{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P7Z2Z7ELE577CNGERJOZIEWIHP","short_pith_number":"pith:P7Z2Z7EL","canonical_record":{"source":{"id":"1301.3188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-15T00:15:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"db9e2e0359dac481c7d0f7e2a4363305a203edbac3103cb573c053754cb20a15","abstract_canon_sha256":"a419273a23593b1d32d9e4251687c08b7e10fe9de3a3d9e3ab31b2e49c08b942"},"schema_version":"1.0"},"canonical_sha256":"7ff3acfc8b277ff134c48a5d9412c83bd9edf1c58ec960d1e456ef9761576fbc","source":{"kind":"arxiv","id":"1301.3188","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3188","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3188v2","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3188","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"P7Z2Z7ELE577","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7Z2Z7ELE577CNGE","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7Z2Z7EL","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P7Z2Z7ELE577CNGERJOZIEWIHP","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-15T00:15:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"db9e2e0359dac481c7d0f7e2a4363305a203edbac3103cb573c053754cb20a15","abstract_canon_sha256":"a419273a23593b1d32d9e4251687c08b7e10fe9de3a3d9e3ab31b2e49c08b942"},"schema_version":"1.0"},"canonical_sha256":"7ff3acfc8b277ff134c48a5d9412c83bd9edf1c58ec960d1e456ef9761576fbc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:59.624032Z","signature_b64":"GOCdQOXP7XNalHOq2ryOcYqVo5gTrz2y0GgMCPBHa92PEcoFCXnaRRSJ2S5W/AAHVQMOMQXv8ban9rx5eUPgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ff3acfc8b277ff134c48a5d9412c83bd9edf1c58ec960d1e456ef9761576fbc","last_reissued_at":"2026-05-18T03:04:59.623503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:59.623503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3188","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HguZKvCSEAXCxMkfKf8SG4OcVnsTmTLlo38dQaUbLgo5LbfFjkdynlkEQdu1ntcyenZR8p5nfAJfXAsmEMUBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:31:00.623460Z"},"content_sha256":"d59c1d0307e0687e1ac44359664fdf06caa8c3af82560138b8a9ecf17f0a18c3","schema_version":"1.0","event_id":"sha256:d59c1d0307e0687e1ac44359664fdf06caa8c3af82560138b8a9ecf17f0a18c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P7Z2Z7ELE577CNGERJOZIEWIHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumerating indices of Schubert varieties defined by inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Michael H. Albert, Robert Brignall","submitted_at":"2013-01-15T00:15:29Z","abstract_excerpt":"By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 35142, 42513, 351624), a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3188","kind":"arxiv","version":2},"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":"2026-05-18T03:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enVbT+0lcSSs/SXwyVivvSnc7KhghefePSkXA9nczlJorICrO8z7NlAJWbUQPijI8MTMa8KQ9DhhYW8JOQ2nDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:31:00.623814Z"},"content_sha256":"1f318af917ca5eb851dfb3d08695fffc24c78be89c8f91c75324726a80f925ca","schema_version":"1.0","event_id":"sha256:1f318af917ca5eb851dfb3d08695fffc24c78be89c8f91c75324726a80f925ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/bundle.json","state_url":"https://pith.science/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/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":"2026-06-12T09:31:00Z","links":{"resolver":"https://pith.science/pith/P7Z2Z7ELE577CNGERJOZIEWIHP","bundle":"https://pith.science/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/bundle.json","state":"https://pith.science/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7Z2Z7ELE577CNGERJOZIEWIHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P7Z2Z7ELE577CNGERJOZIEWIHP","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":"a419273a23593b1d32d9e4251687c08b7e10fe9de3a3d9e3ab31b2e49c08b942","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-15T00:15:29Z","title_canon_sha256":"db9e2e0359dac481c7d0f7e2a4363305a203edbac3103cb573c053754cb20a15"},"schema_version":"1.0","source":{"id":"1301.3188","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3188","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3188v2","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3188","created_at":"2026-05-18T03:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"P7Z2Z7ELE577","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7Z2Z7ELE577CNGE","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7Z2Z7EL","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1f318af917ca5eb851dfb3d08695fffc24c78be89c8f91c75324726a80f925ca","target":"graph","created_at":"2026-05-18T03:04:59Z","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":"By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 35142, 42513, 351624), a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class.","authors_text":"Michael H. Albert, Robert Brignall","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-15T00:15:29Z","title":"Enumerating indices of Schubert varieties defined by inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3188","kind":"arxiv","version":2},"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:d59c1d0307e0687e1ac44359664fdf06caa8c3af82560138b8a9ecf17f0a18c3","target":"record","created_at":"2026-05-18T03:04:59Z","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":"a419273a23593b1d32d9e4251687c08b7e10fe9de3a3d9e3ab31b2e49c08b942","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-15T00:15:29Z","title_canon_sha256":"db9e2e0359dac481c7d0f7e2a4363305a203edbac3103cb573c053754cb20a15"},"schema_version":"1.0","source":{"id":"1301.3188","kind":"arxiv","version":2}},"canonical_sha256":"7ff3acfc8b277ff134c48a5d9412c83bd9edf1c58ec960d1e456ef9761576fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff3acfc8b277ff134c48a5d9412c83bd9edf1c58ec960d1e456ef9761576fbc","first_computed_at":"2026-05-18T03:04:59.623503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:59.623503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GOCdQOXP7XNalHOq2ryOcYqVo5gTrz2y0GgMCPBHa92PEcoFCXnaRRSJ2S5W/AAHVQMOMQXv8ban9rx5eUPgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:59.624032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3188","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d59c1d0307e0687e1ac44359664fdf06caa8c3af82560138b8a9ecf17f0a18c3","sha256:1f318af917ca5eb851dfb3d08695fffc24c78be89c8f91c75324726a80f925ca"],"state_sha256":"2d72618e7e35a203385dc8195b9422953cd4001c9eb3d3e07f408aca627e04a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Pr/+EPmQo0yQcRObk5KnSVG49Mjga7fYmI0CJltxgKTX6o9fx06wqdJHUfMJVyDU4xTrk7+8ac80zwkLOJ6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:31:00.625833Z","bundle_sha256":"da2f545c28bacf802fae119bd45d135b5bac26857015629bceed53853e33b12d"}}