{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LFFIKU3KQW4BZCCCLDGFZPQA6Q","short_pith_number":"pith:LFFIKU3K","canonical_record":{"source":{"id":"1608.04006","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2016-08-13T16:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"3bbefbedefd481a2a7103424353e6696f5a28a815296348877d0a01898a6cd2e","abstract_canon_sha256":"a5772fff4e37e4d733feceb6251f78f4bf47b24169615a500a0054d1bd97ae67"},"schema_version":"1.0"},"canonical_sha256":"594a85536a85b81c884258cc5cbe00f4061a34e14187a11048fd5aadbbb35d84","source":{"kind":"arxiv","id":"1608.04006","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04006","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04006v2","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04006","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"LFFIKU3KQW4B","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LFFIKU3KQW4BZCCC","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LFFIKU3K","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LFFIKU3KQW4BZCCCLDGFZPQA6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04006","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2016-08-13T16:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"3bbefbedefd481a2a7103424353e6696f5a28a815296348877d0a01898a6cd2e","abstract_canon_sha256":"a5772fff4e37e4d733feceb6251f78f4bf47b24169615a500a0054d1bd97ae67"},"schema_version":"1.0"},"canonical_sha256":"594a85536a85b81c884258cc5cbe00f4061a34e14187a11048fd5aadbbb35d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:34.639345Z","signature_b64":"UBgoPikTRYJwXm0KXOrHgMSas791QLNb10UfKiRE/SO2Vb//g+p8O3o9zV1WQncVxhf8PQqN+N4aWLjDAZAsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"594a85536a85b81c884258cc5cbe00f4061a34e14187a11048fd5aadbbb35d84","last_reissued_at":"2026-05-17T23:56:34.638613Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:34.638613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04006","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNBuT0KsBt5i7QzMGjnIzNuVXHujVFgNzwUsoizi2pWU415X8r1o6CsGvKMJ0X1dvYnfDsHOY+wUVa7NJ/tFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:14:04.820858Z"},"content_sha256":"0d0be0b900eb3b99fecd58e75131cffd8813b45a79f1f7fc81c62d3b1446cd19","schema_version":"1.0","event_id":"sha256:0d0be0b900eb3b99fecd58e75131cffd8813b45a79f1f7fc81c62d3b1446cd19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LFFIKU3KQW4BZCCCLDGFZPQA6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Induction and Analogy in a Problem of Finite Sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Ryan Zielinski","submitted_at":"2016-08-13T16:45:39Z","abstract_excerpt":"What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04006","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgaiCW6EmztzCnNGnIx1hRIMbZEo07jfUgBcVCSE0u5grWJf8qHroz2psdi2aIZaZJkloQ+fk21MW5HxU6lXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:14:04.821487Z"},"content_sha256":"68dcb247bd0d7ef47873e6df2d44e9e82bccff0c651a0f0ba3a027e2bb8cc9b2","schema_version":"1.0","event_id":"sha256:68dcb247bd0d7ef47873e6df2d44e9e82bccff0c651a0f0ba3a027e2bb8cc9b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/bundle.json","state_url":"https://pith.science/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T17:14:04Z","links":{"resolver":"https://pith.science/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q","bundle":"https://pith.science/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/bundle.json","state":"https://pith.science/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFFIKU3KQW4BZCCCLDGFZPQA6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LFFIKU3KQW4BZCCCLDGFZPQA6Q","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":"a5772fff4e37e4d733feceb6251f78f4bf47b24169615a500a0054d1bd97ae67","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2016-08-13T16:45:39Z","title_canon_sha256":"3bbefbedefd481a2a7103424353e6696f5a28a815296348877d0a01898a6cd2e"},"schema_version":"1.0","source":{"id":"1608.04006","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04006","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04006v2","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04006","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"LFFIKU3KQW4B","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LFFIKU3KQW4BZCCC","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LFFIKU3K","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:68dcb247bd0d7ef47873e6df2d44e9e82bccff0c651a0f0ba3a027e2bb8cc9b2","target":"graph","created_at":"2026-05-17T23:56:34Z","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":"What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from the point of view of someone who is trying to solve the problem himself. Keywords: analogy, Johann Faulhaber, finite sums, heuristics, inductive reasoning, number theory, George Polya, problem solving, teaching of mathematics","authors_text":"Ryan Zielinski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2016-08-13T16:45:39Z","title":"Induction and Analogy in a Problem of Finite Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04006","kind":"arxiv","version":2},"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":"sha256:0d0be0b900eb3b99fecd58e75131cffd8813b45a79f1f7fc81c62d3b1446cd19","target":"record","created_at":"2026-05-17T23:56:34Z","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":"a5772fff4e37e4d733feceb6251f78f4bf47b24169615a500a0054d1bd97ae67","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2016-08-13T16:45:39Z","title_canon_sha256":"3bbefbedefd481a2a7103424353e6696f5a28a815296348877d0a01898a6cd2e"},"schema_version":"1.0","source":{"id":"1608.04006","kind":"arxiv","version":2}},"canonical_sha256":"594a85536a85b81c884258cc5cbe00f4061a34e14187a11048fd5aadbbb35d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"594a85536a85b81c884258cc5cbe00f4061a34e14187a11048fd5aadbbb35d84","first_computed_at":"2026-05-17T23:56:34.638613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:34.638613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UBgoPikTRYJwXm0KXOrHgMSas791QLNb10UfKiRE/SO2Vb//g+p8O3o9zV1WQncVxhf8PQqN+N4aWLjDAZAsCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:34.639345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04006","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d0be0b900eb3b99fecd58e75131cffd8813b45a79f1f7fc81c62d3b1446cd19","sha256:68dcb247bd0d7ef47873e6df2d44e9e82bccff0c651a0f0ba3a027e2bb8cc9b2"],"state_sha256":"f6de589a09595fffb500254bc15066d0a975d55e4fe08024d33f53c91ea56bfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YtmiItcyEZR4pzjA0r1K2sbZeci0MRXybuHe/YG8Ahu92KT8d8OafUGkdoVfb3G/+QATn8EXFhCU3RcRW0T6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:14:04.825066Z","bundle_sha256":"3c73d8e80943869b3ad7ca9393afa5d479d55bab5e0ea3a40cebbc9795b04933"}}