{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HTLVGHJ2ZYY3KQAL5PR34GWCGB","short_pith_number":"pith:HTLVGHJ2","canonical_record":{"source":{"id":"2506.20792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-25T19:31:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1f1fecec55902dfa40af48d13caa70712823cf5512e57982b780b221f957c727","abstract_canon_sha256":"49bf12ce4e51a5a90543343f09228a4919e59e20f1f7f1443fe3a05fa21637f7"},"schema_version":"1.0"},"canonical_sha256":"3cd7531d3ace31b5400bebe3be1ac23045ab7dd1098f6230b517aae111b55dab","source":{"kind":"arxiv","id":"2506.20792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.20792","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.20792v1","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20792","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"HTLVGHJ2ZYY3","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"HTLVGHJ2ZYY3KQAL","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"HTLVGHJ2","created_at":"2026-07-05T11:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HTLVGHJ2ZYY3KQAL5PR34GWCGB","target":"record","payload":{"canonical_record":{"source":{"id":"2506.20792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-25T19:31:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1f1fecec55902dfa40af48d13caa70712823cf5512e57982b780b221f957c727","abstract_canon_sha256":"49bf12ce4e51a5a90543343f09228a4919e59e20f1f7f1443fe3a05fa21637f7"},"schema_version":"1.0"},"canonical_sha256":"3cd7531d3ace31b5400bebe3be1ac23045ab7dd1098f6230b517aae111b55dab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:34.119821Z","signature_b64":"E4l2pQV9Iw763HLelux/fYe8pUQTGhPG4skOzaazC6wx/hzsRlXLD5zo+TUIqjqLs43Xmemq0kULb9eKxkEdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cd7531d3ace31b5400bebe3be1ac23045ab7dd1098f6230b517aae111b55dab","last_reissued_at":"2026-07-05T11:27:34.119349Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:34.119349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.20792","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":"2026-07-05T11:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yx+FYk5MtBVdOJRbVTqJYQzKCaK6f4ZpwyRBlLCjnT4J3l56+aBglW6jUJcntfruPCBC6kZ58xhHpu7e/y2dDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:20:47.192087Z"},"content_sha256":"c1fe2af790ebaa4b96be8399caeb5cd5a448036601c90c26691df2ee91ed10d0","schema_version":"1.0","event_id":"sha256:c1fe2af790ebaa4b96be8399caeb5cd5a448036601c90c26691df2ee91ed10d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HTLVGHJ2ZYY3KQAL5PR34GWCGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Richardson tableaux and components of Springer fibers equal to Richardson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Martha E. Precup, Steven N. Karp","submitted_at":"2025-06-25T19:31:57Z","abstract_excerpt":"Motivated by the study of Springer fibers and their totally nonnegative counterparts, we define a new subset of standard tableaux called Richardson tableaux. We characterize Richardson tableaux combinatorially using evacuation as well as in terms of a pair of associated reading words. We also characterize Richardson tableaux geometrically, proving that a tableau is Richardson if and only if the corresponding component of a Springer fiber is a Richardson variety, which in turn holds if and only if its positive part is a top-dimensional cell of the totally nonnegative Springer fiber studied by L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20792","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.20792/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:27:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/tM+VhUEsLsxxbtEHzdsBxwAVn0ejJVM6ifW/GCBvsOr+5xb2/hm6uH1RzUUqN3Cz7Y0MqQXnjXkqirrOgNuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:20:47.192589Z"},"content_sha256":"f708c3762d6d4afc7989cba423bb99d185c82408270c93b17a9fed7c30e0449e","schema_version":"1.0","event_id":"sha256:f708c3762d6d4afc7989cba423bb99d185c82408270c93b17a9fed7c30e0449e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/bundle.json","state_url":"https://pith.science/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/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":"2026-08-09T03:20:47Z","links":{"resolver":"https://pith.science/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB","bundle":"https://pith.science/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/bundle.json","state":"https://pith.science/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTLVGHJ2ZYY3KQAL5PR34GWCGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HTLVGHJ2ZYY3KQAL5PR34GWCGB","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":"49bf12ce4e51a5a90543343f09228a4919e59e20f1f7f1443fe3a05fa21637f7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-25T19:31:57Z","title_canon_sha256":"1f1fecec55902dfa40af48d13caa70712823cf5512e57982b780b221f957c727"},"schema_version":"1.0","source":{"id":"2506.20792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.20792","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.20792v1","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20792","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"HTLVGHJ2ZYY3","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"HTLVGHJ2ZYY3KQAL","created_at":"2026-07-05T11:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"HTLVGHJ2","created_at":"2026-07-05T11:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:f708c3762d6d4afc7989cba423bb99d185c82408270c93b17a9fed7c30e0449e","target":"graph","created_at":"2026-07-05T11:27:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.20792/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the study of Springer fibers and their totally nonnegative counterparts, we define a new subset of standard tableaux called Richardson tableaux. We characterize Richardson tableaux combinatorially using evacuation as well as in terms of a pair of associated reading words. We also characterize Richardson tableaux geometrically, proving that a tableau is Richardson if and only if the corresponding component of a Springer fiber is a Richardson variety, which in turn holds if and only if its positive part is a top-dimensional cell of the totally nonnegative Springer fiber studied by L","authors_text":"Martha E. Precup, Steven N. Karp","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-25T19:31:57Z","title":"Richardson tableaux and components of Springer fibers equal to Richardson varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20792","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:c1fe2af790ebaa4b96be8399caeb5cd5a448036601c90c26691df2ee91ed10d0","target":"record","created_at":"2026-07-05T11:27:34Z","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":"49bf12ce4e51a5a90543343f09228a4919e59e20f1f7f1443fe3a05fa21637f7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-25T19:31:57Z","title_canon_sha256":"1f1fecec55902dfa40af48d13caa70712823cf5512e57982b780b221f957c727"},"schema_version":"1.0","source":{"id":"2506.20792","kind":"arxiv","version":1}},"canonical_sha256":"3cd7531d3ace31b5400bebe3be1ac23045ab7dd1098f6230b517aae111b55dab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cd7531d3ace31b5400bebe3be1ac23045ab7dd1098f6230b517aae111b55dab","first_computed_at":"2026-07-05T11:27:34.119349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:34.119349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4l2pQV9Iw763HLelux/fYe8pUQTGhPG4skOzaazC6wx/hzsRlXLD5zo+TUIqjqLs43Xmemq0kULb9eKxkEdAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:34.119821Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.20792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1fe2af790ebaa4b96be8399caeb5cd5a448036601c90c26691df2ee91ed10d0","sha256:f708c3762d6d4afc7989cba423bb99d185c82408270c93b17a9fed7c30e0449e"],"state_sha256":"9509176a59af784870a644f2edb443f477bc5627ee90ccd0476e5e686e20012a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+GOneJtvYbFtDsHeF+cKDPe+dALbdkq66H62w2eJEidiIdSTTzjndc2HefkCH9xiYS+AXYhEU6Cou1IrSGjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:20:47.197501Z","bundle_sha256":"b448551c2104faa83b8a3c1893cade14dfe1cf852f00fc0795c4cf758edd141e"}}