{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KCVC5QB23OQXXU6IE7QY4O3LST","short_pith_number":"pith:KCVC5QB2","canonical_record":{"source":{"id":"1009.4690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T19:41:03Z","cross_cats_sorted":[],"title_canon_sha256":"f5fb308d492ed902e68aa288c4595485f11815cd6a42e5a0f168ec47909b186b","abstract_canon_sha256":"f65fb8a87adaf9cc690203a8e71b21124912588b79549b6204a9d1869815864f"},"schema_version":"1.0"},"canonical_sha256":"50aa2ec03adba17bd3c827e18e3b6b94e0e909b1e7c40b97a0589163149f0f40","source":{"kind":"arxiv","id":"1009.4690","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4690","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4690v3","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4690","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"KCVC5QB23OQX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KCVC5QB23OQXXU6I","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KCVC5QB2","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KCVC5QB23OQXXU6IE7QY4O3LST","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T19:41:03Z","cross_cats_sorted":[],"title_canon_sha256":"f5fb308d492ed902e68aa288c4595485f11815cd6a42e5a0f168ec47909b186b","abstract_canon_sha256":"f65fb8a87adaf9cc690203a8e71b21124912588b79549b6204a9d1869815864f"},"schema_version":"1.0"},"canonical_sha256":"50aa2ec03adba17bd3c827e18e3b6b94e0e909b1e7c40b97a0589163149f0f40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:46.190800Z","signature_b64":"xEj5wWfRflLI4uHjcw2hgz1dYg0zc22PMypQFegmhzoFcgHkKjGhtL8bL8hlatH2OmwcXMEEwuj7dXyJCy0rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50aa2ec03adba17bd3c827e18e3b6b94e0e909b1e7c40b97a0589163149f0f40","last_reissued_at":"2026-05-18T04:18:46.190392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:46.190392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4690","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3H5UoaZ9Sw0q5VDl+LdF5206WQxOX1jmDjTehTF2XBiLxLqvMuSmdewroaNRq6dT1xFDqRCs+sU5JmPindSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:00:10.843499Z"},"content_sha256":"6c23acd7265b9b9eff5f14ecc7183417b991054a7cf6f6f9e8af28670267f8bf","schema_version":"1.0","event_id":"sha256:6c23acd7265b9b9eff5f14ecc7183417b991054a7cf6f6f9e8af28670267f8bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KCVC5QB23OQXXU6IE7QY4O3LST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Stump, Luis Serrano","submitted_at":"2010-09-23T19:41:03Z","abstract_excerpt":"We exhibit a canonical connection between maximal (0,1)-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable, and thus shellable, sphere. In particular, this implies a positivity result for Schubert polynomials. For Ferrers shapes, we moreover construct a bijection to maximal fillings avoiding south-east chains of the same length which specializes to a bijection between k-triangulations of the n-gon and k-fans of Dy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4690","kind":"arxiv","version":3},"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":"2026-05-18T04:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9eEXL+QZKgV2/xvU/0HQrL+VUPjX0zHF6ktb8EnrIzis80wxoFJ1vSJKozKHqrSb4mzlq7Y8D3I0jh3BABe9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:00:10.843836Z"},"content_sha256":"a323c6a1961d2ecf6df1358a1cff743ce2652cc91a1c81e11ff5145c1a32258d","schema_version":"1.0","event_id":"sha256:a323c6a1961d2ecf6df1358a1cff743ce2652cc91a1c81e11ff5145c1a32258d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCVC5QB23OQXXU6IE7QY4O3LST/bundle.json","state_url":"https://pith.science/pith/KCVC5QB23OQXXU6IE7QY4O3LST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCVC5QB23OQXXU6IE7QY4O3LST/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":"2026-07-07T10:00:10Z","links":{"resolver":"https://pith.science/pith/KCVC5QB23OQXXU6IE7QY4O3LST","bundle":"https://pith.science/pith/KCVC5QB23OQXXU6IE7QY4O3LST/bundle.json","state":"https://pith.science/pith/KCVC5QB23OQXXU6IE7QY4O3LST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCVC5QB23OQXXU6IE7QY4O3LST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KCVC5QB23OQXXU6IE7QY4O3LST","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":"f65fb8a87adaf9cc690203a8e71b21124912588b79549b6204a9d1869815864f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T19:41:03Z","title_canon_sha256":"f5fb308d492ed902e68aa288c4595485f11815cd6a42e5a0f168ec47909b186b"},"schema_version":"1.0","source":{"id":"1009.4690","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4690","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4690v3","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4690","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"KCVC5QB23OQX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KCVC5QB23OQXXU6I","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KCVC5QB2","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a323c6a1961d2ecf6df1358a1cff743ce2652cc91a1c81e11ff5145c1a32258d","target":"graph","created_at":"2026-05-18T04:18:46Z","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":"We exhibit a canonical connection between maximal (0,1)-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable, and thus shellable, sphere. In particular, this implies a positivity result for Schubert polynomials. For Ferrers shapes, we moreover construct a bijection to maximal fillings avoiding south-east chains of the same length which specializes to a bijection between k-triangulations of the n-gon and k-fans of Dy","authors_text":"Christian Stump, Luis Serrano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T19:41:03Z","title":"Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4690","kind":"arxiv","version":3},"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":"sha256:6c23acd7265b9b9eff5f14ecc7183417b991054a7cf6f6f9e8af28670267f8bf","target":"record","created_at":"2026-05-18T04:18:46Z","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":"f65fb8a87adaf9cc690203a8e71b21124912588b79549b6204a9d1869815864f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T19:41:03Z","title_canon_sha256":"f5fb308d492ed902e68aa288c4595485f11815cd6a42e5a0f168ec47909b186b"},"schema_version":"1.0","source":{"id":"1009.4690","kind":"arxiv","version":3}},"canonical_sha256":"50aa2ec03adba17bd3c827e18e3b6b94e0e909b1e7c40b97a0589163149f0f40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50aa2ec03adba17bd3c827e18e3b6b94e0e909b1e7c40b97a0589163149f0f40","first_computed_at":"2026-05-18T04:18:46.190392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:46.190392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEj5wWfRflLI4uHjcw2hgz1dYg0zc22PMypQFegmhzoFcgHkKjGhtL8bL8hlatH2OmwcXMEEwuj7dXyJCy0rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:46.190800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4690","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c23acd7265b9b9eff5f14ecc7183417b991054a7cf6f6f9e8af28670267f8bf","sha256:a323c6a1961d2ecf6df1358a1cff743ce2652cc91a1c81e11ff5145c1a32258d"],"state_sha256":"2cced420ec217fd462ade777ea94da2f39cd22370701bdba8c1d3fb5748b3f83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JAiJIcqUnMdCiISuMIxk3Wp0d2gMrKm2WRmI84PLIJ0dAWHjScklwq+wSqix3xHo+qXpyAHTQlAeskiPx5nNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:00:10.845685Z","bundle_sha256":"619fd9c17d8fd1e30fb4e368dac2050f6edcc322c88b9bc5e5efe9b0549cb249"}}