb7giGuksJsiDypLml+YjuwFP998ckDKZ12RuKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:21.509771Z"},"content_sha256":"a13153c51ead07ff5d40011d4dfe022bf82e3a3c0d1e4b0be03a3aaa0bdc8feb","schema_version":"1.0","event_id":"sha256:a13153c51ead07ff5d40011d4dfe022bf82e3a3c0d1e4b0be03a3aaa0bdc8feb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:X54O7MVLZCLJFIGAY6N4OHLJUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of principal evaluations of Schubert polynomials for layered permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro H. Morales, Greta Panova, Igor Pak","submitted_at":"2018-05-11T11:49:19Z","abstract_excerpt":"Denote by $u(n)$ the largest principal specialization of the Schubert polynomial: $\nu(n) := \\max_{w \\in S_n} \\mathfrak{S}_w(1,\\ldots,1) $ Stanley conjectured in [arXiv:1704.00851] that there is a limit $\\lim_{n\\to \\infty} \\, \\frac{1}{n^2} \\log u(n), $ and asked for a limiting description of permutations achieving the maximum $u(n)$. Merzon and Smirnov conjectured in [arXiv:1410.6857] that this maximum is achieved on layered permutations. We resolve both Stanley's problems restricted to layered permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04341","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":"2026-05-18T00:16:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLEzfsd5d4hsOMInQllweFe5mBR5nMP3ckf1DtGxw/v+OmMcjHGArNYzZ1oVL1gRCsNFqOi2y/Sz+Qt7jAwCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:21.510463Z"},"content_sha256":"750449c45c4e3edc5a087e8bfce2b01c50bca9355b7a0dfdb460e76825e18cc1","schema_version":"1.0","event_id":"sha256:750449c45c4e3edc5a087e8bfce2b01c50bca9355b7a0dfdb460e76825e18cc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/bundle.json","state_url":"https://pith.science/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/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":"2026-05-30T22:11:21Z","links":{"resolver":"https://pith.science/pith/X54O7MVLZCLJFIGAY6N4OHLJUG","bundle":"https://pith.science/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/bundle.json","state":"https://pith.science/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X54O7MVLZCLJFIGAY6N4OHLJUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X54O7MVLZCLJFIGAY6N4OHLJUG","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":"b8b96a260780152a54af45561f1a72697074ac833310aa3f1ea6e262601a590e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-11T11:49:19Z","title_canon_sha256":"7e99cacaa85a150c64104e520a1841ad545f7a31a0f38f9d46ca85cda07ae9ec"},"schema_version":"1.0","source":{"id":"1805.04341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04341","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04341v1","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04341","created_at":"2026-05-18T00:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"X54O7MVLZCLJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X54O7MVLZCLJFIGA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X54O7MVL","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:750449c45c4e3edc5a087e8bfce2b01c50bca9355b7a0dfdb460e76825e18cc1","target":"graph","created_at":"2026-05-18T00:16:12Z","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":"Denote by $u(n)$ the largest principal specialization of the Schubert polynomial: $\nu(n) := \\max_{w \\in S_n} \\mathfrak{S}_w(1,\\ldots,1) $ Stanley conjectured in [arXiv:1704.00851] that there is a limit $\\lim_{n\\to \\infty} \\, \\frac{1}{n^2} \\log u(n), $ and asked for a limiting description of permutations achieving the maximum $u(n)$. Merzon and Smirnov conjectured in [arXiv:1410.6857] that this maximum is achieved on layered permutations. We resolve both Stanley's problems restricted to layered permutations.","authors_text":"Alejandro H. Morales, Greta Panova, Igor Pak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-11T11:49:19Z","title":"Asymptotics of principal evaluations of Schubert polynomials for layered permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04341","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:a13153c51ead07ff5d40011d4dfe022bf82e3a3c0d1e4b0be03a3aaa0bdc8feb","target":"record","created_at":"2026-05-18T00:16:12Z","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":"b8b96a260780152a54af45561f1a72697074ac833310aa3f1ea6e262601a590e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-11T11:49:19Z","title_canon_sha256":"7e99cacaa85a150c64104e520a1841ad545f7a31a0f38f9d46ca85cda07ae9ec"},"schema_version":"1.0","source":{"id":"1805.04341","kind":"arxiv","version":1}},"canonical_sha256":"bf78efb2abc89692a0c0c79bc71d69a1933524c92a343d7f10c1654fb54a210c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf78efb2abc89692a0c0c79bc71d69a1933524c92a343d7f10c1654fb54a210c","first_computed_at":"2026-05-18T00:16:12.770627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:12.770627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I1QL24I3EwJv64O2SYZ07lUM8HKfSY/h2iqrruQnlB9aOZIwrhCFJ7MCjzH+HgEC+F09IkQPABA+tekdl5kpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:12.771532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a13153c51ead07ff5d40011d4dfe022bf82e3a3c0d1e4b0be03a3aaa0bdc8feb","sha256:750449c45c4e3edc5a087e8bfce2b01c50bca9355b7a0dfdb460e76825e18cc1"],"state_sha256":"74659bfed9ec908907557fb605ddf9137c3fc77fa773fe0848b4cfa523a2e437"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCl9+C3HguTYEcgOMI7F4qw5v/mmHrexT3wnnMupnEoHRdEkprryf1EnizIArIynqXfF3M644j+unUDP4oL8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:11:21.514219Z","bundle_sha256":"584d9ed9ffeabaa545ae077703028c48ce8d4d6a3be2dcd7193eca8750408cda"}}