{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LUMLIHXWJIOYTCIS7FHIKRYZ6G","short_pith_number":"pith:LUMLIHXW","canonical_record":{"source":{"id":"1412.4496","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-15T08:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"b8d2709319faef7924cd35b7b58470757875323df4a3985a4d3f345a2cba67ab","abstract_canon_sha256":"b9a2f6b2a1f5ce7ff0fbfcc71569c747fe5e8ace3ed1a7e9a5d979bb9826011b"},"schema_version":"1.0"},"canonical_sha256":"5d18b41ef64a1d898912f94e854719f1965ba9438a6d01d0a9358dea4c3e5bdf","source":{"kind":"arxiv","id":"1412.4496","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4496","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4496v4","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4496","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"LUMLIHXWJIOY","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LUMLIHXWJIOYTCIS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LUMLIHXW","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LUMLIHXWJIOYTCIS7FHIKRYZ6G","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4496","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-15T08:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"b8d2709319faef7924cd35b7b58470757875323df4a3985a4d3f345a2cba67ab","abstract_canon_sha256":"b9a2f6b2a1f5ce7ff0fbfcc71569c747fe5e8ace3ed1a7e9a5d979bb9826011b"},"schema_version":"1.0"},"canonical_sha256":"5d18b41ef64a1d898912f94e854719f1965ba9438a6d01d0a9358dea4c3e5bdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:08.750284Z","signature_b64":"aVKIXUSEKVqrefOS3eqtu5ZvRR5KhWlYYdp87gYn3W+uCgFKUJjyR71ZHbx5vVeJRl/N0Vpy5yx0MVTE14NSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d18b41ef64a1d898912f94e854719f1965ba9438a6d01d0a9358dea4c3e5bdf","last_reissued_at":"2026-05-18T00:49:08.749712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:08.749712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4496","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":"2026-05-18T00:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Lp8TcYLnmRAzpnywCbVDDifTNHaYVKKQyRCE5XhWR+lWSkD6Te2ueHEyv0y7BUVdtNY+WZSGLoeNfqMvLgOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:51:16.215730Z"},"content_sha256":"93360ec5cc0cc2287bc81669063819184e012de84381c5170ec267c33952b916","schema_version":"1.0","event_id":"sha256:93360ec5cc0cc2287bc81669063819184e012de84381c5170ec267c33952b916"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LUMLIHXWJIOYTCIS7FHIKRYZ6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Polymatroids satisfying a stronger symmetric exchange property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dancheng Lu","submitted_at":"2014-12-15T08:43:53Z","abstract_excerpt":"In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid satisfies the one-sided strong exchange property, this result provides an alternative proof for one of the main theorems of J. Schweig in \\cite{Sc}, where it is shown that every pruned lattice path polymatroid satisfies White's conjecture. In addition, for two classes of pruned lattice path polymatroidal ideals $I$ and their powers we d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4496","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":"2026-05-18T00:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QDwVFCmXii9T3jLrMUIGMe4lEKFvROBP6jpY/BKuIU+vvnEqFsYFwT79AGHL19B72TnNmL10cc8gKIBcSd6jDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:51:16.216133Z"},"content_sha256":"724ff634859f047827cbc586836c4377dbebd9ba0b3a0617ef90f3586b794c41","schema_version":"1.0","event_id":"sha256:724ff634859f047827cbc586836c4377dbebd9ba0b3a0617ef90f3586b794c41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/bundle.json","state_url":"https://pith.science/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/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":"2026-06-05T03:51:16Z","links":{"resolver":"https://pith.science/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G","bundle":"https://pith.science/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/bundle.json","state":"https://pith.science/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUMLIHXWJIOYTCIS7FHIKRYZ6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LUMLIHXWJIOYTCIS7FHIKRYZ6G","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":"b9a2f6b2a1f5ce7ff0fbfcc71569c747fe5e8ace3ed1a7e9a5d979bb9826011b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-15T08:43:53Z","title_canon_sha256":"b8d2709319faef7924cd35b7b58470757875323df4a3985a4d3f345a2cba67ab"},"schema_version":"1.0","source":{"id":"1412.4496","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4496","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4496v4","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4496","created_at":"2026-05-18T00:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"LUMLIHXWJIOY","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LUMLIHXWJIOYTCIS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LUMLIHXW","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:724ff634859f047827cbc586836c4377dbebd9ba0b3a0617ef90f3586b794c41","target":"graph","created_at":"2026-05-18T00:49:08Z","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 introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid satisfies the one-sided strong exchange property, this result provides an alternative proof for one of the main theorems of J. Schweig in \\cite{Sc}, where it is shown that every pruned lattice path polymatroid satisfies White's conjecture. In addition, for two classes of pruned lattice path polymatroidal ideals $I$ and their powers we d","authors_text":"Dancheng Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-15T08:43:53Z","title":"Discrete Polymatroids satisfying a stronger symmetric exchange property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4496","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":"sha256:93360ec5cc0cc2287bc81669063819184e012de84381c5170ec267c33952b916","target":"record","created_at":"2026-05-18T00:49:08Z","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":"b9a2f6b2a1f5ce7ff0fbfcc71569c747fe5e8ace3ed1a7e9a5d979bb9826011b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-15T08:43:53Z","title_canon_sha256":"b8d2709319faef7924cd35b7b58470757875323df4a3985a4d3f345a2cba67ab"},"schema_version":"1.0","source":{"id":"1412.4496","kind":"arxiv","version":4}},"canonical_sha256":"5d18b41ef64a1d898912f94e854719f1965ba9438a6d01d0a9358dea4c3e5bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d18b41ef64a1d898912f94e854719f1965ba9438a6d01d0a9358dea4c3e5bdf","first_computed_at":"2026-05-18T00:49:08.749712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:08.749712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aVKIXUSEKVqrefOS3eqtu5ZvRR5KhWlYYdp87gYn3W+uCgFKUJjyR71ZHbx5vVeJRl/N0Vpy5yx0MVTE14NSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:08.750284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4496","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93360ec5cc0cc2287bc81669063819184e012de84381c5170ec267c33952b916","sha256:724ff634859f047827cbc586836c4377dbebd9ba0b3a0617ef90f3586b794c41"],"state_sha256":"fabcdc0e490cdce1d197b5ad031733368434a84f7b72662bdb6eabfe601a3d6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f+KCSuvpFpA5Kd+8jGdwo55saF2hh0FQ0KfvR3HgWetShEMMYNdws9ktyQBL2GC/AeTHwYGY7yPfdxtAYO4gCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:51:16.218788Z","bundle_sha256":"837551c6ebc892fb5ec264970521338c1d23fc18b5e3e02c8b8ea2ca0556a761"}}