{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q4BOLLUFN6U5GOKO273AK6ZQHU","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":"d899463a4aa83c16fc1ee45a03368faff6ff60774c97c313a75ad17a30f252d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-28T19:20:28Z","title_canon_sha256":"41fb9400b24e143339e711187673b5297e348932f3f2803ef9922131ab31ceb7"},"schema_version":"1.0","source":{"id":"1708.08493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08493","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08493v1","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08493","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"Q4BOLLUFN6U5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4BOLLUFN6U5GOKO","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4BOLLUF","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:96938749125ab787a40ed55db177115accc2d9900b1d37a3f477ffa3b3610c1c","target":"graph","created_at":"2026-05-18T00:36:27Z","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":"Given a graph $G$ with $n$ vertices and a bijective labeling of the vertices using the integers $1,2,\\ldots, n$, we say $G$ has a peak at vertex $v$ if the degree of $v$ is greater than or equal to 2, and if the label on $v$ is larger than the label of all its neighbors. Fix an enumeration of the vertices of $G$ as $v_1,v_2,\\ldots, v_{n}$ and a fix a set $S\\subset V(G)$. We want to determine the number of distinct bijective labelings of the vertices of $G$, such that the vertices in $S$ are precisely the peaks of $G$. The set $S$ is called the \\emph{peak set of the graph} $G$, and the set of a","authors_text":"Alexander Diaz-Lopez, Erik Insko, Lucas Everham, Mohamed Omar, Pamela E. Harris, Vincent Marcantonio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-28T19:20:28Z","title":"Peaks on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08493","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":"sha256:9cbbdd0226c9c323bcd6f6eb4855c931d397a647d8e5dc65202f43fa03d8e5bf","target":"record","created_at":"2026-05-18T00:36:27Z","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":"d899463a4aa83c16fc1ee45a03368faff6ff60774c97c313a75ad17a30f252d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-28T19:20:28Z","title_canon_sha256":"41fb9400b24e143339e711187673b5297e348932f3f2803ef9922131ab31ceb7"},"schema_version":"1.0","source":{"id":"1708.08493","kind":"arxiv","version":1}},"canonical_sha256":"8702e5ae856fa9d3394ed7f6057b303d1d177e7d4464fd3c44f1485da918f19e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8702e5ae856fa9d3394ed7f6057b303d1d177e7d4464fd3c44f1485da918f19e","first_computed_at":"2026-05-18T00:36:27.581498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:27.581498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ztLk44MZwgzkmVSsTraIX4JrOCABityTeK1jE9VYFPsDUVDjkwunKZHUdhalE3PxGlCvC4kwsmwux3c4O687AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:27.582150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cbbdd0226c9c323bcd6f6eb4855c931d397a647d8e5dc65202f43fa03d8e5bf","sha256:96938749125ab787a40ed55db177115accc2d9900b1d37a3f477ffa3b3610c1c"],"state_sha256":"ccd916ec4f07cdd6627aac9cbd3eb8b333b65da946bf5b4d025c9b4ceb95ee71"}