{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D2QK3QBXN4A6PEPASFAJFJZCPK","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":"599003f028bd0f9243153275e5464219b26c2e45fcdd92e0a8e293f1990864a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-20T15:22:22Z","title_canon_sha256":"5b5476dd0a8d611e540ecd14722586a002acc54af00187f85e95c9e26f367c05"},"schema_version":"1.0","source":{"id":"1906.08690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08690","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08690v1","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08690","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"D2QK3QBXN4A6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D2QK3QBXN4A6PEPA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D2QK3QBX","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:df9b1c1e5b46673d842b43a9a17c8a75a2246a2dbae427dca83fbdbb494c10b7","target":"graph","created_at":"2026-05-17T23:42:49Z","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 introduce the set $\\mathcal{G}^{\\rm SSP}$ of all simple graphs $G$ with the property that each symmetric matrix corresponding to a graph $G \\in \\mathcal{G}^{\\rm SSP}$ has the strong spectral property. We find several families of graphs in $\\mathcal{G}^{\\rm SSP}$ and, in particular, characterise the trees in $\\mathcal{G}^{\\rm SSP}$.","authors_text":"Helena \\v{S}migoc, Jephian C.-H. Lin, Polona Oblak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-20T15:22:22Z","title":"The strong spectral property for graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08690","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:c69d91c9f43825a976fbded91fe200062f5d8878090830c8434176aef90c164d","target":"record","created_at":"2026-05-17T23:42:49Z","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":"599003f028bd0f9243153275e5464219b26c2e45fcdd92e0a8e293f1990864a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-20T15:22:22Z","title_canon_sha256":"5b5476dd0a8d611e540ecd14722586a002acc54af00187f85e95c9e26f367c05"},"schema_version":"1.0","source":{"id":"1906.08690","kind":"arxiv","version":1}},"canonical_sha256":"1ea0adc0376f01e791e0914092a7227a959cba64e7ab7fdc3530a5fa5351260e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ea0adc0376f01e791e0914092a7227a959cba64e7ab7fdc3530a5fa5351260e","first_computed_at":"2026-05-17T23:42:49.565558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:49.565558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tecu/xRZwdLHTd/BaLEhbvq0RTxXPvx8kydlsUpX0PJlwLC/y0tgc7xTRromkXHcwpvZFoaZwGoni7DgGi9Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:49.565995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69d91c9f43825a976fbded91fe200062f5d8878090830c8434176aef90c164d","sha256:df9b1c1e5b46673d842b43a9a17c8a75a2246a2dbae427dca83fbdbb494c10b7"],"state_sha256":"1ebe4ef1ae31f975db88cf87390092cef1e7e0ce4bfa6aece2b7ba62c6e65bd6"}