{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IBQCV5BHN2GR72PNETUFMWSD5T","short_pith_number":"pith:IBQCV5BH","canonical_record":{"source":{"id":"1405.5587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-22T01:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"cfa482244c535393e70a5aaa11ea880e28ea13a07d0a611a9967ffad3e47a084","abstract_canon_sha256":"e403b1453ac87ac07edd1baee326e8298ccf4d26e4d89095175e6d6cbda6636a"},"schema_version":"1.0"},"canonical_sha256":"40602af4276e8d1fe9ed24e8565a43ece57210fc8565150a2c009076c9336ebd","source":{"kind":"arxiv","id":"1405.5587","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5587","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5587v2","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5587","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"IBQCV5BHN2GR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IBQCV5BHN2GR72PN","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IBQCV5BH","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IBQCV5BHN2GR72PNETUFMWSD5T","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-22T01:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"cfa482244c535393e70a5aaa11ea880e28ea13a07d0a611a9967ffad3e47a084","abstract_canon_sha256":"e403b1453ac87ac07edd1baee326e8298ccf4d26e4d89095175e6d6cbda6636a"},"schema_version":"1.0"},"canonical_sha256":"40602af4276e8d1fe9ed24e8565a43ece57210fc8565150a2c009076c9336ebd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:24.031847Z","signature_b64":"gVlbdRlkMSmyS7xYmLCK038qqiphAIaY7DDpP5OJdE76/RC79ofxtFF7KY74yqD81uZ1qp6qycC2tSl3EeZeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40602af4276e8d1fe9ed24e8565a43ece57210fc8565150a2c009076c9336ebd","last_reissued_at":"2026-05-18T01:15:24.031123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:24.031123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5587","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":"2026-05-18T01:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X5WH4vRZNWiJ4R28r3WffBCV8Tu/OXnVI49a4wmUfkTiINaBfNZPpoIWwhBtl8i0OrbaiyXqXEc2KbTSI3/fBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:22:23.643517Z"},"content_sha256":"18a4008efc62f49ad3ad60467c1093148ada006f381185eaa79d356535db8f9a","schema_version":"1.0","event_id":"sha256:18a4008efc62f49ad3ad60467c1093148ada006f381185eaa79d356535db8f9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IBQCV5BHN2GR72PNETUFMWSD5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parking functions, Shi arrangements, and mixed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Ruiz, Ana Berrizbeitia, Claudia Rodriguez, Matthias Beck, Michael Dairyko, Schuyler Veeneman","submitted_at":"2014-05-22T01:22:01Z","abstract_excerpt":"The \\emph{Shi arrangement} is the set of all hyperplanes in $\\mathbb R^n$ of the form $x_j - x_k = 0$ or $1$ for $1 \\le j < k \\le n$. Shi observed in 1986 that the number of regions (i.e., connected components of the complement) of this arrangement is $(n+1)^{n-1}$. An unrelated combinatorial concept is that of a \\emph{parking function}, i.e., a sequence $(x_1, x_2, ..., x_n)$ of positive integers that, when rearranged from smallest to largest, satisfies $x_k \\le k$. (There is an illustrative reason for the term \\emph{parking function}.) It turns out that the number of parking functions of len"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5587","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":"2026-05-18T01:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Om2/YwQT0KyKWC63mDM5JCksGRvR2i5cJbfXmvN/qEMX9HD+ZUCDxpdiQ1nsFG1yftKCLQPKlFzlBSFl7mRdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:22:23.643862Z"},"content_sha256":"adb12050dd50a1dad35246fbdfccdc4aa98c94dab53da6afd8fa9e2e38b761c7","schema_version":"1.0","event_id":"sha256:adb12050dd50a1dad35246fbdfccdc4aa98c94dab53da6afd8fa9e2e38b761c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBQCV5BHN2GR72PNETUFMWSD5T/bundle.json","state_url":"https://pith.science/pith/IBQCV5BHN2GR72PNETUFMWSD5