{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RDBNN5WU455EWK7NZ7A56DDTWW","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":"a5721bea45689e7c4243690eb7df193c51e8da2179ce9f69c4e9bf52b10ff6e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-06-10T22:04:47Z","title_canon_sha256":"6b237bc0322a64539d820ff1f339562df739ca0a37ab0a2f024e3a8f15b2a528"},"schema_version":"1.0","source":{"id":"1406.2731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2731","created_at":"2026-05-18T02:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2731v1","created_at":"2026-05-18T02:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2731","created_at":"2026-05-18T02:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"RDBNN5WU455E","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RDBNN5WU455EWK7N","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RDBNN5WU","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:441b7534051f7381911e63090291eda909f6a3e4111b8c19a787986d239b91e6","target":"graph","created_at":"2026-05-18T02:49:55Z","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":"This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function defined by data or sampling values from a given function, rather than an explicit mathematical formula. The basics of this approach are two averages: arithmetic mean and graphic mean. The arithmetic mean is used to define integral. Area is used to interpret the meaning of an integral. Antiderivative is introduced from integral, and derivative-antiderivative pair","authors_text":"Chris Rasmussen, Dov Zazkis, Kimberly Leung, Samuel S.P. Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-06-10T22:04:47Z","title":"Calculus from a Statistics Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2731","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":"sha256:2ca548eb45bf1abc1f19bf8c9581ba39b76b8ac71023e973be5a61bcd00f5217","target":"record","created_at":"2026-05-18T02:49:55Z","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":"a5721bea45689e7c4243690eb7df193c51e8da2179ce9f69c4e9bf52b10ff6e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-06-10T22:04:47Z","title_canon_sha256":"6b237bc0322a64539d820ff1f339562df739ca0a37ab0a2f024e3a8f15b2a528"},"schema_version":"1.0","source":{"id":"1406.2731","kind":"arxiv","version":1}},"canonical_sha256":"88c2d6f6d4e77a4b2bedcfc1df0c73b5a06d8176a4840b7454586332c6b27251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88c2d6f6d4e77a4b2bedcfc1df0c73b5a06d8176a4840b7454586332c6b27251","first_computed_at":"2026-05-18T02:49:55.307448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:55.307448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z8QKp7YybD5GTyH1NAP55nkZPOqZ8dkd9QA+ritMf6u/cq6ht5Sy8owGDQnkaViVLy8S0+ko9l4gilupdkUpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:55.307993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ca548eb45bf1abc1f19bf8c9581ba39b76b8ac71023e973be5a61bcd00f5217","sha256:441b7534051f7381911e63090291eda909f6a3e4111b8c19a787986d239b91e6"],"state_sha256":"b9e7030ea928ea9762a6b079f09f7839d4e7fc42bb1591be54e408fc2a89cac4"}