{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:46O6TP7NUIVAGHRIZJXZZVTBIU","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":"7b806830b459a4a8db30da4c71d5da3fa328ef3107a49b3d8a29f2e2ebe0bf22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-13T22:15:34Z","title_canon_sha256":"adb728bd7b4b34fb51cc036a78511c2c276b7905a74739d971e1b1253fcbfdc0"},"schema_version":"1.0","source":{"id":"1704.04288","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.04288","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1704.04288v3","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04288","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"46O6TP7NUIVA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"46O6TP7NUIVAGHRI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"46O6TP7N","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:253fe26ddabf83bb1688965b68ebce15872f0dd9294f5c0acb2744f2355e6586","target":"graph","created_at":"2026-05-18T00:12:00Z","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 consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We define a permutation $\\pi$ to be $k$-pass sortable if $\\pi$ is sortable using $k$ passes through the stack. Permutations that are $1$-pass sortable are simply the stack sortable permutations as defined by Knuth. We define the permutation class of $2$-pass sortable permutations in terms of their basis. We also show all $k$-pass sortable classes have finite bases by giving bounds on the length of a basis el","authors_text":"Howard Skogman, Rebecca Smith, Toufik Mansour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-13T22:15:34Z","title":"Passing through a stack $k$ times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04288","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":"sha256:1f03ecedc1763f206aa6271564a0e43c0c58598ce93f046028b4dd0463b19387","target":"record","created_at":"2026-05-18T00:12:00Z","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":"7b806830b459a4a8db30da4c71d5da3fa328ef3107a49b3d8a29f2e2ebe0bf22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-13T22:15:34Z","title_canon_sha256":"adb728bd7b4b34fb51cc036a78511c2c276b7905a74739d971e1b1253fcbfdc0"},"schema_version":"1.0","source":{"id":"1704.04288","kind":"arxiv","version":3}},"canonical_sha256":"e79de9bfeda22a031e28ca6f9cd661452327caece8a0e7bce5429847aeb57041","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e79de9bfeda22a031e28ca6f9cd661452327caece8a0e7bce5429847aeb57041","first_computed_at":"2026-05-18T00:12:00.528863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:00.528863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"89vmeMDNP+BnJveCu8w2uRj/4pM8DTOXZZ7Q5dnIPNuxg889Pe/l8vtEqU4VmzkfmvuI1dC3aQZz3Mwf65s0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:00.529421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.04288","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f03ecedc1763f206aa6271564a0e43c0c58598ce93f046028b4dd0463b19387","sha256:253fe26ddabf83bb1688965b68ebce15872f0dd9294f5c0acb2744f2355e6586"],"state_sha256":"aa8602c69754c69526d03925ac67c51355b744ec4cf48f2b60604b9ee3487b5d"}