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBQCV5BHN2GR72PNETUFMWSD5T/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":"2026-06-03T07:22:23Z","links":{"resolver":"https://pith.science/pith/IBQCV5BHN2GR72PNETUFMWSD5T","bundle":"https://pith.science/pith/IBQCV5BHN2GR72PNETUFMWSD5T/bundle.json","state":"https://pith.science/pith/IBQCV5BHN2GR72PNETUFMWSD5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBQCV5BHN2GR72PNETUFMWSD5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IBQCV5BHN2GR72PNETUFMWSD5T","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":"e403b1453ac87ac07edd1baee326e8298ccf4d26e4d89095175e6d6cbda6636a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-22T01:22:01Z","title_canon_sha256":"cfa482244c535393e70a5aaa11ea880e28ea13a07d0a611a9967ffad3e47a084"},"schema_version":"1.0","source":{"id":"1405.5587","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5587","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5587v2","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5587","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"IBQCV5BHN2GR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IBQCV5BHN2GR72PN","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IBQCV5BH","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:adb12050dd50a1dad35246fbdfccdc4aa98c94dab53da6afd8fa9e2e38b761c7","target":"graph","created_at":"2026-05-18T01:15:24Z","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":"The \\emph{Shi arrangement} is the set of all hyperplanes in $\\mathbb R^n$ of the form $x_j - x_k = 0$ or $1$ for $1 \\le j < k \\le n$. Shi observed in 1986 that the number of regions (i.e., connected components of the complement) of this arrangement is $(n+1)^{n-1}$. An unrelated combinatorial concept is that of a \\emph{parking function}, i.e., a sequence $(x_1, x_2, ..., x_n)$ of positive integers that, when rearranged from smallest to largest, satisfies $x_k \\le k$. (There is an illustrative reason for the term \\emph{parking function}.) It turns out that the number of parking functions of len","authors_text":"Amanda Ruiz, Ana Berrizbeitia, Claudia Rodriguez, Matthias Beck, Michael Dairyko, Schuyler Veeneman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-22T01:22:01Z","title":"Parking functions, Shi arrangements, and mixed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5587","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":"sha256:18a4008efc62f49ad3ad60467c1093148ada006f381185eaa79d356535db8f9a","target":"record","created_at":"2026-05-18T01:15:24Z","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":"e403b1453ac87ac07edd1baee326e8298ccf4d26e4d89095175e6d6cbda6636a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-22T01:22:01Z","title_canon_sha256":"cfa482244c535393e70a5aaa11ea880e28ea13a07d0a611a9967ffad3e47a084"},"schema_version":"1.0","source":{"id":"1405.5587","kind":"arxiv","version":2}},"canonical_sha256":"40602af4276e8d1fe9ed24e8565a43ece57210fc8565150a2c009076c9336ebd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40602af4276e8d1fe9ed24e8565a43ece57210fc8565150a2c009076c9336ebd","first_computed_at":"2026-05-18T01:15:24.031123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:24.031123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVlbdRlkMSmyS7xYmLCK038qqiphAIaY7DDpP5OJdE76/RC79ofxtFF7KY74yqD81uZ1qp6qycC2tSl3EeZeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:24.031847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5587","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18a4008efc62f49ad3ad60467c1093148ada006f381185eaa79d356535db8f9a","sha256:adb12050dd50a1dad35246fbdfccdc4aa98c94dab53da6afd8fa9e2e38b761c7"],"state_sha256":"178863d29bac1b307b93c1111122672eda92bf5c5669a01f4579328ee6f8c28d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbGraBTM4DyIxXgGnZ72KWhvixYhjpt+ykvm3fbMP0yiEio87yf8HOsKgybY+n9nI3rVrA83oBddpTjLpyuPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:22:23.646807Z","bundle_sha256":"481df930c09b784fe994e369f345062dd1861fef20f983d169acb2a230f56f0b"}}