{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FEQ7ZGWDPLQYR2QNERFAN2QGEL","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":"71f6a4b4c4396054dc3359c5e43cdaba785cca3d93b627ea330f7c252b2d5c29","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-10T12:44:32Z","title_canon_sha256":"f149175f017aac268165535bc598b6cb80e9c79360c1f7007291d72044d951dc"},"schema_version":"1.0","source":{"id":"1212.2049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2049","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2049v1","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2049","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"FEQ7ZGWDPLQY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FEQ7ZGWDPLQYR2QN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FEQ7ZGWD","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:0e2694c71e77705114c87687526e8e120f6d1dc309021d33b7a8462df09ed2e7","target":"graph","created_at":"2026-05-18T03:38:54Z","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":"In literature, many important combinatorial properties of subsets of N have been studied both with nonstandard techniques and from the point of view of N. In this thesis we mix these two different approaches in a technique that, at the same time, incorporates nonstandard tools and ultrafilters.","authors_text":"Lorenzo Luperi Baglini","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-10T12:44:32Z","title":"Hyperintegers and Nonstandard Techniques in Combinatorics of Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2049","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":"sha256:4bf00bf8cd7e92f42713fa2e09d60bf5b611c653ed290e2b01727d263589fb0c","target":"record","created_at":"2026-05-18T03:38:54Z","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":"71f6a4b4c4396054dc3359c5e43cdaba785cca3d93b627ea330f7c252b2d5c29","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-10T12:44:32Z","title_canon_sha256":"f149175f017aac268165535bc598b6cb80e9c79360c1f7007291d72044d951dc"},"schema_version":"1.0","source":{"id":"1212.2049","kind":"arxiv","version":1}},"canonical_sha256":"2921fc9ac37ae188ea0d244a06ea0622ef5a9c85870ce6f0ba1b46a9e4e03a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2921fc9ac37ae188ea0d244a06ea0622ef5a9c85870ce6f0ba1b46a9e4e03a43","first_computed_at":"2026-05-18T03:38:54.508238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:54.508238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NlYG5HhG1cB3gdkrSrDm7Ef1LYn8uhCMohM1uYOVW89+CR+vgKihlaWUwfd7vL0ecs+oNg/s4p/ks4ysA/UUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:54.508663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bf00bf8cd7e92f42713fa2e09d60bf5b611c653ed290e2b01727d263589fb0c","sha256:0e2694c71e77705114c87687526e8e120f6d1dc309021d33b7a8462df09ed2e7"],"state_sha256":"1d035bc5dc3d2abd5e6a151c5a3c9112eb17b55debd51ee25938cc8a57e931d9"}